混沌蚂蚁群优化求解自由节点B样条曲线拟合

B样条曲线拟合问题中,将节点作为自由变量可大幅提高拟合精度,但这就使曲线拟合问题转化为求解困难的连续多峰值、多变量非线性优化问题,当待拟合的曲线是不连续、有尖点情况,就更为困难。针对这一问题,基于混沌蚂蚁群优化算法CASO,提出了一种新的B样条曲线拟合算法CASO-DF。该算法结合B样条曲线拟合原理,通过蚁群中蚂蚁个体的混沌行为,调整自由节点位置,通过蚁群的自组织行为自适应地调整内部节点数目,解决了B样条曲线拟合问题。仿真结果表明了CASO-DF算法能够有效实现自由节点B样条曲线拟合,且性能优于其他同类算法。     

基于遗传算法的B样条曲线拟合改进算法

B样条曲线拟合应用于绘制离散数据点的变化趋势,一般采用数据逼近或者迭代的方法得到,是图像处理和逆向工程中的重要内容。针对待拟合曲线存在多峰值、尖点、间断等问题,提出一种基于遗传算法的B样条曲线拟合算法。首先利用惩罚函数将带约束的曲线优化问题转换为无约束问题,然后利用改进的遗传算法来选择合适的适应度函数,再结合模拟退火算法自适应调整节点的数量和位置,在寻优的过程中找到最优的节点向量,持续迭代直到产生最终的优良重建曲线为止。实验结果表明,该算法有效地提高了精度并加快了收敛速度。     

数据点加权最小二乘渐进迭代逼近及其B样条曲线拟合

为了使B样条拟合曲线插值部分数据点且逼近其余数据点,提出数据点加权的最小二乘渐进迭代逼近(DW-LSPIA)算法,证明了其收敛性并以它为基础提出一种B样条曲线拟合算法.首先赋初始权重于每个数据点,用DW-LSPIA算法生成初始拟合曲线;然后根据待插值点与拟合曲线上对应点的误差调整待插值点的权重,并重新运用DW-LSPIA算法生成新的拟合曲线;如此迭代,直至拟合曲线达到插值要求.实例结果表明,该拟合算法鲁棒、高效,也可使拟合曲线保形.     

基于二次B样条曲线拟合的新算法

针对由四点拟合成一条三次B样条曲线过程中计算量大的缺点,提出了一种简单的二次B样条曲线拟合算法。即用两条二次B样条曲线近似一条三次B样条曲线,以期达到计算量小,光滑度也达到要求,提高B样条曲线的绘制速度。     

开放均匀B样条曲线反算的一种通用算法

已知型值点反求控制多边形在计算机辅助几何设计(CAGD)等领域的实际应用中经常涉及,开放均匀B样条曲线的反算过程相对复杂.基于此,提出了一种通用的反算算法,并以三次样条曲线为例,分析了开放均匀B样条曲线反算的过程,详细给出了B样条基函数、反算矩阵,并求出了控制顶点,解决了开放均匀B样条曲线拟合中的反算问题.     

一种简单的二次B样条曲线拟合算法

针对双圆弧拟合算法绘制一条B样条曲线,需要反复多次计算各坐标分量的3次多项式,计算量大,绘制拟合速度极慢,难以满足实际需要等情况,该算法提出了一种简单的二次B样条曲线拟合算法,该算法提高了B样条曲线的绘制速度,有效地解决了4个点以上控制点的拟合问题。     

一种改进的B 样条翼型参数化方法

翼型设计是空气动力学研究的一项重要内容,翼型的参数化结果将影响翼型的优化设计。为了减少翼型优化中的设计变量,保证优化结果的光滑性与C2 连续,在优化过程中控制翼型几何特性的变化范围,提出了一种改进的B 样条参数化方法。用一条三次非均匀B 样条曲线表示翼型,翼型数据的参数化过程中主要运用了B 样条曲线拟合算法,并且在一般的B 样条曲线拟合算法的基础上加入了对曲线的法向约束,通过迭代得到最终的参数化结果。实验结果表明,该方法可以很好的拟合典型的翼型数据,得到的翼型参数化结果不仅光滑,满足C2 条件,而且所得翼型函数的参数个数比传统的参数化方法有了进一步的减少,更有利于之后翼型的优化设计。     

用改进遗传算法确定B样条曲线的节点矢量

文章研究了在给定误差要求下,用最少控制顶点的B样条曲线拟合测量数据的问题,提出了采用改进的遗传算法确定节点矢量,从而使拟合得到的B样条曲线不仅满足精度要求,而且具有较少的控制顶点。设计了新的适应度函数,对传统的遗传算法进行了改进,通过实例证明了算法的有效性。     

一种新的语音数据压缩算法

提出了一种基于B样条曲线拟合的语音压缩算法，为语音数据的压缩提供了新的思路。在PCM语音文件中，采用分段直线的方法对语音样本数据进行拟合，其处理结果与ADPCM的处理结果相近，如果采用高次的B样条曲线来拟合语音数据，在压缩率略有下降的情况下，话音质量将明显提高。算法具有实现简单、效率高的特点。     

用LS-SVMs整体构造B样条曲线

由给定的空间数据点集构造B样条曲线是CAGD中一个重要研究课题,常用的逼近方法实质上是基于“经验风险”意义下的最小二乘逼近。文章讨论了基于“结构风险”意义下用最小二乘支持向量回归机整体构造B样条曲线的逼近问题,其出发点是最小化结构风险,而不是传统学习的经验风险最小化,从而在理论上保证了好的推广能力,能够实现对原始曲线的逼近而不仅仅是对测量数据点的逼近。文章建立了B样条曲线拟合的数学模型,并构造了一种特殊的核函数来保证曲线的B样条表示形式。该方法为曲线拟合问题提供了新思路,数值实验证实了可行性。     

基于安德森加速的快速 B 样条拟合算法

曲线拟合技术已被广泛地应用于图像处理、工程实验等领域。其中,B 样条曲线拟 合是曲线拟合中最常见的方法,它具有局部性好、连续性好等优点,但拟合精度一般较低。在实 际应用中,B 样条曲线拟合对于精度和速度的要求都较高。为了提升平面 B 样条曲线拟合速度, 将安德森加速的想法应用到曲线拟合的方法之中,提出一种基于安德森加速的拟牛顿方法。首先 设定一个初始形状,然后根据初始形状找到其每个数据点的投影点的位置参数,然后利用安德森 加速计算出控制点的相应位置,迭代进行以上 2 步,直到结果收敛。实验结果表明,该方法在收 敛速度和迭代时间上均优于其他方法。     

Shape modeling based on specifying the initial B-spline curve and scaled BFGS optimization method

In this paper, we consider the problem of fitting the B-spline curves to a set of ordered points, by finding the control points and the location parameters. The presented method takes two main steps: specifying initial B-spline curve and optimization. The method determines the number and the position of control points such that the initial B-spline curve is very close to the target curve. The proposed method introduces a length parameter in which this allows us to adjust the number of the control points and increases the precision of the initial B-spline curve. Afterwards, the scaled BFGS algorithm is used to optimize the control points and the foot points simultaneously and generates the final curve. Furthermore, we present a new procedure to insert a new control point and repeat the optimization method, if it is necessary to modify the fitting accuracy of the generated B-spline fitting curve. Associated examples are also offered to show that the proposed approach performs accurately for complex shapes with a large number of data points and is able to generate a precise fitting curve with a high degree of approximation.     

Contour curve reconstruction from cloud data for rapid prototyping

In this study, a method for generation of sectional contour curves directly from cloud point data is given. This method computes contour curves for rapid prototyping model generation via adaptive slicing, data points reducing and B-spline curve fitting. In this approach, first a cloud point data set is segmented along the component building direction to a number of layers. The points are projected to the mid-plane of the layer to form a 2-dimensional (2D) band of scattered points. These points are then utilized to construct a boundary curve. A number of points are picked up along the band and a B-spline curve is fitted. Then points are selected on the B-spline curve based on its discrete curvature. These are the points used as centers for generation of circles with a user-define radius to capture a piece of the scattered band. The geometric center of the points lying within these circles is treated as a control point for a B-spline curve fitting that represents a boundary contour curve. The advantage of this method is simplicity and insensitivity to common small inaccuracies. Two experimental results are included to demonstrate the effectiveness and applicability of the proposed method.     

Reconstruction of B-spline curves and surfaces by adaptive group testing

Point clouds as measurements of 3D sensors have many applications in various fields such as object modeling, environment mapping and surface representation. Storage and processing of raw point clouds is time consuming and computationally expensive. In addition, their high dimensionality shall be considered, which results in the well known curse of dimensionality. Conventional methods either apply reduction or approximation to the captured point clouds in order to make the data processing tractable. B-spline curves and surfaces can effectively represent 2D data points and 3D point clouds for most applications. Since processing all available data for B-spline curve or surface fitting is not efficient, based on the Group Testing theory an algorithm is developed that finds salient points sequentially. The B-spline curve or surface models are updated by adding a new salient point to the fitting process iteratively until the Akaike Information Criterion (AIC) is met. Also, it has been proved that the proposed method finds a unique solution so as what is defined in the group testing theory. From the experimental results the applicability and performance improvement of the proposed method in relation to some state-of-the-art B-spline curve and surface fitting methods, may be concluded.     

基于B样条隶属函数的模糊推理系统

隶属函数和推理规则的确定是模糊推理的难点。通过研究模糊推理过程和B样条函数的特性,对应用B样条函数拟合模糊隶属函数进行推理的方法进行改进。通过对误差极值点、曲率极值点的计算和筛选,得到B样条函数的型值点。反算求得控制点之后,通过自适应增加控制点对曲线进行调整,增加曲线对隶属函数的拟合度,解决了B样条函数对隶属函数的拟合问题。建立B样条推理规则,构造实现了B样条推理系统,并求出该系统的最终结果为B样条超曲面。最后,通过实验验证了该方法的有效性和可行性。     

隐式B-样条曲线重建的直接Greville纵标法

提出了一种以隐式B-样条曲线为表达形式,基于直接Greville纵标的曲线重建方法。根据点云建立有向距离场,并作为B-样条函数的Greville纵标,然后根据高影响区内的平均代数误差优化Greville纵标;得到一个隐式B-样条函数,该函数的零点集即为重建曲线。该方法具有模型简单,重建速度快,无多余分支,无需手工调节任何参数的优点。实验结果证实了该直接法的效率明显高于点拟合法和普通场拟合法,以几何误差为准则的精度亦优于普通场拟合方法。     

Constructing iterative non-uniform B-spline curve and surface to fit data points

In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc     

基于遗传算法的B样条曲线和Bézier曲线的最小二乘拟合

考虑用B样条曲线拟合平面有序数据使得最小二乘拟合误差最小.一般有两种考虑,一种是保持B样条基函数的节点不变,选择参数使得拟合较优.参数的选择方法包括均匀取值、累加弦长法、centripetal model、Gauss-Newton迭代法等.另一种则是先确定好参数值(一般用累加弦长法),然后再用.某一算法计算出节点,使得拟合较优.同时把两者统一考虑,用遗传算法同时求出参数、节点使得拟合在最小二乘误差意义下最优.与Gauss-Newton迭代法、Piegl算法相比,本方法具有较好的鲁棒性(拟合曲线与初始值无关)、较高的精度及控制顶点少等优点.实验结果说明采用遗传算法得到的曲线逼近效果更好.用遗传算法对Bezier曲线拟合平面有序数据也进行了研究.     

基于差分进化算法的B 样条曲线曲面拟合

应用B 样条曲线曲面拟合内在形状带有间断或者尖点的数据时,最小二乘法得到的 拟合结果往往在间断和尖点处误差较大,原因在于最小二乘法将拟合函数B 样条的节点固定。本 文在利用3 次B 样条曲线和曲面拟合数据时,应用差分进化算法设计出一种能够自适应地设置B 样条节点的方法,同时对节点的数量和位置进行优化,使得B 样条拟合曲线曲面在间断和尖点处 产生拟多重节点,实现高精度地拟合采样于带有间断或尖点的曲线和曲面数据。