{"status":"public","_id":"60396","type":"journal_article","author":[{"orcid":"0000-0003-2340-3462","id":"114904","last_name":"Campen","first_name":"Marcel","full_name":"Campen, Marcel"},{"first_name":"Hanxiao","full_name":"Shen, Hanxiao","last_name":"Shen"},{"first_name":"Jiaran","full_name":"Zhou, Jiaran","last_name":"Zhou"},{"full_name":"Zorin, Denis","first_name":"Denis","last_name":"Zorin"}],"extern":"1","publication":"ACM Transactions on Graphics 39, 1, (2019)","date_created":"2025-06-26T08:10:54Z","department":[{"_id":"969"}],"doi":"10.1145/3360511","abstract":[{"text":"Seamless global parametrization of surfaces is a key operation in geometry\r\nprocessing, e.g. for high-quality quad mesh generation. A common approach is to\r\nprescribe the parametric domain structure, in particular the locations of\r\nparametrization singularities (cones), and solve a non-convex optimization\r\nproblem minimizing a distortion measure, with local injectivity imposed through\r\neither constraints or barrier terms. In both cases, an initial valid\r\nparametrization is essential to serve as feasible starting point for obtaining\r\nan optimized solution. While convexified versions of the constraints eliminate\r\nthis initialization requirement, they narrow the range of solutions, causing\r\nsome problem instances that actually do have a solution to become infeasible.\r\nWe demonstrate that for arbitrary given sets of topologically admissible\r\nparametric cones with prescribed curvature, a global seamless parametrization\r\nalways exists (with the exception of one well-known case). Importantly, our\r\nproof is constructive and directly leads to a general algorithm for computing\r\nsuch parametrizations. Most distinctively, this algorithm is bootstrapped with\r\na convex optimization problem (solving for a conformal map), in tandem with a\r\nsimple linear equation system (determining a seamless modification of this\r\nmap). This initial map can then serve as valid starting point and be optimized\r\nwith respect to application specific distortion measures using existing\r\ninjectivity preserving methods.","lang":"eng"}],"user_id":"117512","external_id":{"arxiv":["1810.02460"]},"citation":{"short":"M. Campen, H. Shen, J. Zhou, D. Zorin, ACM Transactions on Graphics 39, 1, (2019) (2018).","ama":"Campen M, Shen H, Zhou J, Zorin D. Seamless Parametrization with Arbitrarily Prescribed Cones. <i>ACM Transactions on Graphics 39, 1, (2019)</i>. Published online 2018. doi:<a href=\"https://doi.org/10.1145/3360511\">10.1145/3360511</a>","mla":"Campen, Marcel, et al. “Seamless Parametrization with Arbitrarily Prescribed Cones.” <i>ACM Transactions on Graphics 39, 1, (2019)</i>, 2018, doi:<a href=\"https://doi.org/10.1145/3360511\">10.1145/3360511</a>.","apa":"Campen, M., Shen, H., Zhou, J., &#38; Zorin, D. (2018). Seamless Parametrization with Arbitrarily Prescribed Cones. <i>ACM Transactions on Graphics 39, 1, (2019)</i>. <a href=\"https://doi.org/10.1145/3360511\">https://doi.org/10.1145/3360511</a>","bibtex":"@article{Campen_Shen_Zhou_Zorin_2018, title={Seamless Parametrization with Arbitrarily Prescribed Cones}, DOI={<a href=\"https://doi.org/10.1145/3360511\">10.1145/3360511</a>}, journal={ACM Transactions on Graphics 39, 1, (2019)}, author={Campen, Marcel and Shen, Hanxiao and Zhou, Jiaran and Zorin, Denis}, year={2018} }","ieee":"M. Campen, H. Shen, J. Zhou, and D. Zorin, “Seamless Parametrization with Arbitrarily Prescribed Cones,” <i>ACM Transactions on Graphics 39, 1, (2019)</i>, 2018, doi: <a href=\"https://doi.org/10.1145/3360511\">10.1145/3360511</a>.","chicago":"Campen, Marcel, Hanxiao Shen, Jiaran Zhou, and Denis Zorin. “Seamless Parametrization with Arbitrarily Prescribed Cones.” <i>ACM Transactions on Graphics 39, 1, (2019)</i>, 2018. <a href=\"https://doi.org/10.1145/3360511\">https://doi.org/10.1145/3360511</a>."},"date_updated":"2025-07-14T12:45:03Z","language":[{"iso":"eng"}],"title":"Seamless Parametrization with Arbitrarily Prescribed Cones","year":"2018"}