三角形网格细分采样

Subdivision remeshing of triangle meshes

提出了一个网格细分采样方法.对于具有任意拓扑的亏格为零的流形三角形网格,首先在单位球面上对其进行全局参数化,然后将一个简单的正多面体进行适应性细分从而得到细分采样网格,将采样网格进行中心投影到参数单位球面上,并在采样网格顶点处对参数化网格进行重采样,从而得到一个具有细分拓扑结构和原始网格形状的新网格.具有细分结构的重采样网格不仅可用于网格简化和几何压缩,而且有利于采用细分小波对定义于其顶点上的各种数字几何信号进行处理.

Remeshing of triangle meshes is widely used in mesh simplification, geometry compression and digital geometry processing, etc., this paper proposes an novel remeshing method. For a given manifold triangle mesh with zero genus and arbitrary topology, it is firstly parameterized onto a unit sphere globally, and then a sampling mesh with subdivision topology is achieved by subdividing a icosahedron. This sampling mesh is center projected onto uint sphere, and the original mesh is re-sampled at the vertices of the sampling mesh to produce a new mesh with subdivision topology. This kind of remeshing not only can be used in geometry simplification and compression, but also is useful for processing all kinds of geometry signals defined on the vertices of meshes with subdivision wavelets.