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?