网格曲面上两相离曲线段的光滑过渡

将欧氏空间中两非均匀B样条曲线间G1连续条件拓展到曲面空间,提出一种构造网格曲面上两相离曲线光滑过渡曲线的方法.网格曲面上的曲线采用测地B样条表示,具有与欧氏空间中传统B样条相一致的明确数学模型.基于三角网格模型的拓扑邻接关系,提出一种网格曲面上测地线的延长线离散逼近算法,以此为基础,建立两测地B样条曲线间G1连续条件,将边界连续条件转化为控制顶点的位置约束,从而构建两曲线间的光滑过渡曲线.试验结果表明,所提方法健壮、高效,不依赖于参数化和投影技术,即使对于具有尖锐特征的曲面亦有很强的适应性.     

基于边界控制的Gn连续过渡曲面的构造

讨论了基于重新参数化局部基曲面线性组合构造G^n连续过渡曲面时重新参数化局部基曲面的形状对于过渡曲面的边界和形状的影响；提出了采用能量最小法使过渡曲面的边界弯曲最小来确定重新参数化局部基曲面参数域的方法，并提出相应的重新参数化局部基曲面的确定方法，从而构造较好的过渡曲面。     

过渡曲面构造方法探索

针对模具过渡曲面构造过程中存在的问题，提出了运用NURBS曲线、曲面构造方法，在缺少一条边信息的条件下构造过渡曲面，用这种方法构造的曲面能够满足过渡曲面的工艺要求。     

三角网格曲面上的等距曲线构造

为了用明确的数学形式表示三角曲面网格中的基曲线和等距曲线,提出一种流形网格曲面上曲线等距线的计算方法,网格曲面上的曲线用测地B样条表示,具有明确的数学表示形式。采用节点插入技术将源曲线分解为分段Bezier曲线,并进行线性化逼近,通过曲线细分策略使其误差控制在给定的容差ε1内;提出一种给定源点和初始方向的离散化测地线构造算法,以该算法为基础,按照顶点等距方法获得源曲线的初始等距线;以初始等距线作为控制多边形并适当插入一些顶点,构造满足给定容差ε2的G1连续分段Bezier曲线作为源曲线的等距线。等距曲线的整体逼近误差由ε1和ε2之和构成,因此可以实现误差的全局控制。针对曲面上曲线自交点计算工作量大的问题,提出先识别局部自交区域再求自交点的策略,减少了线段求交的计算量。实验结果表明,所提方法健壮、有效,能满足曲面上曲线的等距计算要求。     

复杂型腔环切拐角过渡刀轨生成技术

针对环切刀轨中存在的拐角及残区问题,提出采用三段式Clothiod曲线光滑拼接的方法进行过渡优化。首先,借鉴骨架线提取的原理判断拐角残区并提取出残区步长;然后,在残区步长的基础上,选取过渡控制点和初始插入点作为曲线过渡的特征点;最后,在特征点的约束下,将曲线和直线进行过渡连接,并保证过渡曲线的C2阶连续。仿真加工测试结果表明,该方法能有效切除环切拐角残余并实现刀轨的平稳过渡,同时能很好地缩短加工时间和提高整体的加工质量。     

曲面相贯线上的圆角过渡实用算法

圆柱体相贯线上的圆角表示法是CAD和计算机辅助设计中众所周知的难题。所有的CAD/CAM软件中都没有这一功能。本文借助"滚球法",以二次圆弧曲线的NURBS生成原理为基础,利用NURBS方法可精确表示圆及圆弧的特点,给出了构造圆柱体相贯线上圆角过渡曲面的实用算法,同时给出了过渡曲面的NURBS表示。     

一种基于离散数据的自由曲面建模方法

提出一种基于离散数据的自由曲面建模方法。该算法采用平行网格构造曲面，利用三次样条函数和参数样条对列表点进行行列两个方面的插补，采用局部回弹法进行曲线光顺，从而构造出适于数控加工的网格曲面，由于采用参数样条进行插补，可保证插值曲线通过所有型值点，曲线具有一、二阶导数连续的性质，可保证曲线的整体连续平滑。该方法的特点是方便了直角坐标下平行行切加工的数控编程。     

注塑机合模装置连杆过渡结构设计分析

针对注塑机双曲肘内翻式合模装置十字头连杆过渡结构应力集中现象和出现断裂问题,以双曲肘内翻式合模装置为研究对象进行分析,研究并提出了一种采用曲面过渡的设计方法。对合模装置十字头连杆进行了动力学、静力学仿真分析表明过渡处应力集中明显,超出安全系数1.5的许用应力值,是导致十字头连杆断裂的原因。根据圆过渡设计方法中的半径和出现最大应力值位置的关系,提出了一种过渡曲线方程,以该曲线构造过渡曲面,降低过渡结构最大应力值。通过与圆过渡设计方法和楔形面过渡设计方法对比,研究结果表明,该方法对降低过渡处最大应力值具有有效性。     

基于截面轮廓的NURBS曲面重建

提出了一种基于变截面轮廓线族重建NURBS曲面的方法。用自动跟踪法反求出轮廓线组的脊线,并用脊线自动调整各轮廓线的起始点位置。然后插值各个轮廓线,构造封闭的样条曲线,以特征点处的节点为分段点实现多条样条曲线的分段相容,并蒙皮构造封闭的B样条曲面。对于有特征点的轮廓线,通过设置特征点的重数及在曲线构造和曲面蒙皮中的相应处理,可以在曲面上保留轮廓线中的特征。     

反求工程中过渡曲面特征提取算法研究

针对反求工程中常见的过渡曲面特征，提出了一种过渡曲面特征的提取算法。该算法包括数据分块和过渡曲面参数提取两部分，在数据分块算法中，通过数据精简，曲率估算和曲率比较等步骤，将过渡区域的数据点从原努点云数据中分离出来，在过渡曲面参数提取算法中，通过圆柱拟合和过渡区域跟踪算法，计算出一系列过渡曲面的截面线，该算法和已有的过渡曲面特征提取算法相比，无需人工交互，而且适用于等半径过渡曲面特征和变半径过渡曲面特征。     

基于等切共轭的弧齿锥齿轮差曲面建立与解析

对弧齿锥齿轮提出了一种新的共轭求解方法,来更方便地求解共轭小轮的齿面方程,在此基础上进行了齿面接触分析。在分析过程中提出了一种新的ease-off差曲面计算方法,即用对应点的转角误差替代直线误差进行差曲面求解,使得传动误差解析、齿面修形量的确定更为直观和准确。提取了ease-off曲面上的差曲线,以方便地确定出接触路径和边缘接触点。根据全程差曲线得到了齿面接触印痕分布情况。     

A new automatic contact point detection algorithm for AFM force curves

A new method for estimating the contact point in AFM force curves, based on a local regression algorithm, is presented. The main advantage of this method is that can be easily implemented as a computer algorithm and used for a fully automatic detection of the contact points in the approach force curves on living cells. The estimated contact points have been compared to those obtained by other published methods, which were applied either for materials with an elastic response to indentation forces or for experiments at high loading rates. We have found that the differences in the values of the contact points estimated with three different methods were not statistically significant and thus the algorithm is reliable. Also, we test the convenience of the algorithm for batch‐processing by computing the contact points of a force curve map of 625 (25×25) curves. Microsc. Res. Tech. 76:870–876, 2013. © 2013 Wiley Periodicals, Inc.     

基于B样条曲面的点云孔洞拟合填充

为了后续曲面重构的需要,针对有孔洞的点云数据,提出了一种孔洞拟合填充的自适应方法。由于孔洞与其周围离散点有一定的连续性,该算法首先从孔洞周围已有的点云数据中选取离散点,用新的参数化方法对得到的离散点参数化后,用最小二乘法进行自适应曲面拟合,对得到的拟合曲面通过迭代法逐步逼近优化,考虑曲率变化的影响在曲面上取点,实现了孔洞光滑填充。实例表明,改进的参数化方法使算法的复杂度减低,进一步迭代优化提高了曲面拟合精度,在面上取点时考虑了曲率变化,因此该方法可以应用于具有复杂曲面形状的点云中的孔洞填充。     

裁剪B样条曲面重建算法研究

提出了具有不规则边界的裁剪B样条曲面重建方法。采用基准平面对数据点进行参数化，并建立以B样条曲面控制顶点为未知量的超定方程组；提出了基于有效点判别条件的孔洞识别算法，通过对孔洞区域的控制顶点施加顶点形状保持约束,确保方程组最小二乘解的存在；基于误差控制重构B样条曲面整体覆盖数据区域，通过边界线提取或曲面求交剪裁来重构裁剪曲面的边界。该方法具有符合设计意图、曲面在孔洞区域具有良好的形状一致性、曲面重构精度高等特点。     

螺旋锥齿轮拟合齿面啮合特性分析方法

已知齿面测量的采样点，利用微分几何及Ferguson参数样条曲面原理，建立了螺旋锥齿轮齿面拟合的数学模型。根据优化求极值复合形方法和共轭理论，通过变定义域，快速求解齿轮副拟合齿面接触点，并运用V—H接触区调整方法，研究了拟合齿面接触迹、接触区和运动误差曲线的求解算法，绘制出相关图形并给出了实例。     

Generating parametric G2 non-four-sided blending surfaces

A method of generating n-sided (n=3, 5, 6) G² blending surfaces (except that the 3-sided blending surface is C⁰ continuous at the three vertexes and the 5-sided blending surface is C⁰ continuous at a vertex) is presented in this paper. When this method is used to generate n-sided (n=3, 5, 6) G² blending surfaces between the base surfaces, the base surfaces are expressed as n-sided (n=3, 5, 6) by reparameterising the base surfaces; then the n-sided (n=3, 5, 6) G² blending surfaces are convex combinations of the base surfaces expressed as n-sided (n=3, 5, 6) surfaces. When the contact curves are arbitrary curves in the base surfaces, the regions near the contact curves in the base surfaces are reparameterised and expressed as n-sided (n=3, 5, 6) surfaces; then the n-sided (n=3, 5, 6) G² blending surfaces are convex combinations of the reparameterised local base surfaces expressed as n-sided (n=3, 5, 6) surface styles. The shape of the n-sided (n=3, 5, 6) blending surfaces can be adjusted by changing the size of the reparameterised local base surfaces and the combination weights. An example of a 5-sided surface generated between an aerofoil, the body and the fringe surface of a missile is given.     

CONSTRUCTION OF G^2 CONTINUOUS CURVES ON SURFACE WITH PLANAR CUBIC BEZIER CURVES

The problem of constructing curve on parametric surface (or surface that can be parameterized) such that it interpolates a sequence of points with prescribed tangent direction and curvature vector (or geodesic curvature) at every point and the issue of curve blending on this kind of surface are researched. The mapping and tangent mapping from the surface to its parametric plane are introduced and thus several conclusions with differential geometry are deduced. Based on those conclusions, the problem of interpolating (or blending) curve on a parametric surface is converted to a similar one on its parametric plane. The final solution curve of either interpolation or blending issue is explicit and can still be expressed by parametric form. And so, unlike existing methods, the presented method needs not to use any surface/surface intersection algorithms, usually a troublesome process, for displaying such interpolation curve. Experiment results show the presented methods are feasible and applicable to CAD/CAM and computer graphics.     

CONSTRUCTION OF G~2 CONTINUOUS CURVES ON SURFACE WITH PLANAR CUBIC BZIER CURVES

The problem of constructing curve on parametric surface (or surface that can be parameterized) such that it interpolates a sequence of points with prescribed tangent direction and curvature vector (or geodesic curvature) at every point and the issue of curve blending on this kind of surface are researched. The mapping and tangent mapping from the surface to its parametric plane are introduced and thus several conclusions with differential geometry are deduced. Based on those conclusions, the problem of interpolating (or blending) curve on a parametric surface is converted to a similar one on its parametric plane. The final solution curve of either interpolation or blending issue is explicit and can still be expressed by parametric form. And so, unlike existing methods, the presented method needs not to use any surface/ surface intersection algorithms, usually a troublesome process, for displaying such interpolation curve. Experiment results show the presented methods are feasible and applicable to CAD/CA     

基于支持向量机的点云曲面刀具路径规划

针对单值散乱点云曲面刀具路径规划问题,提出了一种基于最小二乘支持向量机的计算方法。在计算过程中,将点云数据向平面投影,得到二维点集。应用网格划分和边界网格内测量点高斯映射技术,提取平面区域内的边界特征点。用边界特征点定义点云曲面的实际加工区域,在此区域内规划平行等间距刀具路径。应用最小二乘支持向量机拟合点云数据,求得被加工曲面的连续表达模型,经此模型将二维刀具路径数据向三维空间映射,求出刀触点数据。将刀触点经法向偏置计算,求得刀位点。实例验证证明,该方法能较好地解决信息不完备散乱点云曲面刀具路径生成问题。