反求工程CAD混合建模理论与方法研究
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摘要
反求工程是将实物模型转化为工程概念和CAD模型的一系列技术方法的总称,已经发展成为现代设计方法学中的一个重要分支。随着计算机技术和几何造型技术的发展,反求工程己不再满足于简单的产品仿制,而是基于实物模型的产品创新。为了增强反求模型的二次设计能力,从而支持产品创新,本文研究了反求工程CAD混合建模方法及其关键技术。
混合建模即将正向设计和反求工程相结合,从测量数据中提取出可以重新进行参数化设计的特征、约束及设计意图,进行再设计,完成CAD模型。本文给出了基于该建模方法的基本框架,特征和约束的定义、分类及表达。在模型分析基础上引入树的概念,建立反求工程CAD建模树,确定建模方法和步骤。讨论了混合建模方法的主要研究内容,并研究了二次曲面特征和过渡曲面特征提取。
自由曲面重构是反求工程重要研究内容之一,重构曲面质量的影响因素包括逼近精度和光顺性,除此而外,还要求重构曲面与周边相邻曲面达到一定的连续性。文中给出了重构区域划分原则和基于切片法的重构区域边界定义方法,详细研究了应用点云切片技术的蒙皮曲面重构、无约束的自由曲面逼近重构和带有边界约束的双三次B样条曲面重构方法,并给出曲面重构的基本过程。给出了应用最小二乘逼近数学模型的逼近曲面迭代求解方法,在优化目标函数中加入简化的曲面能量模型控制曲面光顺性。
在曲面光顺中,研究了能量法、次数升阶、小波分解三种B样条曲面光顺方法,对比分析了不同方法的优缺点和适用场合。为了保证光顺后曲面模型的整体连续性,提出了带位置约束和跨边界切矢约束的B样条曲面能量光顺方法。
针对曲面连续性编辑,研究和提出了多种曲面局部协调设计方案,恢复曲面模型的G~1连续性。具体包括相邻两曲面的公共边界处位置和法矢调整、曲面搭接,多曲面间矩形拓扑裁剪区域的局部孔斯混合、局部B样条插值和局部B样条逼近。设计中,采用二次逼近进行裁剪区域边界条件预处理,松弛边界约束,使局部设计区域与周边曲面达到近似G~1连续,符合工程要求。插值和逼近则充分利用裁剪区域的曲面信息,分别对设计曲面精度和光顺性进行控制。
反求工程CAD混合建模方法及相关技术已成功应用于反求工程CAD软件RE-SOFT中,结合实例论证了其可行性和适用性。最后在总结全文工作的基础上,指出了有待进一步研究的内容。
Reverse Engineering (RE) is a discipline of transforming physical parts into engineering concepts and CAD model, covers a series of methods and techniques. It has been an important branch of modern design methodology. With the developing of computer and measurement technique, RE concentrates on no longer product copy but innovation. In order to operate the CAD model constructed by RE method, a hybrid CAD modeling method and some related key techniques are studied in this dissertation.Hybrid CAD modeling method is a kind of integration of RE and conventional design in which the product features, geometric constraints and design intent are addressed by inheriting and developing the initial design of a physical prototype. Fundamental theory included in this method, such as modeling strategy, feature and constraint definition, classification and representation, are researched in chapter two. Based on model analysis, modeling procedures are described by RE modeling tree, which is introduced from the graph theory. Main contents in relation to the hybrid modeling method are discussed, and some key techniques such as quadric surface feature extraction and blend surface feature extraction are addressed in details.Free form surface reconstruction plays a key role in RE. The reconstructed surface not only needs to meet approximating precision and looks smooth, but also needs to reach certain continuity with adjacent surfaces. Reconstruction region is defined by point cloud slicing method and should satisfy the given principle. When the curve network is ready, B-spline surface skinning based on point cloud slicing, optimization bicubic B-spline surface reconstruction method with or without boundary constraint is proposed. The objective function consists of least squares approximating term and simplified surface energy term, which affect the precision and fairing of the reconstructed surface respectively. It can be solved by iteration approaches.Surface fairing techniques, including energy based surface fairing, order elevation surface fairing and wavelet decomposition surface fairing, are introduced. Pros and cons of various fairing method are also described. In order to keep whole surface model G~1 continuous, an energy based fairing method with boundary constraint of curves or cross boundary derivatives is presented.In the process of RE modeling, it is always necessary to do some further surface
混合建模即将正向设计和反求工程相结合,从测量数据中提取出可以重新进行参数化设计的特征、约束及设计意图,进行再设计,完成CAD模型。本文给出了基于该建模方法的基本框架,特征和约束的定义、分类及表达。在模型分析基础上引入树的概念,建立反求工程CAD建模树,确定建模方法和步骤。讨论了混合建模方法的主要研究内容,并研究了二次曲面特征和过渡曲面特征提取。
自由曲面重构是反求工程重要研究内容之一,重构曲面质量的影响因素包括逼近精度和光顺性,除此而外,还要求重构曲面与周边相邻曲面达到一定的连续性。文中给出了重构区域划分原则和基于切片法的重构区域边界定义方法,详细研究了应用点云切片技术的蒙皮曲面重构、无约束的自由曲面逼近重构和带有边界约束的双三次B样条曲面重构方法,并给出曲面重构的基本过程。给出了应用最小二乘逼近数学模型的逼近曲面迭代求解方法,在优化目标函数中加入简化的曲面能量模型控制曲面光顺性。
在曲面光顺中,研究了能量法、次数升阶、小波分解三种B样条曲面光顺方法,对比分析了不同方法的优缺点和适用场合。为了保证光顺后曲面模型的整体连续性,提出了带位置约束和跨边界切矢约束的B样条曲面能量光顺方法。
针对曲面连续性编辑,研究和提出了多种曲面局部协调设计方案,恢复曲面模型的G~1连续性。具体包括相邻两曲面的公共边界处位置和法矢调整、曲面搭接,多曲面间矩形拓扑裁剪区域的局部孔斯混合、局部B样条插值和局部B样条逼近。设计中,采用二次逼近进行裁剪区域边界条件预处理,松弛边界约束,使局部设计区域与周边曲面达到近似G~1连续,符合工程要求。插值和逼近则充分利用裁剪区域的曲面信息,分别对设计曲面精度和光顺性进行控制。
反求工程CAD混合建模方法及相关技术已成功应用于反求工程CAD软件RE-SOFT中,结合实例论证了其可行性和适用性。最后在总结全文工作的基础上,指出了有待进一步研究的内容。
Reverse Engineering (RE) is a discipline of transforming physical parts into engineering concepts and CAD model, covers a series of methods and techniques. It has been an important branch of modern design methodology. With the developing of computer and measurement technique, RE concentrates on no longer product copy but innovation. In order to operate the CAD model constructed by RE method, a hybrid CAD modeling method and some related key techniques are studied in this dissertation.Hybrid CAD modeling method is a kind of integration of RE and conventional design in which the product features, geometric constraints and design intent are addressed by inheriting and developing the initial design of a physical prototype. Fundamental theory included in this method, such as modeling strategy, feature and constraint definition, classification and representation, are researched in chapter two. Based on model analysis, modeling procedures are described by RE modeling tree, which is introduced from the graph theory. Main contents in relation to the hybrid modeling method are discussed, and some key techniques such as quadric surface feature extraction and blend surface feature extraction are addressed in details.Free form surface reconstruction plays a key role in RE. The reconstructed surface not only needs to meet approximating precision and looks smooth, but also needs to reach certain continuity with adjacent surfaces. Reconstruction region is defined by point cloud slicing method and should satisfy the given principle. When the curve network is ready, B-spline surface skinning based on point cloud slicing, optimization bicubic B-spline surface reconstruction method with or without boundary constraint is proposed. The objective function consists of least squares approximating term and simplified surface energy term, which affect the precision and fairing of the reconstructed surface respectively. It can be solved by iteration approaches.Surface fairing techniques, including energy based surface fairing, order elevation surface fairing and wavelet decomposition surface fairing, are introduced. Pros and cons of various fairing method are also described. In order to keep whole surface model G~1 continuous, an energy based fairing method with boundary constraint of curves or cross boundary derivatives is presented.In the process of RE modeling, it is always necessary to do some further surface
引文
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