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

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},
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{-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.}};

-
I'm not sure what you mean, the web page doesn't truncate it for me. I copy and paste the above from this window into my notebook, and then temp is defined as a list with 1071 elements. When I import the original file, it is also a list of 1071 elements. –  user5789 Feb 7 '13 at 19:33
I wanted to just link to the data, but don't know a good hosting site that allows hotlinking and is free. –  user5789 Feb 7 '13 at 19:38
@Jimbo You could post your solution as an answer and accept it. –  Alexey Popkov Feb 8 '13 at 6:21
Crash confirmed on v9.0.1 OS X 64 bit. –  Szabolcs Feb 8 '13 at 21:21
A comment from sunt05: This problem occurs only on 64-bit systems. I tested the problem on different machines with 32-bit systems and found they all work. Is this a bug? –  Mr.Wizard Feb 25 '13 at 12:52

## 3 Answers

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]


-
That's great. Would there be any downside to having the program automatically initialize this option for a few commonly used functions? If I wanted to have the line SetOptions[ListContourPlot, Method -> {"DelaunayDomainScaling" -> True}]; read in every time the kernel is initialized, what file do I need to edit? –  user5789 Feb 9 '13 at 0:56
@Jimbo, you would need to edit the kernel init.m file. It is located in the folder given by FileNameJoin[{\$UserBaseDirectory, "Kernel"}]. I'm not sure about any unwanted side effects, the fact that this is an option rather than hard-coded into ListContourPlot suggests that there are probably cases where you don't want it. –  Simon Woods Feb 9 '13 at 8:57

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}]]]

-

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.

-
Thanks for this. I'm glad they fixed this in later versions, it is sad to have to add noise to the data in order to plot it. –  user5789 Feb 7 '13 at 19:14
FWIW, it crashed on v9.0.1 on OS X 10.8.2, so it doesn't seem like it's localized to v7 –  rm -rf Feb 7 '13 at 19:20
@rm-rf reproduced on 9.0.1 on Windows, too. And even 8.0.4. The latter takes absolutely ages but does eventually crash. –  Oleksandr R. Feb 7 '13 at 20:02
Weird, I get no error on Windows in versions 8.0.1.0 and 9.0.0.0 –  user5789 Feb 7 '13 at 20:15
InterpolationOrder->1 in my similar case mathematica.stackexchange.com/questions/45155/… does not work –  alessandro Apr 1 at 13:12