Reflection Models I

1. Reflection Models I • Today • Types of reflection models • The BRDF and reflectance • The reflection equation • Ideal reflection and refraction • Fresnel effect • Ideal diffuse • Next lecture • Glossy and specular reflection models • Rough surfaces and microfacets • Self-shadowing • Anisotropic reflection models University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

2. Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency. • Properties • Spectra and Color [Moon Spectra] • Polarization • Directional distribution • Theories • Phenomenological • Physical University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

3. Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror • Ideal Diffuse • Lambert’s Law • Matte • Specular • Glossy • Directional diffuse University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

4. Materials Plastic Metal Matte From Apodaca and Gritz, Advanced RenderMan University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

5. The Reflection Equation University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

6. The BRDF • Bidirectional Reflectance-Distribution Function University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

7. The BSSRDF • Bidirectional Surface Scattering Reflectance-Distribution Function Translucency University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

8. Gonioreflectometer University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

9. Properties of BRDF’s • 1. Linearity • 2. Reciprocity principle From Sillion, Arvo, Westin, Greenberg University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

10. Properties of BRDF’s • 3. Isotropic vs. anisotropic • 4. Energy conservation Reciprocity and isotropy University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

11. Energy Conservation University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

12. The Reflectance • Definition: Reflectance is ratio of reflected to incident power • Conservation of energy: 0 <r< 1 • 3 by 3 set of possibilities: • Units: r [dimensionless], fr [1/steradians] University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

13. Law of Reflection University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

14. Ideal Reflection (Mirror) University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

15. Snell’s Law University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

16. Total internal reflection: Law of Refraction University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

17. Optical Manhole Total internal reflection From Livingston and Lynch University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

18. Fresnel Reflectance Metal (Aluminum) Dielectric (N=1.5) Gold F(0)=0.82 Silver F(0)=0.95 Glass n=1.5 F(0)=0.04 Diamond n=2.4 F(0)=0.15 Schlick Approximation University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

19. Experiment • Reflections from a shiny floor From Lafortune, Foo, Torrance, Greenberg, SIGGRAPH 97 University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

20. Approximated Reflectance Cook-Torrance approximation Cook-Torrance Model for Metals Reflectance of Copper as a function of wavelength and angle of incidence Measured Reflectance Light spectra Copper spectra University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

21. Lambert’s Cosine Law Ideal Diffuse Reflection • Assume light is equally likely to be reflected in any output direction (independent of input direction). University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

22. “Diffuse” Reflection • Theoretical • Bouguer - Special micro-facet distribution • Seeliger - Subsurface reflection • Multiple surface or subsurface reflections • Experimental • Pressed magnesium oxide powder • Almost never valid at high angles of incidence • Paint manufactures attempt to create ideal diffuse University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

23. Phong Model R(E) E R(L) E N N L L Reciprocity: Distributed light source! University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

24. s Phong Model Diffuse Mirror University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell

25. Properties of the Phong Model • Energy normalize Phong Model University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell