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0 0
0 0
x
x
0 y y · = 0 z z 0
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z/d Chapter 5: 3D – Projections, Camera, and Lighting w component not equal to one!
Result is in clip coordinates 19 Perspective Division
• Perspective division gives normalized device coordinates
• Divide projected x,y,z,w components by projected w. x
xp y yp P · = z zp 1
wp xn
xp /wp yn yp /wp = zn zp /wp wn
1
ECS 175 Chapter 5: 3D – Projections, Camera, and Lighting 20 Perspective Projection
• We use the projection matrix to map normalized coordinates to the canonical clip volume [1,1]3
zn (−near) = −1 AND zn (−far) = 1
far + near
2 · far · near
1
zn = −
·z−
·−
far − near
far − near
z
xn (xp = left) = −1 xn = ECS 175 AND xn (xp = right) = 1 AND 2 · near
right + left
·x+
·z
right − left
right − left Chapter 5: 3D – Projections, Camera, and Lighting near · x
xp =
−z 1
·−
z
21 Perspective Projection
• Full perspective projection matrix:
zn = xn = P = ECS 175
− 2 · near
right + left
·x+
·z
right...
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 Spring '08
 Staff

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