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.     

Triangular nomograms for symmetrical coupler curvesHoмoгpaммa тpeyгoльнoй фopмы длы cиммeтpичныч мaтyнныч кpaивычNomogrammes triangulaires pour les courbes symmetriques

Triangular nomograms have been constructed as a simple means of finding symmetrical coupler curves of the crank-rocker linkage. A nomogram of this kind has been presented by the author of this article during a Conference of the Institution of Mechanical Engineers at London in 1972. Twenty-seven versions have now been developed and fully worked out.They are dimensionless and have then three angles as parameters to determine the type of curve with all its properties.The curve types are concerned with those characteristics which the crank-rocker linkage yields for symmetrical coupler curves such as: curves with one or two points of reversal; with internal contact; 8-shaped curves; curves with 2 equal radii of curvature; curves with one or two undulation points on the axis of symmetry; curves with two undulation points oriented symmetrically in relation to each other and a top angle; curves with Burmester points, where the second derivative of the radius of curvature is zero; and curves with one or two tangents which touch the curve at three different points each.The 27 triangular nomograms refer to the symmetrical coupler curves of the 4-bar linkage and are used for selection of the type of curve and corresponding data for the linkage.This article will deal with three of them which relate to coupler curves with the property that a tangent touches the curve at three separate points, while two more examples of the various verions of the nomogram will be presented.A example of the application of the nomogram is given by the design of a transfer mechanism, where use has been made of a curve with two cusps and further modification to a 6-bar linkage.     

CNC codes conversion from linear and circular paths to NURBS curves

A novel approach is proposed for converting NC files of G01/G02/G03 codes into NURBS curves. The NC points are first acquired from an NC file composed of lines and arcs. A segmentation algorithm based on the angles and lengths evaluated from adjacent points is then used to subdivide the entire group of points into segments. An error-bounded constrained curve fitting algorithm is implemented to fit each segment of points into a curve, maintaining the accuracy, smoothness and boundary continuity between the curves. The chord errors between the NC points and the fitted curves are controlled, which ensures the accurate recovery of NC paths. Also, a knot insertion algorithm is proposed to determine the appropriate number of control points automatically, allowing effective fitting of all segments. Several examples are presented to demonstrate the feasibility of the proposed approach.     

基于三次Q-Bézier曲线的车灯造型设计

用一条三次Q-Bézier曲线描述了汽车车灯造型轮廓;提出首先由设计师在平面视图中绘制并编辑汽车车灯造型的二维三次Q-Bézierr曲线轮廓图,然后将其投影到汽车车身上,最后通过对曲面进行修剪获得车灯造型轮廓的方法。该方法基于三次Q-Bézier曲线生成及拼接原理,可以迅速从全局或局部调整车灯轮廓线条,获得光顺的曲线效果,从而快速获得多个车灯轮廓的造型方案。     

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。     

Adaptive tool-path generation on point-sampled surfaces

In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.     

基于角度分割的截面线数据匹配点对建立算法

研究了从截面线数据到B样条曲面拟合的过程中,建立最佳匹配数据点对的问题。提出了一种基于角度分割建立截面线数据匹配点对的算法,该算法利用各层截面线的公共几何中心,计算各点到中心的斜率,再利用基于斜率的插值获取给定角度在原参数曲线上的参数值。最后运用德布尔点的递推公式得到参数对应的坐标。当处理完所有的截面线数据,就得到了一组采样个数统一的匹配点对。该算法在进行截面线数据重采样的同时就完成了对数据点的对正处理,不仅适用于对凸轮廓的处理,而且也能处理层间形状变化较大的截面线数据。     

A Machine Vision Approach for Detecting and Inspecting Circular Parts

In this paper, we present a machine vision approach for detecting and inspecting circular parts and parts with circular arcs on the contours. The method uses the Hough transform technique and uses the directional information of a normal to the circle at each boundary point. Cubic polynomial curve fitting is used to estimate the normal, and determine the concavity of the fitted curve at each given boundary point. The proposed Hough transform method is a two-stage pro-cedure. The first stage uses a 2D accumulator array to detect circle centres. The second stage uses a 1D accumulator array to detect the radii of circles. The proposed method is robust for detecting circular parts with partial occlusion such as peripheral defects or burrs. For an image of size N × N, the storage requirements are N 2 and the time complexity is bounded by (N+m)n, where m is the number of circle centres detected in the first stage and n is the number of boundary points in the image.     

FREE-FORM SURFACE RECON-STRUCTION BASED ON NURBS TO SERIAL CROSS-SECTIONS

A new method for recovering shape from cross-sectional contours with complex branchingstructures is presented. First, each branching problem by providing an intermediate contour using dis-tance function and image processing technology is solved. Then, all contours are divided into severalgroups of simple contours. For each group, a NURBS curve is fitted to contour points in each sectionwithin a given accuracy on a common knot vector.Finally, the NURBS surface skinning of these con-tours is performed for providing a smooth geometric model. The method is suitable to reproduce theobject by NC machining or rapid prototyping. Some results demonstrate its usefulness and feasibility.     

UG点集处理技术在直接切片中的应用

在UG环境下利用点集处理技术,完成对切片过程中界面轮廓出现的圆锥曲线、三次Bezier曲线等不规则曲线,进行参数化直线处理;仅仅使用一种直线线型描述切片结果,这样可在很大程度上简化RP数据处理软件的设计.     

The feature-based posterior crown design in a dental CAD/CAM system

This paper presents a newly developed CAD approach for a quick and accurate design of a dental posterior prosthesis. The approach arises from the basic idea that every human tooth has its own specific features. Based upon the features of the standard posterior tooth, the initial data containing the defined feature points are firstly acquired from the scanned points of the standard tooth. The standard prosthetic profile is thereby formulated using the bicubic Nurbs surface fitting technique. This profile has the two functions of possessing the same features with the patient’s missing posterior tooth, and the adjustability with the feature points and the defined B-spline profile feature curves. For the purpose of the adjustment of the established model, the global and occlusal feature curves are proposed considering the individual patient’s original information. According to these curves, the corresponding standard prosthetic profile is locally adjusted to meet the fit of the global size and occlusal surface. Finally, a close and continuous profile of a posterior crown is generated. Using this design, a posterior prosthesis is successfully manufactured in the computer-aided machining process.     

非均匀有理B样条曲线多分辨率特征几何建模研究

NURBS曲线的几何建模,传统方法是通过模型的控制顶点对曲线进行操作、编辑和处理,繁琐费时,使NURBS曲线的设计变得十分困难。基于一种新的半正交非均匀B样条小波多分辨率技术将单一尺度几何空间变换到多尺度空域和频域空间,NURBS曲线的整体结构和局部细节被转化为曲线的多尺度整体特征和细节特征。通过对这种多尺度特征的编辑、操作和处理有效实现NURBS曲线的几何建模。     

A Comparative Study on Open Circuit Voltage Models for Lithium-ion Batteries

The current research of state of charge(SoC) online estimation of lithium-ion battery(LiB) in electric vehicles(EVs)mainly focuses on adopting or improving of battery models and estimation filters. However, little attention has been paid to the accuracy of various open circuit voltage(OCV) models for correcting the SoC with aid of the ampere-hour counting method. This paper presents a comprehensive comparison study on eighteen OCV models which cover the majority of models used in literature. The low-current OCV tests are conducted on the typical commercial LiFePO_4/graphite(LFP) and LiNiMnCoO_2/graphite(NMC) cells to obtain the experimental OCV-SoC curves at different ambient temperature and aging stages. With selected OCV and SoC points from experimental OCV-SoC curves, the parameters of each OCV model are determined by curve fitting toolbox of MATLAB 2013. Then the fitting OCV-SoC curves based on diversified OCV models are also obtained. The indicator of root-mean-square error(RMSE) between the experimental data and fitted data is selected to evaluate the adaptabilities of these OCV models for their main features, advantages,and limitations. The sensitivities of OCV models to ambient temperatures, aging stages, numbers of data points,and SoC regions are studied for both NMC and LFP cells. Furthermore, the influences of these models on SoC estimation are discussed. Through a comprehensive comparison and analysis on OCV models, some recommendations in selecting OCV models for both NMC and LFP cells are given.     

快速成型中封闭PS曲线边界补偿重建算法研究

对快速成型数据处理中封闭PS边界曲线补偿重建算法进行了研究,分析了已有的几种PS边界曲线补偿重建算法的特点。根据快速成型数据处理过程中截面多边形补偿的特点,提出了基于有效交叉点搜索的补偿边界重建的新算法;并在已开发的RP数据处理软件中成功应用,提高了该数据处理软件的稳定性。     

A practical sampling method for profile measurement of complex blades

Blade is one of the most important parts in turbine machinery. The complex geometry of blades not only makes them difficult to fabricate, but also leads them difficult to inspect. Typically, the surface of blades is measured by using coordinate measuring machine (CMM). Since the measurement time and cost increase proportionally as the increase of measurement points, it is essential to sample measurement points which can represent entire blade with sufficient confidence and accuracy. In order to achieve a certain allowable deviation with a suitable set of points, a practical sampling method for surface measurement of blades was studied. Firstly, the leading edge curve and trailing edge curve were supposed to represent the twisted and bend information of blades. A sampling method based on maximum chordal deviation for leading edge curve and trailing edge curve was researched. Further, a fusion approach for sampling points on both edge curves, which determine the cross-sections, was proposed. Secondly, the inspection points sampling method for sectional curves were investigated. Finally, two simulation and one experimental examples were used to demonstrate the sampling methodology. The results indicated that the approach of this study can ensure the measurement precision at high curvature potion by measuring a small number of points.     

Unconstrained and constrained curve fitting for reverse engineering

Curve fitting is commonly used in reverse engineering for the reconstruction of curves from measured points, and it is critically important to provide various kinds of curve-fitting algorithms to acquire curves that satisfy different constraint conditions. We divide the curve-fitting problem into unconstrained and constrained types. For the unconstrained type, three curve-fitting algorithms are investigated: general, smooth and extended curve fitting. The general curve fitting considers only the accuracy of the fitted curve; the smooth curve fitting can control both the accuracy and the fairness of the fitted curve, while the extended curve fitting can acquire a curve longer than the range of the measured points. For the constrained type, we propose three curve-fitting conditions: fixed end-points, closed curve and continuity to adjacent curves. Detailed discussion for each of the above cases is presented. Associated examples are also provided to illustrate the feasibility of the proposed algorithms.     

基于 AUTOCAD 的面向机械装配图的关键技术及其应用

提出了基于ＡＵＴＯＣＡＤ生成装配图的技术关键及解决方案；设计了零件的统一表示模式；引入了一种新的轮廓自动识别算法，将内外轮廓识别统一起来。采用线段端点分类及交点排序的策略，快速可靠地解决需要消除的部分。最后给出一个稳定可靠的任意多边形裁剪算法。上述方法已成功地应用于机械工程装配图。     

Artefacts in restored images due to intensity loss in three-dimensional fluorescence microscopy

Computational algorithms for three-dimensional deconvolution have proven successful in reducing blurring and improving the resolution of fluorescence microscopic images. However, discrepancies between the imaging conditions and the models on which such deconvolution algorithms are based may lead to artefacts and/or distortions in the images restored by application of the algorithms. In this paper, artefacts associated with a decrease of fluorescence intensity with time or slice in three-dimensional wide-field images are demonstrated using simulated images. Loss of intensity, whether due to photobleaching or other factors, leads to artefacts in the form of bands or stripes in the restored images. An empirical method for correcting the intensity losses in wide-field images has been implemented and used to correct biological images. This method is based on fitting a decreasing function to the slice intensity curve computed by summing all pixel values in each slice. The fitted curve is then used for the calculation of correction factors for each slice.     

自适应细分曲面算法及在快速成型

为提高快速成型制造中STL模型切片轮廓的光滑性,提出了一种基于Loop模式的自适应曲面细分算法,首先分割出网格模型中的曲面和平面,对和尖锐边相邻的曲面三角面设计了特殊的细分规则.通过三角面顶点的平坦度和容差平坦度决定三角面是否做进一步细分,以达到自适应细分的目的.该算法在保留零件模型上尖锐特征的同时,提高了模型上曲面部分的光顺性,从而可以利用模型的全局信息获得光滑的2维切片数据.     

基于空间栅格支撑与曲率云图引导的点云表面构线

针对已有的点云表面构线方法在处理多层点云曲面模型时出现的弱鲁棒性问题,以及构线过程中缺乏直观点云形状特征引导的现象,提出一种基于空间栅格支撑与曲率云图引导的点云表面构线方法。首先,将点云划入规则分布的空间栅格并基于三参数Shepard曲面估算点云曲率;其次,依据曲率云图反映的点云几何形状特征选择构线点,并搜索沿构线点投影方向与之相交的最近非空栅格(即含有测量点的栅格),继而以最近非空栅格为中心,构建其k-最近邻域点集作为点投影算法的目标点云计算构线点的投影点;然后,插值构线点列经投影计算得到的投影点序列,获得初始曲线;最后,构造与初始曲线节点分布一致的法矢曲线作为曲线投影的方向,结合二分法与基于空间栅格支撑的点投影算法将初始曲线投影至点云曲面。实例对比表明,空间栅格的引入显著增强了点投影算法的稳定性,而曲率云图的引导则提高了用户交互选点构线过程中对点云所蕴涵形状特征的识别与分析能力。