article

Fast exact and approximate geodesics on meshes

Authors:

Vitaly Surazhsky,

Tatiana Surazhsky,

Danil Kirsanov,

Steven J. Gortler,

Hugues HoppeAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 24, Issue 3

Pages 553 - 560

https://doi.org/10.1145/1073204.1073228

Published: 01 July 2005 Publication History

Abstract

The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of the exact "single source, all destination" algorithm presented by Mitchell, Mount, and Papadimitriou (MMP). We show that the algorithm runs much faster in practice than suggested by worst case analysis. Next, we extend the algorithm with a merging operation to obtain computationally efficient and accurate approximations with bounded error. Finally, to compute the shortest path between two given points, we use a lower-bound property of our approximate geodesic algorithm to efficiently prune the frontier of the MMP algorithm. thereby obtaining an exact solution even more quickly.

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Cited By

Chen SHei NHu SYue ZHe Y(2024)Convex Quadratic Programming for Computing Geodesic Distances on Triangle MeshesMathematics10.3390/math1207099312:7(993)Online publication date: 27-Mar-2024
https://doi.org/10.3390/math12070993
Li YHe SZhang YHuang Q(2024)Modeling and Analysis of Creeping Wave Diffraction of Complex Target Surface Based on Planar Mesh Model2024 Photonics & Electromagnetics Research Symposium (PIERS)10.1109/PIERS62282.2024.10618116(1-5)Online publication date: 21-Apr-2024
https://doi.org/10.1109/PIERS62282.2024.10618116
Grigorev IMursalimov E(2024)Method of Forming Paths for Uniform Surface Treatment for Objects of Complex Shape2024 IEEE 25th International Conference of Young Professionals in Electron Devices and Materials (EDM)10.1109/EDM61683.2024.10614983(1650-1655)Online publication date: 28-Jun-2024
https://doi.org/10.1109/EDM61683.2024.10614983
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Index Terms

Fast exact and approximate geodesics on meshes
1. Computing methodologies
  1. Computer graphics
    1. Image manipulation
    2. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 24, Issue 3

July 2005

826 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1073204

Issue’s Table of Contents

Copyright © 2005 ACM.

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Association for Computing Machinery

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Publication History

Published: 01 July 2005

Published in TOG Volume 24, Issue 3

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Cited By

Chen SHei NHu SYue ZHe Y(2024)Convex Quadratic Programming for Computing Geodesic Distances on Triangle MeshesMathematics10.3390/math1207099312:7(993)Online publication date: 27-Mar-2024
https://doi.org/10.3390/math12070993
Li YHe SZhang YHuang Q(2024)Modeling and Analysis of Creeping Wave Diffraction of Complex Target Surface Based on Planar Mesh Model2024 Photonics & Electromagnetics Research Symposium (PIERS)10.1109/PIERS62282.2024.10618116(1-5)Online publication date: 21-Apr-2024
https://doi.org/10.1109/PIERS62282.2024.10618116
Grigorev IMursalimov E(2024)Method of Forming Paths for Uniform Surface Treatment for Objects of Complex Shape2024 IEEE 25th International Conference of Young Professionals in Electron Devices and Materials (EDM)10.1109/EDM61683.2024.10614983(1650-1655)Online publication date: 28-Jun-2024
https://doi.org/10.1109/EDM61683.2024.10614983
Qiao HTan JYan JSun CYin XLi ZWu JGuan HWen SZhang MXu SJin L(2024)A comprehensive evaluation of the phenotype-first and data-driven approaches in analyzing facial morphological traitsiScience10.1016/j.isci.2024.10932527:3(109325)Online publication date: Mar-2024
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Bulut VOnan ASenyayla B(2024)Obtaining the optimal shortest path between two points on a quasi-developable Bézier-type surface using the Geodesic-based Q-learning algorithmEngineering Applications of Artificial Intelligence10.1016/j.engappai.2024.108821136(108821)Online publication date: Oct-2024
https://doi.org/10.1016/j.engappai.2024.108821
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https://doi.org/10.1016/j.cpc.2024.109333
Liu WWang PChen SXin STu CHe YWang W(2024)Towards geodesic ridge curve for region-wise linear representation of geodesic distance fieldComputer Aided Geometric Design10.1016/j.cagd.2024.102291111(102291)Online publication date: Jun-2024
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Ryckelynck DCasenave FAkkari NRyckelynck DCasenave FAkkari N(2024)Industrial Application: Uncertainty Quantification in Lifetime Prediction of Turbine BladesManifold Learning10.1007/978-3-031-52764-7_5(71-95)Online publication date: 21-Feb-2024
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Huang QHe SZhang YZhu GChen H(2023)Research on the computational method of creeping waves diffraction of arbitrary complex target based on the planar mesh modelOptics Express10.1364/OE.47745331:4(6426)Online publication date: 8-Feb-2023
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Loth FKiel TBusch KKristensen P(2023)Surface roughness in finite-element meshes: application to plasmonic nanostructuresJournal of the Optical Society of America B10.1364/JOSAB.47688340:3(B1)Online publication date: 12-Jan-2023
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