Shadow of a solid on the PH

Find the shadow of the solid (cylinder, centre (14, 5, 3.5)) on the horizontal plane with parallel light of direction (1, 0, -1).

Step-by-step solution

Project every vertex of the solid from the focus (or along the light direction) onto the PH.
The shadow is the convex hull of all those points.
Clip the shadow to the part of the plane that actually exists (y ≥ 0).
Check that the shadow cannot be larger than the projection of the solid from the light.

Result: shadow with 34 vertices.

The shadow of a convex solid is the convex hull of the shadows of its vertices: there is no need to compute it face by face.