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The heat method for distance computation

Authors:

Clarisse Weischedel,

Max WardetzkyAuthors Info & Claims

Communications of the ACM, Volume 60, Issue 11

Pages 90 - 99

https://doi.org/10.1145/3131280

Published: 24 October 2017 Publication History

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Abstract

We introduce the heat method for solving the single- or multiple-source shortest path problem on both flat and curved domains. A key insight is that distance computation can be split into two stages: first find the direction along which distance is increasing, then compute the distance itself. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard sparse linear systems. These systems can be factored once and subsequently solved in near-linear time, substantially reducing amortized cost. Real-world performance is an order of magnitude faster than state-of-the-art methods, while maintaining a comparable level of accuracy. The method can be applied in any dimension, and on any domain that admits a gradient and inner product---including regular grids, triangle meshes, and point clouds. Numerical evidence indicates that the method converges to the exact distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where greater regularity is desired.

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Index Terms

The heat method for distance computation
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image Communications of the ACM

Communications of the ACM Volume 60, Issue 11

November 2017

95 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/3154816

Editor:
Andrew A. Chien
Association for Computing Machinery, New York, NY

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Copyright © 2017 ACM.

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Publication History

Published: 24 October 2017

Published in CACM Volume 60, Issue 11

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https://dl.acm.org/doi/10.1177/10943420241261981
Liu TZhang TChen YHuang YWang C(2024)Neural Slicer for Multi-Axis 3D PrintingACM Transactions on Graphics10.1145/365821243:4(1-15)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658212
Blandano GBurger JCappella ADolci CFacchi GPedersini FSforza CTartaglia GHong JPark J(2024)Gender Classification via Graph Convolutional Networks on 3D Facial ModelsProceedings of the 39th ACM/SIGAPP Symposium on Applied Computing10.1145/3605098.3636039(482-489)Online publication date: 8-Apr-2024
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