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ACM"],"published-print":{"date-parts":[[2017,10,24]]},"abstract":"<jats:p>\n            We introduce the\n            <jats:italic>heat method<\/jats:italic>\n            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.\n          <\/jats:p>","DOI":"10.1145\/3131280","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T14:19:33Z","timestamp":1509027573000},"page":"90-99","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":165,"title":["The heat method for distance computation"],"prefix":"10.1145","volume":"60","author":[{"given":"Keenan","family":"Crane","sequence":"first","affiliation":[{"name":"Carnegie Mellon University"}]},{"given":"Clarisse","family":"Weischedel","sequence":"additional","affiliation":[{"name":"University of G\u00f6ttingen"}]},{"given":"Max","family":"Wardetzky","sequence":"additional","affiliation":[{"name":"University of G\u00f6ttingen"}]}],"member":"320","published-online":{"date-parts":[[2017,10,24]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964997"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/1496770.1496882"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12611"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of Workshop on Vision, Modeling, and Visualization (VMV)","author":"Bommes D.","year":"2007","unstructured":"Bommes , D. , Kobbelt , L. 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