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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| Format: | Article |
| Language: | English |
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MDPI AG
2016-02-01
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| Series: | Computers |
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| Online Access: | http://www.mdpi.com/2073-431X/5/1/4 |
| _version_ | 1798040237048332288 |
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| author | Xiaowu Li Zhinan Wu Linke Hou Lin Wang Chunguang Yue |
| author_facet | Xiaowu Li Zhinan Wu Linke Hou Lin Wang Chunguang Yue |
| author_sort | Xiaowu Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:04:41Z |
| format | Article |
| id | doaj.art-fa5a10fa2a3a4be698f067e324cbc02e |
| institution | Directory Open Access Journal |
| issn | 2073-431X |
| language | English |
| last_indexed | 2024-04-11T22:04:41Z |
| publishDate | 2016-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computers |
| spelling | doaj.art-fa5a10fa2a3a4be698f067e324cbc02e2022-12-22T04:00:47ZengMDPI AGComputers2073-431X2016-02-0151410.3390/computers5010004computers5010004The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical TorusXiaowu Li0Zhinan Wu1Linke Hou2Lin Wang3Chunguang Yue4College of Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaSchool of Mathematics and Computer Science, Yichun University, Yichun 336000, ChinaCenter for Economic Research, Shandong University, Jinan 250100, ChinaCollege of Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaCollege of Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaWe 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.http://www.mdpi.com/2073-431X/5/1/4point projectionelliptical torusmajor planar circleminor planar ellipsethe long axisthe minor axisintersection |
| spellingShingle | Xiaowu Li Zhinan Wu Linke Hou Lin Wang Chunguang Yue The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus Computers point projection elliptical torus major planar circle minor planar ellipse the long axis the minor axis intersection |
| title | The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus |
| title_full | The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus |
| title_fullStr | The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus |
| title_full_unstemmed | The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus |
| title_short | The Accurate Method for Computing the Minimum Distance between a Point and an Elliptical Torus |
| title_sort | accurate method for computing the minimum distance between a point and an elliptical torus |
| topic | point projection elliptical torus major planar circle minor planar ellipse the long axis the minor axis intersection |
| url | http://www.mdpi.com/2073-431X/5/1/4 |
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