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Graph."],"published-print":{"date-parts":[[2020,12,31]]},"abstract":"<jats:p>\n            This paper introduces a new approach to computing geodesics on polyhedral surfaces---the basic idea is to iteratively perform\n            <jats:italic>edge flips<\/jats:italic>\n            , in the same spirit as the classic Delaunay flip algorithm. This process also produces a triangulation conforming to the output geodesics, which is immediately useful for tasks in geometry processing and numerical simulation. More precisely, our FlipOut algorithm transforms a given sequence of edges into a locally shortest geodesic while avoiding self-crossings (formally: it finds a geodesic in the same\n            <jats:italic>isotopy class<\/jats:italic>\n            ). The algorithm is guaranteed to terminate in a finite number of operations; practical runtimes are on the order of a few milliseconds, even for meshes with millions of triangles. The same approach is easily applied to curves beyond simple paths, including closed loops, curve networks, and multiply-covered curves. We explore how the method facilitates tasks such as straightening cuts and segmentation boundaries, computing geodesic B\u00e9zier curves, extending the notion of\n            <jats:italic>constrained Delaunay triangulations (CDT)<\/jats:italic>\n            to curved surfaces, and providing accurate boundary conditions for partial differential equations (PDEs). Evaluation on challenging datasets such as\n            <jats:italic>Thingi10k<\/jats:italic>\n            indicates that the method is both robust and efficient, even for low-quality triangulations.\n          <\/jats:p>","DOI":"10.1145\/3414685.3417839","type":"journal-article","created":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T21:51:05Z","timestamp":1606513865000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":65,"title":["You can find geodesic paths in triangle meshes by just flipping edges"],"prefix":"10.1145","volume":"39","author":[{"given":"Nicholas","family":"Sharp","sequence":"first","affiliation":[{"name":"Carnegie Mellon University"}]},{"given":"Keenan","family":"Crane","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University"}]}],"member":"320","published-online":{"date-parts":[[2020,11,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3144567"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2019.1566927"},{"key":"e_1_2_2_3_1","unstructured":"E. 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