Bézier曲面在三角域和矩形域上的互化

Bezier曲面是CAD/CAM中应用最为广泛的曲面之一。它可分为两类:矩形域上张量积形式的Bezier曲面:三角域上的Bezier曲面:     

矩形域及三角域上Bezier曲面的转换

本文讨论了矩形域及三角域上Ｂｅｚｉｅｒ曲面的相互关系，从几何变换的角度给出了显式的转换公式及几何解释，同时也给出了相应的算法。     

三角域上C~1插值的两种表示

在有限元计算中,散乱数据插值以及曲面设计和表示等问题常常需要构造三角域上C~1连续的分片插值多项式.Zenisek证明了闭三角域上整体具有m阶光滑的双变量插值多项式至少是4m+1次的.在实际问题中最常用到的是三角域上C~1连续五次双变量插值多项式的表示.     

三角域上Bernsterin—Bezier曲面的一种推广

本文给出了三角域上Ｂｅｒｎｓｔｅｉｎ－Ｂｅｚｉｅｒ曲面的一种推广，并研究了这种曲面的性质和算法。     

一种细分格式生成极限曲面的法向量的求法

在Levin给出的三角域上生成极限曲面的法向量求法基础上,给了同拟蝴蝶形细分在矩形域上生成极限曲面的情况,并得到了两个自由度,可以对法向量进行优化选取,这对讨论曲面的等距面有广泛的实际意义。     

三角域上带两个形状参数的Bézier曲面的扩展

给出了三角域上带双参数λ1,λ2的类三次Bernstein基函数,它是三角域上三次Bernstein基函数的扩展.分析了该组基的性质并定义了三角域上带有两个形状参数λ1,λ2的类三次Bernstein-Bézier(B-B)参数曲面.该基函数及参数曲面分别具有与三次Bernstein基函数及三次B-B参数曲面类似的性质.当λ1,λ2取特殊的值时,可分别得到三次Bernstein基函数及三次B-B参数曲面以及参考文献中所定义的类三次Bernstein基函数及类三次B-B参数曲面.由实例可知,通过改变形状参数的取值,可以调整曲面的形状.     

Bézier曲面在三角域和矩形域上的互化

Bezier曲面是CAD/CAM中应用最为广泛的曲面之一。它可分为两类:矩形域上张量积形式的Bezier曲面:三角域上的Bezier曲面:     

矩形域上的插值曲面及其协调性方程

在CAGD中,曲面片的光滑拼接是一个重要问题,而在多片(三片以上)曲面的光滑拼接过程中,将不可避免的要遇到光滑拼接条件的协调性(又称相容性)问题,[4]中系统地讨论了单形上超限多项式插值及相容性问题,本文主要讨论矩形域上多项式曲面片光滑拼接的协调性方程,并在此基础上讨论了矩形域上插值曲面的构造问题.     

n次三角域Bézier曲面片GC~1拼接的对称条件

1.引言曲面造型是计算几何领域中一个重要的研究课题,在工程和制造中有着广泛的应用。Bezier曲面是当前曲面造型的重要方法之一,具有装配灵活,适应性强的优点。用矩形域和三角域Bezier曲面片混合造型,几乎可以构造任意形状的曲面。但Bezier曲面造型也     

三角域上Bernstein—Bézier曲面的一种推广

本文给出了三角域上Bernstein—Bezier曲面的一种推广,并研究了这种曲面的性质和算法。     

Adaptive methods for piecewise polynomial collocation for ordinary differential equations

Various adaptive methods for the solution of ordinary differential boundary value problems using piecewise polynomial collocation are considered. Five different criteria are compared using both interval subdivision and mesh redistribution. The methods are all based on choosing sub-intervals so that the criterion values have (approximately) equal values in each sub-interval. In addition to the main comparison it is shown by example that at least when accuracy is low then equidistribution may not give a unique solution. The main results that using interval size times maximum residual as criterion gives very much better results than using maximum residual itself. It is also shown that a criterion based on a global error estimate while giving very good results in some cases, is unsatisfactory in other cases. The other criteria considered are that given by De Boor and the last Chebyshev series coefficient. AMS subject classification (2000)  65L10, 65L50, 65L60     

Gröbner bases, H-bases and interpolation

The paper is concerned with a construction for H-bases of polynomial ideals without relying on term orders. The main ingredient is a homogeneous reduction algorithm which orthogonalizes leading terms instead of completely canceling them. This allows for an extension of Buchberger's algorithm to construct these H-bases algorithmically. In addition, the close connection of this approach to minimal degree interpolation, and in particular to the least interpolation scheme due to de Boor and Ron, is pointed out.

     

Optimal local spline interpolants

A constructive proof is given of the existence of a local spline interpolant which also approximates optimally in the sense that its associated operator reproduces polynomials of maximal order. First, it is shown that such an interpolant does not exist for orders higher than the linear case if the partition points of the appropriate spline space coincide with the given interpolation points. Next, in the main result, the desired existence of an optimal local spline interpolant for all orders is proved by increasing, in a specified manner, the set of partition points. Although our interpolant reproduces a more restricted function space than its quasi-interpolant counterpart constructed by De Boor and Fix [1], it has the advantage of interpolating every real function at a given set of points. Finally, we do some explicit calculations in the quadratic case.     

On the Convergence of Iterated Remeshing

In the context of constructing a one-dimensional space-meshby equidistributing a weight function (monitor function) asintroduced by de Boor, we prove that under not too unrealistican approximation to the process as carried out in practice,iterating the remeshing process gives a convergent sequenceof meshes. The limit mesh has useful asymptotic smoothness properties.We suggest ways in which this could be exploited for improvederror control in BVPs. Numerical experiments show the convergencebehaviour, and give preliminary support to the error-controlproposal.     

Conjectures on GCn sets

The paper gives a generalization of the counterexample of C. de Boor on ? ^d and provides an example of GC ₂ set in ?⁴ with three maximal hyperplanes. Also, a conjecture on the number of maximal lines of GC _n sets in ? ^d is discussed and proved that it is true in the case when n = 2, d = 3.     

Quasi-interpolation with translates of a function having noncompact support

We establish a result related to a theorem of de Boor and Jia [1]. Their theorem, in turn, corrected and extended a result of Fix and Strang [5] concerning controlled approximation. In our result, the approximating functions are not required to have compact support, but satisfy instead conditions on their behavior at . Our theorem includes some recent results of Jackson [6] and is closely related to the work of Buhmann [2].Communicated by Carl de Boor     

An improved solution for diffusion waves to overland flow

Diffusion wave equation describes the flood wave propagation which is used in solving overland and open channel flow problems. Therefore, it is important to understand and solve the diffusion wave equations accurately. For this purpose, researchers have previously developed several analytical and numerical methods for the solution of the partial differential equation of diffusion waves. The solution derived by Kazezy?lmaz-Alhan and Medina (2007) [12] can be used to solve overland flow problems during rainfall events with both constant and variable rainfall intensity, and with constant hydraulic diffusivity and wave celerity. In this paper, this method is improved by employing the De Hoog algorithm instead of Stehfest algorithm for Laplace inversion and adapting the solution to variable hydraulic diffusivity and wave celerity. In addition, the performances of the Stehfest and the De Hoog algorithms are compared. Synthetic examples are solved by using both Stehfest and De Hoog algorithms incorporated into the existing analytical solution to present the accuracy of the De Hoog algorithm over the Stehfest algorithm. The examples are also solved by using the new method in order to demonstrate the improvement over the existing method.     

由线性微分算子决定的B-样条

首先,我们引进一些记号及定义.设 t=(t_i)_(-∞)~∞是非减的实数序列,对所有i都有t_i相似文献   

Non-uniform exponential tension splines

We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D ²(D ²–p ²), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each interval. The algorithm provides values of the associated B-splines and their generalized and ordinary derivatives by performing positive linear combinations of positive quantities, described as lower-order exponential tension splines. We show that nothing else but the knot insertion algorithm and good approximation of a few elementary functions is needed to achieve machine accuracy. The underlying theory is that of splines based on Chebyshev canonical systems which are not smooth enough to be ECC-systems. First, by de Boor algorithm we construct exponential tension spline of class C ¹, and then we use quasi-Oslo type algorithms to evaluate classical non-uniform C ² tension exponential splines.      

Urn models and B-splines

Urn models are used to construct normalized B-spline basis functions over arbitrary knot vectors. These stochastic models are then applied to derive some of the basic analytic properties of B-splines. In particular, the Cox-de Boor recursion formula is given a probabilistic interpretation. The connection between urn models, B-splines, and Beta-splines is also discussed.