基于局部协调设计的复杂自由曲面模型拓扑还原技术

针对局部协调设计因引入协调曲面而破坏了模型原有的拓扑结构并同时增加了自由曲面形状造型所需的曲面片数量,提出一种基于局部协调设计的复杂裁剪汇交曲面模型拓扑还原技术。逆向定位汇交点(N面角点)并完整构造出决定还原后N边汇交曲面模型拓扑、几何形状和边界的特征曲线网格。应用自由曲面逼近技术分片逼近经裁剪汇交曲面和协调曲面离散获得的点云数据重建B样条曲面以实现裁剪汇交曲面的拓扑还原。采用自由曲面模型的全局美化技术实现紧公差约束下对点云逼近的N张拓扑还原后汇交曲面的全局美化,保证曲面相邻边界和N面角点处收敛的G1光滑拼接。应用实例表明,该拓扑还原技术不仅较好复现了原始汇交曲面模型的拓扑与几何性质,并且使模型达到整体G1连续。     

基于任意拓扑曲线网的曲面造型技术研究

插值由特征曲线组成的曲线网是最常用的曲面建模思路,而从简单矩形拓扑曲线网到任意拓扑曲线网的扩展不仅增强了曲面设计自由度,而且提高了曲面设计效率。以曲线网建模过程为序,介绍了任意拓扑曲线网的创建和编辑、插值曲面的构造以及曲线网建模系统研究等技术的研究现状,分析了Bezier和NURBS曲面、Gregory曲面片和细分曲面在曲线网插值中的应用特点,指出了今后研究的重点。     

B样条曲面的T样条裁剪法

针对B样条曲面裁剪法中的裁剪曲面定义与裁剪边界修改问题,提出一种T样条曲面裁剪法,并用于多边矩形域上的曲面裁剪。先将B样条曲面转换为一张全行列T样条曲面,然后再利用T样条曲面的局部均匀细分和控制点移除,得到一张T样条裁剪曲面。裁剪后的T样条曲面建立在一个多边T网格上,具有完整的曲面定义,并且可以局部修改其裁剪边界。最后通过实例验证了T样条裁剪曲面在曲面定义和边界修改上都优于B样条裁剪曲面。     

逆向工程中自由曲面拟合方法的分类与比较

阐述了逆向工程中自由曲面拟合的曲面重构和多个曲面整合两方面内容。曲面重构可分为插值和逼近两种方法,其中插值的方法有样条插值、基于散乱点数据的三角曲面插值;而逼近的方法有最小二乘逼近、基于能量原理的曲面逼近、偏微分方程逼近和小波理论的逼近方法等。则多个曲面整合包括几何连续性和参数连续性。本文对他们分别进行了介绍归类和比较,并且得出了有关的结论。     

基于广义延拓逼近法的复杂曲面重构研究

针对逆向工程中复杂曲面重构,基于广义延拓逼近法,提出一种逼近算法.该算法一方面能在分片边界点上满足插值条件,使得各分片之间的变化具有一定的协调性;另一方面,利用分片插值区域周围结点(包括内点)的信息,实现分片区域内部的最佳逼近,同时算法又使曲面形状具有局部可控性、变差减少性和凸包性等特性.仿真实例证实,该算法改善了传统逼近算法方法在重构曲面时产生的失真和运算的不稳定现象,并且得到较高的曲面重构精度,具有计算稳定、快速和方便的优点.     

基于原始曲面信息的变形网格的曲面重构

为了对有限元分析后的模型进行干涉检查和再分析,需对变形后的网格重建实体模型。基于原始曲面的信息,对变形后的网格进行区域分割,针对分割后的每个特征区域,分别对二次曲面和B-样条曲面采用了不同的重构方法。对于二次曲面,提出了一种基于等参数线的二次曲面参数提取的方法;对于B-样条曲面,给出了一种误差控制的B-样条曲面拟合的多步迭代方法。基于原始模型的拓扑结构,对重构后的曲面进行裁剪缝合得到变形后的实体模型。由于利用了原始曲面信息,使得曲面重构得以简化。实验表明,基于原始曲面信息的曲面重构方法可以快速有效地重构出任意复杂拓扑结构的变形后的曲面。     

任意拓扑结构复杂曲面模型重构新方法

分析了采用参数化方法进行复杂曲面模型重构时存在的缺点,给出了应用递归插值分割理论从离散测量点构成的初始控制网格直接构造任意拓扑结构复杂自由曲面模型时计算插值点的统一算法,设计了一种能充分体现这种曲面模型重构方法优点的四叉树型数据结构存储必要的信息,最后给出了复杂自由曲面模型重构的几个实例。从实例可以看出该方法能够避免参数化方法在复杂曲面模型重构时所必须的参数曲面片之间的拼接和裁剪等问题,为复杂自由曲面模型重构提供了有效的新方法。     

基于实物的复杂曲面零件反求工程中未知区域测量数据补充及曲面重构技术

针对基于实物的复杂零件反求工程中含有部分形状未知区域（如裁减曲面中的被裁减部分、测量盲区等）的复杂曲面反求CAD建模问题,提出了三种测量数据补充方法:①局部区域实物填充法。②补充设计数据补充法。③基于逼近曲面或三角曲面的测量数据自动补充法。研究了基于三角曲面模型初始表达的复杂曲面分区NURBS曲面重构方法。最后,给出了结合上述方法和反求工程软件RE-SOFT所解决的摩托车塑料件反求CAD建模实例。实践表明,综合运用所提出的数据补充和曲面重构方法,能够大大缩短实物样件的反求CAD建模时间,提高复杂曲面产品的设计效率。     

基于变分隐式曲面的三角网格孔洞修补

针对三角网格模型存在的孔洞问题提出一种基于变分隐式曲面的孔洞修补算法。首先,利用孔洞边界信息构造插值孔洞边界的变分隐式曲面并将其网格化,得到初始孔洞网格,再利用边界点裁剪初始孔洞网格,最后把裁剪后的孔洞网格与初始网格拓扑合并,完成孔洞修补。算法充分考虑了孔洞周围的信息,使得孔洞网格与原始网格光滑连接,取得了比较好的效果。     

基于变分隐式曲面的三角网格孔洞修补

针对三角网格模型存在的孔洞问题提出一种基于变分隐式曲面的孔洞修补算法。首先，利用孔洞边界信息构造插值孔洞边界的变分隐式曲面并将其网格化，得到初始孔洞网格，再利用边界点裁剪初始孔洞网格，最后把裁剪后的孔洞网格与初始网格拓扑合并，完成孔洞修补。算法充分考虑了孔洞周围的信息，使得孔洞网格与原始网格光滑连接，取得了比较好的效果。     

Contour-parallel offset machining for trimmed surfaces based on conformal mapping with free boundary

The parametric surfaces of some manufactured parts are often subjected to the Boolean operation of other objects; generating suitable NC tool paths from such trimmed surface remains a challenge. This paper presents a new planar development-based method to generate contour-parallel offset paths of trimmed surfaces. To avoid direct frequent identifications and removals of interferences of offset curves on 3D-trimmed surface possibly with multiple holes or restricted regions, the original surface is flattened in the plane domain using a two-stage approach which consists of conformal mapping with free boundary and further nonlinear accuracy improvement. Then, sequent offsets of the boundary curves of the planar region are generated, and the global interferences are detected and removed using an efficient and robust divide-and-conquer strategy. Based on a tree data structure, a tool-path linking algorithm is also given with less or no tool retractions, and subsequently, the resulting planar paths are inversely mapped to the physical space. Illustrated examples have been conducted to testify the affectivity and the applicability of the proposed contour-parallel offset machining method.     

Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining

Reparameterization-based toolpath generation methods are usually adopted for machining triangular meshes, trimmed surfaces and compound surfaces. The quality of the reparameterization has an important effect on that of the surface. In this paper, a combined reparameterization procedure is introduced to generate an optimal mapping between the designed surface and a specified planar circular region with relatively less distortion both in length and in angle. Then, for five-axis sculptured surface machining the mathematical model of spiral guide path with maximum path interval is constructed in the circular region. Cutter contact paths are obtained by inversely mapping the guide path onto the designed surface. Under constraints of gouging and collision, continuous and optimal cutter orientations are subsequently calculated. Finally, the results of simulation and experiment of the machining process are given to illustrate the feasibility and applicability of the proposed method.     

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.     

三坐标测量机检测数据与CAD系统之间的接口技术研究

提出一种需要人工适当干预的曲面处理方法。该方法通过对大量的点位数据进行处理，生成相应的曲线，然后由设计人员对曲线进行修整，生成相应的曲面。并采用ObjectARX为开发工具，在MDT环境下开发了三坐标测量机与CAD系统之间的接口程序。     

基于复合三角Bezier曲面/平面交线的裁剪

提出一种复合三角Ｂｅｚｉｅｒ曲面与平面的求交算法,这种算法能处理多条交线、交线环的情况,在自由曲面数控加工编程中具有广泛的应力场合,对提高汽车等领域的曲面ＮＣ加工精度具有重要的工程价值。将交点作为型值点插入相应的三角网格,通过三角网 重新划分和分离,实现复合曲面的裁剪。试用显示,这种裁剪方法在工程上是行之有效的。     

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。     

基于边界法线插值的两步法细分曲面造型

针对曲面造型中光滑边界曲线的插值要求（位置和法线），提出了两步法插值边界法线细分方法：首先按边界位置插值细分规则对控制网格进行一次迭代细分，分别计算其细分后的V点、E点、F点；然后调整边界点相邻顶点的位置来满足边界法线要求。该方法将插值边界法线先转化为邻城顶点的调整，后转变为单参数的求解问题，并通过实例验证了该方法能有效地控制细分曲面造型的边界形状。该方法对丰富细分曲面造型技术和推广其应用起到一定作用。     

Topology recovery technique for complex freeform surface model after local geometry repair

Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations.Local geometry repair,such as cover holes or replace bad surfaces by adding new surface patches for dealing with inconsistencies among the confluent region,where multiple surfaces meet,is a common technique used in CAD model repair and reverse engineering.However,local geometry repair destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling.Consequently,a topology recovery technique dealing with complex freeform surface model after local geometry repair is proposed.Firstly,construct the curve network which determine the geometry and topology properties of recovery freeform surface model;secondly,apply freeform surface fitting method to create B-spline surface patches to recover the topology of trimmed ones.Corresponding to the two levels of enforcing boundary conditions on a B-spline surface,two solution schemes are presented respectively.In the first solution scheme,non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches.In the other solution scheme,constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G 1 continuity simultaneously.The presented two different schemes are applied to the consistent surface model,which consists of five trimmed confluent surface patches and a local consistent surface patch,and a machine cover model,respectively.The application results show that our topology recovery technique meets shape-preserving and G 1 continuity requirements in reverse engineering.This research converts the problem of topology recovery for consistent surface model to the problem of constructing G 1 patches from a given curve network,and provides a new idea to model repairing study.     

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.