Week 12 Tutorial

Question 1: Radiosity

Consider the 3x3 room below.

We want to use radiosity to light this room. We shall consider each wall to be made of three equal size patches. For the sake of this exercise we will work in 2D only.

We can use the Nusselt Analog to compute the form factors between patches:

The image above illustrates the computation for F[8,5], below

tan(theta) = 1/1.5
theta = 33.69°
cos(theta) = 0.83

tan(phi) = 2/1.5
phi = 53.13°
cos(phi) = 0.6

F[8,5] = (cos(theta) - cos(phi)) / 2
       = 0.12

a) What are the form factors for the other faces. (Hint: you can exploit a lot of symmetry here)

Suppose the window (patch 2) has emmissive energy E[2] = 1 and diffuse reflection coefficient rho[2] = 0
All the other walls have E[i] = 0 and rho[i] = 0.5.

b)Use four iterations of the progressive refinement algorithm to compute radiosity values for the walls.

The progressive refinement algorithm is shown below. It prioritises patches by how much light they have stored up.

for each patch i:
    B[i] = dB[i] = E[i]

iterate:
  select patch i with max dB[i]:
  calculate F[i][j] for all j
  for each patch j:
    dRad = rho[j] * B[i] *
           F[i][j] * A[j] / A[i]
    B[j] += dRad
    dB[j] += dRad
    dB[i] = 0

To compute the form factor Fji for light sent from patch i to patch j, we use the equation

Fji = Fij Aj/Ai

Question 2: Rational Bezier Splines

Evaluate the co-ordinates of a unit circle, with the centre at (0,0) defined by the parametric equation for a circle

x(theta) = cos theta
y(theta) = sin theta

with theta = 90 and theta = 210

Show how a degree 2 rational Bezier spline with the control points and weights in the table below can represent a unit circle at centre (0,0).

Evaluate the co-ordinates of the circle at theta 90 and 210 by using equivalent values of t and the relevant rational bezier spline equations.

Question 3: Sample Exam Questions

a and b are similar in style to Part B of the final exam which are short answer questions. c,d,e and are similar in style to Part C in the final exam which are design questions

1. Explain the advantages and disadvantages of normal mapping (a.k.a. bump mapping) over adding extra polygons to represent detail.
2. We have looked at three methods for simulating shadows: shadow mapping, ray-tracing and radiosity. What are the pros and cons of each technique? When might they be appropriate to employ?
3. Below is an image of M. C. Escher's Three Worlds. We want to render a short animation of this scene. What techniques would we employ?
   

4. For an art project you need to render a polished wooden bowl like the one below. How would you generate this mesh? What method would you use to texture it? What would its material properties be for lighting?
   
   

5. You want to implement a smoky fire in a 3D game. Name (at least) two different approaches to implementing this. What are the pros and cons of each?

If there is any more time left, please go over material from previous weeks tutorials that were not finished or discuss last minute assignment issues.