AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Tsinghua Science and Technology Article
PDF (2.7 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Open Access

The Closest and Farthest Points to an Affine Ellipse or Ellipsoid

Shuangmin Chen, Shiqing Xin, Ying He( ), Guojin Wang†
School of Computer Engineering, Nanyang Technological University, Singapore 639798
State Key Lab of CAD&CG, Zhejiang University, Hangzhou 310054, China
Show Author Information

Abstract

Affine ellipses/ellipsoids based bounding volumes are widely used in various graphics applications, such as ray tracing and collision detection. They provide a much tighter fit than the regular ellipses/ellipsoids. The most important operation involved is to compute the closest/farthest point, on a given ellipse/ellipsoid, with respect to a user specified point. In this paper, we first formulate such a problem for the ellipse case into solving a quartic equation and then for the ellipsoid case by solving a system of quartic equations. The method proposed in this paper is elegant and highly efficient.

Keywords

ellipseellipsoidclosest pointfarthest pointbounding volumecollision detection

References

【1】
【1】
 
 
Crossref Google Scholar
Tsinghua Science and Technology
Volume 17 Issue 4,
August 2012
Pages 481-484
DOI: 10.1109/TST.2012.6297594

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Chen S, Xin S, He Y, et al. The Closest and Farthest Points to an Affine Ellipse or Ellipsoid. Tsinghua Science and Technology, 2012, 17(4): 481-484. https://doi.org/10.1109/TST.2012.6297594

234

Views

25

Downloads

3

Crossref

N/A

Web of Science

3

Scopus

0

CSCD
Received: 15 May 2012
Revised: 15 June 2012
Published: 01 August 2012
© The author(s) 2012.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).