截面轮廓曲线分段约束拟合

本文以线段和圆弧为逼近基元对封闭的截面曲线进行分段拟合,给出了曲线的拟合算法和逼近误差的分析表达式。在对截面曲线分界点进行迭代寻优后,得到了综合累积误差最小的分界点,并以此进行截面曲线的分段拟合;针对拟合所得的曲线,提出了具体的约束修正方法。通过实例分析表明,该算法简单有效,能较好地解决以线段和圆弧为基元的截面曲线拟合问题。     

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。     

自由曲线的双圆弧拟合成形法

用双圆弧拟合离散型值点生成自由曲线是近年来非圆曲线或曲面的零件自动编程与加工中常用的一种数学模型。本文从计算机几何，函数逼近论等数学理论出发，建立了新的双圆弧拟合的计算公式，并给出了推导过程。同时在此基础上，提出了一种实用的分割－拟合的双圆弧拟合自由曲线的成形方法。     

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。     

基于遗传算法的多边形逼近3D数字曲线

首先对3D数字曲线进行简单的数据压缩．通过对该曲线上的点列进行二进制编码定义来表示数字曲线的染色体．二进制串中的每一个位称为基因，每一个逼近多边形和染色体形成1-1映射．目标函数使给定曲线和逼近多边形之间的均方差最小．构造了解决该问题的选择、交叉、变异三个算子．所得最优染色体中基因值为1的基因对应数字曲线的分界点．实验结果表明，该方法能够得到精确的逼近结果．     

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。     

一种用圆弧逼近三次平面Bezier曲线的算法

本文给出一种用圆弧逼近三次平面Ｂｅｚｉｅｒ曲线的算法。该算法的特点是保持曲线的整体光滑性，所用圆弧数量少，并可对逼近精度进行控制。该算法稍加变化后也适用于圆弧逼近其它类型的平面曲线。     

利用梯度信息快速提取直线边缘特征

立足于视觉检测系统的实时性需要,提出一种利用梯度信息的快速直线边缘提取方法。该方法首先利用梯度信息和两点确定一条直线进行线段基元的快速定位和扫描;然后对扫描得到的线段基元进行基于几何距离最小化的最佳直线拟合;最后使用端点投影距离的方法对线段基元进行共线性检测,连接共线的线段基元并对连接结果重新进行最佳直线拟合,得到最终的直线边缘特征。实验结果表明:该方法进行直线边缘特征提取的速度比目前文献中最快的Hough变换改进算法提高了1倍左右,适应能力强,可以满足视觉检测系统对直线边缘特征提取的实时性和精度要求。     

变曲率对称圆弧曲线及其在圆弧样条拟合中的应用

针对数控加工的需要，对圆弧样条拟合曲线的形状进行局部修改和优化，提出了一种新的圆弧样条曲线的基本形式－变曲率对称圆弧曲线，并给出了其计算方法和具体应用，该方法可满足不同运算字长数控系统对拟合后圆弧样条曲线最大曲率半径的要求，同时还可满足随动控制加工对拟合曲率变动量的要求。     

一种线段和圆弧的逼近方法及其在工程图纸矢量 …

本文给出了一种通过数据点逼近生成直线段和圆弧的算法及其证明。此方法的优点是生成的线段和圆弧显式给出，方便应用。本文还讨论了此算法在图纸矢量化中的应用。     

A spline algorithm for modeling cutting errors on turning centers

Turned parts on turning centers are made up of features with profiles defined by arcs and lines. An error model for turned parts must take into account not only individual feature errors but also how errors carry over from one feature to another. In the case where there is a requirement of tangency between two features, such as a line tangent to an arc or two tangent arcs, any error model on one of the features must also satisfy a condition of tangency at a boundary point between the two features. Splines, or piecewise polynomials with differentiability conditions at intermediate or knot points, adequately model errors on features and provide the necessary degrees of freedom to match constraint conditions at boundary points. The problem of modeling errors on features becomes one of least squares fitting of splines to the measured feature errors subject to certain linear constraints at the boundaries. The solution of this problem can be formulated uniquely using the generalized or pseudo inverse of a matrix. This is defined and the algorithm for modeling errors on turned parts is formulated in terms of splines with specified boundary constraints.     

开圆弧样条的保形插值算法

提出一种G1圆弧样条插值算法.该算法选取部分满足条件的型值点构造初始圆,然后过剩下的型值点分别构造相邻初始圆的公切圆.在此过程中,让所有型值点均为相应圆弧的内点,且每段圆弧尽量通过2个型值点.在型值点列满足较弱的条件下,曲线具有在事先给定首末切向的情况下圆弧总段数比型值点个数少且保形的特点.     

基于单义域邻接图的圆弧与圆识别

工程图纸扫描输入与识别理解是ＣＡＤ推广和普及的关键步骤之一,主要解决已有大量图纸再利用问题。在工程图纸扫描图象识别研究中,圆弧识别是识别算法中的重点和难点。传统的圆弧识别多是基于线段逼近。该文提出一种基于单义域邻接图的圆弧及圆识别算法,可以直接提取圆弧,对二值图象作水平黑洲程编码,相关游程基于线宽与拓扑的一致性构成条形域,对其中多义域进行分裂得单义域（线段域和圆弧域）,单义域邻接图可较好描述图象的     

A note on planar minimax arc splines

Arc splines are planar, tangent continuous, piecewise curves made of circular arcs and straight line segments. They are important because they can be used as the cutting paths for numerically controlled cutting machinery. This paper presents an algorithm for finding an arc spline that is a minimax approximation to discrete data.     

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.     

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.     

最大比率圆弧逼近轮廓的匹配方法

提出了一种新的圆孤逼近轮廓曲线进行目标匹配的方法-最大比率法。曲线上两点之间的圆弧和曲线夹成的面积与对应扇形的比值随曲线上点的曲率的变化而变化。通过设置一个阈值算法可以检测曲率的较大的特征点用于圆弧逼近匹配。     

单圆弧样条保形插值算法

该文以插值具有偶数个点的闭多边形为例提出了一种新的圆弧样条插值算法。这种算法具有以下3个特点：（1）生成的圆弧样条曲线具有保形的特点；（2）圆弧样条中圆弧的段数与型值点个数相同。（3）圆弧段之间的连接点不一定在插值的型值点上，这样就能用更多的自由度来控制拟合曲线的形状。同此文中还提出了一个优化的算法来得到光顺的插值曲线，同时还给出了几个例子加以说明。     

Curve fitting and fairing using conic splines

We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. For parts of the G¹ conic spline without an inflection, we can obtain a curvature continuous conic spline by adjusting the tangent direction at the joint point and scaling the weights for every two adjacent rational Bézier curves. The unwanted curvature extrema within conic segments or at some joint points can be removed efficiently by scaling the weights of the conic segments or moving the joint points along the normal direction of the curve at the point. In the end, a fair conic spline curve is obtained that is G² continuous at convex or concave parts and G¹ continuous at inflection points. The main advantages of the method lies in two aspects, one advantage is that we can construct a curvature continuous conic spline by a local algorithm, the other one is that the curvature plot of the conic spline can be controlled efficiently. The method can be used in the field where fair shape is desired by interpolating or approximating a given point set. Numerical examples from simulated and real data are presented to show the efficiency of the new method.