Surface reconstruction using bivariate simplex splines on Delaunay configurations |
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Authors: | Juan Cao Xin Li Guozhao Wang Hong Qin |
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Affiliation: | aInstitute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;bDepartment of Electrical and Computer Engineering and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA;cDepartment of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 11794-4400, USA |
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Abstract: | Recently, a new bivariate simplex spline scheme based on Delaunay configuration has been introduced into the geometric computing community, and it defines a complete spline space that retains many attractive theoretic and computational properties. In this paper, we develop a novel shape modeling framework to reconstruct a closed surface of arbitrary topology based on this new spline scheme. Our framework takes a triangulated set of points, and by solving a linear least-square problem and iteratively refining parameter domains with newly added knots, we can finally obtain a continuous spline surface satisfying the requirement of a user-specified error tolerance. Unlike existing surface reconstruction methods based on triangular B-splines (or DMS splines), in which auxiliary knots must be explicitly added in advance to form a knot sequence for construction of each basis function, our new algorithm completely avoids this less-intuitive and labor-intensive knot generating procedure. We demonstrate the efficacy and effectiveness of our algorithm on real-world, scattered datasets for shape representation and computing. |
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Keywords: | B-splines Simplex splines Surface fitting Delaunay configuration Triangular B-splines Conformal mapping Computational geometry Object modeling Geometric algorithms |
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