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Saddle vertex graph (SVG)

Xiang Ying, Xiaoning Wang, Ying He
2013 ACM Transactions on Graphics  
We would like to thank the anonymous reviewers for their valuable comments and Ms. Qian Sun for her help on the figures. This project was supported by an MOE Tier1 Grant.  ...  Abstract This paper presents the Saddle Vertex Graph (SVG), a novel solution to the discrete geodesic problem.  ...  In moving towards this goal, we propose the Saddle Vertex Graph (or SVG), a novel method for computing the geodesic distance on a triangle mesh.  ... 
doi:10.1145/2508363.2508379 fatcat:3ppvd7b6ifevvkibw5hmhqsqi4

GeodesicEmbedding (GE): A High-Dimensional Embedding Approach for Fast Geodesic Distance Queries [article]

Qianwei Xia, Juyong Zhang, Zheng Fang, Jin Li, Mingyue Zhang, Bailin Deng, Ying He
2021 arXiv   pre-print
We then compute a local embedding for each non-saddle vertex.  ...  In this paper, we develop a novel method for fast geodesic distance queries.  ...  As pointed out in [1] , saddle vertices are crucial in solving the discrete geodesic problem, since they serve as the backbone of saddle vertex graphs (SVG).  ... 
arXiv:2108.13821v2 fatcat:3rx2apxgvffybisldqsyhfvnny

User controllable anisotropic shape distribution on 3D meshes

Xiaoning Wang, Tien Hung Le, Xiang Ying, Qian Sun, Ying He
2016 Computational Visual Media  
Thanks to a recent breakthrough in geodesic computation, the local parameterization can be computed at low cost.  ...  Using a pre-computed lookup table, our method can efficiently detect collision among the shapes to be distributed on the 3D mesh.  ...  [42] proposed the saddle vertex graph (SVG), a sparse graph which encodes the geodesic information in a triangle mesh.  ... 
doi:10.1007/s41095-016-0057-1 fatcat:ctckjmh2pfegjmfe6smbicmimq

A Survey of Algorithms for Geodesic Paths and Distances [article]

Keenan Crane, Marco Livesu, Enrico Puppo, Yipeng Qin
2020 arXiv   pre-print
In spite of the difficulty of this problem, recent literature has developed a wide variety of sophisticated methods that enable rapid queries of geodesic information, even on relatively large models.  ...  Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific  ...  [99] define the Discrete Geodesic Graph DGG, which improves over the SVG by allowing approximated paths to go also through non-saddle vertices.  ... 
arXiv:2007.10430v1 fatcat:3agdtrziqrhyjnr3tceltdkidm

Fast Wavefront Propagation (FWP) for Computing Exact Geodesic Distances on Meshes

Chunxu Xu, Tuanfeng Y. Wang, Yong-Jin Liu, Ligang Liu, Ying He
2015 IEEE Transactions on Visualization and Computer Graphics  
Computing geodesic distances on triangle meshes is a fundamental problem in computational geometry and computer graphics.  ...  We draw only a few representative wavefronts to avoid clutter. The small inset in the middle illustrates the computed geodesic distances using iso-distance contours.  ...  ACKNOWLEDGMENTS We thank Keenan Crane for his code of the heat method. The models are courtesy of Aim@Shape and Stanford University.  ... 
doi:10.1109/tvcg.2015.2407404 pmid:26357244 fatcat:6rlei37ktfhydlhysdxggkwd64

Parallel and Scalable Heat Methods for Geodesic Distance Computation [article]

Jiong Tao, Juyong Zhang, Bailin Deng, Zheng Fang, Yue Peng, Ying He
2019 arXiv   pre-print
Moreover, we employ a similar breadth-first strategy to derive a parallel Gauss-Seidel solver for the diffusion step in the heat method.  ...  To further lower the memory consumption from gradient optimization on faces, we also propose a formulation that optimizes the projected gradients on edges, which reduces the memory footprint by about 50%  ...  Geodesic distance query is then performed by computing a shortest path on the graph. Ying et al. [22] proposed the saddle vertex graph (SVG) for encoding geodesic distance.  ... 
arXiv:1812.06060v3 fatcat:ozaxu5w2u5b3lfmcbr5jl2gjzq

Geodesic Distance Computation via Virtual Source Propagation

Philip Ulrich Trettner, David Bommes, Leif Kobbelt
2021 Symposium on Geometry Processing 2021  
Exact geodesic iso-contours are shown in sharp red lines and ours as color gradients in dark blue to avoid occlusion. Source is the red sphere.  ...  Propagation (GSP), on a large mesh with complex topology.  ...  Acknowledgements This project was funded by the European Regional Development Fund within the "HDV-Mess" project under EFRE-0500038. Open access funding enabled and organized by Projekt DEAL.  ... 
doi:10.18154/rwth-2021-08503 fatcat:h7iflnrykjh2hghpne3i5pagu4

Geodesic Distance Computation via Virtual Source Propagation

P. Trettner, D. Bommes, L. Kobbelt
2021 Computer graphics forum (Print)  
Exact geodesic iso-contours are shown in sharp red lines and ours as color gradients in dark blue to avoid occlusion. Source is the red sphere.  ...  Propagation (GSP), on a large mesh with complex topology.  ...  Acknowledgements This project was funded by the European Regional Development Fund within the "HDV-Mess" project under EFRE-0500038. Open access funding enabled and organized by Projekt DEAL.  ... 
doi:10.1111/cgf.14371 fatcat:rwwaa5bum5dqlarakdvq573mga

Fast and exact discrete geodesic computation based on triangle-oriented wavefront propagation

Yipeng Qin, Xiaoguang Han, Hongchuan Yu, Yizhou Yu, Jianjun Zhang
2016 ACM Transactions on Graphics  
Computing discrete geodesic distance over triangle meshes is one of the fundamental problems in computational geometry and computer graphics.  ...  On the basis of such synchronized window propagation, we design a new geodesic computation algorithm based on a triangle-oriented region growing scheme.  ...  Acknowledgments We would like to thank the anonymous reviewers for their valuable comments.  ... 
doi:10.1145/2897824.2925930 fatcat:hi5py7wbeje5nf63ru6vduhcrm

A unified framework for isotropic meshing based on narrow-band Euclidean distance transformation

Yuen-Shan Leung, Xiaoning Wang, Ying He, Yong-Jin Liu, Charlie C. L. Wang
2015 Computational Visual Media  
While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness.  ...  Our algorithm is parallel and memory-efficient, and can construct the shell space for resolutions up to 2048 3 at interactive speed.  ...  Acknowledgements The NTU authors are partially supported by AcRF  ... 
doi:10.1007/s41095-015-0022-4 fatcat:hisusnmbobckdh4n3ac4ankqaq