Computer Graphics Question

This matrix represents a perspective transformation in homogeneous coordinates for the case of the view plane parallel to the x-y plane and passing through z=0, with the Projection Reference Point on the x-axis at a negative distance from the origin. In summary, the derived transformation matrix accounts for the specific positioning of the view plane and the Projection Reference Point in order to accurately transform points from 3D space to 2D space.
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Problem Statement:

Derive the perspective transformation matrix in homogeneous coordinates for the case of the view plane parallel to the x-y plane and passing through z=0, when the Projection Reference Point is on the x-axis at zprp, where zprp<0.

Attempt to answer:
54mtKkx.png

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Anyone can help me to check whether the solution I do is correct?
Thanks
 
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  • #2
.The transformation matrix can be written as: $\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1/z_{prp} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$where $z_{prp}$ is the distance of the Projection Reference Point from the origin.
 

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Computer graphics is the creation, manipulation, and display of images using computers. It is important because it allows for the visualization and communication of complex ideas and information, and has applications in various industries such as entertainment, education, and research.

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