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Symmetry 2018, 10(5), 164; https://doi.org/10.3390/sym10050164

Integrated Hybrid Second Order Algorithm for Orthogonal Projection onto a Planar Implicit Curve

1,†
,
1,†
,
2,†
,
3,†
,
4,†
and
5,†,*
1
College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
2
Graduate School, Guizhou Minzu University, Guiyang 550025, China
3
School of Mathematics and Computer Science, Yichun University, Yichun 336000, China
4
Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, China
5
Center for Economic Research, Shandong University, Jinan 250100, China
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 17 April 2018 / Revised: 27 April 2018 / Accepted: 8 May 2018 / Published: 15 May 2018
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Abstract

The computation of the minimum distance between a point and a planar implicit curve is a very important problem in geometric modeling and graphics. An integrated hybrid second order algorithm to facilitate the computation is presented. The proofs indicate that the convergence of the algorithm is independent of the initial value and demonstrate that its convergence order is up to two. Some numerical examples further confirm that the algorithm is more robust and efficient than the existing methods. View Full-Text
Keywords: point projection; intersection; planar implicit curve; Newton’s second order method; integrated hybrid second order algorithm point projection; intersection; planar implicit curve; Newton’s second order method; integrated hybrid second order algorithm
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Li, X.; Pan, F.; Cheng, T.; Wu, Z.; Liang, J.; Hou, L. Integrated Hybrid Second Order Algorithm for Orthogonal Projection onto a Planar Implicit Curve. Symmetry 2018, 10, 164.

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