【作者】 周廷方；

【导师】 彭群生； 冯结青；

【作者基本信息】 浙江大学 ， 应用数学， 2005， 硕士

【摘要】 随着计算机硬件和3D扫描技术的快速发展,离散网格及其处理已经成为几何造型和计算机图形学领域中的热点研究内容,其研究成果已广泛应用于制造业,娱乐业,游戏工业等领域。 网格曲面编辑是网格处理的核心技术,其目的是为用户提供直观,高效的曲面编辑手段,实现复杂几何模型的构造.近年来,一些学者相继提出了多种网格曲面编辑算法,归纳起来可分为两类:一类是将曲面嵌入到均匀网格体的FFD方法及其扩展,另一类是基于曲面微分属性的编辑方法.前者的编辑模式直观,效果便于控制,但交互方式不够灵活;后者编辑效果较佳,但表达形式特殊,不便与已有造型系统集成。 可见,研究一种交互方式直观,高效可控,表达方式统一的网格编辑方法是很有意义的.鉴于此,本文研究并提出了一种形式统一且能够体现曲面内在几何属性的多分辨率几何表达方式,该表达方式由逼近曲面的一张光顺的基曲面及定义在该基曲面上的一组局部变量构成.基于该表达方式,我们利用层次B-样条表示基曲面,提出了一个网格曲面编辑框架,并在该框架中实现了自由变形,几何细节迁移等功能.在框架的处理流程中,用户首先交互地在网格上选取编辑区域,程序随后完成所选区域的参数化和均匀重采样,并用层次B-样条光顺拟合这些均匀采样点作为该网格的基曲面,然后计算所选区域中网格顶点相对B-样条基曲面的局部变量(该局部变量具有平移,旋转不变性,可将其视为曲面在编辑过程中的内蕴几何特征),从而可以实现通过编辑层次B-样条基曲面来达到编辑原网格曲面的目的。利用层次B-样条,还可方便地实现多分辨率编辑,借助于直接操纵的DFFD方法,该框架也可对网格曲面进行直接编辑,以精确控制编辑结果。 在曲面编辑过程中分解得到的局部变量可作为曲面的几何细节,将其映射到自身变形后的基曲面上即得到变形后的网格曲面,也可将其映射到不同物体的基曲面上,以实现几何细节的迁移。实验结果表明,该方法主要特点是操作直观方便,无论对整体还是局部编辑,都能取得可控、可靠的编辑效果,且采用B-样条表达方式,易于与已有的造型和动画系统合成。更多还原

【Abstract】 With the rapid development of 3D scanning technology, mesh processing has become one of the hottest topics in geometry modelling as well as computer graphics and its research results have been widely applied into a great deal of areas, such as mechanical manufacture, movie entertainment, game technology and so on.As the core technology of mesh processing, mesh editing aims at the effective construction of complex geometry models with intuitive and high-efficiency editing approach. In recent years, lots of mesh editing algorithms have been promoted, which can be mainly classified into two categories: the FFD based editing methods which embed the surface into 3D uniform lattice volume and surface differential properties based methods. FFD method provides intuitive editing mode and easy-to-control editing style, while its user interaction is not flexible. The differential properties based methods can bring outstanding deformation result, but it is difficult to be integrated into existing technologies duing to its special representation form.So it is great important to investigate on effective mesh editing method featured with intuitive interaction, easy-to-control editing style and unified data representation. Motivated by this, an unified multi-resolution geometry representation form is proposed in this thesis, which precisely denote the internal geometric properties of surface. After the decomposition of original surface, we can get the unified geometry representation form consisting of a smoothing base surface and a group of local variables defined on the base surface. Using hierarchical B-splines to represent the base surface, we construct a comprehensive and powerful mesh editing framework and implement most of mesh editing applications such as freeform deformation, geometric detail transfer and so on. During the pipeline of our framework, First Region Of Interest (ROI) is selected interactively on the mesh. Then the ROI is parameterized and re-sampled uniformly. The re-sampled points are fitted with hierarchical B-spline surfaces. The local coordinates of the vertices in the ROI corresponding to the hierarchical B-spline surfaces are computed(These local variables are translation and rotation invariant, which could be regarded as intrinsic geometric variables for the mesh and remained unchanged during editing). Based on this, the original mesh could be manipulated through editing the B-spline base surface and multi-resolution editing could be archived easily. Gen-eralizing DFFD method to the framework, the direct mesh manipulation could also be implemented effectively.Furthermore, the extractive local variables could be mapped to different meshes’ base surfaces. The framework also can realize the geometric detail transfer. Experimental results demonstrate that our method provides intuitive and powerful operations for both global and local mesh editing. Since the hierarchical B-splines are widely applied, our method can be seamlessly integrated into current animation and modelling systems.更多还原