Plotting a 3D list causes kernel to crash if x and y axes have vastly different scales

Question

Bug introduced in 7.0.1 or earlier and fixed in 10.0.2 or earlier

---

I have access to two versions of Mathematica, version 7.0.1 on Linux and version 8 on Windows. When I try the following two lines on version 7, the kernel quits when it tries to plot. In version 8 it plots just fine. You can import the data using:

temp = Import["http://pastie.org/pastes/6098244/download", "Table"];

Any idea why this crashes in version 7?

ListContourPlot[temp]

It may also crash in Mathematica 7 for Windows too, but I don't personally have a copy of that on my machine.

ETA: Other users have reported this also crashes in some versions 8 and 9 across different platforms, so I changed the name of the post accordingly.

---

If the pastebin link fails, please copy the data from here:

temp={{-0.1,11000,1.00214},{-0.1,11050,0.998176},
{-0.1,11100,0.994088},{-0.1,11150,0.990016},{-0.1,11200,0.986111},
{-0.1,11250,0.982526},{-0.1,11300,0.979411},{-0.1,11350,0.976904},
{-0.1,11400,0.97513},{-0.1,11450,0.974195},{-0.1,11500,0.974179},
{-0.1,11550,0.975137},{-0.1,11600,0.977087},{-0.1,11650,0.98002},
{-0.1,11700,0.983885},{-0.1,11750,0.988602},{-0.1,11800,0.994051},
{-0.1,11850,1.00008},{-0.1,11900,1.00652},{-0.1,11950,1.01315},
{-0.1,12000,1.01975},{-0.1,12050,1.02608},{-0.1,12100,1.03189},
{-0.1,12150,1.03694},{-0.1,12200,1.04098},{-0.1,12250,1.04378},
{-0.1,12300,1.04513},{-0.1,12350,1.04486},{-0.1,12400,1.04282},
{-0.1,12450,1.03889},{-0.1,12500,1.03303},{-0.1,12550,1.02522},
{-0.1,12600,1.01549},{-0.1,12650,1.00392},{-0.1,12700,0.990664},
{-0.1,12750,0.975894},{-0.1,12800,0.959842},{-0.1,12850,0.942777},
{-0.1,12900,0.924999},{-0.1,12950,0.906838},{-0.1,13000,0.888643},
{-0.1,13050,0.870773},{-0.1,13100,0.853588},{-0.1,13150,0.837442},
{-0.1,13200,0.822673},{-0.1,13250,0.809592},{-0.1,13300,0.798481},
{-0.1,13350,0.789577},{-0.1,13400,0.783075},{-0.1,13450,0.779116},
{-0.1,13500,0.777787},{-0.098,11000,0.990164},{-0.098,11050,0.986921},
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{-0.068,12000,0.999991},{-0.068,12050,0.999991},{-0.068,12100,0.999991},
{-0.068,12150,0.999991},{-0.068,12200,0.999991},{-0.068,12250,0.999991},
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{-0.062,12300,0.999999},{-0.062,12350,0.999999},{-0.062,12400,0.999999},
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{-0.06,11550,1.},{-0.06,11600,1.},{-0.06,11650,1.},{-0.06,11700,1.},
{-0.06,11750,1.},{-0.06,11800,1.},{-0.06,11850,1.},{-0.06,11900,1.},
{-0.06,11950,1.},{-0.06,12000,1.},{-0.06,12050,1.},{-0.06,12100,1.},
{-0.06,12150,1.},{-0.06,12200,1.},{-0.06,12250,1.},{-0.06,12300,1.},
{-0.06,12350,1.},{-0.06,12400,1.},{-0.06,12450,1.},{-0.06,12500,1.},
{-0.06,12550,1.},{-0.06,12600,1.},{-0.06,12650,1.},{-0.06,12700,1.},
{-0.06,12750,1.},{-0.06,12800,1.},{-0.06,12850,1.},{-0.06,12900,1.},
{-0.06,12950,1.},{-0.06,13000,1.},{-0.06,13050,1.},{-0.06,13100,1.},
{-0.06,13150,1.},{-0.06,13200,1.},{-0.06,13250,1.},{-0.06,13300,1.},
{-0.06,13350,1.},{-0.06,13400,1.},{-0.06,13450,1.},{-0.06,13500,1.}};

Answer 1

You can use the undocumented Method option "DelaunayDomainScaling" to deal with the problem. I don't know any details but I assume it works by rescaling the data inside the triangulation algorithm:

ListContourPlot[temp, Method -> {"DelaunayDomainScaling" -> True}, PlotRange -> All]

Answer 2

It turns out to indeed be a problem with the triangulation algorithm. I figured it out by plotting the list incrimentally as in ListContourPlot[temp[[;;n]]] and found it would plot for n<103 but then gave an error "The data generates an inconsistent triangulation. You can perturb the data to make it valid." Alexey Popkov gave the suggestion of perturbing the data with some artificial noise, but that isn't necessary in this case.

Searching that error message took me to this page which suggested I could rescale the x and y values to lie between 0 and 1, and then it would plot just fine. Something about the difference in range in the x and y dimensions short-circuited it. I tried the method listed there and it worked just fine.

maxmin={Min[#],Max[#]}&/@Transpose[temp][[{1,2}]];

rescaled=Transpose[{
   Rescale[temp[[All,1]]],Rescale[temp[[All,2]]],temp[[All,3]]
}];

Then to do a contour plot of the rescaled data (which works without error), and apply a rescaling directly to the axis of the resulting plot:

gr=ListContourPlot[rescaled,PlotRange->All];

gr/.GraphicsComplex[a__]:> GeometricTransformation[
      GraphicsComplex[a], RescalingTransform[{{0,1},{0,1}},maxmin]]

A 3D plot like this:

gr=ListPlot3D[rescaled,PlotRange->All];
gr/.GraphicsComplex[a__]:>GeometricTransformation[
      GraphicsComplex[a], RescalingTransform[{{0,1},{0,1},{0,1}},Append[maxmin,{0,1}]]]

Answer 3

I also had such problem in version 7 when the data grid is too regular. I think it is a limitation of the triangulation algorithm used in v.7. To avoid this you could try to perturbate original grid a bit by adding a small random noise to the {x ,y} values: Patrick Scheibe's method, Peter Pein's method. Another possibility is to use Interpolation with InterpolationOrder->1 and ContourPlot instead of ListContourPlot.