2
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I'm trying to plot a Finite Element Solution of a plate with a hole using the function ListContourPlot, but I'm facing a problem in some regions of the plot. When i plot the solution the circular boundary of the hole does not appears.

Here is the code:

data={{700.,0.,0.42875396232391694},{960.842147,297.433445,-37.36615695497536},{702.566555,39.1578526,0.6852999723580719},{922.354298,289.777724,-32.921302483206546},{710.222276,77.6457021,1.2272651242461134},{722.836172,114.805011,1.4860129142809595},{740.192414,149.999975,0.779956736723524},{761.994034,182.628398,-1.5130293945326856},{787.868,212.132,-5.717113487281527},{817.371602,238.005966,-11.737458821188556},{850.000025,259.807586,-18.982640830979022},{885.194989,277.163828,-26.430027673541563},{608.692458,0.,0.02023692134820343},{1000.,343.343137,-28.7995173103202},{555.858732,0.,-1.6915856678101096},{1000.,391.307542,-22.403326277005934},{497.956591,0.,-3.451955910168312},{1000.,444.141268,-18.405768006592677},{434.852286,0.,-5.070814274703965},{1000.,502.043409,-15.77897532781538},{366.494367,0.,-6.487613191833915},{1000.,565.147714,-13.932473155429127},{1000.,1000.,-5.9290637554562755},{71.4285714,1000.,-9.982885734346524},{0.,71.4285714,-10.053631580082289},{928.571429,1000.,-6.08348550647138},{142.857143,1000.,-9.961961169842333},{0.,142.857143,-10.042010588655344},{857.142857,1000.,-6.507074513708224},{214.285714,1000.,-9.97803416153116},{0.,928.571429,-9.996728276601186},{0.,214.285714,-10.026394257904844},{785.714286,1000.,-7.122407771412628},{285.714286,1000.,-9.995650249882374},{0.,857.142857,-9.99149959690205},{0.,285.714286,-10.010004175552332},{714.285714,1000.,-7.826319682554508},{357.142857,1000.,-9.962585529343455},{0.,785.714286,-9.986229414721237},{0.,357.142857,-9.99540146985172},{642.857143,1000.,-8.514460194914406},{428.571429,1000.,-9.826319199954693},{0.,714.285714,-9.980941336634517},{0.,428.571429,-9.984607382642643},{571.428571,1000.,-9.10484451678646},{500.,1000.,-9.54629776929175},{0.,642.857143,-9.977322459785094},{0.,500.,-9.978104919109866},{0.,571.428571,-9.975865874263468},{293.195493,0.,-7.6915814467642525},{1000.,633.505633,-12.50586998503262},{1000.,853.402253,-8.983078010985944},{73.2988733,0.,-9.851467940743001},{219.89662,0.,-8.633573428731918},{146.597747,0.,-9.355098896543701},{1000.,706.804507,-11.276798631313433},{1000.,780.10338,-10.150477366086703},{910.205363,332.183684,-25.97460036606055},{868.003901,317.519566,-22.993130270042556},{830.865369,296.981879,-19.505956912130138},{795.683229,273.614209,-15.495351920638466},{762.184855,245.552232,-11.48928574495261},{730.698516,213.064313,-7.8417717835725185},{704.253655,175.900235,-4.733727267686217},{683.403268,134.767573,-2.1994180457972696},{659.841275,45.8253581,0.6969770552635137},{668.560442,91.3969199,-0.3940912075347751},{948.124782,389.208372,-22.042086233662445},{941.513279,444.367746,-18.186858074067693},{937.296039,506.380641,-15.601526123240786},{558.124853,59.0748099,-2.339276547928968},{498.083274,64.4749564,-4.0621489854515795},{929.283811,928.309738,-7.695645501021768},{858.676835,929.791496,-7.919190286573397},{935.061861,572.071533,-13.807176693769541},{432.568315,67.461616,-5.569213999696164},{788.132559,930.346902,-8.280745308418629},{717.557452,930.276204,-8.711060927621798},{71.0919422,143.416464,-9.904899046288568},{362.558131,69.5914342,-6.860896068365187},{70.1688403,213.994414,-9.948587426036047},{144.693134,71.8763527,-9.420207949438614},{217.25563,71.682884,-8.771359224719983},{290.107887,70.5819819,-7.92213073775015},{144.406863,927.6824,-10.027618344938881},{216.220417,927.906944,-10.06205833219897},{287.550619,928.177171,-10.084874307721305},{359.637119,928.385792,-10.067841842153078},{431.713599,928.546456,-9.980517570984434},{503.842686,928.83322,-9.799146536494549},{646.622226,929.765853,-9.142044221559773},{576.127998,929.548429,-9.510961610815393},{933.504703,641.729194,-12.411350247716463},{932.220342,713.157249,-11.230571011411932},{930.886896,784.940316,-10.12974077286325},{69.1661466,284.698629,-9.991883271115595},{69.0494999,355.664579,-10.026928058570054},{68.7841077,426.520435,-10.050466084978462},{68.8360552,498.076877,-10.062281951214766},{69.3972679,569.995386,-10.063593001180672},{69.9104876,641.803622,-10.056524886854211},{71.1261657,713.318647,-10.046051119343723},{71.2467165,784.985208,-10.03138563538349},{71.9644414,856.517609,-10.01818310622691},{621.041441,104.891055,-2.356485087311265},{847.014746,362.986623,-20.043704096192865},{810.99402,336.14116,-18.780286425353236},{773.321434,313.37371,-16.64862296032539},{637.047914,156.343016,-4.965032735982325},{661.11608,205.437849,-8.100392182909065},{733.23341,285.423743,-14.15512381820734},{694.359845,249.652629,-11.290882531064666},{504.002587,130.296097,-5.6475811825880005},{433.914846,137.572367,-6.7982146354379385},{141.091767,213.240936,-9.754101836594396},{214.639648,142.218807,-9.079625271775646},{139.269704,283.727305,-9.941656235603594},{138.247745,354.296395,-10.097387029865232},{861.938288,788.024547,-10.224141481946425},{361.061956,140.322139,-7.695237012656498},{287.583785,141.275443,-8.451949003716114},{864.170648,716.668164,-11.310040696677895},{790.472549,859.645687,-9.36363113894425},{720.557592,860.233814,-9.63237558973346},{649.946313,859.23878,-9.906091061320275},{578.436229,858.031321,-10.126318237024027},{506.272401,857.160807,-10.265856249652677},{433.714678,857.047102,-10.321652276000787},{361.267526,856.925566,-10.311005539222535},{144.842918,855.779696,-10.086232090150343},{288.630655,856.415949,-10.253115821135804},{144.211171,784.223866,-10.147599484865365},{137.877313,425.667626,-10.207558001588042},{142.734706,712.681506,-10.207966437666556},{141.09758,640.563633,-10.256861582242397},{137.837961,496.681433,-10.264776583343465},{139.22669,568.912889,-10.279026258876264},{866.578232,645.723196,-12.469087019701417},{869.446701,575.028582,-13.827087129361509},{873.488809,504.676772,-15.574457601060127},{881.252019,437.425912,-17.976805036201885},{792.549648,370.355358,-17.807694711092072},{702.931198,334.831284,-15.1975140094407},{649.579139,297.648376,-13.070082210980727},{607.888018,239.230408,-10.025942034800611},{581.905995,178.609965,-6.842419973758177},{795.620656,717.797506,-11.45777135935922},{723.423906,789.43128,-10.587599125723909},{652.48312,787.587228,-10.762250466570068},{580.010007,785.83366,-10.857497006102511},{506.334631,784.205532,-10.858273859720903},{432.500324,784.574053,-10.767756133740377},{209.668024,283.077487,-9.87300057222792},{207.420901,354.024842,-10.206007171012459},{359.693137,785.085124,-10.628752038934953},{287.916309,784.603457,-10.467734398912052},{206.639437,425.17224,-10.43592071131275},{207.103706,496.842811,-10.557477007528618},{208.573953,568.411103,-10.582222643752939},{211.517379,640.701037,-10.533628687528724},{214.503907,712.619879,-10.431990369229043},{814.274583,417.090776,-17.487998685495317},{807.249826,497.328825,-15.540293166030798},{798.70837,645.660086,-12.608417657557622},{802.519899,572.74778,-13.928978390297395},{439.079093,215.49007,-8.622432760655578},{285.372858,213.070458,-9.144953562360852},{360.359637,214.224174,-8.80607835699459},{729.511696,641.546114,-12.742178873154947},{654.921525,714.445849,-11.698895119683042},{581.51989,709.238728,-11.699450783880595},{505.855176,705.006333,-11.54393921587805},{356.487598,712.55908,-10.959490049352882},{430.104499,708.942013,-11.255584549735898},{281.512914,641.006604,-10.863395730685264},{734.288431,567.141339,-13.962914372292857},{739.554952,491.044962,-15.283883720380576},{745.998184,416.897295,-16.413781733649422},{276.327957,355.339039,-10.385597333509649},{274.846997,425.656538,-10.746370184373395},{275.363472,497.106469,-10.929021737714407},{277.489811,569.200686,-10.95500723326394},{592.998744,371.114769,-13.617760709376785},{357.07627,291.125503,-9.939274999662011},{446.46894,312.447107,-10.793883504081435},{343.165323,426.198669,-11.162807153616324},{344.332074,497.455832,-11.39525578874747},{665.207489,558.017045,-13.83586329338504},{592.998744,371.114769,-13.542139922790657},{670.682089,479.418464,-14.808690795228571},{400.756894,365.052702,-11.205655124250482},{585.296389,625.693833,-12.643452312581674},{425.111072,631.205528,-11.68832943732313},{504.0016,611.806422,-12.28476895416098},{347.138821,568.647446,-11.398818614887249},{600.47466,466.376795,-14.00078013734896},{530.846578,531.198601,-13.064791072533476},{465.198553,559.150719,-12.317028435335871},{412.119426,496.903791,-11.952314259788437},{475.669133,500.742001,-12.6098701221251}};
ListContourPlot[data, 
  ColorFunction -> "TemperatureMap", 
  AspectRatio -> Automatic, 
  PlotLegends -> Automatic, 
  PlotRange -> {10, -40}, 
  Contours -> 25]

The solution is looking like this:

enter image description here

While it should look like this(Solution from Ansys):

enter image description here

Any hints?

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  • $\begingroup$ Qualitatively they look very similar. Which part are you dissatisfied with? $\endgroup$ – Marius Ladegård Meyer Jan 8 '17 at 23:32
  • $\begingroup$ There is a hole in the right down corner that is not appearing. $\endgroup$ – Diogo Jan 8 '17 at 23:36
  • 2
    $\begingroup$ That hole seems to be some excluded region from the solution, but without the boundary conditions and equations used to produce the data you provide, then how can we know? $\endgroup$ – Marius Ladegård Meyer Jan 8 '17 at 23:54
  • $\begingroup$ The problem is not with the solution, but with the plot. Note that in the left down corner there is also a blank region $\endgroup$ – Diogo Jan 9 '17 at 0:29
  • 3
    $\begingroup$ Here is the workaround I spoke of: mathematica.stackexchange.com/a/110002/9490 . essentially, you need to restrict the plotting region to the concave hull, or alpha shape, rather than the convex hull $\endgroup$ – Jason B. Jan 9 '17 at 2:03
4
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As user9490 pointed out in the comments, there is missing data around the corners:

Graphics[Point[data[[All, 1 ;; 2]]]]

enter image description here

It looks as though ListContourPlot plots over the convex hull of the data, so to get the corners I think we need to manually extrapolate.

missingpts = {{0, 0}, {0, 1000}, {1000, 300}};
newvals = Mean /@ Nearest[data[[All, 1 ;; 2]] -> data[[All, 3]], missingpts, 2];

newdata = MapThread[Append, {missingpts, newvals}]
{{0, 0, -9.95255}, {0, 1000, -9.98981}, {1000, 300, -33.0828}}
data = Join[data, newdata];

Lastly, we can remove the extraneous data near the circle with the option RegionFunction -> Function[{x, y}, ! Element[{x, y}, Disk[{1000, 0}, 300]].

Here's the resulting plot:

ListContourPlot[data, ColorFunction -> "TemperatureMap", 
 AspectRatio -> Automatic, PlotLegends -> Automatic, 
 PlotRange -> {10, -40}, Contours -> 25, 
 RegionFunction -> Function[{x, y}, ! Element[{x, y}, Disk[{1000, 0}, 300]]]]

enter image description here

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2
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Update

Let's look at your data space with an normal 3D plot.

ListPlot3D[data,
 PlotTheme -> "ZMesh",
 PlotStyle -> White,
 Boxed -> False,
 Axes -> False,
 ClippingStyle -> None,
 ViewPoint -> {0, 0, 100},
 SphericalRegion -> True,
 Lighting -> "Neutral"]

3Dplot

You can see you have really nasty behavior at the bottom right. Because you tell us nothing about how you obtained the data points, I don't know whether your data truly reflects the physics of the problem or is exhibiting artifacts of your computation method. But it is clear to me that the contour plot made by

ListContourPlot[data,
  ColorFunction -> "BrightBands",
  PlotRange -> {-26.5, -2.5},
  PlotLegends -> Automatic,
  MaxPlotPoints -> 100,
  InterpolationOrder -> 1,
  Contours -> Range[-29.5, .5, 3],
  FrameStyle -> White,
  Background v Black,
  ImageMargins v 5]

contours

gives an accurate visualization of your data. Placing a black sector of a circle on the lower right area seems to me to be just covering the bad area with a bit of carpeting.

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  • $\begingroup$ 's thank you for the answer, but this os not what i want. I need the circular boundary to be show.. $\endgroup$ – Diogo Jan 9 '17 at 1:53
  • $\begingroup$ m_goldberg, I think the issue might be that Mathematica is plotting in a region where there are no points.... $\endgroup$ – Jason B. Jan 9 '17 at 1:57
  • 1
    $\begingroup$ I agree with @user9490. Executing ListPlot[data[[All, {1, 2}]], AspectRatio -> 1] shows the circular region that the OP wants excluded. However, regions to be excluded are in the mind of the beholder. There are lots of potential data gaps in the interior of the data (at least there are in my mind). But Mathematica can only exclude areas if you tell it that there's a hard border. That information is not intrinsic to the set of data points. $\endgroup$ – JimB Jan 9 '17 at 6:44
0
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I found an improvised solution. I plot a disk in the region were the solution shouldn't exists. But still there is the corners problem. Here is the code:

data = {{700., 0., 0.42875396232391694}, {960.842147, 
297.433445, -37.36615695497536}, {702.566555, 39.1578526, 
0.6852999723580719}, {922.354298, 
289.777724, -32.921302483206546}, {710.222276, 77.6457021, 
1.2272651242461134}, {722.836172, 114.805011, 
1.4860129142809595}, {740.192414, 149.999975, 
0.779956736723524}, {761.994034, 
182.628398, -1.5130293945326856}, {787.868, 
212.132, -5.717113487281527}, {817.371602, 
238.005966, -11.737458821188556}, {850.000025, 
259.807586, -18.982640830979022}, {885.194989, 
277.163828, -26.430027673541563}, {608.692458, 0., 
0.02023692134820343}, {1000., 
343.343137, -28.7995173103202}, {555.858732, 
0., -1.6915856678101096}, {1000., 
391.307542, -22.403326277005934}, {497.956591, 
0., -3.451955910168312}, {1000., 
444.141268, -18.405768006592677}, {434.852286, 
0., -5.070814274703965}, {1000., 
502.043409, -15.77897532781538}, {366.494367, 
0., -6.487613191833915}, {1000., 
565.147714, -13.932473155429127}, {1000., 
1000., -5.9290637554562755}, {71.4285714, 
1000., -9.982885734346524}, {0., 
71.4285714, -10.053631580082289}, {928.571429, 
1000., -6.08348550647138}, {142.857143, 
1000., -9.961961169842333}, {0., 
142.857143, -10.042010588655344}, {857.142857, 
1000., -6.507074513708224}, {214.285714, 
1000., -9.97803416153116}, {0., 
928.571429, -9.996728276601186}, {0., 
214.285714, -10.026394257904844}, {785.714286, 
1000., -7.122407771412628}, {285.714286, 
1000., -9.995650249882374}, {0., 
857.142857, -9.99149959690205}, {0., 
285.714286, -10.010004175552332}, {714.285714, 
1000., -7.826319682554508}, {357.142857, 
1000., -9.962585529343455}, {0., 
785.714286, -9.986229414721237}, {0., 
357.142857, -9.99540146985172}, {642.857143, 
1000., -8.514460194914406}, {428.571429, 
1000., -9.826319199954693}, {0., 
714.285714, -9.980941336634517}, {0., 
428.571429, -9.984607382642643}, {571.428571, 
1000., -9.10484451678646}, {500., 1000., -9.54629776929175}, {0., 
642.857143, -9.977322459785094}, {0., 
500., -9.978104919109866}, {0., 
571.428571, -9.975865874263468}, {293.195493, 
0., -7.6915814467642525}, {1000., 
633.505633, -12.50586998503262}, {1000., 
853.402253, -8.983078010985944}, {73.2988733, 
0., -9.851467940743001}, {219.89662, 
0., -8.633573428731918}, {146.597747, 
0., -9.355098896543701}, {1000., 
706.804507, -11.276798631313433}, {1000., 
780.10338, -10.150477366086703}, {910.205363, 
332.183684, -25.97460036606055}, {868.003901, 
317.519566, -22.993130270042556}, {830.865369, 
296.981879, -19.505956912130138}, {795.683229, 
273.614209, -15.495351920638466}, {762.184855, 
245.552232, -11.48928574495261}, {730.698516, 
213.064313, -7.8417717835725185}, {704.253655, 
175.900235, -4.733727267686217}, {683.403268, 
134.767573, -2.1994180457972696}, {659.841275, 45.8253581, 
0.6969770552635137}, {668.560442, 
91.3969199, -0.3940912075347751}, {948.124782, 
389.208372, -22.042086233662445}, {941.513279, 
444.367746, -18.186858074067693}, {937.296039, 
506.380641, -15.601526123240786}, {558.124853, 
59.0748099, -2.339276547928968}, {498.083274, 
64.4749564, -4.0621489854515795}, {929.283811, 
928.309738, -7.695645501021768}, {858.676835, 
929.791496, -7.919190286573397}, {935.061861, 
572.071533, -13.807176693769541}, {432.568315, 
67.461616, -5.569213999696164}, {788.132559, 
930.346902, -8.280745308418629}, {717.557452, 
930.276204, -8.711060927621798}, {71.0919422, 
143.416464, -9.904899046288568}, {362.558131, 
69.5914342, -6.860896068365187}, {70.1688403, 
213.994414, -9.948587426036047}, {144.693134, 
71.8763527, -9.420207949438614}, {217.25563, 
71.682884, -8.771359224719983}, {290.107887, 
70.5819819, -7.92213073775015}, {144.406863, 
927.6824, -10.027618344938881}, {216.220417, 
927.906944, -10.06205833219897}, {287.550619, 
928.177171, -10.084874307721305}, {359.637119, 
928.385792, -10.067841842153078}, {431.713599, 
928.546456, -9.980517570984434}, {503.842686, 
928.83322, -9.799146536494549}, {646.622226, 
929.765853, -9.142044221559773}, {576.127998, 
929.548429, -9.510961610815393}, {933.504703, 
641.729194, -12.411350247716463}, {932.220342, 
713.157249, -11.230571011411932}, {930.886896, 
784.940316, -10.12974077286325}, {69.1661466, 
284.698629, -9.991883271115595}, {69.0494999, 
355.664579, -10.026928058570054}, {68.7841077, 
426.520435, -10.050466084978462}, {68.8360552, 
498.076877, -10.062281951214766}, {69.3972679, 
569.995386, -10.063593001180672}, {69.9104876, 
641.803622, -10.056524886854211}, {71.1261657, 
713.318647, -10.046051119343723}, {71.2467165, 
784.985208, -10.03138563538349}, {71.9644414, 
856.517609, -10.01818310622691}, {621.041441, 
104.891055, -2.356485087311265}, {847.014746, 
362.986623, -20.043704096192865}, {810.99402, 
336.14116, -18.780286425353236}, {773.321434, 
313.37371, -16.64862296032539}, {637.047914, 
156.343016, -4.965032735982325}, {661.11608, 
205.437849, -8.100392182909065}, {733.23341, 
285.423743, -14.15512381820734}, {694.359845, 
249.652629, -11.290882531064666}, {504.002587, 
130.296097, -5.6475811825880005}, {433.914846, 
137.572367, -6.7982146354379385}, {141.091767, 
213.240936, -9.754101836594396}, {214.639648, 
142.218807, -9.079625271775646}, {139.269704, 
283.727305, -9.941656235603594}, {138.247745, 
354.296395, -10.097387029865232}, {861.938288, 
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708.942013, -11.255584549735898}, {281.512914, 
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491.044962, -15.283883720380576}, {745.998184, 
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479.418464, -14.808690795228571}, {400.756894, 
365.052702, -11.205655124250482}, {585.296389, 
625.693833, -12.643452312581674}, {425.111072, 
631.205528, -11.68832943732313}, {504.0016, 
611.806422, -12.28476895416098}, {347.138821, 
568.647446, -11.398818614887249}, {600.47466, 
466.376795, -14.00078013734896}, {530.846578, 
531.198601, -13.064791072533476}, {465.198553, 
559.150719, -12.317028435335871}, {412.119426, 
496.903791, -11.952314259788437}, {475.669133, 
500.742001, -12.6098701221251}};

lp=ListContourPlot[data, 
  ColorFunction -> "TemperatureMap", 
  AspectRatio -> Automatic, 
  PlotLegends -> Automatic, 
  PlotRange -> {10, -40}, 
  Contours -> 25]
    lpd = Show[
       Graphics[{GrayLevel[1], Disk[{1000, 0}, 300]}, 
        AspectRatio -> Automatic]];
    Show[lp, lpd] 

enter image description here

$\endgroup$
  • 1
    $\begingroup$ The problem with the corners is that you don't have a data point at the corners - look at the results of ListPlot[ data[[All,{1,2}]] ] $\endgroup$ – Jason B. Jan 9 '17 at 5:15

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