UNSTRUCTURED GRID GENERATION AND A SIMPLE TRIANGULATION ALGORITHM FOR ARBITRARY 2-D GEOMETRIES USING OBJECT ORIENTED PROGRAMMING

This paper describes the logic of a dynamic algorithm for a general 2D Delaunay triangulation of arbitrarily prescribed interior and boundary nodes. The complexity of the geometry is completely arbitrary. The scheme is free of speciÞc restrictions on the input of the geometrical data. The scheme generates triangles whose associated circumcircles contain Ôno nodal points except their vertices. There is no predeÞned limit for the number of points and the boundaries. The direction of generation of the triangles cannot be determined a priori as opposed to the moving front techniques. An automatic node placement scheme reßecting the initial boundary point spacings is used. The successive reÞnement scheme results in such a point distribution that the triangulation algorithm need not perform any geometric intersection check for overlapped triangles and penetrated boundaries. Further computational saving is provided by using a special binary tree (ADT) in which the points are ordered such that contiguous points in the list are neighbours in physical space. The method consists of a set of simple rules to understand. The dynamic nature of the Object Oriented Programming (OOP) of the algorithms provides e¦cient memory management on the insertion, deletion and searching processes. The computational e¤ort bears a linear relation-ship between the CPU time and the total number of nodes. Some of the existing methods in the literature regarding triangular mesh generation are discussed in context.