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Most of the existing solutions for this problem use constructions with limited degrees-of-freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.<\/jats:p>","DOI":"10.1115\/1.4051121","type":"journal-article","created":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T06:31:10Z","timestamp":1620714670000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":5,"title":["A Local Approach for Computing Smooth B-Spline Surfaces for Arbitrary Quadrilateral Base Meshes"],"prefix":"10.1115","volume":"22","author":[{"given":"Dennis","family":"Mosbach","sequence":"first","affiliation":[{"name":"Image Processing Department, Fraunhofer ITWM, Kaiserslautern 67663, Germany"}]},{"given":"Katja","family":"Schladitz","sequence":"additional","affiliation":[{"name":"Image Processing Department, Fraunhofer ITWM, Kaiserslautern 67663, Germany"}]},{"given":"Bernd","family":"Hamann","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Davis, CA 95616"}]},{"given":"Hans","family":"Hagen","sequence":"additional","affiliation":[{"name":"Computer Graphics and HCI Group, University of Kaiserslautern, Kaiserslautern 67663, Germany"}]}],"member":"33","published-online":{"date-parts":[[2021,7,13]]},"reference":[{"volume-title":"Fundamentals of Computer Aided Geometric Design","year":"1993","author":"Hoschek","key":"2021071309350702900_CIT0001"},{"key":"2021071309350702900_CIT0002","volume-title":"Curves and Surfaces for CAGD: A Practical Guide","author":"Farin","year":"2002","edition":"5th ed."},{"issue":"1","key":"2021071309350702900_CIT0003","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.cagd.2009.09.003","article-title":"On the Complexity of Smooth Spline Surfaces From Quad Meshes","volume":"27","author":"Peters","year":"2010","journal-title":"Comput. 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