Simple finite element-based computation of distance functions in unstructured grids

• Published in: International journal for numerical methods in engineering Vol. 72; no. 9; pp. 1095 - 1110
• Main Authors: Elias, Renato N., Martins, Marcos A. D., Coutinho, Alvaro L. G. A.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 26.11.2007; Wiley
• Subjects: Computational techniques; distance function; Eikonal solvers; Exact sciences and technology; finite elements; Fundamental areas of phenomenology (including applications); level set; Mathematical methods in physics; Physics; reinitialization; Finite element method; Computer vision; Unstructured mesh; distance function; Eikonal solvers; level set; Contour line; Modelling; reinitialization; Mesh generation; finite elements; Cartesian coordinates
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2079

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 (∥∇φ∥ = 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 © 2007 John Wiley & Sons, Ltd.