Assignment 2

Coordinate Systems and 3D Projection

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

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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

(u₁,v₁)
(u₂,v₂)
(u₃,v₃)
(u₄,v₄)

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