IntegraI型Lupas-Bézier算子收敛阶的估计

运用概率型算子的概率性质,研究了局部有界函数f的Integral型Lupas-Bézier算子收敛阶,得到更精确的估计。其研究对于Bézier型算子逼近的研究工作,以及提高运用Bézier法的计算机辅助设计几何造型的精度的估计有重要意义。     

Durrmeyer-Bézier算子收敛阶的新估计

运用概率型算子的概率性质,由Boj anic-Cheng的分解法,研究了有界变差函数f 的 Durrmeyer-Bézier算子收敛阶的精确估计。其研究对于Bézier型算子逼近的研究工作,以及提高运用Bézier法的计算机辅助设计几何造型精度的估计有重要意义。     

Integral型Lupas-Bézier算子的收敛阶

在Zeng等人对函数f的Integral型Lupas-Bézier算子在区间[0,∞)上收敛于α 11f(x ) αα 1f(x-)的收敛阶进行研究的基础上,利用基函数的概率性质等方法,对其所给的积分型Lupas-Bézier算子收敛阶估计结果作进一步的改进,得到其收敛阶的精确估计.     

积分型Szász-Bézier算子的逼近阶

对局部有界函数f的积分型Szász-Bézier算子的逼近阶进行估计.在Zuo和Zeng关于积分型Szász-Bézier算子的逼近阶估计公式研究的基础上,得到更精确估计公式.     

局部有界函数的Integral型Lupas-Bzier算子的收敛阶

对局部有界函数f的Integral型Lupas-Bzier算子在区间[0,∞)上收敛于[f(x+)+αf(x-)]/(α+1)的收敛阶进行研究,利用Cauch-Schwarz不等式和Lupas基函数的概率性质等方法,对前人关于Integral型Lupas-Bzier算子收敛阶的系数估计作了进一步的改进,得到了较优的系数估计。     

Durrmeyer-Bezier算子收敛阶的新估计

运用概率型算子的概率性质,由Boj anic-Cheng的分解法,研究了有界变差函数f 的 Durrmeyer-Bezier算子收敛阶的精确估计。其研究对于Bezier型算子逼近的研究工作,以及提高运用Bezier法的计算机辅助设计几何造型精度的估计有重要意义。     

Bézier曲线的光滑拼接

Bézier曲线是计算机图形学研究的主要内容.曲线的拼接是曲线曲面造型中的关键技术之一.基于Bézier曲线的拼接原理,在Visual C＋＋6.0环境下开发Bézier曲线的拼接程序,将曲线拼接在界面中动态实现.     

同曲线的同次均匀B样条与Bézier控制顶点转换

主要研究B样条与Bézier控制顶点的转换问题,从样条曲线基函数的角度推导出低次均匀B样条与Bézier控制顶点的转换矩阵,给出转换矩阵的一些相应性,从而利于工业造型的样条曲线造型系统转换。     

C^2连续的有理三次Bézier样条插值曲线

有理Bézier曲线具有很多良好的性质,是曲线曲面设计的重要方法.根据给定的型值点,通过构造有理Bézier样条插值曲线的公式,给出了计算方法,并且分析了重节点情形曲线的形状和特点,最后通过数值实例验证了方法的有效性.     

BBH-Bézier算子的点态逼近估计

利用经典的Zeng分解方法,并结合Bleimann-Butzer and Hahn算子基函数的界,讨论了Bleimann-Butzer and Hahn-Bézier算子在0＜α＜1时对一般有界函数的逼近,得到比较好的收敛阶估计,所得结果拓展了在α≥1时对有界变差函数逼近的研究工作.     

Improvement of the termination criterion for subdivision of the rational Bézier curves

By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.     

Improvement of the termination criterion for subdivision of the rational Bézier curves

By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed. Project supported by the National Natural Science Foundation of China (No. 60173034) and the Foundation of State Key Basic Research(973) Program (No. G1998030600), China     

BBH—Bezier算子的点态逼近估计

利用经典的Zeng分解方法,并结合Bleimann-ButzerandHahn算子基函数的界,讨论了Bleimann-ButzerandHahn-B6zier算子在O〈α〈1时对一般有界函数的逼近,得到比较好的收敛阶估计,所得结果拓展了在α≥1时对有界变差函数逼近的研究工作．     

PH-spline approximation for Bézier curve and rendering offset

In this paper,a G1, C1, C2 PH-spline is employed as an approximation for a given Bézier curve within error bound and further renders offset which can be regarded as an approximate offset to the Bézier curve. The errors between PH-spline and the Bézier curve, the offset to PH-spline and the offset to the given Bézier curve are also estimated. A new algorithm for constructing offset to the Bézier curve is proposed.     

Constrained multi-degree reduction of rational Bezier curves using reparametenzation

Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bezier curves to the algorithms of constrained multi-degree reduction for rational Bezier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bezier curves, which are used to make uniform the weights of the rational Bezier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of ＂cancelling the best linear common divisor＂ and ＂shifted Chebyshev polynomial＂, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.     

Bézier曲线等分作图算法的包络性分析

Bézier曲线是一种最重要且最简便的构造控制参数曲线方法,是计算机图形学的重要内容。Bézier曲线的等分作图算法是一种简便、计算量小的算法;同时Bézier曲线在一些实际应用中可由包络形成因而具有包络性。本文给出了二次三次及n次Bézier曲线等分图算法的包络性证明,证明了Bézier曲线的包络性,为理解Bézier曲线的等分图算法提供了新的方式。     

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)     

PH-spline approximation for Bézier curve and rendering offset

In this paper, a G¹, C¹, C² PH-spline is employed as an approximation for a give Bézier curve within error bound and further renders offset which can be regarded as an approximate offset to the Bézier curve. The errors between PH-spline and the Bézier curve, the offset to PH-spline and the offset to the given Bézier curve are also estimated. A new algorithm for constructing offset to the Bézier curve is proposed. Project supported by the National Natural Foundation of China (No. 60073023) and the National Basic Research Program (973) of China (No. 2002CB312101)