Appearance Models for Graphics

1. Appearance Models for Graphics COMS 6998-3, Lecture 2 BRDFs and Radiometry Many slides courtesy Pat Hanrahan: http://graphics.stanford.edu/courses/cs348b-02/lectures/lecture4/illumination.pdf

3. Radiometry • Physical measurement of electromagnetic energy • We consider light field • Transport theory • Radiance, Irradiance • Reflection functions: BRDF • Examples, Properties • Simple BRDF models

4. Transport Theory • Flow of stuff. In this case, stuff = photons of light • Consider particle flow through small area [CW18] density

7. Radiance • Power per unit projected area perpendicular to the ray per unit solid angle in the direction of the ray • Symbol: L(x,ω)(W/m2 sr) • Flux given by dΦ = L(x,ω) cos θ dω dA

8. Radiance properties • Radiance is constant as it propagates along ray • Derived from conservation of flux • Fundamental in Light Transport.

11. Radiance properties • Sensor response proportional to surface radiance (constant of proportionality is throughput) • Far away surface: See more, but subtends smaller angle • Wall is equally bright across range of viewing distances Consequences • Radiance associated with rays in a ray tracer • All other radiometric quantities derived from radiance

14. Irradiance, Radiosity • Irradiance E is the radiant power per unit area • Integrate incoming radiance over hemisphere • Projected solid angle (cos θ dω) • Uniform illumination: Irradiance = π [CW 24,25] • Units: W/m2 • Radiosity • Power per unit area leaving surface (like irradiance)

17. BRDF • Reflected Radiance proportional to Irradiance • Constant proportionality: BRDF [CW pp 28,29] • Bidirectional Reflection Distribution Function • (4 Vars) • Reflectance Equation [CW pp 30]

20. Mirror

21. Lambertian

22. Reflectance/Energy Conservation

30. Retroreflection

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

32. Representations

33. Reparameterizations