NURBS skinning surface for ship hull design based on new parameterization method

Surface reconstruction from sets of cross-sectional data is important in a variety of applications. The problem of generating a ship hull surface from non-regular cross-sectional curves is addressed. Generating non-uniform rational B-splines (NURBS) surfaces that represent cross-sectional curves is a challenge, since the number of control points is growing due to the non-avoidable process of having compatible cross-sectional curves. A new NURBS parameterization method that yields a minimum number of control points, and is adequate in generating a smooth and fair NURBS surface for ship hulls is proposed. This method allows for multiple knots and close domain knots. The results of applying different parameterization methods on the forward perpendicular (FP) region of a ship hull (organized in eight sections) shows that the proposed method reduces the number of control points and generates a smooth and fair NURBS surface, without sacrificing the original object shape of the FP region.     

基于NURBS的自由曲面精确拟合方法研究

提出了一类卷曲模型的NURBS曲面建模新方法。借助提出的截面轮廓设计技术,构造了点云数据的系列截面轮廓线,并以蒙皮操作为基础得到了能反映点云基本几何特征的基面。应用参数校正技术,给出了一种合理且比较有效的基面参数化方法,并由此用加权最小二乘算法实现了基于迭代的NURBS曲面的精确拟合。实际的算例结果验证了方法的实用性及精确性,非常适于模具型腔建模。     

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。     

NURBS approximation to the flank-milled surface swept by a cylindrical NC tool

In this paper, a method to approximate the flank-milled surface swept by a cylindrical cutter with a non-uniform rational basis spline (NURBS) surface is presented. The swept surface produced by the moving tool can be calculated as a collection of points organized as a series of grazing curves along the surface. The generated NURBS surface closely matches the grazing surface. The deviation between this surface and the grazing surface is calculated and is controlled by increasing the number of control points used to represent the surface.     

Global Continuity Adjustment and Local Shape Optimization Technique for Complex Trimmed Surface Model

Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering.In recent years,a lot of progress has been made in smooth join of non-trimmed surface patches,while there has been seldom research on smoothly stitching trimmed surface patches together.This paper studies the problem of global continuity adjustment,damaged hole repair and local shape optimization for complex trimmed surface model,and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region.Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G1 continuity,and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch.The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole,and the result demonstrates the validation of our method.Furthermore,on the premise of global continuity,the proposed locally repairing damaged surface model provides a better foundation for following research work,such as topology recovery technique for complex surface model after geometric repair.     

基于NURBS曲线的数控机床几何误差实时补偿研究

阐述了一种基于NURBS曲线的数控机床几何误差补偿技术,利用误差模型计算预设的NURBS路径与控制点之间的位置偏移能得到NRUBS误差补偿函数控制点,通过插入新的节点产生新的函数控制点,并提高NURBS曲线表达误差补偿函数的柔度,从而得到更高的补偿精度。结果表明,在公差精度为0．00057mm的情况下,沿3种不同工作路径的误差补偿精度都小于1mm。     

Fast and accurate NURBS fitting for reverse engineering

Fast and accurate fitting of non-uniform rational B-spline (NURBS) curves and surfaces through large sets of measured data is an important problem in applications such as reverse engineering and geometric modelling. This paper presents a method for realising significant improvements in the computational efficiency of this task. The basic idea is that the sparsity structures of the relevant matrices that are specific to the problem of NURBS fitting can be precisely defined and that full exploitation of these structures leads to significant savings in both computational and storage requirements. These savings allow for a large number of control points to be used in order to define the surface and consequently to improve the accuracy of shape representation. The achieved computational complexity is linear in both the number of measured points and the number of control points while the storage requirements of the algorithm are linear with the number of control points only. The complexity analysis, as well as the analysis of actual running times is presented. The results demonstrate that, using this approach, highly complex shapes may be modelled accurately with a single NURBS surface.     

基于矢量分析的数控加工轨迹设计方法研究

描述了基于矢量分析和NURBS的数控加工轨迹设计方法。基于给定的被加工曲面在其参数域上的优化走刀方向集合,并依据标量场与梯度场的转化关系,建立了精确逼近离散方向矢量的走刀矢量场拟合模型,由此给出了数控加工轨迹的矢量表达形式。以NURBS作为发生矢量场的流函数并借助其较强的局部调控能力,通过调整控制点列,可望实现数控加工轨迹拓扑形状的整体优化调控。验证实例表明该方法能够进行复杂形状数控加工轨迹的精细设计,有利于保证精度指标下曲面加工效率的最大化。     

A Novel Method of Efficient Machining Error Compensation Based on NURBS Surface Control Points Reconstruction

A novel method to improve the efficiency of error compensation in free-form surface machining based on the Non-Uniform Rational B-Splines (NURBS) surface control points reconstruction is proposed in this article. With the presented method, a relatively small number of inspection points are needed to be measured for error compensation. The machined surface is obtained by reconstructing the control points of the designed surface based on the on-machine measurement data. The machining error of the surface is obtained by calculating the difference between the machined surface and the designed one. Then a compensate surface is achieved using the mirror symmetry model and surface modification method to compensate the machining error. Experimental validation for the milling of a NURBS surface shows that the machining accuracy of the surface is improved by 62.57% through use of the proposed method.     

A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry

In an attempt to construct an isogeometric analysis-suited geometry for isogeometric analysis, a new surface parameterization method using the one-step inverse forming (SPIA) is proposed. Initial generation of watertight analysis-suitable geometry (NURBS surfaces) with complex shapes can be a significant bottleneck for isogeometric analysis because computer-aided design models often include ambiguities such as gaps and overlaps. Most of traditional surface parameterization techniques are based on geometric method and limited to finite meshes, while SPIA is a physics-based method using sheet metal forming technique with large elastic–plastic deformation and robust enough and rapid to deal with the finite elements mesh with over 100,000 nodes within 2 min without the necessity to simplify the meshes. Using Coons surface parameterization, global mesh parameterization, and NURBS reconstruction, we can rebuild new computer-aided design models with errors under any tolerance to which isogeometric analysis can be applied. The NURBS surfaces after reconstruction are also used for computer-aided manufacturing.     

Accuracy improvement method for flank milling surface design

In this paper, a variation of the method of designing surfaces for flank milling proposed by Li et al. 2006 (Surface design for flank milling. Submitted to CAD, July) is presented. Li’s method is based on the premise that the surface flank milled by a cylindrical tool can be represented by a NURBS surface and can be used by designers to build efficient impellers, blades and other engineering parts. In the proposed method, a four control point curve is used to approximate the grazing curves and for subsequent generation of a polynomial surface. This eliminates the need of weights for the interior control points and still results in a good surface. The accuracy of the surface can be controlled by adding control points. Examples are given to demonstrate the proposed surface design method.     

An Approximate Lofting Approach for B-Spline Surface Fitting to Functional Surfaces

Owing to their specific functionality, surfaces are often given as bivariate functions including non-polynomial or higher-orde polynomial terms. It is necessary to represent them in standard formats such as non-uniform rational B-splines (NURBS) for approximation. As most such surfaces require fine quality of surfacing and high precision of manufacturing, accuracy should be guaranteed in their representations. As high accuracy is likely to result in bulky and redundant representations, it is also important to make them more com-pact. For NURBS surfaces, control points must be reduced without sacrificing accuracy. This paper presents an approximate lofting method for B-spline surface fitting to a functional surface within a specified accuracy. It adopts adaptive sampling and multiple B-spline curve fitting. The method is very effective when the surface shape is longish or the cross-sectional curves vary regularly in shape along a specific direction. Some experimental results demonstrate its usefulness and quality.This revised version with a corrected online cover date was published online in April 2004.     

An algorithm of NURBS surface fitting for reverse engineering

Reverse engineering is an approach for constructing a CAD model from a physical part through dimensional measurement and a surface model. Different from conventional methods, this paper develops a new algorithm by which a desired fitted surface is obtained with less computation. Let selected m×n measured points be control points to construct B-spline or NURBS surface, then modify this constructed surface by using all the measured points and least squares minimization. A new algorithm for parameterization for measured points is also presented in this paper. The effectiveness and efficiency of these proposed algorithms are demonstrated.     

High accurate interpolation of NURBS tool path for CNC machine tools

Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.     

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.     

基于逼近理论的逆向工程曲面柔性重构技术研究

为减少通用曲面重构在处理非均匀扫描数据点时,曲线曲面形状的失真和不稳定,提出了一种曲面逼近方法。首先对彼此相互独立的每行数据点作逐行的曲线逼近,并根据被传递的候选节点矢量作节点选择,然后根据所需误差精度来控制曲线的控制顶点数,从而合成曲面。彼此相互独立合成的曲线减少了曲面形状的不稳定,同时通过节点矢量传递的柔韧性,可以获得较满意的参数化过程,节点矢量的柔性选择又会使控制点的增加得到有效的控制。实际应用证明,该方法是一种行之有效的曲面拟合方法。     

A novel approach for computing C2-continuous offset of NURBS curves

Computing offset curves is an important geometric operation in areas of CAD/CAM, robotics, cam design and many industrial applications. In this paper, an algorithm for computing offsets of NURBS curves using C²-continuous B-spline curves is presented. The progenitor curve in database is initially approximated by a line-fitting curve, and then the exact offset of this line-fitting curve is introduced as an initial offset. Based on the initial offset and a set of selected knots, an intended C²-continuous B-spline curve is subsequently constructed. The method uses a new error-measuring scheme, which is based on the convex hull property of Bézier curves and the idea of cumulative errors, to calculate the global error bound of offset approximation. The method obtains offset curves with C² continuity and guarantees that the actual error bound is precisely within the prescribed tolerance. In addition, it also allows one to selectively parametrize the offset curve.     

NURBS curve and surface fitting for reverse engineering

Reverse engineering is an approach for constructing a computer-aided design (CAD) model from a physical part through dimensional measurement and surface modelling. This paper presents alternatives for reverse engineering of free-form parts using Non-Uniform Rational B-Spline (NURBS) surfaces. A two-step linear approach is employed for fitting NURBS curves and surfaces using the measured points. During the first step, the weights of the control points are identified from a homogeneous system using symmetric eigenvalue decomposition. The control points are further processed in a way similar to B-spline curve and surface fitting. Some examples are presented to illustrate both the steps of reverse engineering and the process of NURBS curve and surface fitting.     

Optimum design of ship design system using neural network method in initial design of hull plate

Manufacturing of complex surface plates in stern and stem is a major factor in cost of a preliminary ship design by computing process. If these hull plate parts are effectively classified, it helps to compute the processing cost and find the way to cut-down the processing cost. This paper presents a new method to classify surface plates effectively in the preliminary ship design using neural network. A neural-network-based ship hull plate classification program was developed and tested for the automatic classification of ship design. The input variables are regarded as Gaussian curvature distributions on the plate. Various applicable rules of network topology are applied in the ship design. In automation of hull plate classification, two different numbers of input variables are used. By observing the results of the proposed method, the effectiveness of the proposed method is discussed. As a result, high prediction rate was achieved in the ship design. Accordingly, to the initial design stage, the ship hull plate classification program can be used to predict the ship production cost. And the proposed method will contribute to reduce the production cost of ship.     

B-spline surface reconstruction and direct slicing from point clouds

The issue of surface reconstruction and slicing from point clouds has been receiving extensive attention recently. When using the B-spline surface fitting technique, the difficulty of parameterization exists. At the same time, for interfacing between reverse engineering and rapid prototyping, the point clouds are usually converted to an stereolithography (STL) model. This leads to a huge file size and requires expert modeling skills. The objective of this work is to establish a base surface parameterization and direct slicing strategy for scattered data based on a cross-sectional design technique. We first present a new method of directly extracting sectional contours from point clouds. Then, we create a base surface by skinning the primary boundary curves and interior sectional curves. Based on a good parameterization, the final surface is achieved with tight tolerance. Several practical examples have demonstrated the feasibility of the proposed method. It can be widely used in Number Control (NC) machining and rapid prototyping.