共查询到18条相似文献,搜索用时 78 毫秒
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圆域B样条曲线的节点去除 总被引:1,自引:0,他引:1
在圆域算术的基础上,引入了圆域B样条曲线的概念,并讨论了它的一些基本性质.研究了圆域B样条曲线的节点去除问题,即用去除一个节点后的圆域B样条曲线包住原曲线,采用拟线性规划和最佳逼近2种方法,分别给出了该问题的解析解. 相似文献
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多形状参数的二次非均匀双曲B-样条曲线 总被引:1,自引:0,他引:1
给出了一类带多个形状参数的二次非均匀双曲B-样条曲线,这类曲线具有二次多项式B-样条曲线的许多重要性质.根据形状参数的不同取值,能整体或局部地调控曲线的形状;无需重节点技术或解线性方程组,就能使曲线直接插值于某些控制点或控制边.此外,这类曲线能精确地表示双曲线. 相似文献
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《计算机辅助设计与图形学学报》2016,(4)
广义B样条曲线具备了B样条曲线的各种优良性质,又因为其独具的核函数为形状设计带来更加丰富的可能性,文中提出了广义B样条曲线的节点去除与光顺算法.首先给出了构造广义B样条对偶基的新方法,其时间计算复杂度得到了很好的控制;其次摘除需去除的节点,再利用对偶基的最佳逼近性质,采用广义B样条的对偶基求得新的广义B样条曲线的控制顶点;在广义B样条曲线光顺中引入跳跃值的概念,如果某个节点附近的跳跃值较大,则去除相应的节点,从而实现在此节点处的光顺.最后通过大量的数值实例,展示了算法的有效性. 相似文献
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基于改进L-系统的植物形态建模方法研究 总被引:1,自引:0,他引:1
L-系统是表达植物拓扑形态结构的重要方法之一。然而传统的L-系统表达植物枝条弯曲的方法复杂,产生式难以提炼,生成的枝条结构生硬。为了更好地模拟植物枝条弯曲的形态结构,对传统的L-系统进行改进。改进的L-系统将B-样条曲线的数学表达式转化为L-系统的规则产生式,以生长节点为中心,结合B-样条曲线表达,灵活控制枝干的弯曲性,并且采用生长节点的动态数据结构设计,最终实现植物枝条形态的逼真模拟效果。 相似文献
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本文研究了调整一个节点对B样条曲线产生的影响。调整B样条曲线的一个节点,引起两个节点区间改变。讨论了这两个节点区间上有定义的B样条基函数所发生的变化,以及对B样条曲线产生的影响。研究表明,通过调整一个节点可以方便地调整B样条曲线的形状,为B样条曲线形状调整提供了一种简便有效的方法,这在很大程度上丰富了B样条曲
线形状调整的方法。 相似文献
线形状调整的方法。 相似文献
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讨论了任意边界下的极小曲面造型问题,提出了一个用B-样条函数做任意有界区域上极小曲面造型的新方法.基本思想是:对B-样条函数加权,权函数为节点到区域边界的距离函数,使用加权的B-样条函数空间作为有限元子空间,从而可以得到极小曲面在任意边界上的B-样条曲面近似解.结果表明,新方法得到的极小曲面具有良好的光顺性,且计算精度高. 相似文献
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为解决移动机器人在避障时的曲线优化问题,提出了基于最小变量的B-样条路径规划方法.对该方法从数学模型上进行了推导,指出了该方法相对于其它B-样条方法的优点,并对该方法进行了优化,给出了相应的优化算法.研究表明:具有最小变量的B-样条函数比只用B-样条函数定义的曲线具有更优化的线性约束,其曲线具有更好的光滑性. 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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Yu-Hua Gu Tjahjadi T. 《IEEE transactions on systems, man, and cybernetics. Part A, Systems and humans : a publication of the IEEE Systems, Man, and Cybernetics Society》1999,29(4):358-367
In this paper, we consider the problem of matching 2D planar object curves from a database, and tracking moving object curves through an image sequence. The first part of the paper describes a curve data compression method using B-spline curve approximation. We present a new constrained active B-spline curve model based on the minimum mean square error (MMSE) criterion, and an iterative algorithm for selecting the “best” segment border points for each B-spline curve. The second part of the paper describes a method for simultaneous object tracking and affine parameter estimation using the approximate curves and profiles. We propose a novel B-spline point assignment algorithm which incorporates the significant corners for interpolating corresponding points on the two curves to be compared. A gradient-based algorithm is presented for simultaneously tracking object curves, and estimating the associated translation, rotation and scaling parameters. The performance of each proposed method is evaluated using still images and image sequences containing simple objects 相似文献
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Convexity-preserving fairing 总被引:4,自引:0,他引:4
This paper develops a two-stage automatic algorithm for fairing C2-continuous cubic parametric B-splines under convexity, tolerance and end constraints. The first stage is a global procedure, yielding a C2 cubic B-spline which satisfies the local-convexity, local-tolerance and end constraints imposed by the designer. The second stage is a local finefairing procedure employing an iterative knot-removal knotreinsertion technique, which adopts the curvature-slope discontinuity as the fairness measure of a C2 spline. This procedure preserves the convexity and end properties of the output of the first stage and, moreover, it embodies a globaltolerance constraint. The performance of the algorithm is discussed for four data sets. 相似文献
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为解决移动机器人在避障时的曲线优化问题,提出了基于最小变量的B-样条路径规划方法。对该方法从数学模型上进行了推导,指出了该方法相对于其它B-样条方法的优点,并对该方法进行了优化,给出了相应的优化算法。研究表明:具有最小变量的B-样条函数比只用B-样条函数定义的曲线具有更优化的线性约束,其曲线具有更好的光滑性。 相似文献
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《Advances in Engineering Software》2000,31(2):107-118
This paper presents a method for the direct manipulations of B-spline and non-uniform rational B-splines (NURBS) curves using geometric constraints. A deformable model is developed to define the deformation energy functional of B-spline and NURBS curves. The finite element method is used to minimize the deformation energy functional and solve for the deformed shape of curves subjected to constraints. This approach results in a set of linear equations for a B-spline curve and a set of non-linear equations for a NURBS curve. A perspective mapping is used to linearize the NURBS formulations. NURBS curves are first mapped from the 3D Cartesian coordinate space to the 4D homogeneous coordinate space, and transformed to 4D B-spline curves. After the manipulation in the 4D homogeneous coordinate space, the modified NURBS curves are then mapped back to the 3D Cartesian coordinate space. The approach is implemented by a prototype program, which is written in C, and runs under WINDOWS. Several examples are presented to demonstrate the capabilities of this approach. 相似文献
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Wen-Ke Wang Hui Zhang Hyungjun Park Jun-Hai Yong Jean-Claude Paul Jia-Guang Sun 《Computer aided design》2008,40(10-11):999-1008
A new algorithm for reducing control points in lofted surface interpolation to rows of data points is presented in this paper. The key step of surface lofting is to obtain a set of compatible B-spline curves interpolating each row. Given a set of points and their parameterization, a necessary and sufficient condition is proposed to determine the existence of interpolating B-spline curves defined on a given knot vector. Based on this condition, we first properly construct a common knot vector that guarantees the existence of interpolating B-spline curves to each row of points. Then we calculate a set of interpolating B-spline curves defined on the common knot vector by energy minimization. Using this method, fewer control points are employed while maintaining a visually pleasing shape of the lofted surface. Several experimental results demonstrate the usability and quality of the proposed method. 相似文献