Skip to main content

plotting - ListContourPlot interpolation screws up on concave set of data


I want to create ListContourPlots for sets of Data (from a physics simulation) given as Triplets {x, y, f(x, y)}. Certain parameter regions in the x-y-plane are excluded by experiments. The list of triplets simply does not contain any Triplets with excluded x-y-parameters. ListPointPlot3D shows that this is not the problem.



The problem is that ListContourPlot (which I prefer to use, since I have to correlate exclusions from different quantities) interpolates values into regions where no data points are given, as soon as the shape of the data-filled region becomes concave.


I already tried creating a list that is only defined in the excluded regions and painting it over the original plot, however, my dataset is not entirely concave, so that overpainting will cut off some of the interesting parts of the plot...


I figure it has something to do with the "Method" option of ListContourPlot, but those things are really badly documented.


Here is a list of 140 data triplets that show the problem.


l= {{14., 2.1, 125.433}, {14., 2.1375, 125.957}, {14., 2.175, 
  126.58}, {14., 2.2125, 127.354}, {14., 2.25, 128.415}, {14.5, 
  2.1125, 125.698}, {14.5, 2.15, 126.315}, {14.5, 2.1875, 
  127.087}, {14.5, 2.225, 128.152}, {15., 2.1, 125.593}, {15., 2.1375,
   126.238}, {15., 2.175, 127.061}, {15., 2.2125, 128.256}, {15.5, 
  2.1125, 125.886}, {15.5, 2.15, 126.669}, {15.5, 2.1875, 

  127.783}, {16., 2.1, 125.73}, {16., 2.1375, 126.534}, {16., 2.175, 
  127.708}, {16.5, 2.1125, 126.054}, {16.5, 2.15, 127.082}, {17., 2.1,
   125.829}, {17., 2.1375, 126.85}, {17.5, 2.1, 125.858}, {17.5, 
  2.1375, 127.016}, {18., 2.1, 125.868}, {18., 2.1375, 
  127.185}, {18.5, 2.1125, 126.243}, {18.5, 2.15, 128.277}, {19., 
  2.125, 126.76}, {19.5, 2.1125, 126.183}, {20., 2.1, 125.633}, {20., 
  2.1375, 127.686}, {20.5, 2.125, 126.573}, {21., 2.1125, 
  125.763}, {21.5, 2.1, 125.093}, {21.5, 2.1375, 127.062}, {22., 
  2.125, 125.806}, {22.5, 2.1125, 124.979}, {22.5, 2.15, 
  127.707}, {23., 2.125, 125.111}, {23.5, 2.1, 124.03}, {23.5, 2.1375,

   125.248}, {24., 2.1, 123.738}, {24., 2.1375, 124.82}, {24.5, 2.1, 
  123.445}, {24.5, 2.1375, 124.411}, {24.5, 2.175, 126.896}, {25., 
  2.125, 123.689}, {25., 2.1625, 124.924}, {25.5, 2.1125, 
  123.092}, {25.5, 2.15, 123.987}, {25.5, 2.1875, 125.801}, {26., 
  2.125, 123.022}, {26., 2.1625, 123.937}, {26., 2.2, 125.892}, {26.5,
   2.125, 122.703}, {26.5, 2.1625, 123.512}, {26.5, 2.2, 
  124.901}, {27., 2.1125, 122.198}, {27., 2.15, 122.848}, {27., 
  2.1875, 123.782}, {27., 2.225, 125.874}, {27.5, 2.125, 
  122.095}, {27.5, 2.1625, 122.745}, {27.5, 2.2, 123.676}, {27.5, 
  2.2375, 125.734}, {28., 2.125, 121.808}, {28., 2.1625, 

  122.394}, {28., 2.2, 123.198}, {28., 2.2375, 124.563}, {28.5, 
  2.1125, 121.39}, {28.5, 2.15, 121.87}, {28.5, 2.1875, 
  122.506}, {28.5, 2.225, 123.412}, {28.5, 2.2625, 125.253}, {29., 
  2.125, 121.29}, {29., 2.1625, 121.747}, {29., 2.2, 122.372}, {29., 
  2.2375, 123.256}, {29., 2.275, 124.961}, {29.5, 2.125, 
  121.036}, {29.5, 2.1625, 121.454}, {29.5, 2.2, 122.006}, {29.5, 
  2.2375, 122.762}, {29.5, 2.275, 123.966}, {30., 2.1, 120.465}, {30.,
   2.1375, 120.896}, {30., 2.175, 121.334}, {30., 2.2125, 
  121.862}, {30., 2.25, 122.595}, {30., 2.2875, 123.735}, {30.5, 2.1, 
  120.187}, {30.5, 2.1375, 120.599}, {30.5, 2.175, 121.065}, {30.5, 

  2.2125, 121.525}, {30.5, 2.25, 122.157}, {30.5, 2.2875, 
  123.07}, {30.5, 2.325, 124.9}, {31., 2.125, 120.167}, {31., 2.1625, 
  120.593}, {31., 2.2, 121.078}, {31., 2.2375, 121.561}, {31., 2.275, 
  122.237}, {31., 2.3125, 123.247}, {31., 2.35, 126.014}, {31.5, 
  2.125, 119.881}, {31.5, 2.1625, 120.285}, {31.5, 2.2, 
  120.747}, {31.5, 2.2375, 121.268}, {31.5, 2.275, 121.808}, {31.5, 
  2.3125, 122.628}, {31.5, 2.35, 124.034}, {32., 2.1125, 
  119.484}, {32., 2.15, 119.849}, {32., 2.1875, 120.264}, {32., 2.225,
   120.742}, {32., 2.2625, 121.268}, {32., 2.3, 121.85}, {32., 2.3375,
   122.72}, {32.5, 2.1125, 119.213}, {32.5, 2.15, 119.558}, {32.5, 

  2.1875, 119.949}, {32.5, 2.225, 120.396}, {32.5, 2.2625, 
  120.911}, {32.5, 2.3, 121.431}, {33., 2.1, 118.846}, {33., 2.1375, 
  119.16}, {33., 2.175, 119.512}, {33., 2.2125, 119.91}, {33., 2.25, 
  120.365}, {33., 2.2875, 120.871}, {33.5, 2.125, 118.783}, {33.5, 
  2.1625, 119.101}, {33.5, 2.2, 119.458}, {33.5, 2.2375, 
  119.856}, {34., 2.1, 118.333}, {34., 2.1375, 118.614}, {34., 2.175, 
  118.923}, {34., 2.2125, 119.261}};

ListPlot@l[[All, 1 ;; 2]]


Mathematica graphics



Answer



f = Interpolation[l3= (Last /@ Sort /@ GatherBy[l[[All, 1 ;; 2]], #[[1]] &])]
ListContourPlot[l, RegionFunction -> (#2 < f[#1] &)]

Mathematica graphics


Edit


If you want a smoother curve, you could use for example whuber's method here for getting something similar to an "envolvent" curve:


l4 = {(#[[1]] - 14) 2 + 1, #[[2]]} & /@ l3;
nrow = 32;

i = Image[SparseArray[Flatten[Table[{i, IntegerPart@#1} -> #2, {i, 1, nrow}] & @@@ l4]]] 
                                                                                   // ImageAdjust

Mathematica graphics


{minima, maxima} = Flatten[Position[First[ImageData[#[i]]], 1]] & /@ {MinDetect, MaxDetect};

f1 = Interpolation[N@{(#[[1]] - 1)/2 + 14, #[[2]]} & /@ l4[[maxima]], InterpolationOrder -> 1]

f2[x_] = Max[f[x], f1[x]]


The "envolvent":


Quiet@Show[ListLinePlot@l3, Plot[f2[x], {x, 14, 34}]]

Mathematica graphics


Quiet@ListContourPlot[l, RegionFunction -> (#2 < f2[#1] &)]

Mathematica graphics


Quiet@ListPlot3D[l, RegionFunction -> (#2 < f2[#1] &), 
                 ColorFunction -> "SouthwestColors", MeshFunctions -> {#3 &}]


Mathematica graphics


Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more