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) → (σ,τ)=(0,0) (s,t)=(1,0) → (σ,τ)=(π ,0)
(s,t)=(1,1) → (σ,τ)=(π,π) 33
2
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 f1 , f3 and non-convex face f2 . The two convex faces f , f have areas equal to 1 m2 and the non-convex face f has area equal to 2
131 3 2 m . Given 𝐹𝐹 = 0.6. Derive the form factor matrix.
2
b) Face𝑓𝑓1isanemitterwith𝐸𝐸1=0.4w/m.Faces f2 isanemitterwith𝐸𝐸2=0.9w/m.Face
22
𝑓𝑓 is a pure reflector. Let the reflectivity factors for all three faces be 0.5. Use the progressive
3
refinement radiosity method to calculate the radiosity of f3
c) Give two advantages of the progressive radiosity method compared with the standard radiosity method.
1
in the second iteration.