反求工程中基于变形的自由形状特征重构
摘要
第一章绪论
阐述了曲面变形的基本理论、方法及研究现状，并从产品设计的背景出发探讨了变形技术的工业需求及目前方法的不足。通过对自由曲面反求建模策略的论述及其研究现状的分析总结，阐明了自由形状表达的细节特征即自由形状特征建模过程中存在的问题，提出利用曲面变形技术解决其重构和后续修改设计问题的思路。最后给出了论文的主要研究内容和基本框架。
第二章反求工程中的自由形状特征重构
研究了反求工程中自由形状特征的定义和分类，通过总结正向设计中自由形状特征的表达引出反求建模中可行的自由形状特征表达方式，提出基于变形的自由形状特征重构策略，分析并给出其中的关键技术及相关基础算法。
第三章基于力密度方法的NURBS曲线和曲面约束变形
基于力密度方法提出了一种统一的求解框架，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，建立了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。针对曲面上曲线的离散表达模型，给出基于文中变形框架的曲面上曲线的形状调整和光顺算法。
第四章基于曲线驱动的曲面局部形状特征变形重构
提出一种新的基于曲线驱动的曲面局部变形方法，支撑自由形状特征中的变形特征重构及重构模型的后续设计修改。通过对形状控制曲线和限定曲线之间的相容性分析，阐述了缓释区域的由来。通过对变形前后限定曲线邻域内微分属性的分析，引入了限定带的概念，并由此概念出发在变形目标函数中引入对限定带的逼近项，实现对曲面变形范围的有效控制。与传统方法相比，可在限定曲线的局部邻域内获得品质较高的曲面模型，同时大大简化优化求解过程中的矩阵存储规模和运算复杂性。
第五章基于曲面变形的置换特征重构
针对与基曲面以过渡特征相连的自由形状特征即置换特征的曲面重构问题进行研究，提出一种将反求和设计相结合、基于约束的建模方法。利用离散求交从点云中提取限定曲线，并以限定曲线和形状控制曲线为约束变形构造目标曲面。为提高重构曲面的质量，详细探讨了初始曲面的构建方法、控制顶点的配置原则以及曲面边界形状优化等内容。而后利用圆弧拟合和概率统计分析等手段提取过渡特征参数，设计重构过渡曲面。其间对点云切片、过渡特征参数提取等一系列支撑算法进行了研究。
第六章RE-SOFT7.0系统架构、实现及建模实例分析
深入探讨了基于特征的反求工程系统RE-SOFT7.0的体系架构策略及功能分解方案，系统介绍了其中的主要功能模块和关键技术。以手机振动膜零件的曲面重构为例，展现了以特征为核心的反求建模策略，并对以往难以构建的自由形状特征以本文方法高品质快速重构。
对本文的主要研究工作和贡献进行了总结，并对该领域未来的研究工作进行了展望
阐述了曲面变形的基本理论、方法及研究现状，并从产品设计的背景出发探讨了变形技术的工业需求及目前方法的不足。通过对自由曲面反求建模策略的论述及其研究现状的分析总结，阐明了自由形状表达的细节特征即自由形状特征建模过程中存在的问题，提出利用曲面变形技术解决其重构和后续修改设计问题的思路。最后给出了论文的主要研究内容和基本框架。
第二章反求工程中的自由形状特征重构
研究了反求工程中自由形状特征的定义和分类，通过总结正向设计中自由形状特征的表达引出反求建模中可行的自由形状特征表达方式，提出基于变形的自由形状特征重构策略，分析并给出其中的关键技术及相关基础算法。
第三章基于力密度方法的NURBS曲线和曲面约束变形
基于力密度方法提出了一种统一的求解框架，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，建立了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。针对曲面上曲线的离散表达模型，给出基于文中变形框架的曲面上曲线的形状调整和光顺算法。
第四章基于曲线驱动的曲面局部形状特征变形重构
提出一种新的基于曲线驱动的曲面局部变形方法，支撑自由形状特征中的变形特征重构及重构模型的后续设计修改。通过对形状控制曲线和限定曲线之间的相容性分析，阐述了缓释区域的由来。通过对变形前后限定曲线邻域内微分属性的分析，引入了限定带的概念，并由此概念出发在变形目标函数中引入对限定带的逼近项，实现对曲面变形范围的有效控制。与传统方法相比，可在限定曲线的局部邻域内获得品质较高的曲面模型，同时大大简化优化求解过程中的矩阵存储规模和运算复杂性。
第五章基于曲面变形的置换特征重构
针对与基曲面以过渡特征相连的自由形状特征即置换特征的曲面重构问题进行研究，提出一种将反求和设计相结合、基于约束的建模方法。利用离散求交从点云中提取限定曲线，并以限定曲线和形状控制曲线为约束变形构造目标曲面。为提高重构曲面的质量，详细探讨了初始曲面的构建方法、控制顶点的配置原则以及曲面边界形状优化等内容。而后利用圆弧拟合和概率统计分析等手段提取过渡特征参数，设计重构过渡曲面。其间对点云切片、过渡特征参数提取等一系列支撑算法进行了研究。
第六章RE-SOFT7.0系统架构、实现及建模实例分析
深入探讨了基于特征的反求工程系统RE-SOFT7.0的体系架构策略及功能分解方案，系统介绍了其中的主要功能模块和关键技术。以手机振动膜零件的曲面重构为例，展现了以特征为核心的反求建模策略，并对以往难以构建的自由形状特征以本文方法高品质快速重构。
对本文的主要研究工作和贡献进行了总结，并对该领域未来的研究工作进行了展望
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