An Improved Algorithm to Compute the Mu-Bases of Tensor-Product Rational Surfaces with Respect to One Variable

The method of moving planes and moving quadrics expresses the implicit equation of a rational parametric surface as a compact determinant. Efficient computation of the moving planes and moving quadrics of a rational surface has gained much attention in the past two decades. Recent development suggests that a promising approach is to compute a mu-basis of a rational surface with respect to one variable -- a minimal basis of the syzygy of a univariate polynomial matrix generated from the parametric equation of the rational surface. This paper proposes an efficient algorithm to compute a mu-basis for a tensor product rational surface with respect to one variable from a set of moving planes. It is shown that the algorithm is superior to several recently developed methods by computational complexity analysis and examples, especially for surfaces with relatively high degree.