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] = 0Note:Nusselt's Analog computes the form factor Fij for light entering the patch i from every patch j.
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.
Control point | Weight |
---|---|
(0, -1) | 1 |
(-sqrt(3), -1) | 0.5 |
(-sqrt(3)/2, 1/2) | 1 |
(0, 2) | 0.5 |
(sqrt(3), 1/2) | 1 |
(sqrt(3), -1) | 0.5 |
(0,-1) | 1 |
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
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?
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.