1
Assignment 4
Qn 1
A texture space with coordinates (s, t) is mapped to the cylinder below:
𝑋𝑋 = 𝑐𝑐𝑐𝑐𝑐𝑐 𝜎𝜎 + 5
𝑌𝑌 = 2𝜏𝜏
𝑍𝑍 = 𝑐𝑐𝑠𝑠𝑠𝑠 𝜎𝜎 + 5
The surface is projected orthographically to (𝑋𝑋,𝑌𝑌).
The following mapping is defined:
(s, t) = (0, 0) → )0,0(),( =τσ
(s, t) = (1, 0) → )0,
2
(),(
π
τσ =
(s, t) = (1, 1) → )
3
,
3
(),(
ππ
τσ =
Pixel order scanning is used. Find the mapping transformation from (𝑋𝑋,𝑌𝑌) to (𝑐𝑐, 𝑡𝑡).
Qn 2 (This question requires knowledge of radiosity)
a) A three face enclosure consists of convex faces 1f , 3f and non-convex face 2f . The two
convex faces 1f , 3f have areas equal to 1 m
2 and the non-convex face 2f has area equal to 2
m2. Given 𝐹𝐹13 = 0.6. Derive the form factor matrix.
b) Face 𝑓𝑓1 is an emitter with 𝐸𝐸1 = 0.4 w/m2. Faces 2f is an emitter with 𝐸𝐸2 = 0.9 w/m
2. Face
𝑓𝑓3 is a pure reflector. Let the reflectivity factors for all three faces be 0.5. Use the progressive
refinement radiosity method to calculate the radiosity of 3f in the second iteration.
c) Give two advantages of the progressive radiosity method compared with the standard
radiosity method.