Visibility problems for polyhedral terrains
Journal of Symbolic Computation
Efficient point location in a convex spatial cell-complex
SIAM Journal on Computing
On the zone of a surface in a hyperplane arrangement
Discrete & Computational Geometry
Ray shooting and parametric search
SIAM Journal on Computing
Ray Shooting Amidst Convex Polyhedra and PolyhedralTerrains in Three Dimensions
SIAM Journal on Computing
Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
Proceedings of the twenty-second annual symposium on Computational geometry
Lines and Free Line Segments Tangent to Arbitrary Three-Dimensional Convex Polyhedra
SIAM Journal on Computing
Linear Data Structures for Fast Ray-Shooting amidst Convex Polyhedra
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Line transversals of convex polyhedra in R3
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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We consider the problem of ray shooting in a threedimensional scene consisting of k (possibly intersecting) convex polyhedra with a total of n facets. That is, we want to preprocess them into a data structure, so that the first intersection point of a query ray and the given polyhedra can be determined quickly. We describe data structures that require Õ(npoly(k)) preprocessing time and storage, and have polylogarithmic query time, for several special instances of the problem. These include the case when the ray origins are restricted to lie on a fixed line l0, but the directions of the rays are arbitrary, the more general case when the supporting lines of the rays pass through l0, and the case of rays orthogonal to z-axis with arbitrary origins. In all cases, this is a significant improvement over previously known techniques (which require Ω(n2) storage, even when k ≪ n).