1. 0 Assignment 1 (Due: 3/9) The projections of two parallel lines, l 1 and l 2, which lie on the ground plane G, onto the image plane I converge at a point p. Give the image coordinates of p and its height.

2. Hint: (1) Define reference frames: ＊ Camera coordinate system ＊ Image coordinate system (2) Using the perspective projection equations and limit theory to derive the coordinates of the vanishing point

3. Consider the camera equipped with a lens, with its image plane at position z' and the plane of scene points in focus at position z. Now suppose that the image plane is moved to. Show that the diameter of corresponding blur circle is, where d is the lens diameter. Use this result to show that the depth of field is given by and conclude that, for a fixed focal length, the depth of filed increases as the lens diameter decreases, and thus the f number increases. Assignment 2 (Due:3/17)

4. A rigid transformation is formulated as: Show that a rigid transformation preserves the angle between two vectors. Assignment 3 (Due:23)

5. Derive the paraperspective projection matrix M. Assignment 4 (Due: 4/6)

6. (Ch. 5) Assignment 6 (Due: 4/27) Show the maximum value of BRDF is.

7. Assignment 7 (Due: 5/4) Derive the radiosity B(P) at point P on a surface due to the thin cylindrical light source with diameter

8. Hand in: (1) The journal paper to be presented in the class, which must be a recent publication within two years. (2) The reading report of the paper. (3) The powerpoint for presentation by (date: 5/18). Assignment 8 (Due: 5/11)

9. Assignment 9 (Due: 6/2)