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The perspective projection matrix, on the view plan z=d where the centre of projection is the origin (0, 0, 0) shall be

  1. $\begin{bmatrix} 0 & 0 & 0 & d \\ 0 & 0 & d & 0 \\ 0 & d & 0 & 0 \\  d & 0 & 0 & 1 \end{bmatrix}$
  2. $\begin{bmatrix} d & 0 & 0 & 0 \\ 0 & d & 0 & 0 \\ 0 & 0 & d & 0 \\  0 & 0 & 1 & 0 \end{bmatrix}$
  3. $\begin{bmatrix} 0 & 0 & 0 & d \\ 0 & 0 & d & 0 \\ 0 & d & 0 & 0 \\  1 & 0 & 0 & 0 \end{bmatrix}$
  4. $\begin{bmatrix} d & 0 & 0 & 0 \\ 0 & d & 0 & 0 \\ 0 & 0 & d & 0 \\  0 & 0 & 0 & 1 \end{bmatrix}$
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ans will be B

c) Derive the matrix for perspective projection with centre of projection at origin and projection plane at z=d.

Perspective projection is a linear projection where three dimensional objects are projected on a picture plane. This has the effect that distant objects appear smaller than nearer objects.

Projection matrix is

D  0  0  0

0  D  0  0

0  0  D  0

0  0  1   0

http://www.niecdelhi.ac.in/uploads/Notes/btech/4sem/it/cg.docx

 

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