MATEMATIKAV ANIMOVANEacuteMFILMU
Milan JarošŠKOMAM 2020
| Funkce a jejich grafy
| Matematickyacute obraz
| Proceduraacutelniacute textura
| Renderovaacuteniacute
MATEMATIKA V ANIMOVANEacuteM FILMU
bdquoJe důležiteacute si uvědomit že umělci a designeacuteři vidiacute tvary a obrazy kdežto počiacutetače pracujiacute s čiacutesly a rovnicemi K propojeniacute těchto dvou světů se využiacutevaacute exaktniacute věda kterou nazyacutevaacuteme matematikaldquo
MATEMATIKA V ANIMOVANEacuteM FILMU
Tony DeRose
| Lineaacuterniacute funkce Směrnicovyacute tvar rovnice přiacutemky
FUNKCE A JEJICH GRAFY
119910 = 119896119909 + 119902
119910 = 119909 119910 = minus119909
| Absolutniacute hodnota
119910 = |119909| 119910 = minus|119909|
FUNKCE A JEJICH GRAFY
| Druhaacute a třetiacute mocnina
119910 = 1199092 119910 = 1199093
FUNKCE A JEJICH GRAFY
| Převraacutecenaacute hodnota
119910 =1
119909119910 = minus
1
119909
FUNKCE A JEJICH GRAFY
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Funkce a jejich grafy
| Matematickyacute obraz
| Proceduraacutelniacute textura
| Renderovaacuteniacute
MATEMATIKA V ANIMOVANEacuteM FILMU
bdquoJe důležiteacute si uvědomit že umělci a designeacuteři vidiacute tvary a obrazy kdežto počiacutetače pracujiacute s čiacutesly a rovnicemi K propojeniacute těchto dvou světů se využiacutevaacute exaktniacute věda kterou nazyacutevaacuteme matematikaldquo
MATEMATIKA V ANIMOVANEacuteM FILMU
Tony DeRose
| Lineaacuterniacute funkce Směrnicovyacute tvar rovnice přiacutemky
FUNKCE A JEJICH GRAFY
119910 = 119896119909 + 119902
119910 = 119909 119910 = minus119909
| Absolutniacute hodnota
119910 = |119909| 119910 = minus|119909|
FUNKCE A JEJICH GRAFY
| Druhaacute a třetiacute mocnina
119910 = 1199092 119910 = 1199093
FUNKCE A JEJICH GRAFY
| Převraacutecenaacute hodnota
119910 =1
119909119910 = minus
1
119909
FUNKCE A JEJICH GRAFY
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
bdquoJe důležiteacute si uvědomit že umělci a designeacuteři vidiacute tvary a obrazy kdežto počiacutetače pracujiacute s čiacutesly a rovnicemi K propojeniacute těchto dvou světů se využiacutevaacute exaktniacute věda kterou nazyacutevaacuteme matematikaldquo
MATEMATIKA V ANIMOVANEacuteM FILMU
Tony DeRose
| Lineaacuterniacute funkce Směrnicovyacute tvar rovnice přiacutemky
FUNKCE A JEJICH GRAFY
119910 = 119896119909 + 119902
119910 = 119909 119910 = minus119909
| Absolutniacute hodnota
119910 = |119909| 119910 = minus|119909|
FUNKCE A JEJICH GRAFY
| Druhaacute a třetiacute mocnina
119910 = 1199092 119910 = 1199093
FUNKCE A JEJICH GRAFY
| Převraacutecenaacute hodnota
119910 =1
119909119910 = minus
1
119909
FUNKCE A JEJICH GRAFY
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Lineaacuterniacute funkce Směrnicovyacute tvar rovnice přiacutemky
FUNKCE A JEJICH GRAFY
119910 = 119896119909 + 119902
119910 = 119909 119910 = minus119909
| Absolutniacute hodnota
119910 = |119909| 119910 = minus|119909|
FUNKCE A JEJICH GRAFY
| Druhaacute a třetiacute mocnina
119910 = 1199092 119910 = 1199093
FUNKCE A JEJICH GRAFY
| Převraacutecenaacute hodnota
119910 =1
119909119910 = minus
1
119909
FUNKCE A JEJICH GRAFY
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Absolutniacute hodnota
119910 = |119909| 119910 = minus|119909|
FUNKCE A JEJICH GRAFY
| Druhaacute a třetiacute mocnina
119910 = 1199092 119910 = 1199093
FUNKCE A JEJICH GRAFY
| Převraacutecenaacute hodnota
119910 =1
119909119910 = minus
1
119909
FUNKCE A JEJICH GRAFY
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Druhaacute a třetiacute mocnina
119910 = 1199092 119910 = 1199093
FUNKCE A JEJICH GRAFY
| Převraacutecenaacute hodnota
119910 =1
119909119910 = minus
1
119909
FUNKCE A JEJICH GRAFY
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Převraacutecenaacute hodnota
119910 =1
119909119910 = minus
1
119909
FUNKCE A JEJICH GRAFY
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Logaritmickaacute a exponenciaacutelniacute funkce
119910 = 119897119900119892119886119909 119910 = 119886119909
FUNKCE A JEJICH GRAFY
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Goniometrickeacute funkce
119910 = sin 119909 119910 = cos 119909
FUNKCE A JEJICH GRAFY
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Středovaacute rovnice kružnice
119909 minus 11990902 + 119910 minus 1199100
2 = 1199032
FUNKCE A JEJICH GRAFY
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
ANIMACE - MATH DANCE
httpswwwyoutubecomwatchv=oeCc6A2WYfQ
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Matematickyacute obraz| Žaacutednaacute mesh žaacutedneacute modely žaacutednyacute renderer žaacutedneacute globaacutelniacute osvětleniacute
| Matematickeacute vyacuterazy definujiacute tvary umiacutestěniacute barvu a světlo stiacuteny pohyb
| bdquoBatmanův vzorecldquo pro dospěleacute (Inigo Quilez)
MATEMATIKA A SHADERY
httpss1135photobucketcomusercabby24mediaBlender20Pics202012shoepnghtmlsrc=pb
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
MATEMATICKYacute OBRAZ
httpswwwshadertoycomview4tByz3
Inigo Quilez
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Shader| = počiacutetačovyacute program kteryacute je součaacutestiacute vykreslovaciacuteho řetězce (renderingu)
| Druhy vertex pixel geometry shader hellip
| Tvorba za pomociacute programovaciacutech jazyků (GLSL pro OpenGL) grafickeacuteho rozhraniacute (node editor v Blenderu)
MATEMATIKA A SHADERY
httpswwwshadertoycomview4tByz3
Inigo Quilez
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
CO JE BLENDER 28
blenderorgblenderorg
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| materiaacutel - kolekce shaderů ktereacute popisujiacute povrch objektu
| shader - definice za pomociacute node editoru v Blenderu (SVM GLSL)
| textura - obraacutezek ze souboru (image) přidaacuteva detail do shaderu a nemaacute žaacutedneacute fyzikaacutelniacute vlastnosti
| proceduraacutelniacute textura ndash definice za pomociacute matematickyacute vzorcůfunkciacute
CO JE MATERIAacuteL
materiaacutel(shader node)
editor
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PŘIacuteKLADY PROCEDURAacuteLNIacuteCH TEXTUR
httpschiuhans111githubioNodevember2019
Hans Chiu
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 +
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - KRUŽNICE119909 minus 1199090
2 + 119910 minus 11991002 + 119911 minus 1199110
2 = 1199032
httpsb3dinterplanetyorgencreating-procedural-textures-in-blender
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
MANDELBROTOVA MNOŽINA
119872 = 119888|119875119888119899(0) ne infinforall119899 rarr infin 119888 119911 isin 119914
kde 119875119888 119911 = 1199112 + 119888
11987510 0 = 0
11987511 0 = 02 + 1 = 1
11987512 1 = 12 + 1 = 2
11987513 2 = 22 + 1 = 5
11987514 5 = 52 + 1 = 26
Přiacuteklad
= 2D fraktaacutel Benoit B Mandelbrot (1979)
119888 = 1 119888 = 1198941198751198940 0 = 0
1198751198941 0 = 119894
1198751198942 119894 = minus1 + 119894
1198751198943 minus1 + 119894 = minus119894
1198751198944 minus119894 = minus1 + 119894
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| = 3D fraktaacutel Daniel White a Paul Nylander (2009)
| White a Nylanderův vzorec pro n-tou mocninu vektoru
| Mandelbulbova množina
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
v
kde
httpswwwblendernationcom20180724how-to-make-mandelbulb-fractals-in-blender-eevee
119872 = c| c isin 1198773
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PROCEDURAacuteLNIacute TEXTURA - MANDELBULB
Jonas Dichelle
httpswwwyoutubecomwatchv=YtDG1_76_2k
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
RENDEROVAacuteNIacute
httpswwwyoutubecomwatchv=mN0zPOpADL4
httpswwwyoutubecomwatchv=WhWc3b3KhnYhttpswwwyoutubecomwatchv=RJnKaAtBPhA
httpswwwyoutubecomwatchv=Y-rmzh0PI3c
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
RENDEROVAacuteNIacute STATE-OF-THE-ART
Up(2009 PixarDisney)
Kung Fu Panda 2(2011 DreamWorks)
Big Hero 6(2014 Disney)
Point based global illumination (Christensen 2008)
Trolls(2016 DreamWorks)
Path-tracing (Kajiya 1986)
| Path-tracing renderery
In-house Hyperion (Disney)
In-house MoonRay V3 (DreamWorks)
In-house Manuka (WetaDigital)
Solid Angle Arnold renderer (Sony Pictures Imageworks ILM hellip)
Blender Cycles
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
SVĚTLO V ANIMOVANYacuteCH FILMECH
Dan OBrien
Dan OBrien
Dan OBrien
Dan OBrien
Špioacuteni v převleku (2019)
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
FOTOCG
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
Andrew Price
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
FOTO NEBO POČIacuteTAČOVAacute GRAFIKA
CGFOTO
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
PATH-TRACING
0
1
light
object
Samples
11
076
051
016
084
062
0665
Pixel ResultSamples
Toward Real-Time Ray Tracing A Survey on Hardware Acceleration and Microarchitecture Techniques Yangdong Deng et al ACM 2017
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
Zobrazovaciacute rovnice a jejiacute řešeniacute za pomociacute Monte Carlo metody
| ωo is direction of outgoing ray
| ωi is direction of incoming ray
| Lo is spectral radiance emitted by the source
from point x in direction ωo
| Le is emitted spectral radiance from point x
in direction ωo
| Ω is the unit hemisphere in direction of normal
vector n with center in x over which we integrate
| Li is spectral radiance coming inside to x in direction ωi
| fr(x ωi ωo) is distribution function of the image
(BRDF) in point x from direction ωi to direction ωo
| ωi n is angle between ωi and surface normal
PATH-TRACING (KAJIYA 1986)
GlossyDiffuse The Cycles Encyclopedia
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Co je problematickeacuteho na teacuteto rovnici
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
Redukce šumu v obraze vyžaduje vysokyacute počet samplůa tiacutem i dlouhyacute čas vyacutepočtu
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
Zobrazovaciacute rovnice
PATH-TRACING (KAJIYA 1986)
1 sample 100 samplů
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Mooreův zaacutekonPočet tranzistorů ktereacute mohou byacutet umiacutestěny na integrovanyacute obvod se přizachovaacuteniacute stejneacute ceny zhruba každyacutech 18 měsiacuteců zdvojnaacutesobiacute
| Shrekův zaacutekonPočet renderovaciacutech procesorovyacutech hodin potřebnyacutech k dokončeniacuteprojektu se zdvojnaacutesobiacute ve srovnaacuteniacute s množstviacutem času potřebneacuteho napředchoziacutem projektu
| Shrek 1 (2001) 5 milioacutenů procesorovyacutech hodin
| Shrek 2 (2004) 10 milioacutenů procesorovyacutech hodin
| Shrek 3 (2007) 20 milioacutenů procesorovyacutech hodin
| Shrek Forever 3D (2010) 50 milioacutenů procesorovyacutech hodin
SHREKŮV ZAacuteKON
httpswwwintelcomcontentdamdoccase-studyhigh-performance-computing-xeon-5600-dreamworks-animation-case-studypdf
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
| Big Hero 6 199 milioacutenů jaacutedro hodin
| 1 osobniacute PC se 4 jaacutedry200Mhod 4 cores = 50Mhod = 21Mdni = 5707 let
| Superpočiacutetač s 1000 PC se 48 jaacutedry200Mhod 48000 cores = 6 měsiacuteců
SUPERPOČIacuteTANIacute (HPC)
Big Hero 6(2014 Disney)
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
45
| Salomon 1008 nodes 2x Intel Xeon E5-2680v3 25 GHz 12 cores
(Haswell) w 128GB InfiniBand FDR56 7D Enhanced hypercube 576 nodes wo accelerator 432 nodes with 2x Intel Xeon Phi 7120P 61
cores 16 GB RAM
| Barbora 192 nodes wo an accelerator 8 nodes with 4x NVIDIA Tesla V100 2x Intel Xeon Cascade Lake 26 GHz 18 cores 192GB InfiniBand HDR 200Gbs (100Gbs per node) 30 GBs LUSTRE storage
| Anselm 209 nodes 2x Intel Xeon E5-2665 24 GHz 8 cores
(Sandy Bridge) 64GB InfiniBand FDR56 7D Enhanced hypercube 180 nodes wo accelerator 4 nodes with MIC accelerator (1x Intel Xeon Phi
5110P) 23 nodes with NVIDIA Kepler K20 | NVIDIAreg DGX-2 SERVER
16 Teslatrade V100 32 GB GPUs 512 GB of GPU HBM2
HPC NA VŠB-TUO
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz
Milan Jarošmilanjarosvsbcz
IT4Innovations naacuterodniacute superpočiacutetačoveacute centrumVŠB ndash Technickaacute univerzita OstravaStudentskaacute 62311B708 00 Ostrava-Porubawwwit4icz