任意拓扑三角形网格的全局参数化

提出了一种零亏格的任意拓扑流形三角形网格自动全局参数化方法 .算法首先采用顶点对合并的网格简化方法构造一个网格的累进表示 ,在进行网格简化的同时 ,对被删除的顶点相对于顶点合并操作所得到的新顶点的邻域进行局部参数化 ,由此得到一个带局部参数化信息的累进网格 ;然后将网格简化所得到的基网格进行中心投影到一个单位球面上 ,并采用累进恢复的方法将删除的顶点按与删除时相反的顺序逐次添加回网格上来 ,所添加顶点的坐标不再是其删除前的坐标值 ,而是由局部参数化信息计算得到 ,并且保证是位于单位球面上的 .由此得到原始网格的单位球面参数化网格

Global Parameterization of Triangle Meshes with Arbitrary Topology

Mesh parameterization is a primary task in many computer graphics applications, such as texture mapping, digital geometry processing and geometry compression, etc. This paper proposes a global parameterization method of meshes with arbitrary topology. For a given manifold triangle mesh with zero genus, it is firstly turned into a PM representation by means of edge collapse, the two vertices of the age to collapse are locally parameterized over the neighborhood of the new vertex obtained through pair contraction. Edge collapse is iteratively carried out until a simple convex base mesh with local parameterization information is reached, then this base mesh is center protected onto a unit sphere, and vertices deleted during edge collapse are added back and positioned on the unit sphere according to the local parameterization information one by one with an inverse order which they are deleted until an isomorphic mesh of original mesh is produced. By this means, global parameterization over the unit sphere of the original mesh is completed. To avoid fold back, relaxation operator is adopted.