{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T16:14:26Z","timestamp":1782317666905,"version":"3.54.5"},"reference-count":69,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T00:00:00Z","timestamp":1500508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2017,8,31]]},"abstract":"<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>\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>\n          <jats:p>\n            We present a class of surface constructions (T-splines with\n            <jats:italic>halfedge knots<\/jats:italic>\n            ) and a class of parametrizations (\n            <jats:italic>seamless similarity maps<\/jats:italic>\n            ) that are, in a sense, a perfect match for the task: for\n            <jats:italic>any<\/jats:italic>\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.\n          <\/jats:p>","DOI":"10.1145\/3072959.3073647","type":"journal-article","created":{"date-parts":[[2017,7,21]],"date-time":"2017-07-21T12:24:07Z","timestamp":1500639847000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":43,"title":["Similarity maps and field-guided T-splines"],"prefix":"10.1145","volume":"36","author":[{"given":"Marcel","family":"Campen","sequence":"first","affiliation":[{"name":"New York University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denis","family":"Zorin","sequence":"additional","affiliation":[{"name":"New York University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2017,7,20]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Ralph Abraham Jerrold E Marsden and Tudor Ratiu. 1988. 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