Geometric algorithm for point projection and
inversion onto Bézier surfaces |
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Authors: | Jinting XU Weijun LIU Hongyou BIAN Lun LI Jianhuang WU |
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Affiliation: | 1.School of Automotive
Engineering, Dalian University of Technology, Dalian 116024, China;Shenyang Institute
of Automation, Chinese Academy of Sciences, Shenyang 110016, China; 2.Shenyang Institute
of Automation, Chinese Academy of Sciences, Shenyang 110016, China; 3.Centre for Human
Computer Interaction, Shenzhen Institution of Advanced Integration
Technology, Chinese Academy of Sciences, Shenzhen 518067, China; |
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Abstract: | This paper presents an accurate and efficient method for the computation of both point projection and inversion onto Bézier surfaces. First, these two problems are formulated in terms of solution of a polynomial equation with u and v variables expressed in the Bernstein basis. Then, based on subdivision of the Bézier surface and the recursive quadtree decomposition, a novel solution method is proposed. The computation of point projection is shown to be equivalent to the geometrically intuitive intersection of a surface with the u-v plane. Finally, by comparing the distances between the test point and the candidate points, the closest point is found. Examples illustrate the feasibility of this method. |
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Keywords: | point projection point inversion Bé zier surface |
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