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为了解决Catumull-Clark细分曲面在工程上难以推广的问题,给出了一种基于C-B样条的Catumull-Clark细分曲面的算法,C-B样条曲线是B样条曲线的拓广,但它们的形状依赖于参数α,由于新的曲面细分方法充分利用C-B样条能够精确表示圆,椭圆等规则形体的特性,因而使通过此方法生成的细分曲面,除了在奇异点处能保持二阶导数连续外,还能够像C-B样条曲线,曲面一样,精确地表示圆柱等常规曲面,统一工程曲面等的造型,同时它仍然保持细分曲面的造型特点,即能够解决NURBS曲面难以处理的任意拓扑结构的造型问题,另外,还可依赖控制参数α的调节作用来增加造型的自由度,而且当α→0时,它们就退化成Catmul-Clark细分曲面,在工程图形上的应用实例表明,这种算法简单,有效。 相似文献
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研究均匀B样条曲线细分生成的几何作图问题,给出了采用p-nary细分法细分生成任意次均匀B样条曲线的递归细分算法。在此基础上,研究了任意次均匀B样条曲线p-nary细分生成的几何作图方法。利用这种几何作图法,可以直观地在计算机上通过编程来快速准确地绘制B样曲线,更重要的是,可以使基于几何方法的任意次B样曲线的手工绘制成为可能。 相似文献
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带有给定切线多边形的B-样条曲线 总被引:23,自引:0,他引:23
51.引言在任意曲线的分析和逼近中,B6zier曲线的分段表示和B样条曲线非常有用I‘-’].Hering.L描述了以给定凸多边形为切线多边形的闭(C‘一和C’一连续)分段三(四)次B6Zier曲线和三(四)次B样条曲线*,并且给出了重要的应用背景.对一般的切线多边形,问描述了闭(G‘一连续)分段三次B6zier曲线.问中描述的算法必须求解大型线性方程组得到所有B6zier点,计算量很大,且曲线容易出现多余拐点,而相应的B样条曲线是由已求出的B6zier点反算deBoor点直接得到.问中描述的算法是通过三次B6zier曲线段G’连接的条件计算每… 相似文献
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三次均匀B样条曲线的扩展 总被引:53,自引:21,他引:53
给出四次多项式调配函数,它是三次B样条函数的扩展.基于给出的调配函数,建立一种带形状参数的分段多项式曲线的生成方法.通过改变形状参数的取值,可以调整曲线接近其控制多边形的程度;可以调整曲线从三次均匀B样条曲线的两侧逼近三次均匀B样条曲线.选取不同的形状参数值,可以得到不同位置的C^2连续的曲线,且所给曲线与三次均匀B样条曲线有相同的端点性质.最后给出了曲线设计的计算实例. 相似文献
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局部调整插值点的三次样条曲线表示 总被引:1,自引:0,他引:1
给出了带局部形状参数的三次样条曲线生成方法.所给方法以Hermite型插值曲线和非均匀三次B样条曲线为特殊情形,将插值于控制点的曲线和逼近于控制多边形的非均匀B样条曲线统一起来.一个形状参数只影响两条曲线段,曲线表达式保持了三次Bezier曲线表达式的简单结构.改变形状参数的值或调整Bezier控制点,可以局部调整曲线的形状.基于所给样条曲线,给出了带局部形状参数的双三次样条曲面. 相似文献
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局部能量最优法与曲线曲面的光顺 总被引:13,自引:6,他引:13
龙小平 《计算机辅助设计与图形学学报》2002,14(12):1109-1113
曲线光顺处理的方法主要有选点修改法和优化方法,而Kjellander方法是最常的选点修改法之一,文中提出一种选点修改法-局部能量最优法,该方法在三次均匀参数曲线法顺问题上进一步改进了Kjellander方法,具有更好的光顺效果,对三次B样条曲面给出了一个与此相关的曲面光顺方法。 相似文献
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提出了Bézier样条曲线利用分割技术近似弧长参数化的一种方法,并给出了相应的算法。通过求出曲线上所谓的‘最坏点’并在相应点处进行分割,可得到两条Bézier样条曲线。让这两条Bézier样条曲线具有与它们的近似弧长成比例的权,并对所得到的新的Bézier样条曲线进行同样的工作最终可得到一条由多条Bézier样条曲线所构成的新曲线。将这多条Bézier样条曲线合并成为一条Bézier样条曲线并通过节点插入技术将所得Bézier样条曲线转化为B-样条曲线的形式可得到全局参数域,其中各条Bézier曲线在全局参数域中所占子区间的长度与它们的权成比例,这样便得到了一条近似弧长参数化曲线。 相似文献
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为便于对均匀B样条曲线进行形状修改,利用二次均匀B样条基函数所需满足的条件,扩展二次均匀B样条基函数,构造出三次多项式调配函数.基于给出的调配函数,建立1种带形状参数的分段多项式曲线.调整形状参数可使三次多项式曲线在二次均匀B样条曲线两侧摆动.最后给出实例,构造出带局部调节参数G^1的连续曲线.该方法可以通过调整参数扩大二次均匀B样条曲线的调整范围. 相似文献
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本文给出了一种表示任意形状区域的方法--用B样条来拟合图像灰度曲面.在加权最小均方误差准则下,用B样条曲面拟合图像的灰度值曲面,再对B样条参数进行编码.该方案与分块DCT表示任意形状区域的方法相比,其压缩率得到很大提高;对于一个较大的区域,用B样条拟合的压缩率可达到分块DCT方法的10倍以上.而在同样码率时,特别是在低码率的情况下恢复后的图像质量优于分块DCT方法. 相似文献
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This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main
contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for
creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction
method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis
(FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration
is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline
curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models
of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape
optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming
are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach.
Received January 27, 2000
Communicated by J. Sobieski 相似文献
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A method to approximate a circular arc of any sweep angle with integral B-spline curves of any degree is presented. The idea is to interpolate end derivatives as well as some internal points with integral B-splines of given degree and continuity. The critical element is the choice of the right end derivative directions and magnitudes. The points and the derivatives at these locations are sampled uniformly using the trigonometric equation of the circle. The method is very general in that any degree and any level of parametric continuity can be specified. 相似文献
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运用能量优化的思想,提出一种B样条曲线变形的新方法,可用于B样条曲线的变形。首先将B样条曲线段类比为有限单元法中线单元,并将作用在B样条曲线段的外载荷等效成线单元的端点力,分别建立B样条曲线内部能量、外载荷能量函数方程;外载荷的改变将引起B样条曲线能量的变化,通过求解一个使曲线能量的变化量为最小的优化问题,得到变形后的B样条曲线。运用该方法实现了B样条曲线的局部、整体等变形操作。 相似文献
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以管道工程领域的结构应力分析要求为研究对象,针对通用有限元分析软件的命令众多、操作复杂的特点,提出了以Visual Basic开发用户图形化操作界面的方法来打包和封装参数化过程命令,在后台调用分析软件进行计算,并输出结果至用户界面,从而建立了管道应力参数化计算机辅助分析平台,该平台大大简化了分析过程并提高了工程设计效率,方便工程人员进行及时的分析和操作。 相似文献
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目的 为了同时解决传统多项式B样条曲线在形状调控、精确表示常见工程曲线以及构造插值曲线时的不足,提出了一类集多种特性的三次三角伪B样条。方法 首先构造了一组带两个参数的三次三角伪B样条基函数,然后在此基础上定义了相应的参数伪B样条曲线,并讨论了该曲线的特性及光顺性问题,最后研究了相应的代数伪B样条,并给出了最优代数伪B样条的确定方法。结果 参数伪B样条曲线不仅满足C2连续,而且无需求解方程系统即可自动插值于给定的型值点。当型值点保持不变时,插值曲线的形状还可通过自带的两个参数进行调控。在适当条件下,该参数伪B样条曲线可精确表示圆弧、椭圆弧、星形线等常见的工程曲线。相应的代数伪B样条具有参数伪B样条曲线类似的性质,利用最优代数伪B样条可获得满意的插值效果。结论 所提出的伪B样条同时解决了传统多项式B样条曲线在形状调控、精确表示常见工程曲线以及构造插值曲线时的不足,是一种实用的曲线造型方法。 相似文献
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In this paper, we propose a method for constructing a new class of copulas. They are called linear B-spline copulas which are a good approximation of a given complicated copula by using finite numbers of values of this copula without the loss of some essential properties. Moreover, rigorous analysis shows that the empirical linear B-spline copulas are more effective than empirical copulas to estimate perfectly dependent copulas. For the cases of nonperfectly dependent copulas, simulations show that the empirical linear B-spline copulas also improve the empirical copulas to estimate the underlying copula structure. Furthermore, we compare the performance of parametric estimation of copulas based on the empirical copulas with that based on the empirical linear B-spline copulas by simulations. In most of the cases, the latter are better than the former. 相似文献
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《Computer Methods in Applied Mechanics and Engineering》2002,191(17-18):1791-1826
Periodic dynamic loadings may cause dynamic instability of a structure through parametric resonance. In this paper, a B-spline finite strip method (FSM) is presented for the dynamic instability analysis of composite laminated rectangular plates and prismatic plate structures, based on the use of first-order shear deformation plate theory (SDPT). The equations of motion of a structure are established by using Lagrange's formulation and they are a set of coupled Mathieu equations. The boundary parametric resonance frequencies of the motion are determined by using the method suggested by Bolotin through a novel development which incorporates the Sturm sequence method and the multi-level substructuring technique to achieve reliability, efficiency and accuracy. Various loading patterns, arbitrary lamination and general boundary conditions are accommodated. A variety of numerical applications is presented to test the developed method and to study the dynamic instability behaviour of single plates and of complicated plate structures under various types of dynamic loading. A dynamic instability index (DII) is devised to measure the degree of instability against certain parameters which include the thickness-to-length ratio, the degree of orthotropy, the fibre orientation, the loading pattern and the boundary conditions. 相似文献
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《国际计算机数学杂志》2012,89(11):2353-2371
In this paper, numerical solutions of a coupled modified Korteweg–de Vries equation have been obtained by the quadratic B-spline Galerkin finite element method. The accuracy of the method has been demonstrated by five test problems. The obtained numerical results are found to be in good agreement with the exact solutions. A Fourier stability analysis of the method is also investigated. 相似文献