Storing the subdivision of a polyhedral surface

Authors:
D Mount
Affiliations:
Department of Computer Science and University of Maryland Institute for Advanced Computer Studies, University of Maryland, College Park, MD
Venue:
SCG '86 Proceedings of the second annual symposium on Computational geometry
Year:
1986

Citing 4
Cited 2

Optimal point location in a monotone subdivision

SIAM Journal on Computing
The discrete geodesic problem

SIAM Journal on Computing
Primitives for the manipulation of general subdivisions and the computation of Voronoi

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On shortest paths in polyhedral spaces

STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing

Voronoi diagrams—a survey of a fundamental geometric data structure

ACM Computing Surveys (CSUR)
On the shortest paths between two convex polyhedra

Journal of the ACM (JACM)

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Abstract

A common structure arising in computational geometry is the subdivision of a plane defined by the faces of a straight line planar graph. We consider a natural generalization of this structure on a polyhedral surface. The regions of the subdivision are bounded by geodesics on the surface of the polyhedron. A method is given for representing such a subdivision that is efficient both with respect to space and the time required to answer a number of different queries involving the subdivision. For example, given a point @@@@ on the surface of the polyhedron, the region of the subdivision containing x can be determined in logarithmic time. If n denotes the number of edges in the polyhedron, and m denotes the number of geodesics in the subdivision, then the space required by the data structure is &Ogr;((n + m) log (n + m)). Combined with existing algorithms for computing Voronoi diagrams on the surface of polyhedra, this structure provides an efficient solution to the nearest neighbor query problem on polyhedral surfaces.