CS 426 Exercises   3D Primitives and Transformations

1. What is the volume of a 3D point? a 3D ray? a 3D line? a 3D polygon? a 3D sphere?
2. What issues must be addressed by a 3D rendering system but not by a 2D rendering system?
3. Why does a 3D line not have a convenient implicit represenation?
4. What is the implicit representation for a 3D plane?  What are the geometric interpretations of each parameter?
5. What types of 3D transformations can be represented with a 3x3 matrix?
6. What types of 3D transformation can be represented by a 4x4 matrix and 3D homogeneous coordinates?
7. Why do we represent transformations with matrices?
8. Which of the following 3D points with homogenous coordinates is closer to the origin: (8, 4, 2) or (4, 2, 1)?
9. What is a linear transformation?  What are its properties?
10. What is an affine transformation?  Which properties of linear transformation do not apply to affine transformations?
11. What is a projective transformation?  Which properties of affine transformation do not apply to projective transformations?
12. Write a sequence of transformation matrices that scales 3D points based on their distances from an arbitrary origin O = (Ox, Oy, Oz).
13. Write a sequence of transformation matrices that rotates 3D points counter-clockwise by theta degrees about an arbitrary 3D line defined by P1 and P2.