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Computers 2016, 5(1), 4; https://doi.org/10.3390/computers5010004

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

1,â€ ,* , 2,â€
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3,â€ ,* , 1,â€
and
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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
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These authors contributed equally to this work.
*
Authors to whom correspondence should be addressed.
Academic Editor: Pedro Alonso JordÃ¡
Received: 20 December 2015 / Revised: 14 February 2016 / Accepted: 16 February 2016 / Published: 24 February 2016
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# 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. View Full-Text
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Li, X.; Wu, Z.; Hou, L.; Wang, L.; Yue, C. The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus. Computers 2016, 5, 4.

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