*CIS 736 (**Computer Graphics)*

Due: Friday, February 2, 2001 (by midnight)

This written assignment is designed to apply your theoretical understanding of the analytic geometry and linear algebra towards principles of computer graphics (CG), and to help you synthesize your own examples of CG problems and methodologies.

Refer to the course intro handout for guidelines on working
with other students. Your solutions should be produced them* only from your
personal notes* (not common work or sources other than the textbook or *properly
cited* references).

** Note**: Remember to

__Warm-up / refresher exercises (basic linear algebra)__

1.
(15 points total) **Coordinate
systems.**

a)
(10 points) **Change of coordinate
system****.**** ***In ***R ^{3}**

b)
(5 points) **Homogeneous coordinates.** Another reason that
homogeneous coordinates are attractive is that 3D points at infinity in Cartesian
coordinates can be represented explicitly in homogeneous coordinates. __How
can this be done?__

__Basic Raster Graphics__

2.
(10 points) **Scan Conversion****.** __Modify__
the midpoint algorithm for scan converting lines to handle lines at any angle.
(You may assume that vertical and horizontal lines, i.e., slope 0 and *¥,
are still detected and handled separately.)*

3.
(10 points) **Transformations. **

4.
(15 points) **Analysis.** * Aliasing, the appearance
of artifacts due to sampling (discretization) error over any function of a continuous
variable that contains sharp changes in intensity, is a serious problem in that
it produces unpleasant or even misleading visual artifacts. Discuss
situations in which these artifacts matter, and those in which they do not.
Discuss various ways to minimize the effects of jaggies, and explain
what the “costs” or those remedies might be.*

__Extra credit__ (5 points) **Clipping****.** *Explain
why the Sutherland-Hodgman polygon clipping algorithm works only for convex
clipping regions. (To receive credit for this problem, you must explain what
happens in the case of concave regions.)*

**Class participation:**

a) (Required)
__Post your “turn-to-a-partner” exercise__ from Wednesday, January 17, 2001,
or a follow-up containing your thoughts on this exercise, to the CIS736 web
board.

b) (Optional)
__Post any unclear points__ regarding basic scan conversion, matrix transformations,
mathematical foundations of CG, or examples that you would like to see covered
in lecture or explained again on the class web board.