@article{Chen2012, 
author = {Shuangmin Chen and Shiqing Xin and Ying He and Guojin Wang},
title = {The Closest and Farthest Points to an Affine Ellipse or Ellipsoid},
year = {2012},
journal = {Tsinghua Science and Technology},
volume = {17},
number = {4},
pages = {481-484},
keywords = {ellipse, ellipsoid, closest point, farthest point, bounding volume, collision detection},
url = {https://www.sciopen.com/article/10.1109/TST.2012.6297594},
doi = {10.1109/TST.2012.6297594},
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.}
}