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Algorithms 2016, 9(1), 15; doi:10.3390/a9010015

A Geometric Orthogonal Projection Strategy for Computing the Minimum Distance Between a Point and a Spatial Parametric Curve

1,* , 2,†
,
3,†
,
1,†
,
1,* and 4,†
1
College of Information Engineering, Guizhou Minzu University, Guiyang 550025, China
2
School of Mathematics and Computer Science, Yichun University, Yichun 336000, China
3
Center for Economic Research, Shandong University, Jinan 250100, China
4
College of Mathematics and Statistics, Yili Normal University, Yining 835000, China
These authors contributed equally to this work.
*
Authors to whom correspondence should be addressed.
Received: 25 November 2015 / Accepted: 2 February 2016 / Published: 6 February 2016
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
View Full-Text   |   Download PDF [252 KB, uploaded 17 February 2016]   |  

Abstract

A new orthogonal projection method for computing the minimum distance between a point and a spatial parametric curve is presented. It consists of a geometric iteration which converges faster than the existing Newton’s method, and it is insensitive to the choice of initial values. We prove that projecting a point onto a spatial parametric curve under the method is globally second-order convergence. View Full-Text
Keywords: point projection; Newton’s method; global convergence; osculating sphere; osculating circle; convergence analysis point projection; Newton’s method; global convergence; osculating sphere; osculating circle; convergence analysis
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Li, X.; Wu, Z.; Hou, L.; Wang, L.; Yue, C.; Xin, Q. A Geometric Orthogonal Projection Strategy for Computing the Minimum Distance Between a Point and a Spatial Parametric Curve. Algorithms 2016, 9, 15.

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