CS 426 Exercises

  1. Write the radiosity equation. For each of the terms (B, E, rho, and F) describe its meaning and give suitable units.
  2. The radiosity equation is system of equations. What are the variables to be solved for? Is the system of equations linear?
  3. Which of the following assumptions must be true for the basic radiosity equation to be a good approximation to the rendering equation: a) all surfaces are diffuse, b) all surfaces are planar, c) the radiosity is the same at all points on a patch element, d) there are no occlusions resulting from one patch blocking light transfers between any other two patches.
  4. If we write the radiosity equation as Ax=b, consider the properties of A: What are the values on the diagonal for planar patch elements? Is the matrix diagonal dominant? Is it symmetric? When can it be singular? Is it positive definite?
  5. The radiosity method studied in class simulates which types of lighting effects: a) shadows, b) direct illumination from area light sources, c) direct illumination from point light sources, d) indirect illumination due to reflections off specular surfaces, e) indirect illumination due to reflections off diffuse surfaces?
  6. Write an an expression for the form factor F_ij for two mutually visible patch elements i and j. Give a short intuitive explanation for each term. How does the expression change if the two patch elements are partially occluded by blockers?
  7. What is the relationship between F_ij and F_ji if we assume uniform light reflection?
  8. What is radiance? How is it different than radiosity?
  9. Is the progressive radiosity method assymptotically more efficient than Gauss-Seidel iteration? If so, why? If not, why do people use progressive refinement?