{"abstract":[{"lang":"eng","text":"<jats:p>Global surface parametrization often requires the use of cuts or charts due to non-trivial topology. In recent years a focus has been on so-called<jats:italic>seamless</jats:italic>parametrizations, where the transition functions across the cuts are rigid transformations with a rotation about some multiple of 90°. Of particular interest, e.g. for quadrilateral meshing, paneling, or texturing, are those instances where in addition the translational part of these transitions is integral (or more generally: quantized). We show that finding not even the optimal, but just an arbitrary valid quantization (one that does not imply parametric degeneracies), is a complex combinatorial problem. We present a novel method that allows us to solve it, i.e. to find valid as well as good quality quantizations. It is based on an original approach to quickly construct solutions to linear Diophantine equation systems, exploiting the specific geometric nature of the parametrization problem. We thereby largely outperform the state-of-the-art, sometimes by several orders of magnitude.</jats:p>"}],"doi":"10.1145/2816795.2818140","author":[{"orcid":"0000-0003-2340-3462","id":"114904","last_name":"Campen","first_name":"Marcel","full_name":"Campen, Marcel"},{"first_name":"David","full_name":"Bommes, David","last_name":"Bommes"},{"last_name":"Kobbelt","full_name":"Kobbelt, Leif","first_name":"Leif"}],"extern":"1","date_created":"2025-06-27T10:19:04Z","department":[{"_id":"969"}],"citation":{"chicago":"Campen, Marcel, David Bommes, and Leif Kobbelt. “Quantized Global Parametrization.” <i>ACM Transactions on Graphics</i> 34, no. 6 (2015): 1–12. <a href=\"https://doi.org/10.1145/2816795.2818140\">https://doi.org/10.1145/2816795.2818140</a>.","bibtex":"@article{Campen_Bommes_Kobbelt_2015, title={Quantized global parametrization}, volume={34}, DOI={<a href=\"https://doi.org/10.1145/2816795.2818140\">10.1145/2816795.2818140</a>}, number={6}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Campen, Marcel and Bommes, David and Kobbelt, Leif}, year={2015}, pages={1–12} }","ieee":"M. Campen, D. Bommes, and L. Kobbelt, “Quantized global parametrization,” <i>ACM Transactions on Graphics</i>, vol. 34, no. 6, pp. 1–12, 2015, doi: <a href=\"https://doi.org/10.1145/2816795.2818140\">10.1145/2816795.2818140</a>.","mla":"Campen, Marcel, et al. “Quantized Global Parametrization.” <i>ACM Transactions on Graphics</i>, vol. 34, no. 6, Association for Computing Machinery (ACM), 2015, pp. 1–12, doi:<a href=\"https://doi.org/10.1145/2816795.2818140\">10.1145/2816795.2818140</a>.","apa":"Campen, M., Bommes, D., &#38; Kobbelt, L. (2015). Quantized global parametrization. <i>ACM Transactions on Graphics</i>, <i>34</i>(6), 1–12. <a href=\"https://doi.org/10.1145/2816795.2818140\">https://doi.org/10.1145/2816795.2818140</a>","short":"M. Campen, D. Bommes, L. Kobbelt, ACM Transactions on Graphics 34 (2015) 1–12.","ama":"Campen M, Bommes D, Kobbelt L. Quantized global parametrization. <i>ACM Transactions on Graphics</i>. 2015;34(6):1-12. doi:<a href=\"https://doi.org/10.1145/2816795.2818140\">10.1145/2816795.2818140</a>"},"issue":"6","publication_identifier":{"issn":["0730-0301","1557-7368"]},"status":"public","_id":"60442","type":"journal_article","page":"1-12","intvolume":"        34","volume":34,"publication_status":"published","user_id":"117512","publication":"ACM Transactions on Graphics","publisher":"Association for Computing Machinery (ACM)","date_updated":"2025-07-14T12:41:34Z","language":[{"iso":"eng"}],"title":"Quantized global parametrization","year":"2015"}