The Closest and Farthest Points to an Affine Ellipse or Ellipsoid |
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Authors: | Shuangmin Chen Shiqing Xin Ying He Guojin Wang |
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Institution: | School of Computer Engineering,Nanyang Technological University,Singapore 639798;State Key Lab of CAD&CG,Zhejiang University,Hangzhou 310054,China |
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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. |
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Keywords: | ellipse ellipsoid closest point farthest point bounding volume collision detection |
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