On the Complexity of Umbra and Penumbra

  • Demouth, Julien
  • Devillers, Olivier
  • Everett, Hazel
  • Glisse, Marc
  • Lazard, Sylvain
  • Seidel, Raimund
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Publication date
January 2009
Publisher
Elsevier BV

Abstract

International audienceComputing shadow boundaries is a difficult problem in the case of non-point light sources. A point is in the umbra if it does not see any part of any light source; it is in full light if it sees entirely all the light sources; otherwise, it is in the penumbra. While the common boundary of the penumbra and the full light is well understood, less is known about the boundary of the umbra. In this paper we prove various bounds on the complexity of the umbra and the penumbra cast on a fixed plane by a segment or convex polygonal light source in the presence of convex polygonal or polyhedral obstacles in $\mathbb{R}^3$. In particular, we show that a single segment light source may cast on a plane, in the presence of two disj...

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