逆向工程中数据分片及模型重建研究
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摘要
本文是作者在逆向工程中数据分片和模型重建方面所进行的一系列理论研究及软件开发的总结。主要内容包括:网格数据的数据分割及矩形片的提取、多个B样条曲面间光滑拼接、任意模型的多个B样条曲面拟合的分块快速算法、基于二元三次样条函数在TYPE-Ⅱ分割下的曲面重建方法、基于约束和层次结构的模型表示及一个小型逆向工程软件系统的建立等。
本文首先综述了逆向工程的现状,分析了逆向工程中的主要步骤,着重介绍了由不同类型的数据(空间点云、轮廓数据、多边形网格)重建不同类型曲面模型的技术,重建曲面的类型主要有分片线性曲面、参数曲面、隐式曲面及细分曲面。
数据分片工作一直是逆向工程研究中的一个热点也是一个难点,到目前为此还没有一种可以通用的分片方法。通常的做法是手工在模型上指定分割边界或者通过网格化简来进行数据分片:手工的方法非常耗时,而通过网格化简的结果是其分片数量过多。对于网格类型的数据,为改进上述不足,本文给出了一种利用网格上的尖锐特征来提取矩形片的方法,对于点云数据以及特征不明显的网格,作者编制的一个小型的软件工程系统CTMod提供了特征手工指定及分隔边界创建的交互方法。相比较传统的手工方法[81],本文的方法大大提高了分片的速度,相比较网格简化方法[49][13][12],本文的算法得到的数据分片数量大大减少,同时兼顾了网格上的尖锐特征(Sharp Feature),使得分片结果更理想。
多个B样条曲面之间光滑拼接是模型重建过程中的另一个重要问题,由于奇异点的存在,由目前的算法拟合得到的曲面一般只达到了G~1的连续。对于三次B样条曲面,在分析了任意拓扑模型曲面重建过程中曲面之间关系的基础上,本文提出了一种G~1和G~2混合连续拼接方法,即沿同一条边界,曲面之间除了在奇异点附近满足G~1连续之外,其它部分满足G~2连续。重建后的模型曲面之间尽可能地满足了更高的光滑连续性。在算法的实现过程中,采用了基于检查点的线性约束条件添加办法。相比较[81],本文采用了不同的光滑约束方程,算法同时可以自动计算约束方程中的各项系数:相比较非线性的约束条件方法[85],本文算法的求解过程更稳定。对于复杂模型,进行全局优化的曲面重建时,需要同时反求大量的曲面控制点。这个拟合过程需要求解庞大的线性方程组,由于数据采样以及B样条基函数本身的特性等原因,该系数矩阵常常会呈现病态,导致拟合结果失真。对此,本文提出了基于分块思想的快速算法。相比较[79,80]直接求解大规模线性方程组得到的结果,这里给出的分块快速拟合方案在不丢失拟合精度的前提下大大地提高了曲面重建速度。
本文还研究了二元三次样条函数在曲面重建中的应用问题,在TYPE-Ⅱ型剖分下,对于三次样条插值曲面的C~1-拼接问题,许多学者在这方面展开了大量的研究[121][119].但关于C~2-拼接的研究相对较少,本文使用二元三次样条函数来插值重建曲面,使得重建曲面达到了C~2-拼接,在给出样条函数分片表达式的同时也给出了其误差估计。
在模型存储中,本文提出了一种基于约束和层次结构的模型表示方法。该数据模型使用BREP/CSG表示方法,同时包含了多重层次的约束,约束集成在于模型特征之间。这种模型可以满足不同层次建模的需求,特别对于虚拟制造,在目前虚拟现实设备的输入和输出分辨率都很有限的情况下,对于复杂模型的建模,其优点显得尤为突出。
最后,作者编制了一个小型的逆向工程软件系统,实现前面提出的一些逆向工程的算法。该系统使用VC++语言,基于MFC框架以及OpenGL技术开发,可以处理点云、轮廓以及网格类型的采样数据,重建模型可以输出为WavefrontOBJ文件。在系统的实现过程中,不可避免地需要处理各种曲线、曲面。同时还给出了一种Bézier曲线的快速绘制算法。
This paper is mainly focused on data segmentation and model reconstruction problems in Reverse Engineering fields,The main contents include Sharp Featurebased quadrilateral domain extraction from a mesh model,connectivity between multiple B-spline surfaces,fast algorithm for fitting multiple B-spline surfaces on model with arbitrary topology,setting up a hierarchically structured constraintbased data model and binary cubic interpolation of splines with C~2 connectivity for type-Ⅱtriangulations on rectangular domain.
First this paper reviews the application of reverse engineering and main processes of reverse engineering are discussed and problems on data segmentation and model reconstruction are analyzed in detail.
To segment a mesh data and extract quadrilateral domains,we take use of sharp features of the mesh.The procedure starts from an optimal triangulation based on the network of sharp features,and a method named idea angle reservation is provided to pre-treat the triangulated domains.Later,all triangles are converted into quadrilaterals under some defined rules for definite type of connected triangular patches.For unorganized points or mesh without any sharp feature,our software system named CTMod provides a user-interface for defining sharp features and creating boundaries.Comparing with manual method,our algorithm increases the partition speed greatly;Comparing with methods based on mesh simplification,our algorithm get fewer reasonable patches over sharp feature.
The connectivity between surfaces is still one important problem for model reconstruction in the realm.After analyzing relationship between surfaces around normal corner or extraordinary corner,we present an algorithrn to setup combined connectivity which means G~1 connectivity is maintained near the extraordinary corner and G~(k-2) connectivity is achieved in the left.In the implementation of our algorithm,linear constraints on check points are added avoiding deal with non-linear problems.While dealing with complex module reconstruction, we should face to calculate a quantity of control points,and solve a huge linear equation problem.For the reason of deficiency on data sampling and features of spline base,the coefficient matrix of the linear equations often turns to be ill.In order to get steady solution we present a fast algorithm based on dividing and controlling technique,this method can quickly solve the problem without loosing precision.
The author also studies the problems of smooth connection between surfaces in type-Ⅱtriangulations using B-Net method.Spline surfaces have a great application on CAD,till now C-connectivity between surfaces are only related to high degree splines.In this chapter we discussed the existence,uniqueness and approximation degree of binary cubic splines with C~2 connectivity for type-Ⅱtriangulations on rectangular domain,and we also gave a analysis of approximation of the interpolation splines.
A hierarchically structured and constraint-based data model for intuitive and precise solid modeling is also presented.The data model is based on a hybrid BREP/CSG strueture.Constraints are embedded in the solid model and are organized at hierarchical levels as feature constraints among internal feature elements,part constraints among internal features and assembly constraints between individual parts The proposed data model permits modeling on different levels and works well especially for virt(?)al prototype on a VR environment.
At last the author developed a small reverse engineering software system to show the presented algorithms work well.Choosing VC++ as the developing language and making use of MFC framework and OpenGL techniques,the system can use point cloud,point contour and mesh data as input files,and processed models can be output in OBJ format.A Curve rendering technique is also presented.
本文首先综述了逆向工程的现状,分析了逆向工程中的主要步骤,着重介绍了由不同类型的数据(空间点云、轮廓数据、多边形网格)重建不同类型曲面模型的技术,重建曲面的类型主要有分片线性曲面、参数曲面、隐式曲面及细分曲面。
数据分片工作一直是逆向工程研究中的一个热点也是一个难点,到目前为此还没有一种可以通用的分片方法。通常的做法是手工在模型上指定分割边界或者通过网格化简来进行数据分片:手工的方法非常耗时,而通过网格化简的结果是其分片数量过多。对于网格类型的数据,为改进上述不足,本文给出了一种利用网格上的尖锐特征来提取矩形片的方法,对于点云数据以及特征不明显的网格,作者编制的一个小型的软件工程系统CTMod提供了特征手工指定及分隔边界创建的交互方法。相比较传统的手工方法[81],本文的方法大大提高了分片的速度,相比较网格简化方法[49][13][12],本文的算法得到的数据分片数量大大减少,同时兼顾了网格上的尖锐特征(Sharp Feature),使得分片结果更理想。
多个B样条曲面之间光滑拼接是模型重建过程中的另一个重要问题,由于奇异点的存在,由目前的算法拟合得到的曲面一般只达到了G~1的连续。对于三次B样条曲面,在分析了任意拓扑模型曲面重建过程中曲面之间关系的基础上,本文提出了一种G~1和G~2混合连续拼接方法,即沿同一条边界,曲面之间除了在奇异点附近满足G~1连续之外,其它部分满足G~2连续。重建后的模型曲面之间尽可能地满足了更高的光滑连续性。在算法的实现过程中,采用了基于检查点的线性约束条件添加办法。相比较[81],本文采用了不同的光滑约束方程,算法同时可以自动计算约束方程中的各项系数:相比较非线性的约束条件方法[85],本文算法的求解过程更稳定。对于复杂模型,进行全局优化的曲面重建时,需要同时反求大量的曲面控制点。这个拟合过程需要求解庞大的线性方程组,由于数据采样以及B样条基函数本身的特性等原因,该系数矩阵常常会呈现病态,导致拟合结果失真。对此,本文提出了基于分块思想的快速算法。相比较[79,80]直接求解大规模线性方程组得到的结果,这里给出的分块快速拟合方案在不丢失拟合精度的前提下大大地提高了曲面重建速度。
本文还研究了二元三次样条函数在曲面重建中的应用问题,在TYPE-Ⅱ型剖分下,对于三次样条插值曲面的C~1-拼接问题,许多学者在这方面展开了大量的研究[121][119].但关于C~2-拼接的研究相对较少,本文使用二元三次样条函数来插值重建曲面,使得重建曲面达到了C~2-拼接,在给出样条函数分片表达式的同时也给出了其误差估计。
在模型存储中,本文提出了一种基于约束和层次结构的模型表示方法。该数据模型使用BREP/CSG表示方法,同时包含了多重层次的约束,约束集成在于模型特征之间。这种模型可以满足不同层次建模的需求,特别对于虚拟制造,在目前虚拟现实设备的输入和输出分辨率都很有限的情况下,对于复杂模型的建模,其优点显得尤为突出。
最后,作者编制了一个小型的逆向工程软件系统,实现前面提出的一些逆向工程的算法。该系统使用VC++语言,基于MFC框架以及OpenGL技术开发,可以处理点云、轮廓以及网格类型的采样数据,重建模型可以输出为WavefrontOBJ文件。在系统的实现过程中,不可避免地需要处理各种曲线、曲面。同时还给出了一种Bézier曲线的快速绘制算法。
This paper is mainly focused on data segmentation and model reconstruction problems in Reverse Engineering fields,The main contents include Sharp Featurebased quadrilateral domain extraction from a mesh model,connectivity between multiple B-spline surfaces,fast algorithm for fitting multiple B-spline surfaces on model with arbitrary topology,setting up a hierarchically structured constraintbased data model and binary cubic interpolation of splines with C~2 connectivity for type-Ⅱtriangulations on rectangular domain.
First this paper reviews the application of reverse engineering and main processes of reverse engineering are discussed and problems on data segmentation and model reconstruction are analyzed in detail.
To segment a mesh data and extract quadrilateral domains,we take use of sharp features of the mesh.The procedure starts from an optimal triangulation based on the network of sharp features,and a method named idea angle reservation is provided to pre-treat the triangulated domains.Later,all triangles are converted into quadrilaterals under some defined rules for definite type of connected triangular patches.For unorganized points or mesh without any sharp feature,our software system named CTMod provides a user-interface for defining sharp features and creating boundaries.Comparing with manual method,our algorithm increases the partition speed greatly;Comparing with methods based on mesh simplification,our algorithm get fewer reasonable patches over sharp feature.
The connectivity between surfaces is still one important problem for model reconstruction in the realm.After analyzing relationship between surfaces around normal corner or extraordinary corner,we present an algorithrn to setup combined connectivity which means G~1 connectivity is maintained near the extraordinary corner and G~(k-2) connectivity is achieved in the left.In the implementation of our algorithm,linear constraints on check points are added avoiding deal with non-linear problems.While dealing with complex module reconstruction, we should face to calculate a quantity of control points,and solve a huge linear equation problem.For the reason of deficiency on data sampling and features of spline base,the coefficient matrix of the linear equations often turns to be ill.In order to get steady solution we present a fast algorithm based on dividing and controlling technique,this method can quickly solve the problem without loosing precision.
The author also studies the problems of smooth connection between surfaces in type-Ⅱtriangulations using B-Net method.Spline surfaces have a great application on CAD,till now C-connectivity between surfaces are only related to high degree splines.In this chapter we discussed the existence,uniqueness and approximation degree of binary cubic splines with C~2 connectivity for type-Ⅱtriangulations on rectangular domain,and we also gave a analysis of approximation of the interpolation splines.
A hierarchically structured and constraint-based data model for intuitive and precise solid modeling is also presented.The data model is based on a hybrid BREP/CSG strueture.Constraints are embedded in the solid model and are organized at hierarchical levels as feature constraints among internal feature elements,part constraints among internal features and assembly constraints between individual parts The proposed data model permits modeling on different levels and works well especially for virt(?)al prototype on a VR environment.
At last the author developed a small reverse engineering software system to show the presented algorithms work well.Choosing VC++ as the developing language and making use of MFC framework and OpenGL techniques,the system can use point cloud,point contour and mesh data as input files,and processed models can be output in OBJ format.A Curve rendering technique is also presented.
引文
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