Title of article :
The Closest and Farthest Points to an Affine Ellipse or Ellipsoid
Author/Authors :
Chen, Shuangmin Nanyang Technological University - School of Computer Engineering, Singapore , Xin, Shiqing Nanyang Technological University - School of Computer Engineering, Singapore , He, Ying Nanyang Technological University - School of Computer Engineering, Singapore , Wang, Guojin Zhejiang University - State Key Lab of CAD CG, China
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 :
ellipse , ellipsoid , closest point , farthest point , bounding volume , collision detection
Journal title :
Tsinghua Science and Technology
Journal title :
Tsinghua Science and Technology
