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N?ther’s theorem of algebraic curves plays an important role in classical algebraic geometry. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. N?ther-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the N?ther-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented. This work was supported by National Natural Science Foundation of China (Grant Nos. 60373093, 60533060, 10726068, 10801024) and the Innovation Foundation of Key Laboratory of High Temperature Gasdynamics of Chinese Academy of Sciences, China  相似文献
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Pythagorean-hodograph (PH) curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs'' constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by $C^1$ Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.  相似文献
3.
In this paper, we study the problem of regular decomposition in integer programming. We apply the radical of binomial ideal and universal Gr¨obner bases to get the regular decomposition forms of a finite integer lattice point set. We indicate the relationship between state polytope and regular decompositions, i.e., an edge of state polytope corresponds to a binomial which decides one of regular decomposition forms of a finite integer lattice point set.  相似文献
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