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Mathematical Problems in Engineering
Volume 2015, Article ID 394246, 11 pages
Research Article

Symbolic Computation of the Orthogonal Projection of Rational Curves onto Rational Parameterized Surfaces

School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

Received 28 April 2015; Revised 25 June 2015; Accepted 1 July 2015

Academic Editor: Mitsuhiro Okayasu

Copyright © 2015 Zhiwang Gan and Meng Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper focuses on the orthogonal projection of rational curves onto rational parameterized surface. Three symbolic algorithms are developed and studied. One of them, based on regular systems, is able to compute the exact parametric loci of projection. The one based on Gröbner basis can compute the minimal variety that contains the parametric loci. The remaining one computes a variety that contains the parametric loci via resultant. Examples show that our algorithms are efficient and valuable.