On finite element mesh reconstruction from nodal coordinates

Abstract In several applications it is necessary to describe continuous fields on domains of arbitrary geometry for which there are discrete data (coordinates and properties) available on a large number of points. In some instances this data is recorded from field observations made by hydrographic stations and released as charts. A common practice to input these coordinates into a computing environment is to use digital tables. Assuming there is properly distributed yet unstructured data, a finite element mesh representation of it would be a multi-purpose and valuable tool. In fact, it can be used as the input of many other tasks of finite element analysis, pre-processing, contour plotting, etc. Establishing the connectivity of a finite element mesh, when generated manually, is a tedious process limited to a few tens of points, and gives rise to a large number of errors. Therefore, an automatic process to do this job is fundamental. This is, however, a rather difficult and tricky problem to solve efficiently. In this paper we are concerned with an algorithm for the automatic generation of meshes of straight-sided quadrilaterals and eventually some triangles from given (unchanged) nodal coordinates. The technique is applicable to non-convex hulls of points.