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Line crossing a solid

Find the entry and exit points of line r (through P(11, 6, 4), direction (2, 1, 2)) in the solid.

Step-by-step solution

1. Put the line inside an auxiliary projecting plane.
2. Find the section of the solid by that plane.
3. Where the line cuts the section outline are the entry and exit points.
4. Check the edge cases: tangent (one point) or outside line (none).

Result: it enters at E(8.99, 5, 1.99) and leaves at S(12, 6.5, 5); chord = 4.51 u.

The chord between entry and exit is the part of the line inside the solid.

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