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Exam: shadows and light angle

With a focus at (10, 9, 18): 1) find the shadow of P(10, 10, 6) on the PH; 2) the shadow of the cube (centre (12, 8, 3)) on the PH; 3) its shadow on plane π (normal (1, 1, 3), constant -9); 4) the angle of the light direction with the PH.

Step-by-step solution

1. Project P from the focus onto the PH.
2. Project every vertex of the cube and take the convex hull.
3. Project the cube onto π and clip each face with the receiving plane.
4. The angle of the light with the PH is measured between the light-centre direction and the horizontal plane.

Result: P′(10, 10.5, 0); cube shadow with 4 vertices; shadow on π with 4 vertices; light at 81.52° to the PH.

Each shadow has its own receiving plane: do not mix the PH shadow with the inclined-plane shadow.

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