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arXiv · 1204.6216

Geodesics in Heat

Keenan Crane·Clarisse Weischedel·Max Wardetzky
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Abstract

We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The method represents a significant breakthrough in the practical computation of distance on a wide variety of geometric domains, since the resulting linear systems can be prefactored once and subsequently solved in near-linear time. In practice, distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We provide numerical evidence that the method converges to the exact geodesic distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where more regularity is required.

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Keenan Crane, Clarisse Weischedel, Max Wardetzky. 2012-09-12. Geodesics in Heat. https://doi.org/10.1145/2516971.2516977

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