自由曲面的局部美化技术

针对反求工程中由多张B-样条曲面构成的边界表示模型在局部区域会出现的形状不规则性的问题,提出利用局部美化技术来消除这种外形的不规则性的方法.首先根据边界表示模型的拓扑给出局部美化的模式,并阐述曲面光顺与模型局部美化之间的区别和联系.然后,通过分析可接受的形状优化准则及其局部微分几何特性,给出局部美化的数学模型.最后,在利用形状分析方法构造局部形状不规则性区域的方法后,借鉴离散的非线性优化方法来保证形状修改的局部性和保持模型的拓扑.给出应用实例揭示了局部美化技术在反求工程中的意义.     

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B样条曲面裁剪计算的局部协调设计

在反求工程曲面重构中,为了对跨多张曲面的局部矩形拓扑裁剪区域进行重新设计,提出了两种基于矩形拓扑区域的曲面局部协调设计方法:自动截面线蒙皮和最小二乘逼近。两种方法均插值于边界曲线和跨界切矢,保证了模型的整体G1连续性,并逼近或插值裁剪区域数据,具有较好的保形性,实际应用效果良好。     

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。     

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。     

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。     

反求工程中复杂曲面边界线的自动提取技术

复杂曲面零件表面的几何模型构造是反求工程的研究重点之一,根据零件表面的数字化数据提取零件表面的边界是构造零件几何模型的关键步骤。针对安全散乱的、无组织的“点云”数据,从工程应用的角度出发,提出了一种自动构造曲面边界曲线的方法,它分为两个步骤,首先,利用分者到一条能包围曲面的所有数字化点的曲线,然后将该曲线模拟为橡皮筋,通过能量最小原理自动修正曲线得到理想的曲面边界。实践证明,通过该方法得到的边界曲     

反求工程中复杂曲面边界线的自动提取技术

复杂曲面零件表面的几何模型构造是反求工程的研究重点之一 ,根据零件表面的数字化数据提取零件表面的边界是构造零件几何模型的关键步骤。针对完全散乱的、无组织的“点云”数据 ,从工程应用的角度出发 ,提出了一种自动构造曲面边界曲线的方法 ,它分为两个步骤 ,首先 ,利用分割方法得到一条能包围曲面的所有数字化点的曲线 ,然后将该曲线模拟为橡皮筋 ,通过能量最小原理自动修正曲线得到理想的曲面边界。实践证明 ,通过该方法得到的边界曲线能满足工程应用的需要     

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。     

由3维离散数据反求曲面STL数据文件

介绍由３维离散数据反求曲面ＳＴＬ数据文件的２种途径：一种利用３维离散数据直接构造曲面ＳＴＬ数据文件；二是先通过离散拟合出样条曲面，然后将样条曲面转化成ＳＴＬ格式数据文件。     

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.     

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.     

形貌视觉测量中立体拼接靶标的设计及应用

设计了一种正六棱柱形状的立体拼接靶标,以靶标侧面6个棋盘格的角点作为全局控制点。基于近景摄影测量技术,建立立体靶标的6个单元模型,通过计算模型内摄站间的相对位姿,推导出棋盘格角点在所属单元模型的局部坐标。以公共棋盘格为中介,确立相邻单元模型的坐标系转换关系。建立靶标的全局坐标系于1号棋盘格,推导该棋盘格平面与其像平面间的单应性矩阵,从而确立全局坐标系和1号棋盘格所处单元模型的坐标系的转换关系。依次递推实现全局坐标系和每个单元模型坐标系的转换,进而计算出全部靶标角点的全局坐标,再经光束平差算法获取精确值。以玻璃表面棋盘格的角点间距作为评价指标,拼接精度优于0.15 mm/m。基于立体拼接靶标的拼接试验表明,实体模型表面4个子区域的局部点云可被精确地拼接成整体点云。与基于全局控制点和平面靶标的拼接方法相比,本方法亦具有更高的拼接精度。     

G2 Continuity for Multiple Surfaces Fitting

Fitting 3D known data into sculptured surfaces has received extensive attention. However, most algorithms available are suitable only for an isolated surface. A part typically contains multiple surface regions that must be blended to a degree of continuity. The conventional approach based on blending, lofting, stitching, etc. cannot guarantee the quality of the surface near the jointed area. The purpose of this work is to present a surface-fitting algorithm for multiple sets of data, concentrating on G 2 continuity across the boundary of the fitted surfaces. The proposed surface-fitting algorithm essentially fits several sets of data simultaneously, and yields a B-spline surface for each set of data. The G 0 ,G 1 , and G 2 continuity conditions between B-spline surface patches were addressed. Based on these results, additional constraints were specified to achieve G 2 continuity across the surface boundary. A successful demonstration of the proposed strategy is provided also.     

A hybrid approach to smooth surface reconstruction from 2-D cross sections

This article presents a hybrid approach to smooth surface reconstruction from serial cross sections, where the number of contours varies from section to section. In a triangular surface-based approach taken in most reconstruction methods, a triangular surface is constructed by stitching triangular patches over a triangular net generated from the compiled contours. In the proposed approach, the resulting surface is a G¹ composite surface consisting of three kinds of surfaces: skinned, branched, and capped surfaces. Each skinned surface is first represented by a B-spline surface approximating the serial contours of the skinned region and then is transformed into a mesh of rectangular Bezier patches. On branched and capped regions, triangular G¹ surfaces are constructed such that the connections between the triangular surfaces and their neighbouring surfaces are G¹ continuous. Because each skinned region is represented by an approximated rectangular C² surface instead of an interpolated triangular G¹ surface, the proposed approach can provide more visually pleasing surfaces and realize more efficient data reduction than the triangular surface-based approach. Some experimental results demonstrate its usefulness and quality.     

基于力密度方法的NURBS曲线和曲面变形框架

提出基于力密度方法的统一求解策略,实现NURBS曲线和曲面的精确变形.将控制网格类比为空间索网结构,分别建立外载荷变化最小、外载荷最小、杆阻尼长度最小和节点位移最小等四种表达不同几何和物理意义的最小化模型来驱动变形,并以控制顶点在变形前后的位移为变量,建立统一表达的目标函数方程,便于多个最小化模型组合使用,满足特定的变形需要.由于目标函数的二次性以及约束的线性化处理,优化问题可以通过Lagrange乘子法转化为线性问题进行求解.在计算中引入目标函数快速求解算法,使变形设计可以满足实时交互操作的需要.应用实例表明,该算法可以应用于细节特征设计和反求建模等复杂曲面造型.     

Local Surface Deformation of Precision Airplane-Engine Components

Local surface plastic deformation may potentially be used for precision shaping of components characterized by low and nonuniform rigidity in the control systems of airplane engines. Analysis of options for the control of technological shape inheritance gives rise to methods of effective deformation. By simulating the stress–strain state of the surface layer, a method is proposed for specifying the local deformation conditions so as ensure shape precision of the part’s working surfaces.