The heat method for distance computation (original) (raw)
Published: 24 October 2017 Publication History
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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Communications of the ACM Volume 60, Issue 11
November 2017
95 pages
Copyright © 2017 ACM.
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Publication History
Published: 24 October 2017
Published in CACM Volume 60, Issue 11
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Affiliations
Keenan Crane
Carnegie Mellon University
Clarisse Weischedel
Max Wardetzky