9.Homogeneous coords, ctd. 3D rotations.


1, What is the effect of multiply by the matirx 
|1 0 0 0|
|0 1 0 0|
|0 0 1 0|
|a b c 0|?

2, Express the (planar) symmetry about the line passing through (7; 8)
and (1; 2) as a 3*3 transformation matrix or as a product of 3*3 matrices
(explain what they are).

3,What is a triangle with vertices (0, 0, 1), (1, 2, 1), (1, 0, 0) mapped to by
the transformation with the following matrix in the homogenous coordinates
| 1 1 3 1|
|-1 0 0 2|
| 5 1 1 0|
| 0 0 0 1|  ?

4,The vertices of a triangle project to (0, 0), (1, 3) and (3, 1). Let's
say that the depth values (computed using the perspective transformation
matrix) at these vertices are 1, 3 and 4 (respectively). What is the depth of
the point on that triangle which projects to (1, 1)?

5,Write the matrix (in homogenous coordinates) of the planar transformation
that rotates by 45 degrees around the point (1, 2) and then translate by(1,2,3).