{"date_updated":"2025-07-14T12:47:47Z","language":[{"iso":"eng"}],"title":"Efficient and robust discrete conformal equivalence with boundary","year":"2021","status":"public","_id":"60378","type":"journal_article","intvolume":"        40","page":"1-16","volume":40,"publication_status":"published","user_id":"117512","publisher":"Association for Computing Machinery (ACM)","publication":"ACM Transactions on Graphics","citation":{"mla":"Campen, Marcel, et al. “Efficient and Robust Discrete Conformal Equivalence with Boundary.” <i>ACM Transactions on Graphics</i>, vol. 40, no. 6, Association for Computing Machinery (ACM), 2021, pp. 1–16, doi:<a href=\"https://doi.org/10.1145/3478513.3480557\">10.1145/3478513.3480557</a>.","apa":"Campen, M., Capouellez, R., Shen, H., Zhu, L., Panozzo, D., &#38; Zorin, D. (2021). Efficient and robust discrete conformal equivalence with boundary. <i>ACM Transactions on Graphics</i>, <i>40</i>(6), 1–16. <a href=\"https://doi.org/10.1145/3478513.3480557\">https://doi.org/10.1145/3478513.3480557</a>","short":"M. Campen, R. Capouellez, H. Shen, L. Zhu, D. Panozzo, D. Zorin, ACM Transactions on Graphics 40 (2021) 1–16.","ama":"Campen M, Capouellez R, Shen H, Zhu L, Panozzo D, Zorin D. Efficient and robust discrete conformal equivalence with boundary. <i>ACM Transactions on Graphics</i>. 2021;40(6):1-16. doi:<a href=\"https://doi.org/10.1145/3478513.3480557\">10.1145/3478513.3480557</a>","chicago":"Campen, Marcel, Ryan Capouellez, Hanxiao Shen, Leyi Zhu, Daniele Panozzo, and Denis Zorin. “Efficient and Robust Discrete Conformal Equivalence with Boundary.” <i>ACM Transactions on Graphics</i> 40, no. 6 (2021): 1–16. <a href=\"https://doi.org/10.1145/3478513.3480557\">https://doi.org/10.1145/3478513.3480557</a>.","bibtex":"@article{Campen_Capouellez_Shen_Zhu_Panozzo_Zorin_2021, title={Efficient and robust discrete conformal equivalence with boundary}, volume={40}, DOI={<a href=\"https://doi.org/10.1145/3478513.3480557\">10.1145/3478513.3480557</a>}, number={6}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Campen, Marcel and Capouellez, Ryan and Shen, Hanxiao and Zhu, Leyi and Panozzo, Daniele and Zorin, Denis}, year={2021}, pages={1–16} }","ieee":"M. Campen, R. Capouellez, H. Shen, L. Zhu, D. Panozzo, and D. Zorin, “Efficient and robust discrete conformal equivalence with boundary,” <i>ACM Transactions on Graphics</i>, vol. 40, no. 6, pp. 1–16, 2021, doi: <a href=\"https://doi.org/10.1145/3478513.3480557\">10.1145/3478513.3480557</a>."},"publication_identifier":{"issn":["0730-0301","1557-7368"]},"issue":"6","doi":"10.1145/3478513.3480557","abstract":[{"text":"<jats:p>We describe an efficient algorithm to compute a discrete metric with prescribed Gaussian curvature at all interior vertices and prescribed geodesic curvature along the boundary of a mesh. The metric is (discretely) conformally equivalent to the input metric. 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>","lang":"eng"}],"author":[{"id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","first_name":"Marcel"},{"last_name":"Capouellez","first_name":"Ryan","full_name":"Capouellez, Ryan"},{"first_name":"Hanxiao","full_name":"Shen, Hanxiao","last_name":"Shen"},{"full_name":"Zhu, Leyi","first_name":"Leyi","last_name":"Zhu"},{"full_name":"Panozzo, Daniele","first_name":"Daniele","last_name":"Panozzo"},{"last_name":"Zorin","full_name":"Zorin, Denis","first_name":"Denis"}],"date_created":"2025-06-25T10:08:08Z","department":[{"_id":"969"}],"extern":"1"}