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Johnson, D.E. and Cohen, E. (2005) Distance Extrema for Spline Models Using Tangent Cones. Proceedings of the 2005 Conference on Graphics Interface, Victoria, May 9-11, 2005, 3 p.

has been cited by the following article:

• TITLE: The Analytical Expressions for Computing the Minimum Distance between a Point and a Torus

  AUTHORS: Xiaowu Li, Linke Hou, Juan Liang, Zhinan Wu, Lin Wang, Chunguang Yue

  KEYWORDS: Point Projection, Center Axis of the Torus, Major Planar Circle, Minor Planar Circle, Intersection

  JOURNAL NAME: Journal of Computer and Communications, Vol.4 No.4, April 22, 2016

  ABSTRACT: In this paper, we present the analytical expressions for computing the minimum distance between a point and a torus, which is called the orthogonal projection point problem. If the test point is on the outside of the torus and the test point is at the center axis of the torus, we present that the orthogonal projection point set is a circle perpendicular to the center axis of the torus; if not, the analytical expression for the orthogonal projection point problem is also given. Furthermore, if the test point is in the inside of the torus, we also give the corresponding analytical expression for orthogonal projection point for two cases.