1. Reflection Models (1) Physically-Based Illumination Models (2)

2. Remaining Hard Problems Reflective Diffraction Effects thin films feathers of a blue jay oil on water CDs Anisotropy brushed metals strands pulled materials Satin and velvet cloths

3. Better (Realistic) Local Illumination Models Blinn-Torrance-Sparrow (1977) –isotropic reflectors with smooth microstructure Cook-Torrance (1982) –wavelength dependent Fresnel term Kajiya (1985) Cabral-Max-Springmeyer (1987) –Anisotropic surfaces Wolff (1990) –adds polarization He-Torrance-Sillion-Greenberg (1991) –adds polarization, statistical microstructure, self-reflectance

4. Cook-Torrance Illumination Model (summary) A linear combination of a number of completely different models and approximations AMBIENT term  to approximate global illumination Lambertian DIFFUSE term  model color SPECULAR term: 1.Fresnel term  gives dependence of specular intensity and color on incidence angle 2.Microfacet model term  spreads the specular intensity, giving an “off-specular bump”

5. Cook-Torrance Illumination Model (summary) Microfacet model term  spreads the specular intensity, giving an “off-specular bump” NOT entirely satisfactory It is based on a one-dimensional “cross-sectional” model

6. Better (Realistic) Local Illumination Models Blinn-Torrance-Sparrow (1977) –isotropic reflectors with smooth microstructure Cook-Torrance (1982) –wavelength dependent Fresnel term Kajiya (1985) Cabral-Max-Springmeyer (1987) –Anisotropic surfaces Wolff (1990) –adds polarization He-Torrance-Sillion-Greenberg (1991) –adds polarization, statistical microstructure, self-reflectance

7. An Explicit Microfacet Model Cabral, B., Max, N., Springmeyer, R., Bidirectional Reflection Functions From Surface Bump Maps, SIGGRAPH `87, pp. 273-281 Construction of a surface of triangular microfacets Reflection model: –Pre-calculation (rather than simulation by a parametric distribution or function) –Table of reflectivities

8. What is a BRDF? BRDF is a function of incoming light direction and outgoing view direction In 3D, a direction D can be represented in spherical coordinates (  D,  D ) A BRDF is a 4D function: BRDF(  L,  L,  V,  V ) or BRDF(  i,  i,  o,  o ) N L V θLθL θVθV observer light surface

9. Table of Reflectivities

10. Explicit Microfacet Model (Cabral et al 87) Any surface whose microstructure can be represented can be modeled Microstructure: isotropic or anisotropic Less restricted than using statistical distribution (Cook and Torrance)

11. Nature of the Microstructure Controlled by varying size and vertex perturbation of triangular microfacets Triangular microfaces construction: bump map or height field (2D array of vertex heights) Heights can be distributed in any desired way

12. Bump Mapping Map texture values to perturbations of surface normals

13. Bump Mapping Map texture values to perturbations of surface normals Straight Phong Shading  approximates smoothly curved surface Straight Phong Shading  approximates smoothly curved surface Phong with bump mapping approximates bumpy surface

14. Irradiated Surface Element Area Normal Mirror direction

15. Reflectivity Function Contribute a ‘delta function’  sum of delta functions

16. Reflectivity Function: How to Build the Information?

17. Max, N., "Horizon mapping: shadows for bump-mapped surfaces“ Visual Computer, 1988

18. Illuminating flux density Fresnel factor Energy incident on a microfacet Max, N., "Horizon mapping: shadows for bump-mapped surfaces“ Visual Computer, 1988

19. Fresnel Factor

20. How About for ALL microfacets?

21. N = 24

24. Energy flowing through one cell

25. returns the index of the cell hit by a ray fired in direction R. Mirror direction Kronecker delta function

27. Illuminating flux density Fresnel factor Energy incident on a microfacet Max, N., "Horizon mapping: shadows for bump-mapped surfaces“ Visual Computer, 1988

28. More than one microfacet is likely to contribute energy to cell k

29. Energy flowing through one cell Energy incident to a microfacet Solid angle of cell k

30. Finally…Table of Reflectivities

31. Reflectivity:

32. The fraction of incoming flux reflected by facet S i

33. G i  the fraction of incoming flux reflected by facet S i Energy incident on a microfacet

34. Illuminating flux density Fresnel factor Energy incident on a microfacet Max, N., "Horizon mapping: shadows for bump-mapped surfaces“ Visual Computer, 1988

35. Energy flowing through one cell Energy incident to a microfacet Solid angle of cell k

36. Energy flowing through one cell Energy incident to a microfacet

37. Better (Realistic) Local Illumination Models Blinn-Torrance-Sparrow (1977) –isotropic reflectors with smooth microstructure Cook-Torrance (1982) –wavelength dependent Fresnel term Kajiya (1985) Cabral-Max-Springmeyer (1987) –Anisotropic surfaces Wolff (1990) –adds polarization He-Torrance-Sillion-Greenberg (1991) –adds polarization, statistical microstructure, self-reflectance