The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus

We present an accurate method to compute the minimum distance between a point and an elliptical torus, which is called the orthogonal projection problem. The basic idea is to transform a geometric problem into finding the unique real solution of a quartic equation, which is fit for orthogonal projec...
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Autor*in:	Xiaowu Li [verfasserIn] Zhinan Wu [verfasserIn] Linke Hou [verfasserIn] Lin Wang [verfasserIn] Chunguang Yue [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	point projection elliptical torus major planar circle minor planar ellipse the long axis the minor axis intersection

Übergeordnetes Werk:	In: Computers - MDPI AG, 2013, 5(2016), 1, p 4
Übergeordnetes Werk:	volume:5 ; year:2016 ; number:1, p 4

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DOI / URN:	10.3390/computers5010004

Katalog-ID:	DOAJ079126146

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allfieldsSound	10.3390/computers5010004 doi (DE-627)DOAJ079126146 (DE-599)DOAJfa5a10fa2a3a4be698f067e324cbc02e DE-627 ger DE-627 rakwb eng QA75.5-76.95 Xiaowu Li verfasserin aut The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present an accurate method to compute the minimum distance between a point and an elliptical torus, which is called the orthogonal projection problem. The basic idea is to transform a geometric problem into finding the unique real solution of a quartic equation, which is fit for orthogonal projection of a point onto the elliptical torus. Firstly, we discuss the corresponding orthogonal projection of a point onto the elliptical torus for test points at six different spatial positions. Secondly, we discuss the same problem for test points on three special positions, e.g., points on the z-axis, the long axis and the minor axis, respectively. point projection elliptical torus major planar circle minor planar ellipse the long axis the minor axis intersection Electronic computers. Computer science Zhinan Wu verfasserin aut Linke Hou verfasserin aut Lin Wang verfasserin aut Chunguang Yue verfasserin aut In Computers MDPI AG, 2013 5(2016), 1, p 4 (DE-627)718632389 (DE-600)2662580-5 2073431X nnns volume:5 year:2016 number:1, p 4 https://doi.org/10.3390/computers5010004 kostenfrei https://doaj.org/article/fa5a10fa2a3a4be698f067e324cbc02e kostenfrei http://www.mdpi.com/2073-431X/5/1/4 kostenfrei https://doaj.org/toc/2073-431X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2016 1, p 4
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topic_facet	point projection elliptical torus major planar circle minor planar ellipse the long axis the minor axis intersection Electronic computers. Computer science
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callnumber-first	Q - Science
author	Xiaowu Li
spellingShingle	Xiaowu Li misc QA75.5-76.95 misc point projection misc elliptical torus misc major planar circle misc minor planar ellipse misc the long axis misc the minor axis misc intersection misc Electronic computers. Computer science The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus
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topic_title	QA75.5-76.95 The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus point projection elliptical torus major planar circle minor planar ellipse the long axis the minor axis intersection
topic	misc QA75.5-76.95 misc point projection misc elliptical torus misc major planar circle misc minor planar ellipse misc the long axis misc the minor axis misc intersection misc Electronic computers. Computer science
topic_unstemmed	misc QA75.5-76.95 misc point projection misc elliptical torus misc major planar circle misc minor planar ellipse misc the long axis misc the minor axis misc intersection misc Electronic computers. Computer science
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title	The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus
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title_full	The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus
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title_sort	accurate method for computing the minimum distance between a point and an elliptical torus
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title_auth	The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus
abstract	We present an accurate method to compute the minimum distance between a point and an elliptical torus, which is called the orthogonal projection problem. The basic idea is to transform a geometric problem into finding the unique real solution of a quartic equation, which is fit for orthogonal projection of a point onto the elliptical torus. Firstly, we discuss the corresponding orthogonal projection of a point onto the elliptical torus for test points at six different spatial positions. Secondly, we discuss the same problem for test points on three special positions, e.g., points on the z-axis, the long axis and the minor axis, respectively.
abstractGer	We present an accurate method to compute the minimum distance between a point and an elliptical torus, which is called the orthogonal projection problem. The basic idea is to transform a geometric problem into finding the unique real solution of a quartic equation, which is fit for orthogonal projection of a point onto the elliptical torus. Firstly, we discuss the corresponding orthogonal projection of a point onto the elliptical torus for test points at six different spatial positions. Secondly, we discuss the same problem for test points on three special positions, e.g., points on the z-axis, the long axis and the minor axis, respectively.
abstract_unstemmed	We present an accurate method to compute the minimum distance between a point and an elliptical torus, which is called the orthogonal projection problem. The basic idea is to transform a geometric problem into finding the unique real solution of a quartic equation, which is fit for orthogonal projection of a point onto the elliptical torus. Firstly, we discuss the corresponding orthogonal projection of a point onto the elliptical torus for test points at six different spatial positions. Secondly, we discuss the same problem for test points on three special positions, e.g., points on the z-axis, the long axis and the minor axis, respectively.
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title_short	The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus
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