【作者】 郑路；

【导师】 鲍虎军； 刘新国；

【作者基本信息】 浙江大学 ， 计算机应用技术， 2006， 硕士

【摘要】 随着计算机图形学的深入发展,数字几何处理渐渐成为研究热点,很多研究成果已经得到了广泛的实际应用。 在数字几何处理中三维网格是最常用的物体形状表示方法,网格参数化是网格处理中最基本的技术,它在网格和一个恰当的参数域之间建立起——映射。在纹理映射、重网格化、网格编辑、morphing等诸多算法中都需要首先对网格进行参数化。 目前网格参数化的方法有很多,按照其参数域的形状可以分为:平面参数化、球面参数化、单形参数化,以及新近提出的polycube参数化。Polycube参数化具有相对较小的网格扭曲,因为其参数域能很好地逼近原始网格形状。同时它又是一种真正的无缝参数化方法。但是polycube形状复杂,难以构造,如何自动生成polycube参数化是一个值得研究的问题。 本文从全新的角度—网格变形—去看待polycube参数化的构建,提出了一种基于网格形变的polycube参数化自动构造方法。我们在网格表面定义了描述网格与polycube差距的能量,通过最小化该能量使原始网格形变成我们需要的polycube参数网格。该方法独特之处在于参数域的形状并不事先指定,而是在形变过程中和映射方法同时优化生成。因而在网格扭曲最小的度量下,本文的方法能产生最优的参数域和最优的映射关系。需要指出的是,我们提出了一套完整的polycube自动构造框架,文中细叙述的算法只是该框架的一个实现。 最后本文深入挖掘了polycube的在数字几何处理中的应用,如重网格化,几何压缩等等。更多还原

【Abstract】 With the rapid development of computer graphics, digital geometry processing (DGP) has received lots of interest recently, and more and more practical applications have gained benefit from its products.Mesh is the most popular representation of models in DGP and mesh parameterization which constructs an one-to-one mapping from a suitable domain to the mesh is a fundamental operation in many area, such as texture mapping, remeshing, mesh editing and morphing.According to the parameter domain, all kinds of parameterization methods can be classified into planar parameterization, spherical parameterization, simplicial parameterization or the recently proposed polycube parameterization. The distortion of polycube maps is obviously low thanks to the shape similarity between polycube domain and the original mesh. However complexity of polycube shape makes it hard to build. Constructing with too much user interactivity will limit its practical applications.In this paper, we investigate parameterization from a new point - mesh deformation - and present a framework for deformation driven automatic polycube parameterization, which deforms the original model to polycube mesh automatically by minimizing energy defined on the mesh. Unlike the other parameterization methods which build the domain firstly then map the mesh onto it, our method generates and optimizes polycube domain and mapping at the same time, which is a great characteristic of our method.Furthermore we dig out more applications of polycube, such as remeshing, geometry information compression and so on, base on our framework.更多还原