UM EECS 487 Fall 2008
Homework Assignment 1
DUE DATE Mon, 9/22/2008, 1:40 pm in lab
September 12, 2008
Show your work for all the questions below. If you don’t show your work, you will get only a third
of the points if your answers are correct.
1. Line rasterization: using the mid-point algorithm presented in class, make all modifications neces-
sary and fill out the tables below to draw the lines specified. If you modify the algorithm, include
the modified algorithm in your answer. (5 pts)
(a) (−3,−4) to (−8,−12)
x y d
... ... ...
(b) (3,−7) to (11,−10)
x y d
... ... ...
2. Clipping (4 pts)
Clip a segment AB against a window Wusing the most efficient of either Cohen-Sutherland or
Cyrus-Beck algorithms or parts thereof where:
(a) A= (−10,20), B = (50,−20),and W={(x, y) : 0 ≤x≤80,0≤y≤30}.
(b) A= (−10,20), B = (50,−20),and W={(x, y) : |x|+|y| ≤ 40}.
3. 3D triangle (3 pts)
(a) Find a 3D vector nof unit length and orthogonal to the triangle ABC where
A= (5,3,2), B = (−1,7,2),and C= (0,0,5).
(b) What is the area of the triangle ABC ?
4. Barycentric coordinates (4 pts)
Find the barycentric coordinates of a point M= (10,25) within triangle P QR
where P= (−10,10), Q = (30,15), R = (10,50).
5. Transforms (4 pts)
Apply the linear transformation given by matrix M="2−2
2 2 #to the triangle ABC , where
A= (1,3), B = (4,3),and C= (4,1). Let A0=M A, B0=M B, and C0=MC . Find the area
of triangle A0B0C0. Describe in words what the transformation Mdoes.
1
