带双参数的四次均匀 B 样条

文中给出了带两个形状参数的四次均匀B样条基函数,由其构造的样条曲线可以通过改变形状参数λ,μ的取值调整曲线的形状,其中参数λ控制整条曲线位置,参数μ对曲线作局部调整.     

两类带参数的四次三角Bézier曲线

本文构造了两种带参数的四次三角基函数,它具有Bernstein基函数的几何性质:非负性、权性、对称性和端点性质.由此定义的两类四次三角曲线,通过形状参数取值的不同,可对曲线的性质进行调控.     

一类类Bezier曲线及其扩展

该文研究一类类Bezier曲线及其扩展。主要根据一组三角基函数构造由四个控制顶点组成的类Bezier曲线,随后引入基函数中的形状控制参数得到带形状参数的类Bezier曲线,进而构造了带形状参数的类Bezier插值曲线,这是基于通过混合函数混合参数化的控制多边形及类Bezier曲线得到的一类曲线。它具有局部性、端点性质、几何不变性与仿射不变性、对称性、凸包性、变差缩减性等性质。同时它可以表示Bezier曲线所不能表示的圆锥曲线,最重要的性质是其具有插值性,这样就大大增强了其在实际领域中得到应用的可能性。     

一类类Bézier曲线及其扩展

该文研究一类类Bezier曲线及其扩展。主要根据一组三角基函数构造由四个控制顶点组成的类Bezier曲线,随后引入基函数中的形状控制参数得到带形状参数的类Bezier曲线,进而构造了带形状参数的类Bezier插值曲线,这是基于通过混合函数混合参数化的控制多边形及类Bezier曲线得到的一类曲线。它具有局部性、端点性质、几何不变性与仿射不变性、对称性、凸包性、变差缩减性等性质。同时它可以表示Bezier曲线所不能表示的圆锥曲线,最重要的性质是其具有插值性,这样就大大增强了其在实际领域中得到应用的可能性。     

基于4点分段的FC3连续组合曲线

为了保留B样条方法的局部控制性和自动光滑性,同时提升曲线的连续阶,并赋予曲线独立于控制顶点和节点矢量的形状调整自由度,提出了一种与3次B样条曲线结构相同的新曲线。首先,在代数多项式空间上,以幂基为基底,预设调配函数的初步表达式,其中包含若干待定系数;然后,根据欲定义的曲线的主要性质,反推出调配函数需满足的基本性质,并据此建立关于调配函数中待定系数的方程组;之后,借助MATLAB软件编程计算,确定待定系数之间的关系,从而确定调配函数的原始表达式,其中包含自由参数;最后,对原始表达式进行整理,使其中的自由参数具有明确的几何意义,从而确定调配函数的最终表达式。基于该调配函数,采用与3次B样条曲线相同的分段定义方式,构造了一种基于4点分段的组合曲线。该曲线不仅继承了B样条曲线的诸多优点,而且突破了3次B样条曲线的连续阶,同时拥有了灵活的局部形状调整参数。另外,对曲线中形状参数的取值范围进行扩展,即可构造插值于局部或全部控制顶点的曲线。与3次B样条方法相比,新方法既可以满足形状设计中对连续性方面更高的要求,又可以满足对形状调整以及逼近与插值方面更多的要求。     

具有高阶奇异解的函数组边值问题的推广

定义了一个新的函数类H*λ1,λ2,….,λn。给出了Cauchy核属于此函数类的Cauchy型积分的plemelj公式,推广了经典的plemelj公式,并利用它和插值多项式理论讨论了具有高阶奇异解,即属于H*λ1,λ2,….,λn的函数组的边值问题。     

五次参数插值样条曲线

给定有序的空间点列,Pi(i=0,1,…,n),构造了一类参数五次插值样条曲线,该插值曲线的每一段由四个基函数构成,曲线段之间是C^2连续的,且曲线可以局部修改。     

TC-B样条曲线与λ-B样条曲线的光滑拼接

在CAGD中,人们对曲线曲面的拼接做了大量的研究与分析.本文研究了三次TC-B样条曲线与带参数λ的三次B样条曲线的光滑拼接问题,并讨论了三次TC-B样条曲线与λ-B样条曲线的G0、G1和G2光滑拼接问题.     

一类微分算子特征值的算法

采用Galerkin方法来构造适当的基函数,计算一类微分算子特征值的近似值,且可用第n次近似值来估计第n-1次近似值的精确度.随着n的增大,特征值λk的精确度逐步提高,只要适当选取n,就可以求得所需精确度的特征值的近似值,此算法具有一定的实用价值和理论价值.     

构造函数求交点 巧用交点求参数

在学习了函数之后,常常遇到形如"已知函数f(x)定义域为[m,n](m相似文献   

Wang-Ball曲线的细分变换

本文首先介绍Wang-Ball曲线细分的快速算法;然后利用与Bezier曲线的转换矩阵,推导出Wang-Ball曲线的细分变换为相似变换;同时,并给出了具体的数值实例.     

NURBS curve blending using extension

Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that comer are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G^1- or G^2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth： （1） The parameterization of the original shapes does not change; （2） No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.     

A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter

We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.     

A family of quasi-cubic blended splines and applications

INTRODUCTION Bézier curves and uniform B-spline curves are powerful tools for constructing free form curves and surfaces (FFC/FFS). But they cannot represent the arcs, hyperbola, sphere, cylinders and other transcendental curves and surfaces exactly. In order to avoid the in- conveniences, many bases are presented in other new spaces (Zhang, 1996; Pe?a, 1997; Walz, 1997; Sánchez-Reyes, 1998; Mainar et al., 2001). Note that, these existing methods can deal with both polynomial curve…     

Curve smoothing using a continuous function

Current curve smoothing technologies provide a smoothed curve by joining together separate curves that have certain degrees of continuity at junctions. These technologies have found many applications in science and engineering. However, none of them can provide a smoothed curve using a single continuous function for arbitrary segmental curves. This paper reports a new approach that can be used to construct a single continuous function that joins an arbitrary number of different segmental curves, with the required degree of continuity at all junctions. The smoothness of transition at different junctions can be controlled by separate parameters to suit different needs. The combined continuous function can approach the original segmental functions asymptotically or match the original segmental functions “exactly” inside each segment by adjusting the smoothness parameter. This new approach may also find application outside the scope of curve smoothing/curving fitting in the future.     

C2连续奇异混合插值曲面

利用奇异混合函数将双三次B样条曲面与虚拟曲面片作混合,构造一类可插值给定数据点的插值曲面,该类曲面在边界处可达到C~2连续,参数α可对曲面片整体形状进行调控。进一步,构造了可局部调控形状的带形状参数的插值曲面。     

Bézier curves with shape parameter

In this paper, Bezier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bezier curves with shape parameter. The Bezier basis curves with shape parameter have most properties of Bemstein basis and the Bezier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bezier curves with shape parameter approximate to the control polygon. In the last, the Bezier surface with shape parameter is also constructed and it has most properties of Bezier surface.     

椭圆弧的多项式逼近

提出一种用三次Bézier曲线逼近椭圆弧的方法,根据椭圆弧和Bézier曲线的对称性确定带参数的控制顶点,再由误差函数的零点分布情况确定参数的值,从而得到误差函数的值.与已有的方法相比较,逼近阶都是6阶,但是具有更好的逼近精度.     

基于多级夹角函数的傅里叶形状描述子(英文)

为了描述形状由全局信息到局部变化的层次信息,提出一种有效的形状签名,即多级夹角函数.多级夹角函数具有内在的旋转、平移和缩放不变性.对轮廓上每一点,其多级夹角函数通过轮廓的非等弧长分割所得的成对线段计算得到.然后利用多级夹角函数推导出傅里叶描述子,以进行高效的形状检索.使用标准的性能评价方法对所提出的描述子在3个形状图像库上进行了测试,包括MPEG-7图像库、Kimia-99图像库和Swedish树叶图像库.形状检索实验结果表明,基于多级夹角函数的傅里叶描述子优于已有的傅里叶描述子,且具有较低的计算复杂度.与其他类型的形状描述方法相比,所提出的描述子在相同查全率时具有最高的查准率,证明了该描述子的有效性.     

Bézier curves with shape parameter

In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and the Bézier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier surface with shape parameter is also constructed and it has most properties of Bézier surface. Project supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973) of China (No. G2002CB12101)