*To be handed in at the beginning of class on
Wednesday, October 5, 2005*

1)

Draw
the left-handed coordinate system KLM having axes K, L, and M.

Add notation to indicate the direction of positive rotation around each axis.

2)

Answer the following questions given the following:

- a single point located at X=1.75 feet, Y= 10 feet, Z= 3 feet relative to the center of the CAVE

- a user with head position at (0,0,6), facing the front wall of the CAVE
- a distance of 0.5 between the eyes of the user

a) Use a graph of the YZ plane to
determine the Z location of the point on the front CAVE wall for each eye

b) Use a graph of the XY plane to
determine the X location of the point on the front CAVE wall for each eye

c) Use a graph of the XZ plane to draw the
point as it is rendered on the front CAVE wall for each eye

3)

Given
a texture of size X=100 by Y=200 and a polygon with the four texture
coordinates

(u_{1},v_{1})

(u_{2},v_{2})

(u_{3},v_{3})

(u_{4},v_{4})

in
counter-clockwise order

a) Assign texture coordinates such that
the right half of the texture (X>50) covers the polygon

b) What coordinates bound the area of the texture
displayed given texture coordinates:

(0,0)

(0.25,0)

(0.5,0.75)

(0.25,0.75)

c) Assign texture coordinates such that
the texture is repeated a total of two times in the Y direction