Lecture_Chapter5_b

Z z 0 1 zd chapter 5 3d projections camera and

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Unformatted text preview: 0 0 0 0 0 x x 0 y y · = 0 z z 0 1 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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