By P.L. George
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1. Quadtree-octree type methods Assuming the data of a polygonal discretization of the contour of the given domain (the two-dimensional case is considered for a simplified discussion), it is easy to construct a regular grid enclosing this polygon. Then a possible mesh can be obtained from this grid by considering its cells. Firstly, the latter are classified as follows: * those enclosed within the domain, * those which are outside the domain, * and those which are intersected by the contour or close to it.
6. The three retained patterns and associated constructions. 120 PL. George CHAPTER I in two dimensions and, * remove the faces belonging to the tetrahedron now formed, * add those which are not shared by two elements existing now, in three dimensions. The main difficulties when implementing such a method are: * determining the type of situation encountered when it is not evident, * finding an adequate location for a point when such a point must be created, or deciding what point must be connected when all points are already known.
7 (courtesy of Cisigraph) and Fig. 8 (courtesy of SDRC) illustrate two other examples of surface meshes created by the two mentioned CAD-CAM systems. CHAPTER III Automatic Method (1): Advancingfront Type Mesh Generation Introduction This class of mesh generators, adapted to arbitrary geometries, has been studied by GEORGE , L6HNER and PARIKH [1988a,b], PERAIRE, PEIRO, FORMAGGIA, MORGAN and ZIENKIEWICZ , and, more recently, by GOLGOLAB . This kind of mesh generator constructs the mesh of the domain from its boundary.