rendering equation computer graphics rendering equation 2009 fabio pellacini 1

Transcription

1 rendering equation computer graphics rendering equation 2009 fabio pellacini 1

2 phsicall-based rendering snthesis algorithms that compute images b simulation the phsical behavior of light computer graphics rendering equation 2009 fabio pellacini 2

3 phsicall-based rendering advantages predictive simulation can be used for architecture, engineering, photorealistic if simulation if correct, images will look real disadvantages reall slow simulation of phsics is computationall ver epensive need accurate geometr, materials and lights otherwise just a correct solution to the wrong problem computer graphics rendering equation 2009 fabio pellacini 3

4 models of light geometric optics light particles travel in straight lines light particles do not interact with each other describes: emission, reflection/refraction, absorption [Stam et al., 1996] computer graphics rendering equation 2009 fabio pellacini 4

5 models of light wave optics light particles interact with each other describes: diffraction, interference, polarization [Gondek et al., 1997] computer graphics rendering equation 2009 fabio pellacini 5

6 models of light quantum optics light particles are like an other quantum particles captures: fluorescence, phosphorescence [Glassner et al., 1997] computer graphics rendering equation 2009 fabio pellacini 6

7 rendering equation describe phsical behavior of light in vacuum filled with objects based on geometric optics principles can be etended to describe participating media can be etended to describe wavelenght dep. computer graphics rendering equation 2009 fabio pellacini 7

8 power and irradiance power: energ per unit time measured in Watts Joules/sec Φ irradiance: power per unit area measured in Watts/meter 2 E dq dt dφ da computer graphics rendering equation 2009 fabio pellacini 8

9 radiance power per unit projected area and solid angle depends on position and direction 5D Θ d da Φ d Φ 2 2 dωθ dacosθθdωθ cosθθ N Θ de cosθ dω Θ Θ [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 9

10 radiance most sensors readings and our ees are proportional to radiance computer graphics rendering equation 2009 fabio pellacini 10

11 radiance notation notation follows [Dutré, Bekaert, Bala] radiance leaving from point in direction Θ Θ radiance coming to point from direction solid angle for a direction in general dω Θ Θ computer graphics rendering equation 2009 fabio pellacini 11

12 radiance radiance is a function of wavelenght Θ λ spectrum Θ,λ in practice, write equations for RGB we will use simplified notation without carr around the wavelength eplicitl computer graphics rendering equation 2009 fabio pellacini 12

13 radiance formulation between two points da 2 d Φ cosθ dω 2 d Φ da da r 2 cosθ cosθ dω da cosθ r 2 [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 13

14 radiance properties invariance on straight paths in vacuum from energ conservation corollar: radiance does not change with distance [Shirle] computer graphics rendering equation 2009 fabio pellacini 14

15 material properties materials differ in the wa the scatter energ need phsical description of light scattering [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 15

16 BRDF bidirectional surface distribution function d Θ ρ, Θ de d Θ dω cosθ [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 16

17 BRDF properties reciprocit ρ, Θ ρ, Θ energ conservation : Θ Ω d Θcosθ dω Θ Θ de : Θ Ω ρ, Θcosθ dω Θ Θ 1 computer graphics rendering equation 2009 fabio pellacini 17

18 hemispherical formulation need outgoing radiance in a given direction from BRDF definition ρ, Θ d Θ dω cosθ determine reflected radiance r b integration over all incoming light r Θ d Θ Ω ρ, Θ cosθ dω computer graphics rendering equation 2009 fabio pellacini 18

19 hemispherical formulation need outgoing radiance in a given direction also consider light spontaneousl emitted b surface e Θ total radiance is the sum of emitted and reflected Θ e Θ + Θ r Θ + Ω e Θ + ρ, Θcos, dω N computer graphics rendering equation 2009 fabio pellacini 19

20 hemispherical formulation Θ + Ω e Θ + ρ, Θcosθ dω [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 20

21 intuition behind rendering equation Θ + Ω e Θ + ρ, Θcosθ dω [Bala] Θ Θ e computer graphics rendering equation 2009 fabio pellacini 21

22 intuition behind rendering equation Θ + Ω e Θ + ρ, Θcosθ dω integral equation indicates radiance at equilibrium computer graphics rendering equation 2009 fabio pellacini 22

23 visible point formulation point visible from in direction r, since energ is conserved in vacuum b substituting previous values in rendering eq. Θ + Ω e Θ + r, ρ, Θcosθ dω computer graphics rendering equation 2009 fabio pellacini 23

24 visible point formulation Θ + Ω e Θ + r, ρ, Θcosθ dω [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 24

25 area formulation compute solid angle visible from to dω da cosθ r 2 [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 25

26 area formulation b changing domain from hemisphere to scene and introducing eplicit visibilit evaluation V Θ + S e Θ + ρ, Θ cosθ 2 r cosθ Θ V, da G, cosθ cosθ Θ 2 r N N 2 computer graphics rendering equation 2009 fabio pellacini 26

27 computer graphics rendering equation 2009 fabio pellacini 27 area formulation Θ + + Θ Θ S e da V G,,, ρ [Dutré, Bekaert, Bala]

28 transport formulation e + T e + T e + TT e +... i 0 T i e [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 28

29 e Te e e + Te computer graphics rendering equation T 2 e 3 T e [Cornell PCG] transport formulation T e e T e e fabio pellacini 29

30 direct and indirect illum. formulation direct illumination: radiance reaching a surface directl from the light often efficient to sample using area formulation indirect illumination: radiance reaching a surface after bouncing at least once on another surface often efficient to sample using hemisphere formulation computer graphics rendering equation 2009 fabio pellacini 30

31 computer graphics rendering equation 2009 fabio pellacini 31 direct and indirect illum. formulation Θ + Θ Θ r e...cos...cos Θ + Θ + Θ i d r e r d d ω θ ρ ω θ ρ

32 computer graphics rendering equation 2009 fabio pellacini 32 direct illumination formulation Ω Θ Θ ω θ ρ d e d cos, Θ Θ surface lights e d da V G,,, ρ rewrite in area formulation Θ Θ l l light e d da V G,,, ρ

33 computer graphics rendering equation 2009 fabio pellacini 33 indirect illumination formulation Ω Θ Θ ω θ ρ d r d cos, since, r r r Ω Θ Θ ω θ ρ d r r d cos,,

34 hemispherical integration 2D square I 1 f da S X f, dd 2D hemisphere I Θ dω f ϕ, θ sinθdϕdθ Θ Θ Ω f 2π π 0 0 computer graphics rendering equation 2009 fabio pellacini 34

35 materials computer graphics rendering equation 2009 fabio pellacini 35

36 phsicall-based materials capture realistic appearance is necessar [Cornell PCG] computer graphics rendering equation 2009 fabio pellacini 36

37 diffuse BRDF light is reflected equall in all directions ρd ρ, Θ π [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 37

38 diffuse BRDF ambertian shading model motivation d Θ ρ, Θ de ρd cosθ π dω C l k d cosθ computer graphics rendering equation 2009 fabio pellacini 38

39 specular BRDF light is reflected onl in one direction ρ, Θ δ, Θ [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 39

40 gloss BRDFs light is reflected in man directions unequall man models eist [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 40

41 gloss BRDFs Phong and Blinn models Phong model ρ, Θ k d + k s cos n θ r k d + k s R Θ n Blinn-Phong model ρ, Θ issues: non reciprocal non energ conserving k + d k s N H n computer graphics rendering equation 2009 fabio pellacini 41

42 gloss BRDFs modified Blinn-Phong model modified Blinn-Phong model ρ, Θ energ conservation ρd n ρs π 2π ρ d + ρ s 1 H Θ n computer graphics rendering equation 2009 fabio pellacini 42

43 gloss BRDFs modified Phong model is modified Phong phsicall accurate? Phong accurate BRDF [afortune et al., 1997] photograph computer graphics rendering equation 2009 fabio pellacini 43

44 gloss BRDFs modified Phong model is modified Phong phsicall accurate? Phong accurate BRDF [afortune et al., 1997] computer graphics rendering equation 2009 fabio pellacini 44

45 gloss BRDFs better models analtic model phsicall motivated hard to capture ever material data-driven measure light reflectance encode in lookup table or fit resample when rendering computer graphics rendering equation 2009 fabio pellacini 45

46 etending the rendering equation computer graphics rendering equation 2009 fabio pellacini 46

47 participating media [Fedkiw et al.] computer graphics rendering equation 2009 fabio pellacini 47

48 subsurface scattering [Jensen et al.] computer graphics rendering equation 2009 fabio pellacini 48

49 [Jensen] subsurface scattering computer graphics rendering equation 2009 fabio pellacini 49

50 subsurface scattering [Jensen et al.] computer graphics rendering equation 2009 fabio pellacini 50