1. Ray Tracing: ------------------a) Give the main idea

------------------b) Describe the dierence from ray casting.

2. Phone Shading Model:

------------------a) Give the formula and the illustration gure;

------------------b) Explain the meaning of each term.

3. 3D Geometric Transformations: Give the matrix representations for translation, rotation, and scaling, using homogenous coordinates.

4. Texture Mapping:

------------------a) Describe the pipeline

------------------b) Clearly dene the space and the mappings between spaces involved.

5. 3D Rendering Pipeline:

------------------a) Give the main modules and their functions

------------------b) Describe the transformation relation of coordinate systems.

6. Theorems:

------------------a) Give the Euler formula and the computation of Euler characteristics number. Describe the terms.

------------------b) Describe the discrete Gauss-Bonnet theorem and the included terms. Give the computation of discrete Gauss curvature for the vertex on triangular mesh.

7. Bezier Curve:

------------------a) Give the explicit formula with 4 given control points

------------------b) Draw an example: P0 = (0,0),P1 = (1,1),P2 = (2,3),P3 = (4,3) using the constructive algorithm.

8. Splines: Give the denitions of Parametric Continuity and Geometric Continuity.