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Its construction is based on theory developed in [Gu et al. 2018b] and [Springborn 2020], relying on results on hyperbolic ideal Delaunay triangulations. Generality is achieved by considering the surface's intrinsic triangulation as a degree of freedom, and particular attention is paid to the proper treatment of surface boundaries. While via a double cover approach the case with boundary can be reduced to the case without boundary quite naturally, the implied symmetry of the setting causes additional challenges related to stable Delaunay-critical configurations that we address explicitly. We furthermore explore the numerical limits of the approach and derive continuous maps from the discrete metrics.<\/jats:p>","DOI":"10.1145\/3478513.3480557","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T18:28:45Z","timestamp":1639160925000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":28,"title":["Efficient and robust discrete conformal equivalence with boundary"],"prefix":"10.1145","volume":"40","author":[{"given":"Marcel","family":"Campen","sequence":"first","affiliation":[{"name":"Osnabr\u00fcck University, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ryan","family":"Capouellez","sequence":"additional","affiliation":[{"name":"NYU"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hanxiao","family":"Shen","sequence":"additional","affiliation":[{"name":"NYU"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leyi","family":"Zhu","sequence":"additional","affiliation":[{"name":"NYU"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniele","family":"Panozzo","sequence":"additional","affiliation":[{"name":"NYU"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denis","family":"Zorin","sequence":"additional","affiliation":[{"name":"NYU"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1998.0988"},{"key":"e_1_2_1_2_1","volume-title":"Conformal Flattening by Curvature Prescription and Metric Scaling. 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