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Mirror Polygons - compgeom - Coauthor

coauthor.csail.mit.edu · 1 words · saved by 1 readers

See Zach’s blog about Tokarski’s polygons with mirrored edges where illuminating one point keeps another point dark. But these examples crucially rely on light rays dying whenever they hit a vertex. Can we define a model of reflection (specifically at vertices) where we get a positive result? I raised the possibility that, if we allow lightrays to reflect from vertices according to some model, then perhaps we could obtain a positive result, e.g., a light source at any interior point illuminates the entire polygon—no dark points. Zach showed that the model I suggested allowed a lightray to bend around a reflex vertex, effectively ruling out that model. Here is a variation on the same idea, which at least avoids bending around. (1) Imagine a vertex 𝑣 v truncated orthogonal to the angle bisector. For 𝑣 v convex, lightrays reflect across the angle bisector. For 𝑣 v reflex, we again truncate orthogonal to the angle bisector. But now, if a ray heads toward 𝑣 v from below the line 𝑎

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