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The Closest and Farthest Points to an Affine Ellipse or Ellipsoid

The Closest and Farthest Points to an Affine Ellipse or Ellipsoid
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摘要 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. 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.
出处 《Tsinghua Science and Technology》 SCIE EI CAS 2012年第4期481-484,共4页 清华大学学报(自然科学版(英文版)
基金 Supported by the National Natural Science Foundation of China (No. 60933007)
关键词 ELLIPSE ELLIPSOID closest point farthest point bounding volume collision detection ellipse ellipsoid closest point farthest point bounding volume collision detection
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