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On the Topology and Isotopic Meshing of Plane Algebraic Curves

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Journal of Systems Science & Complexity 2020年第1期33卷 230-260页

This paper presents a symbolic algorithm to compute the topology of a plane *** is a full version of the authors’CASC15 *** algorithm mainly involves resultant computations and real root isolation for univariate *** to other symbolic methods based on elimination techniques,the novelty of the proposed method is that the authors use a technique of interval polynomials to solve the system f(α,y),?f/?y(α,y)and simultaneously obtain numerous simple roots of f(α,y)=0 on theα*** significantly improves the efficiency of the lifting step because the authors are no longer required to compute the simple roots of f(α,y)=*** the topology is computed,a revised Newton’s method is presented to compute an isotopic meshing of the plane algebraic *** the approximation method is numerical,the authors can ensure that the proposed method is a certified one,and the meshing is topologically *** nontrivial examples confirm that the proposed algorithm performs well.

关键词： Interval polynomial isotopic meshing plane curve topology

Isotopic Meshing of a Real Algebraic Space Curve

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Journal of Systems Science & Complexity 2020年第4期33卷 1275-1296页

This paper presents a new algorithm for computing the topology of an algebraic space *** on an efficient weak generic position-checking method and a method for solving bivariate polynomial systems,the authors give a first deterministic and efficient algorithm to compute the topology of an algebraic space *** to extant methods,the new algorithm is efficient for two *** bit size of the coefficients appearing in the sheared polynomials are greatly *** other is that one projection is enough for most general cases in the new *** the topology of an algebraic space curve is given,the authors also provide an isotopic-meshing(approximation)of the space ***,an approximation of the algebraic space curve can be generated automatically if the approximations of two projected plane curves are first *** is also an advantage of our *** non-trivial experiments show the efficiency of the algorithm.

关键词： curve. method. algebraic

Wu Wen-tsün Formulae for the Blending of Pipe Surfaces

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Northeastern Mathematical Journal 2001年第4期17卷 383-386页

作者：伍铁如雷娜程进三冯果忱 InstituteofMathematics JilinUniversityChangchun130012 不详

One of the central questions in CAGD is blending of pipe surfaces. Wu Wen-tsun[1]studied the problem by using the characteristic set method and derived a sufficient andnecessary condition for the existence of a GC1 bl... 详细信息

关键词： Blending Quadratic surface Geometric continuity