{"alternative_title":["a perfect couple"],"year":"2017","title":"Similarity maps and field-guided T-splines","language":[{"iso":"eng"}],"date_updated":"2025-07-14T12:43:19Z","publication":"ACM Transactions on Graphics","publisher":"Association for Computing Machinery (ACM)","user_id":"117512","publication_status":"published","volume":36,"intvolume":"        36","page":"1-16","type":"journal_article","_id":"60399","status":"public","publication_identifier":{"issn":["0730-0301","1557-7368"]},"issue":"4","citation":{"ama":"Campen M, Zorin D. Similarity maps and field-guided T-splines. <i>ACM Transactions on Graphics</i>. 2017;36(4):1-16. doi:<a href=\"https://doi.org/10.1145/3072959.3073647\">10.1145/3072959.3073647</a>","short":"M. Campen, D. Zorin, ACM Transactions on Graphics 36 (2017) 1–16.","apa":"Campen, M., &#38; Zorin, D. (2017). Similarity maps and field-guided T-splines. <i>ACM Transactions on Graphics</i>, <i>36</i>(4), 1–16. <a href=\"https://doi.org/10.1145/3072959.3073647\">https://doi.org/10.1145/3072959.3073647</a>","mla":"Campen, Marcel, and Denis Zorin. “Similarity Maps and Field-Guided T-Splines.” <i>ACM Transactions on Graphics</i>, vol. 36, no. 4, Association for Computing Machinery (ACM), 2017, pp. 1–16, doi:<a href=\"https://doi.org/10.1145/3072959.3073647\">10.1145/3072959.3073647</a>.","ieee":"M. Campen and D. Zorin, “Similarity maps and field-guided T-splines,” <i>ACM Transactions on Graphics</i>, vol. 36, no. 4, pp. 1–16, 2017, doi: <a href=\"https://doi.org/10.1145/3072959.3073647\">10.1145/3072959.3073647</a>.","bibtex":"@article{Campen_Zorin_2017, title={Similarity maps and field-guided T-splines}, volume={36}, DOI={<a href=\"https://doi.org/10.1145/3072959.3073647\">10.1145/3072959.3073647</a>}, number={4}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Campen, Marcel and Zorin, Denis}, year={2017}, pages={1–16} }","chicago":"Campen, Marcel, and Denis Zorin. “Similarity Maps and Field-Guided T-Splines.” <i>ACM Transactions on Graphics</i> 36, no. 4 (2017): 1–16. <a href=\"https://doi.org/10.1145/3072959.3073647\">https://doi.org/10.1145/3072959.3073647</a>."},"department":[{"_id":"969"}],"date_created":"2025-06-26T08:16:00Z","extern":"1","author":[{"full_name":"Campen, Marcel","first_name":"Marcel","last_name":"Campen","id":"114904","orcid":"0000-0003-2340-3462"},{"last_name":"Zorin","full_name":"Zorin, Denis","first_name":"Denis"}],"abstract":[{"lang":"eng","text":"<jats:p>A variety of techniques were proposed to model smooth surfaces based on tensor product splines (e.g. subdivision surfaces, free-form splines, T-splines). Conversion of an input surface into such a representation is commonly achieved by constructing a global seamless parametrization, possibly aligned to a guiding cross-field (e.g. of principal curvature directions), and using this parametrization as domain to construct the spline-based surface.</jats:p>\r\n          <jats:p>One major fundamental difficulty in designing robust algorithms for this task is the fact that for common types, e.g. subdivision surfaces (requiring a conforming domain mesh) or T-spline surfaces (requiring a globally consistent knot interval assignment) reliably obtaining a suitable parametrization that has the same topological structure as the guiding field poses a major challenge. Even worse, not all fields do admit suitable parametrizations, and no concise conditions are known as to which fields do.</jats:p>\r\n          <jats:p>\r\n            We present a class of surface constructions (T-splines with\r\n            <jats:italic>halfedge knots</jats:italic>\r\n            ) and a class of parametrizations (\r\n            <jats:italic>seamless similarity maps</jats:italic>\r\n            ) that are, in a sense, a perfect match for the task: for\r\n            <jats:italic>any</jats:italic>\r\n            given guiding field structure, a compatible parametrization of this kind exists and a smooth piecewise rational surface with exactly the same structure as the input field can be constructed from it. As a byproduct, this enables full control over extraordinary points. The construction is backward compatible with classical NURBS. We present efficient algorithms for building discrete conformal similarity maps and associated T-meshes and T-spline surfaces.\r\n          </jats:p>"}],"doi":"10.1145/3072959.3073647"}