An Algorithm to Compute the-Bases of Rational Parametric Surfaces with Respect to One Variable  

作　　者：Bingru Huang Falai Chen 

机构地区：[1]Department of Mathematics,University of Science and Technology of China,Hefei 230026,Anhui,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2024年第3期523-541,共19页数学与统计通讯（英文）

基　　金：supported by NSF of China(no.61972368).

摘　　要：The method of moving surfaces is an effective tool to implicitize rational parametric surfaces,and it has been extensively studied in the past two decades.An essential step in surface implicitization using the method of moving surfaces is to compute aμ-basis of a parametric surface with respect to one variable.Theμ-basis is a minimal basis of the syzygy module of a univariate polynomial matrix with special structure defined by the parametric equation of the rational surface.In this paper,we present an efficient algorithm to compute theμ-basis of a parametric surface with respect to a variable based on the special structure of the corresponding univariate polynomial matrix.Analysis on the computational complexity of the algorithm is also provided.Experiments demonstrate that our algorithm is much faster than the general method to compute theμ-bases of arbitrary polynomial matrices and outperforms the F_(5) algorithm based on Gröbner basis computation for relatively low degree rational surfaces.

关 键 词：Rational surface IMPLICITIZATION μ-basis Polynomial matrix factorization 

分 类 号：O17[理学—数学]