Interactive Control of Mesh Topology in Quadrilateral Mesh Generation Based on 2D Tensor Fields
Interactive Control of Mesh Topology in Quadrilateral Mesh Generation Based on 2D Tensor Fields
复制标题
DOI：
10.1007/978-3-642-33191-6_72
复制
发表时间：
2012-07
期刊：
影响因子：
--
通讯作者：
Chongke Bi;Daisuke Sakurai;Shigeo Takahashi;K. Ono
中科院分区：
文献类型：
--
作者：
Chongke Bi;Daisuke Sakurai;Shigeo Takahashi;K. Ono
四边形网格剖分在有限元分析、B样条曲面拟合等工业应用中具有重要意义。然而，在四边形网格中设计适当的顶点连通性，同时考虑目标物体及其边界的形状，仍然是一个具有挑战性的任务。本文提出了一种在四边形网格中通过在目标物体内部引入二维扩散张量场来交互编辑这种网格拓扑的方法。其基本思想是首先跟踪张量场的两个主方向，然后构造四边形网格的对偶图，这样就可以通过设计底层的二维扩散张量场来控制网格的拓扑结构。我们的方法通过编辑目标对象边界上张量样本的方向来提供这种网格拓扑的交互式控制。此外，它还允许我们有意地将简并嵌入对象内部以引入异常（即，非四度）顶点。
Generating quadrilateral meshes is very important in many industrial applications such as finite element analysis and B-spline surface fitting. However, it is still a challenging task to design appropriate vertex connectivity in the quadrilateral meshes by respecting the shapes of the target object and its boundary. This paper presents an approach for interactively editing such mesh topology in quadrilateral meshes by introducing a 2D diffusion tensor field to the interior of the target object. The primary idea is to track the two principal directions of the tensor field first and then construct the dual graph of the quadrilateral mesh, so that we can control the mesh topology through the design of the underlying 2D diffusion tensor field. Our method provides interactive control of such mesh topology through editing the orientations of the tensor samples on the boundary of the target object. Furthermore, it also allows us to intentionally embed degeneracy inside the object to introduce extraordinary (i.e., non-degree-four) vertices according to user requirements.