共查询到19条相似文献,搜索用时 93 毫秒
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HU Qianqian & WANG Guojin Department of Mathematics Zhejiang University Hangzhou China State Key Laboratory of CAD&CG Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2005,48(9):1209-1222
Using algebraic and geometric methods,functional relationships between a point on a conic segment and its corresponding parameter are derived when the conic segment is presented by a rational quadratic or cubic Bézier curve.That is,the inverse mappings of the mappings represented by the expressions of rational conic segments are given.These formulae relate some triangular areas or some angles,determined by the selected point on the curve and the control points of the curve,as well as by the weights of the rational Bézier curve.Also,the relationship can be expressed by the corresponding parametric angles of the selected point and two endpoints on the conic segment,as well as by the weights of the rational Bézier curve.These results are greatly useful for optimal parametrization,reparametrization,etc.,of rational Bézier curves and surfaces. 相似文献
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实分片代数曲线的拓扑结构 总被引:3,自引:0,他引:3
The piecewise algebraic curve is a kind generalization of the classical algebraic curve.By analyzing the topology of real algebraic curves on the triangles,a practi-caUy algrithm for analyzing the topology of piecewise algebraic curves is given.The algrithm produces a planar graph which is topologically equivalent to the piecewise algebraic curve. 相似文献
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Many works have investigated the problem of reparameterizing rational Bézier curves or surfaces via Mbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after Mbius transformation. What's more the users of computer aided design softwares may require some guidelines for designing rational Bézier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway.The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational Bézier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal parametric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational Bézier surfaces with compact derivative bounds. 相似文献
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The existing results of curve degree elevation mainly focus on the degree of algebraic polynomials. The paper considers the elevation of degree of the trigonometric polynomial, from a Bzier curve on the algebraic polynomial space, to a C-B′ezier curve on the algebraic and trigonometric polynomial space. The matrix of degree elevation is obtained by an operator presentation and a derivation pyramid. It possesses not a recursive presentation but a direct expression. The degree elevation process can also be represented as a corner cutting form. 相似文献
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The aim of this paper is to study numerical realization of the conditions of Max Nother's residual intersection theorem. The numerical realization relies on obtaining the inter- section of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determin- ing the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic, even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time. 相似文献
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The aim of this paper is to study numerical realization of the conditions of Max Nther's residual intersection theorem. The numerical realization relies on obtaining the intersection of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determining the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic,even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time. 相似文献
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Estimation of the Bezout number for piecewise algebraic curve 总被引:3,自引:0,他引:3
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper.a coniecture on trianguation is confirmed The relation between the piecewise linear algebraiccurve and four-color conjecture is also presented.By Morgan-Scott triangulation, we will show the instabilityof Bezout number of piecewise algebraic curves. By using the combinatorial optimization method,an upper 相似文献
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Rational Bézier surface is a widely used surface fitting tool in CAD. When all the weights of a rational Bézier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bézier surfaces. In this paper, we study on the degenerations of the rational Bézier surface with weights in the exponential function and indicate the difference of our result and the work of Garc′?a-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bézier surface with weights in the exponential function is defined, which is just the limit of the surface.Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster. 相似文献
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The monotonicity of a rational Bézier curve, usually related to an explicit function,is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized monotonicity, called direction monotonicity, is introduced for rational Bézier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine coordinate systems, and it includes the traditional monotonicity as a subcase. By means of it,proper affine coordinate systems may be chosen to make some rational Bézier curves monotonic.Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well. 相似文献
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任意次的F-Bézier基统一了三角多项式空间上的C-Bézier基和双曲多项式空间上的H-Bézier基,我们证明这种基函数具有类似于基函数的优良性质,包括端点性质、对称性、升阶性质、线性无关性等,并且证明当形状参数趋于零时F-Bézier基收敛Bernstein基. 相似文献
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Malik Zawwar Hussain Maria Hussain 《Journal of Applied Mathematics and Computing》2011,35(1-2):281-293
A local C 1 positivity preserving scheme is developed using Bernstein-Bézier rational cubic function. The domain is triangulated by Delaunay triangulation method. Simple sufficient conditions are derived on the inner and boundary Bézier ordinates to preserve the shape of positive data. These inner and boundary Bézier ordinates involve weights in their definition. In any triangular patch if the Bézier ordinates do not satisfy the derived conditions of positivity, then these are modified by the weights (free parameters) involved in the construction of Bernstein-Bézier rational cubic function to preserve the shape of positive scattered data. 相似文献
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提出了点集Bézier曲线的概念,给出了点集Bézier曲线的性质及细分算法.按照点集算术的定义,当点集是长方形闭域或圆盘时,点集Bézier曲线就是区间Bézier曲线或圆盘Bézier曲线,因此,点集Bézier曲线是对区间Bézier曲线和圆盘Bézier曲线的推广. 相似文献
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研究了用一条样条曲线把两条不相连接的样条曲线光滑连接起来的问题,给出了连接两条一元n次参数样条曲线为一条新的一元n次参数样条曲线的条件,适用于参数样条曲线添加控制顶点的情形,进一步得到了两条一次、二次、三次Bézier样条曲线在几何连续性下实现自然光滑连接的条件. 相似文献
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F. Bihan 《Advances in Mathematics》2002,169(2):177-186
The Viro method is a powerful construction method of real nonsingular algebraic hypersurfaces with prescribed topology. It is based on polyhedral subdivisions of Newton polytopes. A combinatorial version of the Viro method is called combinatorial patchworking and arises when the considered subdivisions are triangulations. B. Sturmfels has generalized the combinatorial patchworking to the case of real complete intersections. We extend his result by generalizing the Viro method to the case of real complete intersections. 相似文献
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WuHongyi 《高校应用数学学报(英文版)》2000,15(1):109-121
Abstract. This paper presents two new families of the generalized Ball curves which include theI~zier curve, the generalized Ball curves defined by Wang and Said independently and some in-termediate curves. The relative degree elevation and reduction schemes, recursive algorithmsand the Bernstein-Bezier representation are also given. 相似文献