中轴变换是一种重要的隐式形状表达方法，中轴网格则是中轴变换的一种扩展。与传统的中轴变换相比，中轴网格具有表达的精确性，简洁性，对称性以及多分辨率等优点。本申请拟研究中轴网格的计算理论、算法及其在几何领域的应用。主要研究内容包括，一、研究使用相对稀疏的采样点生成初始中轴网格的计算方法，研究如何在对中轴网格进行简化的过程中保持尖锐特征的算法。二、研究三维动画序列模型的统一中轴网格的计算与简化方法，探索用中轴网格取代当前流行的三维动画骨骼框架的可能性。三、研究如何利用中轴网格进行三维模型的分割、协同分割以及检索的新方法。四、研究如何利用中轴网格表达以及双边蓝噪声采样算法进行三维多孔材料的合成。本申请详细论述了这些研究内容的意义和价值，并提供了可行的研究方案。预计本项目顺利开展将会形成一系列关于中轴网格计算以及在计算机图形学领域应用的新理论和新方法。

The medial axis transform (MAT) is an important implicit function for shape representation. The medial mesh is an extension to the medial axis transform. Comparing to the original MAT, the medial mesh shares many merits including its conciseness, precision, symmetry and multiresolution. We’d like to investigate the computation theory and algorithms of the medial mesh for 3D models and its applications. Firstly, we would investigate the method of using sparse sampling points to generate the initial medial mesh, and then we’d like to investigate how to keep sharp features during the simplification procedure of the medial mesh. Secondly, this project would study how to compute a unified medial mesh sequence for 3D models of an animation sequence and develop algorithms to globally decimate the unified medial mesh sequence. This study might provide an alternative to the popular skeleton based 3D model animation research. Thirdly, we’d like to device some algorithms to make use of the characteristics of medial mesh to help geometry processing such as mesh segmentation, mesh co-segmentation and shape retrieval. Fourthly, we would investigate the method to synthesize 3D porous material by examples, which would take the advantage of medial mesh and employing the bilateral blue noise sampling algorithm. We discuss the motivations and the values of these studies in this proposal and provide feasible schemes. We expect to achieve a series of new theories and new algorithms for the computation of medial mesh and its applications in the field of computer graphics.