In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the ...In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.展开更多
Optimal parameterization of specified segment on the algebraic curves is a hot issue in CAGD and CG. Take the optimal approximation of arc-length parameterization as the criterion of optimal parameterization, and the ...Optimal parameterization of specified segment on the algebraic curves is a hot issue in CAGD and CG. Take the optimal approximation of arc-length parameterization as the criterion of optimal parameterization, and the optimal or close to optimal rational parameterization formula of any specified segment on the conic curves is obtained. The new method proposed in this paper has ad- vantage in quantity of calculation and has strong self-adaptability. Finally, a experimental comparison of the results obtained by this method and by the traditional parametric algorithm is conducted.展开更多
This paper deals with Hilbert's 16th problem and its generalizations. The configurations of all closed branches of an algebraic curve of degree n are discussed. The maximum number of sheets for an algebraic eq...This paper deals with Hilbert's 16th problem and its generalizations. The configurations of all closed branches of an algebraic curve of degree n are discussed. The maximum number of sheets for an algebraic equation of degree n and the maximum number of limit cycles for a planar algebraic autonomous system are achieved. The author also considers different generalizations and some related problems.展开更多
In this paper, we rewrote the equation of algebraic curve segmentswith the geometric informationonboth ends. The optimal or nearly optimal rationalparametric equation is determinedbythe principle that parametricspeeds...In this paper, we rewrote the equation of algebraic curve segmentswith the geometric informationonboth ends. The optimal or nearly optimal rationalparametric equation is determinedbythe principle that parametricspeedsat both endsareequal. Comparing withotherliteratures, the methodofthis paper has advantage in efficiency andiseasy to realize. The equation of optimal rational parameterization can be obtained directly by the information of both ends. Large numbers ofexperimental data show that our method hasbeen given withmore self-adaptability and accuracy than that ofotherliteratures, and if the parametricspeedat any end reaches its maximum or minimum value, the parameterization is optimal; otherwise itis close tooptimal rational parameterization.展开更多
In this paper, a type of preserving GC1 quadratic algebraic polynomial curve approximate implicitization method for parametric curves is presented The coefficients of the implicit polynomial are determined by the GC1...In this paper, a type of preserving GC1 quadratic algebraic polynomial curve approximate implicitization method for parametric curves is presented The coefficients of the implicit polynomial are determined by the GC1 continuity conditions and an optimal function's minimization Numerical examples show that this method is effective展开更多
基金This paper is partially supported by the National Fundamental Research 973 Program of China under Grant No.2004CB318000.
文摘In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.
文摘Optimal parameterization of specified segment on the algebraic curves is a hot issue in CAGD and CG. Take the optimal approximation of arc-length parameterization as the criterion of optimal parameterization, and the optimal or close to optimal rational parameterization formula of any specified segment on the conic curves is obtained. The new method proposed in this paper has ad- vantage in quantity of calculation and has strong self-adaptability. Finally, a experimental comparison of the results obtained by this method and by the traditional parametric algorithm is conducted.
文摘This paper deals with Hilbert's 16th problem and its generalizations. The configurations of all closed branches of an algebraic curve of degree n are discussed. The maximum number of sheets for an algebraic equation of degree n and the maximum number of limit cycles for a planar algebraic autonomous system are achieved. The author also considers different generalizations and some related problems.
文摘In this paper, we rewrote the equation of algebraic curve segmentswith the geometric informationonboth ends. The optimal or nearly optimal rationalparametric equation is determinedbythe principle that parametricspeedsat both endsareequal. Comparing withotherliteratures, the methodofthis paper has advantage in efficiency andiseasy to realize. The equation of optimal rational parameterization can be obtained directly by the information of both ends. Large numbers ofexperimental data show that our method hasbeen given withmore self-adaptability and accuracy than that ofotherliteratures, and if the parametricspeedat any end reaches its maximum or minimum value, the parameterization is optimal; otherwise itis close tooptimal rational parameterization.
基金the Younger Foundation of ShanghaiEducation Committee
文摘In this paper, a type of preserving GC1 quadratic algebraic polynomial curve approximate implicitization method for parametric curves is presented The coefficients of the implicit polynomial are determined by the GC1 continuity conditions and an optimal function's minimization Numerical examples show that this method is effective
