1. Computer Graphics (Spring 2003) COMS 4160, Lecture 18: Shading 2 Ravi Ramamoorthi http://www.cs.columbia.edu/~cs4160 Guest Lecturer: Aner Benartzi

2. Building up the BRDF Bi-Directional Reflectance Distribution Function Function based on viewing direction. Tells us how bright a surface is. Why should a surface be bright? –Incoming Hemisphere –Incoming Intensity Relates incoming light energy to outgoing light energy.

3. Function of Viewing “direction” A direction in 3-D, in relation to a point on a surface, can be given with 2 angles –, –same as the angles in spherical coordinates –r is not needed for direction only

4. Solid Angels Not enough to view an object from a single line of sight. –infinitesimally small viewing area leads to 0 incoming energy. –need a range of directions. In 2D the span of directions is an angle. In 3D the equivalent value is a solid angle

5. Differential Solid Angles

6. BRDF as a Ratio Just a ratio of the incoming light to the outgoing light. –4D function.

7. The Reflection Equation

8. Brdf Viewer plots Diffuse bv written by Szymon Rusinkiewicz Torrance-Sparrow Anisotropic

9. Incoming vs. Outgoing Energy Desirable properties of BRDF: –Ratio between Zero and One. –Linear –Reciprocity (Hemholtz reciprocity)

10. Properties of BRDF’s

11. Emperical BRDF Sample many incoming and outgoing directions. Store the results in a 4D data structure

12. Analytical BRDF: TS example One famous analytically derived BRDF is the Torrance-Sparrow model. T-S is used to model specular surface, like the Phong model. –more accurate than Phong –has more parameters that can be set to match different materials –derived based on assumptions of underlying geometry. (instead of ‘because it works well’)

13. Torrance-Sparrow Assume the surface is made up grooves at the microscopic level. Assume the faces of these grooves (called microfacets) are perfect reflectors. Take into account 3 phenomena Shadowing MaskingInterreflection

14. Torrance-Sparrow Result Fresnel term: allows for wavelength dependency (ignore for now) Geometric Attenuation: reduces the output based on the amount of shadowing or masking that occurs. Distribution: distribution function determines what percentage of microfacets are oriented to reflect in the viewer direction. How much of the macroscopic surface is visible to the light source How much of the macroscopic surface is visible to the viewer

15. Other BRDFs Toon Shaders –view independent –discrete in lighting dependance Anisotropic –some BRDFs depend on the orientation of the surface. –Hair, Brushed Steel

16. Anisotropic vs. Isotropic The 4D BRDF we’ve seen so far can handle anisotropic surfaces. Most surfaces are isotropic –Appear the same when rotated about the normal –The overall orientation in the phi direction doesn’t matter –only need to worry about the difference between –BRDF becomes a 3D function:

17. Complex Lighting So far we’ve looked at simple, discrete light sources. Real environments contribute many colors of light from many directions. The complex lighting of a scene can be captured in an Environment map. –Just paint the environment on a sphere.

18. Environment Maps Instead of determining the lighting direction by knowing what lights exist... Determine what light exists by knowing the lighting direction. Blinn and Newell 1976, Miller and Hoffman, 1984 Later, Greene 86, Cabral et al. 87

19. Limitations Carefully constructed BRDFs can create very realistic scenes. A good BRDF alone still has limitations: –The silhouettes of objects are still polygonal. –The resolution of surface normals is only as fine as the number of polygons. Can use bump maps –Nothing takes into account objects shadowing themselves. Can use shadow maps

20. Limitations (cont) More limitations of modeling appearance only with a BRDF: –Any reflections or transparency can’t include other scene objects. requires ray-tracing –Sometimes light leaves a different point from the one it entered (subsurface scattering). –Some objects contribute significantly to the lighting in the scene. requires global illumination