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Cast shadow on an inclined plane

Find the shadow of the solid (cylinder, centre (12, 5, 3.5)) on plane π with normal (2, 2, 3) and constant -12, with a focus at (12, 5, 10.5).

Step-by-step solution

1. Project every vertex of the solid from the focus onto the receiving plane.
2. Clip each projection to the part of the plane that exists.
3. The shadow is the convex hull of all projected points.
4. Check that the shadow lies on the plane and does not invade the lit area.

Result: shadow with 32 vertices on π.

On an inclined plane you cannot just project onto the PH: the actual receiving plane must be used.

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