Author(s)

Xiaowu Li^1*, Linke Hou^2*, Juan Liang^3*, Zhinan Wu⁴, Lin Wang¹, Chunguang Yue^1*

¹College of Information Engineering, Guizhou Minzu University, Guiyang, China.
²Center for Economic Research, Shandong University, Jinan, China.
³Department of Science, Taiyuan Institute of Technology, Taiyuan, China.
⁴School of Mathematics and Computer Science, Yichun University, Yichun, China.

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.

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

Li, X. , Hou, L. , Liang, J. , Wu, Z. , Wang, L. and Yue, C. (2016) The Analytical Expressions for Computing the Minimum Distance between a Point and a Torus. Journal of Computer and Communications, 4, 125-133. doi: 10.4236/jcc.2016.44011.