面向普通用户的三维模型设计方法研究

发布时间：2018-03-08 12:20

本文选题：3D打印　切入点：内部空腔设计　出处：《浙江大学》2016年博士论文　论文类型：学位论文

【摘要】：三维模型的设计是计算机图形学中最基本的研究问题之一。三维模型设计工具在产品设计和影视动画等多个领域中都有着广泛的应用。3D打印技术的日渐兴起激发了普通用户对三维模型设计的需求。人们想要设计和制造个性化的物品,却又缺乏使用专业三维设计软件所需的技能。因此,为普通用户开发简单易用的三维模型设计工具成为了近年图形学领域中的一个研究热点。本文针对普通用户的操作习惯,研究了如何利用交互式界面、物理仿真集成和优化算法等手段开发便于普通用户使用的三维模型设计工具,具体包括:·一个基于三角形面网格的内部空腔生成算法,用于设计具有特定质量分布的三维模型。我们借用形状优化领域中半欧拉导数的概念,将优化问题中的能量函数联系到空腔边界上的速度场上,通过迭代地移动空腔边界来生成满足功能性设计目标的最优空腔形状。除了将该算法应用在可稳定站立和可稳定旋转模型的设计问题上,我们还提出了一个设计可漂浮模型的新应用。· 一个既能满足三维模型功能性设计需要,又无需使用3D打印支撑结构的内部空腔生成算法。我们使用具有免支撑性质的斜六面体结构作为空间体素化的基本单元,并设计了体素结构之间的合并算法。通过推导体素上体积分的参数化公式,我们为模型的功能性设计目标构造了优化函数,并交替进行优化求解和体素合并两个过程来生成最终的空腔形状。我们用这个方法设计了可稳定站立和可稳定旋转的三维模型,并打印了实物模型对算法进行了验证。·一个集成结构强度分析的三维模型形状编辑系统,为用户提供即时的物理仿真反馈。我们将四面体网格划分为网格域,并以网格域作为形状编辑和有限元系统更新的基本单元。通过为刚度矩阵中的元素推导参数化公式,并以网格域为单位对有限元系统进行局部更新,我们的系统能够快速地完成有限元系统和四面体网格之间的同步,实时地计算模型上的应力分布情况。系统还包括一个基于网格域的优化算法,能够自动地改变模型的局部形状来降低模型上的最大等效应力。·一个基于勾画的三维模型旋转动画设计系统。我们设计了一种新的交互界面,允许用户通过勾画曲线的方式设定模型进行旋转运动时的角速度变化轨迹。系统能够通过求解优化问题自动地生成最贴近用户输入的轨迹曲线,同时又满足关键帧朝向约束的旋转动画。
[Abstract]:The design of 3D model is one of the most basic research problems in computer graphics. 3D model design tools have been widely used in many fields, such as product design and film animation. People want to design and manufacture personalized objects. Therefore, the development of simple and easy to use 3D model design tools for ordinary users has become a research hotspot in the field of graphics in recent years. This paper studies how to use interactive interface, physical simulation integration and optimization algorithms to develop 3D model design tools for common users, including: 路an internal cavity generation algorithm based on triangular mesh. By using the concept of semi-Euler derivative in the field of shape optimization, the energy function of the optimization problem is related to the velocity field on the boundary of the cavity. The optimal cavity shape is generated by iteratively moving the cavity boundary to meet the functional design objectives. In addition, the proposed algorithm is applied to the design of stable standing and stable rotation models. We also propose a new application for the design of floatable models. We also do not need to use the 3D printing support structure of the internal cavity generation algorithm. We use an oblique hexahedron structure with no support as the basic unit of spatial voxelization. By pushing the parameterized formula of the upper body integral of the conductor element, we construct the optimization function for the functional design objective of the model. In order to generate the final cavity shape, we design a three dimensional model which can stand stably and rotate stably. And print the physical model to verify the algorithm. 路A three-dimensional model shape editing system integrated with structural strength analysis provides immediate physical simulation feedback for users. We divide tetrahedron mesh into grid domain. Taking the grid domain as the basic element of shape editing and finite element system updating, the parameterized formula is derived for the elements in the stiffness matrix, and the local updating of the finite element system is carried out in the grid domain. Our system can quickly synchronize the finite element system and tetrahedron mesh and calculate the stress distribution on the model in real time. The system also includes an optimization algorithm based on mesh domain. Can automatically change the local shape of the model to reduce the maximum equivalent stress on the model. 路A 3D model rotation animation design system based on sketch. We designed a new interactive interface. The system can automatically generate the trajectory closest to the user's input by solving optimization problems. At the same time, it meets the key frame orientation constraints of the rotation animation.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41

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