Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
Computerized girth determination for custom footwear manufacture
Computers and Industrial Engineering
A multi-resolution surface distance model for k-NN query processing
The VLDB Journal — The International Journal on Very Large Data Bases
Parameterization of 3D Surface Patches by Straightest Distances
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Indexing land surface for efficient kNN query
Proceedings of the VLDB Endowment
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Point cloud surfaces using geometric proximity graphs
Computers and Graphics
Scalable shortest paths browsing on land surface
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Finding shortest path on land surface
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Expansion-Based algorithms for finding single pair shortest path on surface
W2GIS'04 Proceedings of the 4th international conference on Web and Wireless Geographical Information Systems
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Straightest paths on meshes by cutting planes
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Proximity graphs for defining surfaces over point clouds
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
| Hi-index | 0.00 |
A new algorithm is proposed for calculating the approximate shortest path on a polyhedral surface. The method mainly uses Dijkstra's algorithm and is based on selective refinement of the discrete graph of a polyhedron. Although the algorithm is an approximation, it has the significant advantages of being fast, easy to implement, high approximation accuracy, and numerically robust. The approximation accuracy and computation time are compared between this approximation algorithm and the extended Chen & Han (ECH) algorithm that can calculate the exact shortest path for non-convex polyhedra. The approximation algorithm can calculate shortest paths within 0.4% accuracy to roughly 100-1000 times faster than the ECH algorithm in our examples. Two applications are discussed of the approximation algorithm to geometric modeling.