On shortest paths in polyhedral spaces
SIAM Journal on Computing
SIAM Journal on Computing
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
A Note on the Complexity of Dijkstra's Algorithm for Graphs with Weighted Vertices
IEEE Transactions on Computers
New results on shortest paths in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
Proceedings of the twenty-second annual symposium on Computational geometry
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Shortest Path Problems on a Polyhedral Surface
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A Level Set Formulation of Geodesic Curvature Flow on Simplicial Surfaces
IEEE Transactions on Visualization and Computer Graphics
Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Efficiently Computing Exact Geodesic Loops within Finite Steps
IEEE Transactions on Visualization and Computer Graphics
A global algorithm to compute defect-tolerant geodesic distance
SIGGRAPH Asia 2012 Technical Briefs
Hi-index | 0.00 |
As a fundamental concept, geodesics play an important role in many geometric modeling applications. However, geodesics are highly sensitive to topological changes; a small topological shortcut may result in a significantly large change of geodesic distance and path. Most of the existing discrete geodesic algorithms can only be applied to noise-free meshes. In this paper, we present a new algorithm to compute the meaningful approximate geodesics on polygonal meshes with holes. Without the explicit hole filling, our algorithm is completely intrinsic and independent of the embedding space; thus, it has the potential for isometrically deforming objects as well as meshes in high dimensional space. Furthermore, our method can guarantee the exact solution if the surface is developable. We demonstrate the efficacy of our algorithm in both real-world and synthetic models.