Series
Clipping — the series
2 essays on one idea, from the one that introduces it to the one that assumes the rest.
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What happens behind the eye
A point behind the camera has a perfectly plausible image. Dividing by a negative fourth coordinate flips both signs, so the point lands through the principal point on the far side of the frame, and a segment crossing the eye plane is drawn straight, inside the frame, and running in exactly the opposite direction — a direction cosine of −1.0000.
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The near plane can be any plane
Rewrite one row of a projection matrix and the near plane stops being perpendicular to the axis and becomes whatever plane is asked for. Every x and every y is untouched — it is the same projection of the same scene from the same eye — and the depth order is wrecked, which is a clean separation of the two things a projection matrix does.