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Fitting unorganized point clouds with active implicit B-spline curves

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Abstract

In computer-aided geometric design and computer graphics, fitting point clouds with a smooth curve (known as curve reconstruction) is a widely investigated problem. In this paper, we propose an active model to solve the curve reconstruction problem, where the point clouds are approximated by an implicit B-spline curve, i.e., the zero set of a bivariate tensor-product B-spline function. We minimize the geometric distance between the point clouds and the implicit B-spline curve and an energy term (or smooth term) which helps to extrude the possible extra branches of the implicit curve. In each step of the iteration, the trust region algorithm in optimization theory is applied to solve the corresponding minimization problem. We also discuss the proper choice of the initial shape of the approximation curve. Examples are provided to illustrate the effectiveness and robustness of our algorithm. The examples show that the proposed algorithm is capable of handling point clouds with complicated topologies.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

    Zhouwang Yang, Jiansong Deng & Falai Chen

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  1. Zhouwang Yang
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  2. Jiansong Deng
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Correspondence to Zhouwang Yang.

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Yang, Z., Deng, J. & Chen, F. Fitting unorganized point clouds with active implicit B-spline curves. Visual Comput 21, 831–839 (2005). https://doi.org/10.1007/s00371-005-0340-0

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