Home exam in advanced topics in Computer Graphics

Three questions:

Q1:

A surface can be represented by a small number of “characteristic” features. A “characteristic” feature, denoted by c-feature, is a point on the surface and its associated quadratic polynomial that locally fits the surface.

A quadratic surface can be represented by (v^t)*M*v + 2*(b^t)v + c = 0, where v = (x, y, z) is the coordinates vector, M is a 3x3 symmetric matrix, b is a 3-vector and c is a nonnegative constant. The coordinates (x,y,z) can be changed to some local frame (local to the characteristic point), so that there is no b^t in the representation. M can be decomposed into U*C*(U^t), where U is an orthogonal matrix (some rotation) and C a diagonal matrix.

Now, two c-features represent locally “similar” surfaces, if their corresponding C matrices are almost similar (one is approximately a scaling of the other). The two c-features represent locally about the same surface (up to rotation) if their C matrices are about the same.

1. Develop this idea and show how to search for a similar piece of surface, given some surface patch.

2. Show how to generate a small but efficient number of c-features for a given 3D mesh (think, for example, about the Stanford bunny). In particular, show where the c-features should be located, how to define them and how to define their number.

Q2.

In the following question you should refer to these papers:

"A Model of Visual Masking for Computer Graphics"
James A. Ferwerda, Sumanta N. Pattanaik, Peter Shirley, Donald P. Greenberg.

http://www.cs.ucf.edu/~sumant/publications/sig97.pdf

"Using Perceptual Texture Masking for Efficient Image Synthesis"
Bruce Walter, Sumanta N. Pattanaik, Donald P. Greenberg.

http://www.cs.ucf.edu/~sumant/publications/EG2002.pdf

"Visibility Culling using Hierarchical Occlusion Maps"
Hansong Zhang, Dinesh Manocha, Tom Hudson, Kenneth E. Hoff III.

Search in: www.acm.org/dl proceedings siggraph97

You may also refer to other papers that you think are relevant.