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首页> 外文期刊>International Journal for Numerical Methods in Engineering >Simple finite element-based computation of distance functions in unstructured grids
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Simple finite element-based computation of distance functions in unstructured grids

机译：非结构化网格中距离函数的基于有限元的简单计算

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摘要

A distance field is a representation of the closest distance from a point to a given surface. Distance fields are widely used in applications ranging from computer vision, physics and computer graphics and have been the subject of research of many authors in the last decade. Most of the methods for computing distance fields are devoted to Cartesian grids while little attention has been paid to unstructured grids. Finite element methods are well known for their ability to deal with partial differential equations in unstructured grids. Therefore, we propose an extension of the fast marching method for computing a distance field in a finite element context employing the element interpolation to hold the Eikonal property (parallel to del phi parallel to = 1). A simple algorithm to develop the computations is also presented and its efficiency demonstrated through various unstructured grid examples. We observed that the presented algorithm has processing times proportional to the number of mesh nodes. Copyright (c) 2007 John Wiley & Sons, Ltd.
机译：距离场表示从点到给定曲面的最接近距离。距离场被广泛用于计算机视觉，物理学和计算机图形学等领域，并且在过去十年中成为许多作者研究的主题。大多数用于计算距离场的方法都专用于笛卡尔网格，而对非结构化网格的关注却很少。有限元方法以其在非结构化网格中处理偏微分方程的能力而闻名。因此，我们提出了一种快速行进方法的扩展，该方法用于在有限元素上下文中使用元素插值来保持Eikonal属性（平行于del phi平行= 1）来计算距离场。还提出了一种用于开发计算的简单算法，并通过各种非结构化网格示例证明了其效率。我们观察到，提出的算法具有与网格节点数量成比例的处理时间。版权所有（c）2007 John Wiley＆Sons，Ltd.

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