SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM (JACM)
Constructing Approximate Shortest Path Maps in Three Dimensions
SIAM Journal on Computing
Minimal Paths in 3D Images and Application to Virtual Endoscopy
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Approximating Shortest Paths on a Nonconvex Polyhedron
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
A multi-resolution surface distance model for k-NN query processing
The VLDB Journal — The International Journal on Very Large Data Bases
Indexing land surface for efficient kNN query
Proceedings of the VLDB Endowment
Finding shortest path on land surface
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
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Finding single pair shortest paths on surface is a fundamental problem in various domains, like Geographic Information Systems (GIS) 3D applications, robotic path planning system, and surface nearest neighbor query in spatial database, etc. Currently, to solve the problem, existing algorithms must traverse the entire polyhedral surface. With the rapid advance in areas like Global Positioning System (GPS), Computer Aided Design (CAD) systems and laser range scanner, surface models are becoming more and more complex. It is not uncommon that a surface model contains millions of polygons. The single pair shortest path problem is getting harder and harder to solve. Based on the observation that the single pair shortest path is in the locality, we propose in this paper efficient methods by excluding part of the surface model without considering them in the search process. Three novel expansion-based algorithms are proposed, namely, Naïve algorithm, Rectangle-based Algorithm and Ellipse-based Algorithm. Each algorithm uses a two-step approach to find the shortest path. (1) compute an initial local path. (2) use the value of this initial path to select a search region, in which the global shortest path exists. The search process terminates once the global optimum criteria are satisfied. By reducing the searching region, the performance is improved dramatically in most cases.