3D Viewing

- Write the parameters describing a pin-hole camera.
- 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).
- To what direction does the camera "towards" vector map during a transformation from the world coordinate system to a right-handed camera coordinate system?
- 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?
- 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?
- Can any parallel projection be described in terms of a perspective projection? Vice-versa?
- 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.
- Under what circumstances are parallel projections mostly used? Same question for perspective projections. Which type of projection produces the most realistic-looking images?