Constrained a Fast Algorithm for Generating Delaunay
004s7949/93 56.00 + 0.00 if) 1993 Pcrgamon Press Ltd A FAST ALGORITHM FOR GENERATING CONSTRAINED DELAUNAY TRIANGULATIONS S. W. SLOAN Department of Civil Engineering and Surveying, University of Newcastle, Shortland, NSW 2308, Australia {Received 4 March 1992) Abstract-A fast algorithm for generating constrained two-dimensional Delaunay triangulations is described. The scheme permits certain edges to be specified in the final t~an~ation, such as those that correspond to domain boundaries or natural interfaces, and is suitable for mesh generation and contour plotting applications. Detailed timing statistics indicate that its CPU time requhement is roughly proportional to the number of points in the data set. Subject to the conditions imposed by the edge constraints, the Delaunay scheme automatically avoids the formation of long thin triangles and thus gives high quality grids. A major advantage of the method is that it does not require extra points to be added to the data set in order to ensure that the specified edges are present. I~RODU~ON to be degenerate since two valid Delaunay triangu- lations are possible. Although it leads to a loss of Triangulation schemes are used in a variety of uniqueness, degeneracy is seldom a cause for concern scientific applications including contour plotting, since a triangulation may always be generated by volume estimation, and mesh generation for finite making an arbitrary, but consistent, choice between element analysis. Some of the most successful tech- two alternative patterns. niques are undoubtedly those that are based on the One major advantage of the Delaunay triangu- Delaunay triangulation. lation, as opposed to a triangulation constructed To describe the construction of a Delaunay triangu- heu~stically, is that it automati~ily avoids the lation, and hence explain some of its properties, it is creation of long thin triangles, with small included convenient to consider the corresponding Voronoi angles, wherever this is possible.
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