Between umbra and penumbra

Computing 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 by a segment or polygonal light source on a plane in the presence of polygon or polytope obstacles. In particular, we show that a single segment light source may cast on a plane, in the presence of two triangles, four connected components of umbra and that two fat convex obstacles of total complexity n can engender Ω(n) connected components of umbra. In a scene consisting of a segment light source and k disjoint polytopes of total complexity n, we prove an Ω(nk2 + k4 ) lower bound on the maximum number of conn...

• Type: Conference
• Year: 2007
• Where: COMPGEOM
• Authors: Julien Demouth, Olivier Devillers, Hazel Everett, Marc Glisse, Sylvain Lazard, Raimund Seidel
• Keywords: COMPGEOM 2007, Connected Components, Discrete Geometry, Light Source, Umbra