B样条曲线C2连续混合

提出了一种新的B样条曲线混合方法。混合曲线是一条整体三次B样条曲线。裁剪后原曲线上的数据点、两个裁剪点、新增数据点以及中间连接点组成数据点列,混合曲线即插值于该数据点列。通过插入新增数据点,使混合曲线上两个裁剪点外侧附近的形状与原曲线完全匹配。混合曲线上两个裁剪点之间的中间部分的形状与光顺性可通过调节两个参数值加以控制。     

Rapid prototyping fabrication and finite element evaluation of the three-dimensional medical pelvic model

This paper presents a non-uniform, periodic closed B-spline approximation algorithm for the fabrication of a medical pelvic model, based on rapid prototyping, and also gives the finite element evaluation of the pelvic model. Rapid prototyping (RP), when used in fabricating medical prosthesis, has a strict requirement for closeness and impermeability of STL files. Incorrect data structure in STL files will cause the subsequent slicing process not to proceed. The non-uniform periodic closed B-spline curve approximation method was applied to processing CT data. The precision and size of STL files was improved to optimize the RP model of the pelvis. Finally, the model of the pelvis was evaluated with the finite element method. Results suggest that a high similarity has been achieved in terms of shape, size and biomechanical properties of the pelvic model and the normal one, which validates our argument that rapid prototyping with non-uniform, periodic closed B-spline algorithm is suitable for the fabrication of a pelvic model, which will prove to be significant in the design of pelvic prostheses .     

基于轮廓约束点的B样条曲面拟合算法

提出了一种面向截面测量数据的B样条曲面拟合算法。首先对原始数据点列进行降噪处理,然后遴选出曲率优势点,并将其作为初始的轮廓约束点,得到插值于约束点的初始曲线。再在需改善拟合精度的区域增加约束点,直至获得满足精度要求的B样条曲线。最后以约束点数目最多的曲线为准,在其余的曲线上增加差额数目的约束点,并进行平均弦长参数化,构造出B样条曲线簇,最终获得B样条拟合曲面。仿真实验结果表明,该方法可显著压缩曲面模型的控制顶点数目,具有较高的曲面重构效率。     

Rough cut tool path planning for B-spline surfaces using convex hull boxes

The objective of this paper is to present a non-uniform layered rough cut plan for B-spline surfaces using convex hull boxes. The tool path plan generated by this method will rapidly remove most redundant material from stock material without overcutting.First, a B-spline surface is decomposed into piecewise Bezier surfaces, of which the convex hull boxes form an approximate model for rough cutting. Then, according to the top planes of those convex hull boxes, the stock material is divided into layers of different thickness. The cavity contour for each layer is obtained using a simplified union Boolean operation on convex hull boxes. Finally, from the top down, each layer is processed like a 2D pocket die cavity.The algorithm is implemented on a personal computer. It is shown that the rough cut plan is very efficient since no computation for solving nonlinear equations is needed, and no overcutting occurs since B-spline surfaces are protected by the convex hull property of Bezier surfaces.     

基于提升格式的B样条曲线光顺技术研究

曲线光顺是曲面光顺的基础,也是自由曲面造型的关键技术之一。在研究经典小波变换的基础之上,提出了基于提升格式的第二代小波光顺技术。通过分割、预测、更新三个步骤组成了一个提升步。以常用的三次准均匀B样条曲线为例,推导准均匀B样条曲线的二代小波表示方法。小波光顺时,通过丢弃细节曲线,保留近似曲线,既保留了原曲线的总体形状,又减少了控制点,最终达到小波光顺的目的。通过实例验证表明,运用第二代小波变换进行曲线光顺,运算简单,易于推广。     

基于交互的B样条曲面重建与误差计算

基于三角网格模型的B样条曲面重建技术得到深入发展,计算与显示重建后的B样条曲面与原始测量三角网格之间的误差对分析曲面重建品质有重要作用。一种较为实用的B样条曲面重建方法是对三角网格模型进行四边界区域划分后进行栅格式采样,再根据采样点进行B样条曲面拟合。针对这种重建方法,研究了一种建立三角网格顶点与四边界区域对应关系的算法,再用离散的方法计算点到对应曲面的距离误差,最后用线性插值方法实现误差彩色．云图的显示。     

A new approach for lofted B-spline surface interpolation to serial contours

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional approach to the problem creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion and performs B-spline surface lofting to get a B-spline surface that interpolates them. The approach tends to result in an astonishing number of control points in the lofted B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for fixing this problem. The approach includes a novel process of obtaining a set of compatible B-spline curves from the given contours. The process is based on universal parameterisation [1, 2], allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realise efficient data reduction and provide a compact representation of a lofted B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.     

超声检测中复杂曲面数字化方法研究

提出了利用超声波检测探头实现自由曲面的路径受控仿形测量方法。针对数据压缩处理引起的各截面曲线上数据点数的不同，提出了一种蒙皮B样条曲面插值方法，该方法在保持插值精度的情况下，减少了曲面重构所需的控制顶点。应用表明，算法计算效率较高。     

非四边(N边)域曲面造型方法的研究及在汽车外形设计中的应用

在J.A.Gregory关于N边域曲面理论研究成果的基础上,提出了一种用B样条曲面理论来构造一般N边域曲面的方法。该方法的优点是,所构造的N边域曲面片能够插值于表达为三次B样条曲线的任意边界及其跨界导矢。首先根据Gregory曲面方法构造N边域曲面片,再利用计算得到的数据构造由n个矩形B样条曲面片构成的一阶几何连续的N边域曲面片。     

截面测量数据的B样条曲面拟合

针对激光扫描仪测量得到的截面型数据,提出了对截面线重新采样的方法,分析了重采样数据拟合曲线的误差,及平方误差随重采样比例变化的规律,从而通过控制误差来确定重采样数目.构造插值于截面数据点的非均匀B样条,再对其进行相同数目的采样,得到了呈矩形分布的点阵,采用双向平均积累弦长参数化方法确定、方向节点矢量,用插值的方法进行曲面拟合.此种方法不仅避免了对轮廓线进行相容性的处理,而且减少了模型数据量,提高了曲面重构的效率.     

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。     

改进B样条曲线应用于6R机器人轨迹优化

利用D-H标架法建立了机器人的运动学模型,并在分析轨迹规划流程基础上将改进B样条曲线用于机器人关节空间轨迹插值;在论述改进原因并详细阐述改进B样条曲线的生成方法后,给出改进B样条曲线应用时的速度与加速度性质及算法实现细节;在MATLAB 2014a平台上进行仿真实验,利用改进方法实现圆弧轨迹运动。结果表明,该方法能够有效提高机器人在关节运动及空间轨迹的平滑性,进而可优化机器人的轨迹运动。     

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented.The symme- try property is realized by using symmetric knot vector and symmetric control points.Firstly,data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points.Then the divided data points are pararaeterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions.Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane.Lastly,the constrained least squares fitting problem is solved with the Lagrange multiplier method.Two examples from industry are given to show that the proposed method is efficient,robust and able to meet the general engineering requirements.     

The Pre-Processing of Data Points for Curve Fitting in Reverse Engineering

Reverse engineering has become an important tool for CAD model construction from the data points, measured by a coordinate measuring machine (CMM), of an existing part. A major problem in reverse engineering is that the measured points having an irregular format and unequal distribution are difficult to fit into a B-spline curve or surface. The paper presents a method for pre-processing data points for curve fitting in reverse engineering. The proposed method has been developed to process the measured data points before fitting into a B-spline form. The format of the new data points regenerated by the proposed method is suitable for the requirements for fitting into a smooth B-spline curve with a good shape. The entire procedure of this method involves filtering, curvature analysis, segmentation, regressing, and regenerating steps. The method is implemented and used for a practical application in reverse engineering. The result of the reconstruction proves the viability of the proposed method for integration with current commercial CAD systems.     

Prediction of surface reconstruction uncertainties for freeform surface inspection

A method is introduced to predict uncertainties of the B-spline freeform surfaces that are reconstructed from the measurement points for inspection of freeform surfaces. The uncertainties of a reconstructed B-spline surface are modeled by variances of coordinates of points on this freeform surface. Prediction of the uncertainty at any location on the reconstructed B-spline surface is carried out in two steps: (1) estimation of variances of the B-spline surface’s control points introduced by the surface reconstruction process, and (2) propagation of the variances from the control points to the points on the B-spline freeform surface. In this research, the variances of the control points of the reconstructed B-spline surface in all three directions are considered to improve the accuracy of uncertainty prediction in the regions with significant changes of geometric shapes. Both the errors and uncertainties at different locations on the reconstructed surface are considered in freeform surface inspection to compare the manufactured surface against the design surface and its tolerance. The developed method has been applied to two case studies to demonstrate its effectiveness.     

基于PI迟滞模型的单压电变形镜开环控制

压电非线性迟滞导致压电变形镜的开环控制精度及闭环工作带宽降低,限制了其在自适应光学系统中的应用。为克服迟滞影响,提出采用PI迟滞模型描述单压电变形镜的迟滞非线性特性,实现单压电变形镜的高精度开环控制。首先建立PI迟滞数学模型,利用最小二乘法辨识PI迟滞模型的权值,计算出PI逆模型的权值和阈值,从而获得消除迟滞后的变形镜控制电压;接着搭建了基于哈特曼波前传感器的自适应光学测试平台,采用单压电变形镜的环形致动器进行离焦面形的开环控制实验。实验结果表明,经过迟滞消除后变形镜的电压-变形迟滞由9.3%降低到1.2%,离焦面形的开环重构精度提高70%以上,证明该迟滞模型可有效应用于单压电变形镜的开环控制。     

A weighted least square based data fusion method for precision measurement of freeform surfaces

The trend towards product miniaturisation and multi-functionality constitutes a driving force for the application of complex surfaces in many fields such as advanced optics. The precision measurement of these surfaces should be carried out at multiple scales, of which process commonly involves several datasets obtained from different sensors. This paper presents a weighted least square based multi-sensor data fusion method for such measurement. The method starts from unifying the coordinate frames of the measured datasets using an intrinsic feature based surface registration method. B-spline surface is used to fit linear surface model to each identified overlapping area of the registered datasets, respectively. By forming a common basis function, the fitted surface models and the corresponding residuals are then combined to construct a weighted least square based data fusion system which is used to generate a fused surface model. An analysis of the uncertainty propagation in data fusion process is also given. Both computer simulation and actual measurement on various freeform surfaces are conducted to verify the validity of proposed method. The results indicate that the proposed method is capable of fusing multi-sensor measured datasets with notable reduction of the measurement uncertainty.     

一种基于椭圆变形模板的唇动跟踪算法

本文给出了一种新的唇动跟踪算法框架，算法结合目标的形状、运动及彩色信息，综合利用可变形模板、光流、Kalman滤波技术，得到一种快速、鲁棒的跟踪结果。该算法使用多条椭圆弧段构成唇模板，基于彩色YCrCb信息进行光流估计，由于利用模型约束的特征光流技术，故不需加入任何附加的平滑性约束；最后借助扩展Kalman（EKF）滤波器将形状与运动信息有机结合起来，给出有效的融合解，而不必直接计算光流；该算法同时利用光流测量方程给出的误差测度及EKF给出的估计方差对虚假边缘点做出判断与舍弃，提高了算法的鲁棒性。文中还给出了相应的实例。     

Airfoil profile reconstruction under the uncertainty of inspection data points

A manufactured aero-engine blade is commonly inspected in sections, and its geometric errors are evaluated from the sectional inspection data points. To maintain consistency in evaluating the geometric errors, in particular, the position and twist errors of the stacked blade sections, reconstruction of valid sectional airfoil profiles from the measurement points is preferred. Considering that inspection data points are subject to measurement uncertainty, profile reconstruction via approximation-based curve fitting, rather than interpolation-based curve reconstruction, is adopted in this work. The fitting error of the approximated airfoil profile is deemed equivalent to the measurement uncertainty in the inspection data points. Thus, according to a given measurement uncertainty value, a progressive curve fitting scheme is proposed to generate the airfoil profile that meets the measurement uncertainty constraint. A closed nonperiodic B-spline curve is utilized to model the reconstructed airfoil profile due to its versatility in closed curve approximation. Typical computational tests have been carried out to demonstrate the effectiveness of the proposed airfoil profile reconstruction method, which is in fact generic and can be equally applied to approximating other closed sectional profiles.     

基于主动轮廓模型的序列图像分割与重建

基于断层测量的表面重建是逆向工程中的重要研究方向,而图像分割是其中的关键性技术。针对这一问题,提出了一种基于Greedy算法的B样条主动轮廓模型,可快速稳定地实现目标图像的分割,适用于基于断层图像的分割与表面重建处理。通过对磁共振序列断层图像的分割与表面重建验证了该方法的有效性。