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3d->2d transformation?

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I know the basics of how this works. you have a 3d vertex, divide the x and the y by the z, and there, you have a distance-related 2d coordinate. But how the heck does one do this in a matrix? I''ve always thought that the perspective matrix does this, but upon closer inspection, it doesn''t appear to convert 3d coords to 2d at all, at least, as far as I can tell. So how the heck does one do this?

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T([x,y,z]) = [x/z, y/z]

This is not a linear transformation, so you don''t do this with a matrix.
There is no way to do this with a matrix.

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that''s what I thought.

ok, thanks. Turns out I don''t really need to convert to screen coordinates anyway.

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