Problem with Delaunay triangulation in Extend Graphics package

*To*: mathgroup at smc.vnet.net*Subject*: [mg39650] Problem with Delaunay triangulation in Extend Graphics package*From*: jrome at mail.com (Jacob Rome)*Date*: Thu, 27 Feb 2003 00:31:25 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I've been using the excellent Delaunay triangulation routine from TWJ's ExtendGraphics package. I started having a problem with the undtion Delaunay[], which would seemingly send the routine into a loop, and it would stop responding. I noticed another problem, too, whereas after triangulating a region "A", a point "B" contained within region "A" was found to not be within any of the delaunay triangles; I have checks in place for collinearity and coincidence, so I could not figure out the problem. While repeatable for a given set of points, these problems would not occur consistently between <i>similar</i> sets of point. So I wrote a routine to run some simple cheks on the algorithm. One set of tests was to see what would happen if I specified repeated points. I wrote the following: << ExtendGraphics`Delaunay` a = {{1, 1}, {2, 2}, {1, 2}, {0, 3}, {4, 1}, {10, 5}, {9, 6}, {5, 5}, {3,5}, {4, 3}}; hull1 = Delaunay[a][[1]]; hull2 = Delaunay[Join[a, {a[[1]]}]][[1]]; h1Plot = Table[a[[hull1[[i]]]], {i, Length[hull1]}]; h2Plot = Table[a[[hull2[[i]]]], {i, Length[hull2]}]; j1 = ListPlot[h1Plot, PlotJoined -> True]; j2 = ListPlot[h2Plot, PlotJoined -> True]; Show[{j1, j2}]; When execting the program, it generates convex hull plots, which should be identical. But they are not. Could this issue with repeated points be at the root of my problem?