CSC 461: Computer Graphics I (Fall 2006)
Assignment 4
Due November 29,
2006 in class
All questions are equally
scored.
- Explain
the following concepts:
- Parallel
projection
- Perspective
projection
- Oblique
projection
- Projection
normalization
- Perspective
normalization
- In
Chapter 5: Viewing of the text, we discuss the perspective projections of
objects. We claim that perspective projections preserve lines: a line will
be projected to a line by perspective projection. Read Sections 5.4.1 and
prove this claim.
- How do
the OpenGL projection matrices change if the COP (Center
of Projection) is not at the
origin? Assume the COP is at (0, 0, 10) and the projection plane is z=0.
- If we
were to use orthogonal projections to draw the coordinate axes, the x- and
y-axes would lie in the plane of the paper, but the z-axis would point out
of the page. Instead, we can draw the x- and y-axes meeting at a 90-degree
angle, with the z-axis going off at -135 degrees from the x-axis. Find the
matrix that projects the original orthogonal-coordinate axes to this view.