The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not self-intersecting. However, due to numerical and/or user error, input surfaces are commonly self-intersecting to some degree. The removal of self-intersection is a burdensome task that complicates workflow and generally slows down the process of creating simulation-ready digital assets. We present a method for the creation of a volumetric embedding hexahedron mesh from a self-intersecting input triangle mesh. Our method is designed for efficiency by minimizing use of computationally expensive exact/adaptive precision arithmetic. Although our approach allows for nearly no limit on the degree of self-intersection in the input surface, our focus is on efficiency in the most common case: many minimal self-intersections. The embedding hexahedron mesh is created from a uniform background grid and consists of hexahedron elements that are geometrical copies of grid cells. Multiple copies of a single grid cell are used to resolve regions of self-intersection/overlap. Lastly, we develop a novel topology-aware embedding mesh coarsening technique to allow for user-specified mesh resolution as well as a topology-aware tetrahedralization of the hexahedron mesh.
翻译:代表输入多边形网格的内部的体积网格的创建体积网格是图形和计算机械应用中常见的一项要求。大多数网格创造技术都假定输入表面不是自我交叉的。然而,由于数字和(或)用户错误,输入表面通常具有某种程度的自我交叉作用。清除自我交叉是一个繁重的任务,它使工作流程复杂化,通常会减缓创建模拟可用数字资产的过程。我们提出了一个方法,用来从自互解输入三角网格中创建体积嵌入六氟赫德罗网格。我们的方法是为了提高效率,尽量减少使用计算成本昂贵的精确/适应精确的计算方法。然而,由于我们的方法几乎没有限制输入表面的自我交叉程度,我们的重点是在最常见的情况下的效率:许多最起码的自我间隙。嵌入的六氟化网格是由统一的背景网格中创建的,由构成电格细胞几何成的六氟化元素组成。一个单一网格格格系的多份副本,用来通过尽量减少计算精确精确精确的精确算法来提高效率。虽然我们的方法几乎没有限制投入表面的内存程度,但我们的内压的内层的内存,但是的内建的内建的内建的内建的内存系统,作为最后用于解的内建的内层的内建的内建的内建的内建的内建的内研。