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1.
利用构造样条基函数的方法得到了一组三角基函数,讨论了这组三角基函数的性质,用这组基得到了一种新的二次三角B样条曲线,并使用研究均匀B样条的方法探讨了这种二次三角曲线,给出了二次三角B样条曲线的一些性质. 相似文献
2.
盛鸿宇 《通化师范学院学报》2014,(4):17-20
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. 相似文献
3.
T-B样条基函数是具有B样条基函数性质的三角基函数。基于T-B样条基函数,构造了一类与给定多边形相切的闭三角多项式曲线,逼近效果好,计算量小,且编程统一,实验表明,具有较好的应用效果。 相似文献
4.
PAN Yong-juan WANG Guo-jin 《浙江大学学报(A卷英文版)》2007,8(8):1199-1209
In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable. 相似文献
5.
MO Guo-liang ZHAO Ya-nan 《浙江大学学报(A卷英文版)》2006,7(12):2043-2049
INTRODUCTION B-spline curves and surfaces have been widely used in Computer Graphics (CG) and Computer Aided Design (CAD) (Hoschek and Lasser, 1993; Piegl and Tiller, 1997). Many practical algorithms, such as those for position and derivatives evaluation, knot insertion, knot deletion and degree elevation, are usually implemented in a CAD system that uses B-spline as a shape design tool. In curve and surface design, a given B-spline curve or surface usually needs to be extended in … 相似文献
6.
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) 相似文献
7.
研究了曲线拟合方法的特点,讨论了三次样条曲线和参数三次样条曲线的拟合方法在螺杆截面廓形拟合中的应用,给出了拟合的方程,并用实例验证了拟合的效果.同时解决了拟合过程中的单调性、失真、端点切向量的确定方法等一些关键技术问题.该方法为精确地生成刀具轨迹提供了光滑的型线方程. 相似文献
8.
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。 相似文献
9.
10.
刘华勇 《宁波职业技术学院学报》2005,9(5):13-15
对新型C-B样条曲线的拟合进行了初步的研究,在能量法的基础上,进一步研究了控制参数对曲线的影响,并给出了通过调整使得曲线的能量最小,以达到光顺拟合的目的. 相似文献
11.
邹序焱 《宜宾师范高等专科学校学报》2013,(12):8-11
提出一种基于带一个形状参数的二次三角函数插值的图像放大算法,给出了插值运算的数学公式.实验结果表明,该算法能有效地应用于数字图像的放大处理,得到的图像轮廓清晰,有效地抑制锯齿现象,放大后的图像满足视觉要求,且不会产生其它明显的人工痕迹,是一种切实可行的图像放大算法. 相似文献
12.
随着离心泵性能参数测试技术的发展,曲线拟合方程化已不再适应高精度的测试点,而应采用三次样条函数的曲线插值方程化,针对三次样条函数中斜率难以确定的问题,提出采用MATLAB语言编写的遗传算法程序进行斜率求解的方法,通过实例表明,遗传算法求解非常有效、准确和快捷。 相似文献
13.
Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called ＂path of AH curve＂ （AH Bezier and AH spline curves） when a changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point. 相似文献
14.
复杂曲面笔式加工的直接插补算法 总被引：2，自引：0，他引：2
针对复杂曲面笔式加工时位于曲面上的空间曲线型刀具轨迹,给出一种直接插补算法.即对以投影方式形成的位于曲面上的空间曲线形式的刀轨,根据导动曲线和刀触点轨迹线之间的几何运动关系,通过泰勒展开近似得到刀触点轨迹线上插补点所对应的导动线的参数,再反求间接得到刀触点坐标,从而生成控制机床运动的指令.该方法的实现扩充了CNC系统的轨迹控制功能,提高了复杂曲面的加工效率.仿真结果表明算法可行而且有效.该算法也可以应用到整体曲面加工中. 相似文献
15.
主要研究了四次样条插值函数的存在唯一性,通过给出三种边界条件,利用三弯矩法的思想,建立求解四次样条插值函数的线性方程组。在等步长的条件下,研究了线性方程组的系数矩阵,在三种边界条件下,证明了系数矩阵在一定条件下是可逆的,从而说明四次样条插值函数的存在唯一性。尤其对第一种边界条件,通过差分方程的方法,证明了在等距节点的条件下四次样条插值函数的存在唯一性与插值点数的奇偶性有关。 相似文献
16.
LI Ya-juan WANG Guo-zhao 《浙江大学学报(A卷英文版)》2006,7(6):1084-1087
INTRODUCTION Modification of knots of a B-spline curve changes the shape of the curve. In some recent pub-lications (Juhász and Hoffmann, 2001; 2003; Hoff-mann and Juhász, 2004; Li and Wang, 2005), the authors studied the effect of the alteration of a single knot on the shape of the curve. Hoffmann (2004) and Li & Wang (2006) applied these theories into the constrained shape modification of B-spline and NURBS curves. Juhász (2001) and Hoffmann & Ju-hász (2005) studied the effe… 相似文献
17.
In this note, we prove that the convergence rate of the modified Gauss-Seidel (MGS) method with preconditional I Sa isa monotonic function of preconditioning parameter a. Based on this result, to achieve better convergence rate we suggest proformingtwice preconditoning when applying the MGS method to solve a linear system whose coefficient matrix is an irreducible non-singularM-matrix. 相似文献
18.
Conventional methods for solving intersections between two offset parametric surfaces often include iteratively using computationally
expensive SSI (surface/surface intersections) algorithm. In addition, these methods ignore the relations between the intersection
curves of parametric surfaces with different offset distances. The algorithm presented in this paper, makes full use of the
topological relations between different intersection loops and calculates intersection loops with the help of previously calculated
intersection loops. It first pre-processes two parametric surfaces to obtain the characteristic points, called topology transition
points (TTPs), which can help in the subsequent finding of the topologies of the intersection curves. Then these points are
categorized into several distinct groups, and we can determine the calculation strategy for searching initial points by analyzing
the properties of these TTPs on the surfaces. Hence, all intersection curves can be marched from initial points by the tracing
algorithm. The proposed algorithm could calculate intersection curves robustly and effectively, and has been tested to be
capable of overcoming the degenerate conditions such as loop and singularities leaking that occur frequently in conventional
algorithms.
Project supported by the National Research Foundation for the Doctoral Program (No. 2000033554) of Higher Education of China
and the Natural Science Foundation of Zhejiang Province, China (No. 6001107) 相似文献
19.
构建了一种带双参数的分段有理三次Hermite插值样条,它是三次Hermite插值样条的推广．讨论了这种样条的逼近性及应用．数值例子表明,对于给定的插值条件,选择合适的参数,生成的插值曲线具有较好逼近效果． 相似文献
20.
连续性是插值函数必须满足的基本条件之一.文[1]定义了一种分段二次插值函数,却不能保证其连续性.文[2]中提出的一种二次样条方法虽能保证插值函数的连续性,但未讨论其收敛性和周期边界条件下解的存在性.本文对文[2]中的二次样条在周期边界条件下解的存在唯一性进行了讨论,并证明了在各种边界条件下插值函数的收敛性. 相似文献