SOME THEORY BEHIND REAL-TIME RENDERING

Transcription

1 SOME THEORY BEHIND REAL-TIME RENDERING Jaroslav Křivánek Charles University in Prague

2 Off-line realistic rendering (not yet in rea-time)

3 Ray tracing 3

4 4

5 Image created by Bertrand Benoit Rendered in Corona Renderer 5

6 Image created by Jeff Patton Rendered in Corona Renderer 6

7 ŠKODA Rapid Catalogue 7

8 8

9 Image created by Weta Digital 20 th Century Fox 9

10 Image created by Weta Digital 20 th Century Fox 10

11 vimeo >> The Great Gatsby 11 VFX

12 vimeo >> The Great Gatsby 12 VFX

13 Global illumination

14 Global illumination Color bleeding Image credit: Michael Bunnell 14 14

15 Global illumination Caustics 15

16 Global illumination in games 16

17 Basic light transport theory

18 Image generation Pixel value = average radiance reflected from surfaces visible through the pixel Generating an image involves (some sort of) light transport simulation Radiance L (x, ω) 18 18

19 Radiance Radiometric quantity measuring amount of light energy along a ray Denoted L (x, ω) x position ω direction ω Units [W / m 2 sr ] Essential properties of radiance Proportional to perceived brightness xxxxx Constant along a ray xxxxxx x 19

20 Light reflection x 20 20

21 Light reflection BRDF Bi-directional Reflectance Distribution Function Obr. Wojciech Matusik 21 21

22 BRDF Formal definition Bidirectional Reflectance Distribution Function outgoing n L i (ω i ) L r (ω o ) dω i reflected θ o θ i incoming f r ( ω ω ) i o = L i dlr ( ωo) ( ω ) cosθ dω i i i [sr 1 ] 22

23 Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) Souce: Ngan et al. Experimental analysis of BRDF models, 23

24 Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) Souce: Ngan et al. Experimental analysis of BRDF models, 24

25 Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) Souce: Ngan et al. Experimental analysis of BRDF models, 25

26 Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) Souce: Ngan et al. Experimental analysis of BRDF models, 26

27 Reflection equation Total reflected radiance: integrate contributions of incident radiance, weighted by the BRDF, over the hemisphere L r ( x, ω ) o = L H ( x) i ( x, ω ) i f r ( x, ω ω ) cosθ dω i o i i upper hemisphere over x n L i (x, ω i ) L r (x, ω o ) θ o θ i dω i CG III (NPGR010) - J. Křivánek 2015

28 But where does the incident radiance come from? Other surfaces in the scene! Rendering Equation x L(r(x,ω i ), ω i ) 28 ω i ω o L i (x,ω i ) 28 + = ) ( i i o i i i o o e o o d cos ), ( ) ),, (r( ), ( ), ( x x x x x H f r L L L ω θ ω ω ω ω ω ω

29 Recursive calculation of rendering equation To calculate L(x, ω o ) I need to calculate L(r(x, ω ), ω ) for all directions ω around the point x. For the calculation of each L(r(x, ω ), ω ) I need to do the same thing recursively At each step, apply Monte Carlo integration to sample the hemisphere etc. r( r(x,ω ), ω ) ω o x ω ω r(x, ω ) 29

30 Monte Carlo integration General approach to numerical evaluation of integrals f(x) Integral: Monte Carlo estimate of I: p(x) x 1 0 x 5 x 3 x 4 x 2 x 6 1 Correct on average : 30

31 Slide credit: Iwan Kawrakov 31

32 Rendering equation Operator form L = L e + T L L = L e + T L L: Equilibrium radiance L e : Emitted radiance T: Transport & scattering operator 32

33 Progressive approximation Each application of T corresponds to one step of reflection & light propagation L + TL e e e e = L T L T L... emission direct illumination OpenGL shading one-bounce indirect illumination two-bounce indirect illumination 33

34 Progressive approximation L e T L e T T Le T T T Le L e L e T L e L e + TLe + T L L e e T Le 34

35 Idea: Distributed ray tracing (Cook 84) 35

36 Path tracing 36

37 Path tracing, Naive getli (x, ω): y = traceray(x, ω) return Le(y, ω) + Lr (y, ω) // emitted radiance // reflected radiance Lr(y, ω): ω = genuniformrandomdir( n(y) ) return getli (y, ω ) * brdf(y, ω, ω ) * dot(ω, n(y)) * 2π 37

38 Path tracing, Naive getli (x, ω): y = traceray(x, ω) return Le(y, ω) + Lr (y, ω) // emitted radiance // reflected radiance Lr(y, ω): ω = genuniformrandomdir( n(y) ) return getli (y, ω ) * brdf(y, ω, ω ) * dot(ω, n(y)) * 2π 38

39 Practical formulas for light transport P. Dutré: Global Illumination Compendium, 39

40 ROBUST GI CALCULATION

41 Path sampling techniques Path tracing Light tracing Bidirectional path tracing 41

42 All possible bidirectional techniques vertex on a light sub-path vertex on en eye subpath 42

43 All possible bidirectional techniques vertex on a light sub-path vertex on en eye subpath no single techniques importance samples all the terms VPLs 43

44 Bidirectional path tracing Use all of the above sampling techniques Combine using Multiple Importance Sampling 44

45 BPT Implementation 45

46 Results Images: Eric Veach BPT, 25 samples per pixel PT, 56 samples per pixel 46

47 Insufficient path sampling techniques Reference solution Bidirectional path tracing 47

48 Insufficient path sampling techniques In BPT, Specular-Diffuse-Specular paths sampled with zero (or very small) probability specular S diffuse D 48

49 PHOTON MAPPING (DENSITY ESTIMATION)

50 Photon mapping (Density estimation) 1. Many fwd walks + store collisions ( photon map ) 2. Radiance estimate: (Kernel) density estimation 50

51 Photon mapping 1. Photon tracing Photon emission Particle tracing Storage in the photon map 2. Rendering with photon map Like path tracing Photon map query instead of recursion 51

52 Photon mapping SDS paths H.W.Jensen Wojciech Jarosz 52

53 Our work: Vertex Connection and Merging BPT + PM combination

54 54 Bidirectional path tracing (30 min)

55 55 Photon mapping (Density estimation) (30 min)

56 56 Vertex connection and merging (30 min)

57 THANK YOU! Questions? [cgg.mff.cuni.cz/~jaroslav]