# CS 426 Exercises   3D Viewing

1. Write the parameters describing a pin-hole camera.
2. Write the matrix that transforms a 3D coordinate system with origin O and orthogonal basis vectors e1, e2, and e3 to the standard cartesian coordinate system with the origin at (0,0,0) and basis vectors (1,0,0), (0,1,0), and (0,0,1).
3. To what direction does the camera "towards" vector map during a transformation from the world coordinate system to a right-handed camera coordinate system?
4. What is a parallel projection?  Write a parameterized matrix that can be used for all possible parallel projections.  What is the geometric interpretation for each of the parameters?
5. What is a perspective projection?  Write a parameterized matrix that converts a perspective view frustum to a canonical viewing volume.  What is the geometric interpretation for each parameter?
6. Can any parallel projection be described in terms of a perspective projection?  Vice-versa?
7. Is it possible to represent a 3D->2D parallel projection with a 3x3 matrix?  If so, write it.  If not, why?  Same question for perspective projection.
8. Under what circumstances are parallel projections mostly used?  Same question for perspective projections.  Which type of projection produces the most realistic-looking images?