Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Arrangements of lines in 3-space: a data structure with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Accelerated occlusion culling using shadow frusta
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Computing nice projections of convex polyhedra
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
| Hi-index | 0.00 |
Let P be a convex polytope in Rd. We discuss the problem of placing a light source at infinity so as to minimize or maximize the shadow area of the polytope. By shadow area we mean the (d-1)-volume of the orthogonal projection of P on a hyperplane normal to the direction of illumination. Let n be the number of (d-1)-dimensional facets of the polytope. We exhibit two algorithms for finding the optimal placement of the light source. One algorithm uses &Ogr;(nd-1) space and time to find the optimal placement. The other uses &Ogr(n) space to find the optimal placement in &Ogr;(nd-1 log n) time. Also, we present an interesting result relating the minimum and maximum shadow areas of P to the radii of the inscribed and circumscribed sphere of a zonotope derived from P.