Geodesics in heat

Keenan Crane, Clarisse Weischedel, Max Wardetzky
2013 ACM Transactions on Graphics  
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
more » ... r 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.
doi:10.1145/2516971.2516977 fatcat:wbk5u3p64vd5dhg7ucxryovhga