Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
On shortest paths amidst convex polyhedra
SIAM Journal on Computing
SIAM Journal on Computing
Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time
SCG '87 Proceedings of the third annual symposium on Computational geometry
The algebraic degree of geometric optimization problems
Discrete & Computational Geometry
Shortest path queries in rectilinear worlds of higher dimension (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Precision-sensitive Euclidean shortest path in 3-space (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Monotonicity of rectilinear geodesics in d-space (extended abstract)
Proceedings of the twelfth annual symposium on Computational geometry
Constructing approximate shortest path maps in three dimensions
Proceedings of the fourteenth annual symposium on Computational geometry
Handbook of discrete and computational geometry
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Scheduling for multi-threaded real-time programs via path planning
EMSOFT '06 Proceedings of the 6th ACM & IEEE International conference on Embedded software
Shortest monotone descent path problem in polyhedral terrain
Computational Geometry: Theory and Applications
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
Flying over a polyhedral terrain
Information Processing Letters
Approximate Euclidean shortest paths amid convex obstacles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Shortest descending paths through given faces
Computational Geometry: Theory and Applications
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
A Genetic Algorithm for Shortest Path Motion Problem in Three Dimensions
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
On the Complexity of Finding Paths in a Two-Dimensional Domain II: Piecewise Straight-Line Paths
Electronic Notes in Theoretical Computer Science (ENTCS)
Euclidean shortest paths in simple cube curves at a glance
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Approximate shortest paths in simple polyhedra
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Computing Geodesic Distances in Tree Space
SIAM Journal on Discrete Mathematics
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We revisit the problem of computing shortest obstacle-avoiding paths among obstacles in three dimensions. We prove new hardness results, showing, e.g., that computing Euclidean shortest paths among sets of "stacked" axis-aligned rectangles is NP-complete, and that computing L1-shortest paths among disjoint balls is NP-complete. On the positive side, we present an efficient algorithm for computing an L1-shortest path between two given points that lies on or above a given polyhedral terrain. We also give polynomial-time algorithms for some versions of stacked polygonal obstacles that are "terrain-like" and analyze the complexity of shortest path maps in the presence of parallel halfplane "walls.