Computer Graphics Fall 2010 group home

Homework 5, Due by email to Peter Honig on Thu Oct 7.

This has lots of little math questions based on the lectures.

1. (1 pt) What is the vector from point (1,2,3) to (4,6,5)?
2. (1) What is the parametric equation of the line from (1,2,3) to (4,6,5)?
3. (1) What is the parametric equation of the line from (1,2,3) in the direction (4,6,5)?
4. (1) What is the parametric equation of the plane with the points (1,0,0), (0,1,0), and (0,0,2)?
5. (1) What is the normal to that plane?
6. (1) Give 3 homogeneous points corresponding to the Cartesian point (2,2,1).
7. (1) Give the Cartesian points corresponding to the homogeneous points (1,3,2,4) and (5,7,8,6).
8. (1) Give 2 homogeneous matrices for the translation by (3,1,2).
9. (1) Here's the Cartesian matrix for a nonuniform scale: {$$ \left(\begin{array}{ccc} 2&0&0\\0&5&0\\0&0&4\end{array}\right) $$} Write the homogeneous matrix for it.
10. (5) Modify gasket3 in the fashion of feedback to store the drawn objects and then list them.