基于遗传算法的以线段和圆弧为基元的曲线拟合

采用线段和圆弧作逼近基元是数字曲线拟合中的一个难点。文中给出一种基于改进遗传算法的拟合方法。通过对点列进行二进制编码，以拟合段数较少和拟合误差较小为优化目标，变异概率和交叉概率自适应生成，并根据相关知识控制分界点间隙，所得最优解中值为1的基因对应数字曲线的分界点，对线段与圆弧相交和相切以及具有噪声等多种情况进行检测，可同时提取尖点和切点，还可得到逼近基元及其之间关系。较好地解决了用线段和圆弧拟合曲线问题。     

基于最小均方误差的圆弧分段曲线拟合方法

提出了一种基于最小均方误差准则的圆弧分段拟合方法。该方法采用自适应高斯滤波器对原始曲线进行平滑处理以消除噪声影响,并提出了一种适合于圆弧曲线拟合的分段算法。在该算法的基础上根据最小均方意味着准则,以圆弧作为基元对曲线进行拟合。实验结果表明,该方法能够较好地消除噪声影响并保留曲线的局部特征。     

二维截面轮廓特征重建方法

针对目前轮廓特征识别算法存在识别结果易受噪声数据干扰、需对每一图形轮廓测量数据进行矢量化等问题,对二维截面轮廓特征重建方法进行研究,提出采用分步方式进行截面轮廓拟合的方法.首先,用平均增量法将测量数据进行直线段分段,并用最小二乘法对分段数据进行拟合,再把拟合结果存入链表内;然后,对于直线段链表内的相邻3条直线段,若相邻2条线段形成的半径满足给定阈值,则进行直线段圆弧拟合处理;最后,搜索拟合的圆弧段,如果存在2个或2个以上的连续圆弧,则将其重构为B样条曲线,得到二维截面轮廓特征的重构图形.该方法能有效减少拟合特征单元的数目,提高拟合精度.     

二次均匀B样条曲线的双圆弧逼近方法*

提出了一种用双圆弧对二次均匀B样条曲线的分段逼近方法。首先,对一条具有n 1个控制顶点的二次均匀B样条曲线按照相邻两节点界定的区间分成n-1段只有三个控制顶点的二次均匀B样条曲线段;然后对每一曲线段构造一条双圆弧进行逼近。所构造的双圆弧满足端点及端点切向量条件,即双圆弧的两个端点分别是所逼近的曲线段的端点,而且双圆弧在两个端点处的切向量是所逼近的曲线段在端点处的单位切向量。同时,双圆弧的连接点是双圆弧连接点轨迹圆与其所逼近的曲线段的交点。这些新构造出来的双圆弧连接在一起构成了一条圆弧样条曲线,即二次均匀B样条曲线的逼近曲线。另外给出了逼近误差分析和实例说明。     

基于成长型神经网络以线段为基元的曲线重建

在逆向工程中,对基于散乱数据点的曲线重建研究有着重要的意义。曲线可用线段基元逼近。提出使用成长型神经网络以线段为基元的曲线重建新算法。给定某一曲线的散乱点集和一初始折线,新算法优化折线上的顶点位置,使折线更好地逼近散乱点;持续分裂折线上活动性强的顶点和删除活动性最弱的顶点,使折线上顶点的分布更符合散乱点数据的概率分布。实验结果表明,新算法能够取得良好的曲线重建效果。     

用双圆弧逼近两条相容圆锥曲线的卷积曲线

基于2条相容圆锥曲线的卷积曲线并不一定能够被有理曲线表示,给出了一种新的逼近该卷积曲线的方法--圆弧逼近方法.先用分段标准圆弧来逼近原来的2条相容的圆锥曲线,再把得到的分段圆弧作卷积运算.该方法不仅能够使得逼近曲线是有理2次,而且能够先验地确定逼近的误差上界.数值例子结果表明,文中方法在数控加工和数控绘图中比较有效.     

基于VB的优化双圆弧拟合误差分析及其算法改进

摘 要：针对数控加工的特点,分析了双圆弧拟合的方式,运用VB实现了双圆弧拟合算法并进行了误差分析;通过对误差分布的分析以及对影响误差因素的研究,探索了双圆弧曲线误差变化的规律,提出了基于步长规划来减小误差的改进拟合算法。     

平面NURBS曲线及其Offset的双圆弧逼近

除直线、圆弧、速端曲线等少数几种曲线外,平面参数曲线的offset曲线通常不能表示成有 理参数形式,因此在实际应用中,为了方便造型系统中数据结构和几何算法的统一表示,offse t曲线通常用低次曲线逼近来表示.通过用双圆弧逼近表示NURBS(non-uniform rational B -spline)曲线及其offset,并利用双圆弧逼近的特有性质,把offset的双圆弧逼近转化为原 曲线的双圆弧逼近,简化了问题的求解.同时考虑了双圆弧逼近算法中分割点的选取、公切点 的确定以及误差估计等主要问题.具体算     

二次Bézier曲线的双圆弧样条插值二分算法*

在数控加工领域,通常需要用尽量少段数的圆弧样条来对曲线进行拟合。采用二分查找算法,用G1连续的双圆弧样条对二次Bézier曲线进行拟合。该算法在给定误差范围内所需的圆弧段数较少。最后给出了具体的实例说明。     

面向高速加工的微小线段平滑过渡算法研究

为满足微小线段高速加工的需求,在分析现有微小线段过渡算法不足的基础上,建立了圆弧过渡矢量夹角数学模型,并给出一种基于过渡圆弧的微小线段平滑过渡算法.该算法能够根据加工精度和微小线段长度确定出微小线段的转角点和过渡圆弧的大小,并可通过机床机械特性来限制过渡圆弧的最大进给速度,从而能够在保证加工精度和满足机床机械特性的条件下,最大限度的提高微小线段加工速度.最后对所提出的过渡算法进行了实际加工验证,验证结果表明该算法具有过渡平稳、误差易控、转角速度高的特点,可实现微小线段的高速和高精加工.     

Recognition of digital curves scanned from paper drawings using genetic algorithms

After analyzing the existing methods, based on holo-extraction method of information, this paper develops a recognition method of digital curves scanned from paper drawings for subsequent pattern recognition and 3D reconstruction. This method is first to construct the networks of single closed region (SCRs) of black pixels with all the information about both segments and their linking points, to classify all the digital contours represented by SCRs into three types: straight-line segments, circular arcs, and combined lines, and then to decompose the combined lines into least basic sub-lines or segments (straight-line segments or circular arcs) with least fitting errors using genetic algorithms with adaptive probabilities of crossover and mutation and to determine their relationships (intersecting or being tangential to each other). It is verified that the recognition method based on the networks of SCRs and the genetic algorithm is feasible and efficient. This method and its software prototype can be used as a base for further work on subsequent engineering drawing understanding and 3D reconstruction.     

Bspline approximation of circle arc and straight line for pocket machining

This article proposes a new method of 2D curve interpolation using non-uniform cubic B-splines particularly adapted to the interpolation of sequences of straight lines and circle arcs. The purpose of this method is to calculate C2 continuous curves adapted to high feedrate pocket machining. Industrially machined pockets usually present simple forms. Generally, the tool path is defined by circle arcs and line segments that introduce slowdowns during machining. Thus, a method for approximating a sequence of line segments and circle arcs using Bspline curves is proposed. The proposed method ensures exact line interpolation, to approach the tool path precisely, to reduce the number of control points and to avoid thickening and oscillation at the connections between line segments and circle arcs. Various applications are presented and numerous tests on machine tools allow the advantages of this method to be illustrated.     

Construction of a hybrid sweep-CSG modeler—The sweep-CSG representation

Applying sweep operations on 2-D closed contours is a well known method for modelling 3-D solid objects. This paper deals with the implementation of a solid modeler with sweep as the basic representational scheme. In the modeler, a solid is defined by sweeping a planar polygon along a linear or curved trajectory. A sculptured solid may also be defined by using a beta-spline curve for the sweep polygon and a cubic B-spline curve for the sweep trajectory. By incorporating Boolean operations, a hybrid sweep-CSG solid modeler is implemented. The current implementation allows translational, rotational, and twisted sweep operations on a planar polygon composited of lines and arcs. In addition, a solid primitive can also be created by sweeping a planar closed beta-spline curve along a cubic B-spline curve.     

基于Freeman链码的自由曲线直线逼近算法

提出一种简单而有效的直线逼近自由曲线算法.自由曲线轮廓采用Freeman链码描述,提出快速分割链码算法,得出逼近节点,从而准确地实现对曲线的逼近.此外,该方法不仅适用于直线、圆弧和非圆曲线,而且还适用于形状复杂,不能用初等解析函数直接表示的自由曲线.实验结果表明,该算法简单、快速、准确,并对自由曲线具有较好的逼近效果.     

G 2 blends of linear segments with cubics and Pythagorean-hodograph quintics

Fillets, also known as blend arcs, are used in CNC machining to round corners. Fillets are normally circular arcs, which have G ¹ contact with the straight line segments to which they are joined. Recent advances in machining technology allow NURBS, including Pythagorean-hodograph (PH) curve segments, to be incorporated in CNC tool paths. This article examines the use of cubic and PH quintic Bézier curve segments that have a single curvature extremum, and which have G ² contact with the straight line segments to which they are joined, as fillets. It is shown how the extreme circle of curvature can be determined. The point of curvature extremum and the corresponding value of the curvature can be changed by adjusting the joining points of the blending curve with the neighbouring straight lines. These blending curves can also be incorporated in computer-aided design packages for curve or surface design.     

基于条形块跟踪的圆弧识别方法研究

本文给出了一种基于条形块跟踪的圆弧矢量化方法，采取条形块跟踪的思想获取圆弧和组合线的低级矢量——型值链，对组合线进行了分隔，在几何意义明显的圆弧形值链基础上，通过检测和验证的方法识别出圆弧。实验结果显示出算法的快速性，识别出的圆弧和原始位图吻合度高，并具有较高的识别率。     

Constrained fitting for 2D profile-based reverse modeling

Profile curve reconstruction is crucial to surface reconstruction in reverse engineering. In this paper, we present a new constrained fitting method involving lines, circular arcs and B-spline curves for profile curve reconstruction. By using similarity transformation, we reduce the condition number of the Hessian matrix involved in the optimization process and, therefore, the numerical stability is significantly improved. Several industrial examples are presented to demonstrate the efficiency of our method. This paper describes a 2D constrained fitting method for profile curve reconstruction in reverse engineering. The method is an extension to the published methods for 2D constrained fitting. Further more, the numerical problem associated with constrained fitting is tackled in our paper. The described method has been implemented in RE-SOFT, which is a feature-based reverse engineering software developed by the CAD/CAE/CAM Lab of Zhejiang University.     

Efficient circular arc interpolation based on active tolerance control

In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G¹ arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.     

基于图像修复的网线绕距测量方法研究

针对网线绕距测量,提出了一种基于图像处理和正交最小二乘曲线拟合的方法。运用彩色空间模型分别提取两条不同颜色的双绞线并将其灰度化。运用阈值分割的方法将图像二值化,运用图像形态学处理填充双绞线内部的孔洞简单修复图像。通过正交最小二乘曲线拟合的方法,拟合出双绞线的中心线,得到两条双绞线的交点并且最终求得网线绕距。实验表明,提出的方法能简单有效地计算出网线绕距。