rendering equation computer graphics rendering equation 2009 fabio pellacini 1

Transcription

1 rendering equation computer graphics rendering equation 2009 fabio pellacini 1

2 physically-based rendering synthesis algorithms that compute images by simulation the physical behavior of light computer graphics rendering equation 2009 fabio pellacini 2

3 physically-based rendering advantages predictive simulation can be used for architecture, engineering, photorealistic if simulation if correct, images will look real disadvantages (really) slow simulation of physics is computationally very expensive need accurate geometry, 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 any other quantum particles captures: fluorescence, phosphorescence [Glassner et al., 1997] computer graphics rendering equation 2009 fabio pellacini 6

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

8 power and irradiance power: energy per unit time measured in Watts = Joules/sec irradiance: power per unit area measured in Watts/meter 2 computer graphics rendering equation 2009 fabio pellacini 8

9 radiance power per unit projected area and solid angle depends on position and direction (5D) [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 9

10 radiance most sensors readings (and your eyes) are proportional to radiance computer graphics rendering equation 2009 fabio pellacini 10

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

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

13 radiance formulation between two points [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 13

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

15 material properties materials differ in the way they scatter energy need physical description of light scattering [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 15

16 BRDF bidirectional surface distribution function [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 16

17 BRDF properties reciprocity energy conservation computer graphics rendering equation 2009 fabio pellacini 17

18 hemispherical formulation need outgoing radiance in a given direction from BRDF definition determine reflected radiance L r by integration over all incoming light computer graphics rendering equation 2009 fabio pellacini 18

19 hemispherical formulation need outgoing radiance in a given direction also consider light spontaneously emitted by surface total radiance is the sum of emitted and reflected computer graphics rendering equation 2009 fabio pellacini 19

20 hemispherical formulation [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 20

21 intuition behind rendering equation x x [Bala] computer graphics rendering equation 2009 fabio pellacini 21

22 intuition behind rendering equation integral equation indicates radiance at equilibrium computer graphics rendering equation 2009 fabio pellacini 22

23 visible point formulation point visible from x in direction Ψ since energy is conserved in vacuum by substituting previous values in rendering eq. computer graphics rendering equation 2009 fabio pellacini 23

24 visible point formulation [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 24

25 area formulation compute solid angle visible from x to y [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 25

26 area formulation by changing domain from hemisphere to scene and introducing explicit visibility evaluation V computer graphics rendering equation 2009 fabio pellacini 26

27 area formulation [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 27

28 transport formulation [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 28

29 [Cornell PCG] transport formulation computer graphics rendering equation 2009 fabio pellacini 29

30 direct and indirect illum. formulation direct illumination: radiance reaching a surface directly 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 direct and indirect illum. formulation computer graphics rendering equation 2009 fabio pellacini 31

32 direct illumination formulation rewrite in area formulation computer graphics rendering equation 2009 fabio pellacini 32

33 indirect illumination formulation since computer graphics rendering equation 2009 fabio pellacini 33

34 hemispherical integration 2D square 2D hemisphere computer graphics rendering equation 2009 fabio pellacini 34

35 materials computer graphics rendering equation 2009 fabio pellacini 35

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

37 diffuse BRDF light is reflected equally in all directions [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 37

38 diffuse BRDF Lambertian shading model motivation computer graphics rendering equation 2009 fabio pellacini 38

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

40 glossy BRDFs light is reflected in many directions unequally many models exist [Dutré, Bekaert, Bala] computer graphics rendering equation 2009 fabio pellacini 40

41 glossy BRDFs Phong and Blinn models Phong model Blinn-Phong model issues: non reciprocal non energy conserving computer graphics rendering equation 2009 fabio pellacini 41

42 glossy BRDFs modified Blinn-Phong model modified Blinn-Phong model energy conservation computer graphics rendering equation 2009 fabio pellacini 42

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

44 glossy BRDFs modified Phong model is modified Phong physically accurate? Phong accurate BRDF [LaFortune et al., 1997] computer graphics rendering equation 2009 fabio pellacini 44

45 glossy BRDFs better models analytic model physically motivated hard to capture every material data-driven measure light reflectance encode in lookup table or fit resample when rendering computer graphics rendering equation 2009 fabio pellacini 45

46 extending 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