SIAM Journal on Computing
Algebraic optimization: the Fermat-Weber location problem
Mathematical Programming: Series A and B
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Fast approximations for sums of distances, clustering and the Fermat--Weber problem
Computational Geometry: Theory and Applications
An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Facility Location Constrained to a Polygonal Domain
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
Aggregate nearest neighbor queries in spatial databases
ACM Transactions on Database Systems (TODS)
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Calculating the meeting point of scattered robots on weighted terrain surfaces
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
Proceedings of the twenty-second annual symposium on Computational geometry
Stable marker-particle method for the Voronoi diagram in a flow field
Journal of Computational and Applied Mathematics
Handling degenerate cases in exact geodesic computation on triangle meshes
The Visual Computer: International Journal of Computer Graphics
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
On finding approximate optimal paths in weighted regions
Journal of Algorithms
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
Isotropic Mesh Simplification by Evolving the Geodesic Delaunay Triangulation
ISVD '11 Proceedings of the 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering
| Hi-index | 7.29 |
Given P, a simple connected, possibly non-convex, polyhedral surface composed of positively weighted triangular faces, we consider paths from generalized sources (points, segments, polygonal chains or polygonal regions) to points on P that stay on P and avoid obstacles (segments, polygonal chains or polygonal regions). The distance function defined by a generalized source is a function that assigns to each point of P the cost of the shortest path from the source to the point. In this paper we present an algorithm for computing approximate generalized distance functions. We also provide an algorithm that computes a discrete representation of the approximate distance function and, as applications, algorithms for computing discrete order-k Voronoi diagrams and for approximately solving facility location problems. Finally, we present experimental results obtained with our implementation of the provided algorithms.