Free transform using 3d projection matrix

MetaMapper

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Mar 14, 2012
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Is it possible to calculate a 3d projection matrix (i.e. the type of 4x4 matrix used in 3d computer graphics) that will transform a rectangle into an arbitrary convex quadrilateral, if so how?

In other words, if I have four (x,y) source coordinates and I want to transform them into four (x,y) destination coordinates using a standard 4x4 3d projection matrix, how do I calculate the 16 elements of the matrix from my 8 input parameters?

Do I even need four coordinate pairs? Can the problem be solved using just three - to project an arbitrary triangle to another arbitrary triangle?
 
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