Skip to main content

plotting - Smooth out contour in RegionPlot/ContourPlot


I would like to smooth out the jagged edges in the outermost contours in the following plot:


Plot with jagged edges.


I have data of values as a function of variables (x,y) in the form


data = {{{x1,y1},z1},{{x2,y2},z2},...};

The figure is produced by


data = << "data.dat";

fnct = Interpolation[data];    
RegionPlot[{fnct[x, y] > 2, fnct[x, y] > 100, fnct[x, y] > 140}, {x, 10^-2, 10^1}, {y, 0, 3},MaxRecursion->5]

The outer edges seem jagged I guess because the data is not very good there. I need to fit a smooth contour instead. I've looked at some other questions like Smoothing ListContourPlot contours but that uses ListContourPlot which for me takes ages and produces a bad result even for the original figure.


Any help appreciated.


The data can be found here:


https://dl.dropboxusercontent.com/u/34796693/data.dat



Answer



First we import the data, which OP is kind enough to leave in his Dropbox for these past 18 months.


data = N@Get["https://dl.dropboxusercontent.com/u/34796693/data.dat"];


Next we look at the data and notice that it is on a rectangular grid,


Dimensions[data]
Dimensions@Gather[data[[All, 1, 1]]]
(* {180901, 2} *)
(* {601, 301} *)

This is going to make all the difference here (if it weren't on a rectangular grid than you wouldn't have been able to do a decent Interpolation anyway).


The plan here is to apply a MovingAverage along the rows and columns of the grid. MovingAverage likes to work on matrices or vectors, not lists like {{{x1,y1},z1},{{x2,y2},z2}....}, so there are a couple of reshaping steps thrown in here for good measure.


npts = 10;

smootheddata = {{#1, #2}, #3} & @@@
   Flatten[
    Transpose[
     MovingAverage[#, npts] & /@
      Transpose[
       MovingAverage[#, npts] & /@
        Partition[Flatten /@ data, 301]
       ]
     ]
    , 1];


Now you just do as you were doing before, create an interpolation function then apply RegionPlot to it, but now you must be aware that you have a smaller range of gridpoints after applying the averaging.


{{xmin, xmax}, {ymin, ymax}} = 
 MinMax /@ Transpose[smootheddata[[All, 1]]]
fnct = Interpolation[smootheddata];
RegionPlot[{fnct[x, y] > 2, fnct[x, y] > 100, fnct[x, y] > 140}, {x, 
  xmin, xmax}, {y, ymin, ymax}, MaxRecursion -> 5]

(* {{0.0107256, 9.66286}, {0.045, 2.955}} *)


enter image description here


You can see that it is probably fine to just average the rows, but the best results come from averaging both rows and columns.


enter image description here


Above I've used 10 as the number of elements to average over, but you can get a smoother plot by including more elements. This will have the effect of decreasing the size of the grid points so you have to choose the best option. Here are a few values for npts


enter image description here


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

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

Is there a way to do conditional matrix loop using 'continue'

I have the following: n = 3; m = 5; ww = RandomReal[{0, 0.1}, {n, n}]; uu = RandomReal[{0, 1}, {m, n}]; pp = RandomReal[{0, 1}, {n, n}]; ss = RandomInteger[{0, 5}, {m, n}]; Grid[{{"ww", "uu", "pp", "ss"}, {ww // TableForm, uu // TableForm, pp // TableForm, ss // TableForm}}, Spacings -> {5, 2}, Dividers -> All] where I would like to look at every element of matrix ss and produce a matrix tt , with zeroes at the locations in ss which have zeroes, and in all other positions do the following: tt = (-1/Subscript[ww, m]) Log[(1 - uu)/(Subscript[pp, m - 1])], where Subscript[ww, m] is the value at index of ww matrix and where Subscript[pp, m - 1] is the value at index-1 of pp matrix. So for example if the first value ever read from matrix ss happens to be 2, then value taken from matrix ww would be from the row 2, but from pp would be from row 1. Also how to tell difference between a 0 as a valid value from within the matrix elemen...
Post a Comment
Read more