The integrity of geometrical boundaries in the two‐dimensional delaunay triangulation

The Delaunay triangulation has recently received attention as a viable method for construction computational meshes. However, an arbitrary boundary definition which must be preserved in the triangulation process will not, in general, satisfy the geometrical definition on which the Delaunay construction is founded. The effect of this is that the integrity of the given boundary edges will be violated and the computational mesh will not conform to the applied geometrical shape. A method is proposed whereby boundary data are supplemented with points to ensure that imposed boundary edges are preserved during the Delaunay triangulation. The method is illustrated on a geometry of an estuary which exhibits highly complex geometrical features.