Unformatted text preview: 0
0 0
0 0
x
x
0 y y Â· = 0 z z 0
1
z/d Chapter 5: 3D â€“ Projections, Camera, and Lighting w component not equal to one!
Result is in clip coordinates 19 Perspective Division
â€¢â€¯ Perspective division gives normalized device coordinates
â€¢â€¯ Divide projected x,y,z,w components by projected w. x
xp y yp P Â· = z zp 1
wp xn
xp /wp yn yp /wp = zn zp /wp wn
1
ECS 175 Chapter 5: 3D â€“ Projections, Camera, and Lighting 20 Perspective Projection
â€¢â€¯ We use the projection matrix to map normalized coordinates to the canonical clip volume [1,1]3
zn (âˆ’near) = âˆ’1 AND zn (âˆ’far) = 1
ï¿¿
ï¿¿
far + near
2 Â· far Â· near
1
zn = âˆ’
Â·zâˆ’
Â·âˆ’
far âˆ’ near
far âˆ’ near
z
xn (xp = left) = âˆ’1 xn = ECS 175 ï¿¿ AND xn (xp = right) = 1 AND 2 Â· near
right + left
Â·x+
Â·z
right âˆ’ left
right âˆ’ left Chapter 5: 3D â€“ Projections, Camera, and Lighting ï¿¿ near Â· x
xp =
âˆ’z 1
Â·âˆ’
z
21 Perspective Projection
â€¢â€¯ Full perspective projection matrix:
zn = xn = P = ECS 175 ï¿¿
ï¿¿ âˆ’ 2 Â· near
right + left
Â·x+
Â·z
right âˆ...
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This document was uploaded on 03/12/2014 for the course ECS 175 at UC Davis.
 Spring '08
 Staff

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