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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.

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