On shortest paths in polyhedral spaces
SIAM Journal on Computing
SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces: 730
Journal of Computational Physics
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
Handling degenerate cases in exact geodesic computation on triangle meshes
The Visual Computer: International Journal of Computer Graphics
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
Convergence of geodesics on triangulations
Computer Aided Geometric Design
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Randomized selection on the GPU
Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics
A global algorithm to compute defect-tolerant geodesic distance
SIGGRAPH Asia 2012 Technical Briefs
Saddle vertex graph (SVG): a novel solution to the discrete geodesic problem
ACM Transactions on Graphics (TOG)
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In many graphics applications, the computation of exact geodesic distance is very important. However, the high computational cost of existing geodesic algorithms means that they are not practical for large-scale models or time-critical applications. To tackle this challenge, we propose the Parallel Chen-Han (or PCH) algorithm, which extends the classic Chen-Han (CH) discrete geodesic algorithm to the parallel setting. The original CH algorithm and its variant both lack a parallel solution because the windows (a key data structure that carries the shortest distance in the wavefront propagation) are maintained in a strict order or a tightly coupled manner, which means that only one window is processed at a time. We propose dividing the CH's sequential algorithm into four phases, window selection, window propagation, data organization, and events processing so that there is no data dependence or conflicts in each phase and the operations within each phase can be carried out in parallel. The proposed PCH algorithm is able to propagate a large number of windows simultaneously and independently. We also adopt a simple yet effective strategy to control the total number of windows. We implement the PCH algorithm on modern GPUs (such as Nvidia GTX 580) and analyze the performance in detail. The performance improvement (compared to the sequential algorithms) is highly consistent with GPU double-precision performance (GFLOPS). Extensive experiments on real-world models demonstrate an order of magnitude improvement in execution time compared to the state-of-the-art.