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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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