Angle	cos	sin
0	1	0
30	√3/2	1/2
45	√2/2	√2/2
60	1/2	√3/2
90	0	1

1) (2 points) We have a tiny 8x4 raster screen. What size frame buffer in bytes is required to store pixel the colors for an RGB system? 8*4*24/8=96 bytes

2) (2 points) Draw the resulting diagram when I make the following GL calls

glBegin(GL_LINES); V1

glVertex3fv(vertex1); *

glVertex3fv(vertex2); V2* *V3

glVertex3fv(vertex3); V4* * V5

glVertex3fv(vertex4);

glVertex3fv(vertex5);

glEnd();

4) Given the following polyline, shade only the interior regions. Show all work.

a) (3 points)Use the odd-even rule.

Crosses even edges exterior

Cross odd edges interior

b) (3 points)Use the non-zero winding rule R to L add one

L to R subtract one

If nonzero, interior

Line algorithms and anti-aliasing

6) (5 points)Consider the line from (7 , 2) to (12 , 4). Use Bresenham’s algorithm to determine the pixels. Plot on the Raster Screen. Show all work.

7 2

K P_k X_k+1 Y_k+1

0 -1 8 2

1 3 9 3

2 -3 10 3

1 1 11 4

4 -5 12 4

ΔX=5 2ΔX=10

ΔY=2 2ΔY=4

M < 1 P₀ = 2ΔY – ΔX = 4-5=-1

If P_k < 0, plot X_k +1, Y_k: P_k+1 = P_k+2ΔY P_k+1 = P_k+4

Else plot X_k +1, Y_k+1: P_k+1 = P_k+2ΔY-2ΔX

P_k+1 = P_k+4-10= P_k-2

				X	X
		X	X
X	X

7) (5 points) Consider the line from (0 , 3) to (2 , 7). Use Bresenham’s algorithm to determine the pixels. Plot on the Raster Screen. Show all work.

ΔX=2 2ΔX=4 ΔY=4 2ΔY=8

M < 1 P₀ = 2ΔX – ΔY = 8-8=0

If P_k < 0, plot X_k, Y_k+1 P_k+1 = P_k+2ΔX P_k+1 = P_k+4

Else plot X_k +1, Y_k+1 P_k+1 = P_k+2ΔX-2ΔY P_k+1 = P_k+4-8= P_k-4

0 3

K P_k X_k+1 Y_k+1

0 0 1 4

1 -4 1 5

2 0 2 6

3 -4 2 7