Contour plot of concave shape from 3 vectors coordinates

Hello,

I'm analyzing a membrane with FEM. The membrane has a rectangular shape with a hole at the center so I've only modeled a quarter of the whole membrane using 60 nodes like in the first image.

I also performed the stress recovery and I have the data arranged in a [Nx3] matrix 'Sxx' , where:

Sxx(:,1) = x coordinate of the node

Sxx(:,2) = y coordinate of the node

Sxx(:,3) = magnitude of the stress

I am trying to make a contour plot of the stress, but due to the hole at the center, the shape is concave and griddata seems to interpolate also across the hole, producing a straight line instead of a quarter of a circle.

This is the code i'm using:

xv1 = min(Sxx(:,1)):max(Sxx(:,1));
yv1 = min(Sxx(:,2)):max(Sxx(:,2));
[X1,Y1] = ndgrid(xv1,yv1);
Z1 = griddata(Sxx(:,1) , Sxx(:,2) , Sxx(:,3) , X1 , Y1);
h1 = pcolor(X1,Y1,Z1);
title('\sigma_{xx}')
c1 = colorbar;
c1.Label.String = '[N/mm^2]';

I also tried every interpolation method of griddata but still doesn't work. All i keep getting is the second image.

I searched online if there's any possibility of limiting the interpolation between points to a certain range but i couldn't find anything that works for me.

I can't transform the stress vector into a matrix due to irregular distances between nodes.

Thank you

[KSSV]

griddata is not inteprolating across the hole, else you would have got some color i.e values at the holes.

USe shading interp after the plot and see.

If you notice the values of Z1 for x < 25 and y < 25, the values would be NaN. griddata is doing good, you may go ahead with your calculations.

[chicken vector]

This is Z1 at the lower left corner

NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN   87.3888   81.0505   74.7122   68.3739   62.0356
       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN   83.7098   85.1843   78.8460   72.5077   66.1694   59.8311
       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN   80.0308   80.6615   82.9798   76.6415   70.3032   63.9649   58.2034
       NaN       NaN       NaN       NaN       NaN       NaN       NaN   76.3518   76.2562   78.3393   80.7753   74.4370   68.0987   62.7671   57.5601
       NaN       NaN       NaN       NaN       NaN       NaN   72.6728   72.5673   73.9341   76.0172   78.5708   72.5377   67.3307   62.1238   56.9168
       NaN       NaN       NaN       NaN       NaN   68.9938   68.8883   69.5289   71.6120   73.6950   77.1014   71.8944   66.6875   61.4805   56.2735
       NaN       NaN       NaN       NaN   65.3148   65.2093   65.1236   67.2067   69.2898   73.1976   72.0822   68.2124   64.3425   60.4727   55.6302
       NaN       NaN       NaN   61.6358   61.5303   61.4248   62.8015   64.8846   66.9677   70.8392   66.9694   63.0995   59.2297   55.3599   51.4900
       NaN       NaN   57.9568   57.8513   57.7458   58.3963   60.4794   62.5624   64.6455   65.7263   61.8565   57.9867   54.1168   50.9474   48.4328
       NaN   54.2778   54.1723   54.0668   53.9910   56.0741   58.1572   60.2403   62.3234   60.6135   57.1716   54.6570   52.1425   49.6279   47.1134
   50.5987   50.4932   50.3877   50.2822   51.6689   53.7520   55.8351   57.9182   59.0665   58.3667   55.8521   53.3376   50.8230   48.3085   45.7939
   46.8142   46.7087   46.6032   47.2637   49.3467   51.4298   53.5129   54

I thought that griddata was interpolating between the two points (0,25) and (25,0), creating a straight line. This seems clear by taking a look at the values on the diagonal between these two points, which increase a constant rate.

If I use 'shading interp' it just removes the black gridlines but the plot still has the straight line.

I'm sure calculations are good so it doesn't really matter, it's just for aesthetics, but i really can't understand how to solve this.

[chicken vector]

From the contour plot is more straightforward.

Answer 1

[KSSV]

To make the plot look neater, you have to increase the number of discretizations.

m = 100 ; n = 100 ; % can be changed 
xv1 = linspace(min(Sxx(:,1)),max(Sxx(:,1)),m);
yv1 = linspace(min(Sxx(:,2)),max(Sxx(:,2)),n);
[X1,Y1] = meshgrid(xv1,yv1);
Z1 = griddata(Sxx(:,1) , Sxx(:,2) , Sxx(:,3) , X1 , Y1);
h1 = pcolor(X1,Y1,Z1);
shading interp 
title('\sigma_{xx}')
c1 = colorbar;
c1.Label.String = '[N/mm^2]';

[chicken vector]

I tried on the first imag but still have the same problem.

I'm trying to solve using 'boundary', if only i can understand how to fill with a color outside a closed curve.

[KSSV]

Okay, then what we can do is....we can pick the points lying outside the arc..i.e in the hole and make the values of those points NaN's ...this would give a good plot. Hope you got it.

[chicken vector]

Yeah that would be great and i think I can do that in this case, but I find difficult to set up a code which can do that for every possible concave shape, since I want this code to be able to analyze every shape.

I can find the points on the matrix which correspond to the boundary using griddata, but how can i define an "inside" and "outside" of a boundary?

THanks for all your time, really appreciate that!

[KSSV]

Read about inpolygon. This will work for any case..you need not to worry.

[chicken vector]

Right now I solved the problem with this function:

https://it.mathworks.com/matlabcentral/fileexchange/10515-fillout

but it's not a very clean approach so i will certainly look deeper into inpolygon.

Thanks for all your help.

Best regards

[KSSV]

Hey....I strictly suggest you inpolygon. This is very easy to use.