6.8 Exercises

1. Compute the form factor for the following configuration. Two identical rectangular plates are positioned parallel to each other (Figure 6.29). Compute the form factor using Monte Carlo integration and compare with the analytical solution. Make a plot of absolute error as a function of the number of sample lines used. Compare empirically stratified, non-stratified, and low-discrepancy sampling (e.g., Halton or Niederreiter; see Section 3.6.7).

   
   

   
   Figure 6.29: Two parallel rectangular plates.

2. Repeat the Exercise 1, but now the plates are perpendicular to each other (Figure 6.30).

   
   

   
   Figure 6.30: Two perpendicular rectangular plates.

3. When comparing the Monte Carlo results of the configurations in Exercises 1 and 2, is there a difference in the convergence speed for the two cases? If there is, explain this difference. If there is no difference in convergence speed, why not?

4. Given is the scene in Figure 6.31 containing 3 diffuse polygons with diffuse reflectivity values of 0 .3, 0 .4 and 0 .5; and 1 diffuse light source emitting 500 watts, covering the complete ceiling.

   
   Figure 6.31: Four diffuse square plates.

   Compute the relevant form factors using the analytic expressions given above, and compute the radiosity solution for this scene. You can solve the linear system by hand or use a mathematical software tool.

1. Increase the diffuse reflectivity for all surfaces in the scene by 10%. What is the result on the new radiosity values? Do the new radiosity values increase by more or less than 10%.?