Plot 2d pressure field

I would like to plot a 2d pressure field, i.e., I have two vectors x, y and the pressure P on each point. I would like to plot a colored map for the pressure field.

I used the scatter function to do it (scatter(x,y,5,P)), but it plots only the points on the coordinates x,y, but the spacing is too large.

I tried to use other functions such as surf or mesh, but it won't work (size(P) must be [length(y),length(x)].

[Sara]

Try looking into contourf. Is that something you would like?

[Thales]

I tried with contourf too. Same error: "Z must be size 2x2 or greater". I don't understand why those surf/mesh/contourf need Z as a matrix, not as a vector, since I have to each point (x(i),y(i)) only one correspondent scalar P(i).

[Sara]

Those functions expect that you provide a 2d matrix of size ny,nx, i.e. a value for each point on a mesh. This also means that x and y contain every element only once if 1d arrays. You can reorganize P in a 2d matrix, so you can use those functions. If you have trouble doing that, I suggest that you attach your arrays here as .m or .mat files so people can post a customized solution.

[Thales]

For instance, I have:

x = [  0,  10,   0,  13,   0,  13, 20, 20]';
y = [  0,   0,  10,   7,  20,  20, 20, 10]';
P = [287, 203, 271, 142, 255, 105,  0,  0];

For simplicity, I've rounded up the numbers. So, for each pair (x(i),y(i)), I have a pressure value P(i) and I want to plot it in some sort of a color map. How can I make P a 2d matrix?

[Sara]

Your data is pretty sparse to have a colormap. Do you mean that for each point x,y you want to show a different color on a 2d map? what is the value of P in the other points on your map? try the following: does it look like something you are trying to obtain? (I've set to zero the value in the points where you didn't provide a value).

clearvars
close all
clc

x = [  0,  10,   0,  13,   0,  13, 20, 20];
y = [  0,   0,  10,   7,  20,  20, 20, 10];
P = [287, 203, 271, 142, 255, 105,  0,  0];

xx = x(x~=0);
dx = min(gcd(x,xx(1)));
xx = min(x):dx:max(x);

yy = y(y~=0);
dy = min(gcd(y,yy(1)));
yy = min(y):dy:max(y);

PP = zeros(numel(yy),numel(xx));
for i = 1:numel(x)
    icell = ceil(y(i)/dy);icell = max(1,icell);icell = min(numel(yy),icell);
    jcell = ceil(x(i)/dx);jcell = max(1,jcell);jcell = min(numel(xx),jcell);

      PP(icell,jcell) = P(i);
  end

surface(xx,yy,PP,'edgecolor','none')
colorbar

[Thales]

Ok, that is what I want...

The only thing now: yes, I have very few data, but that's because I've used a very poorly mesh to calculate the pressures. After solving the problem to how to plot it, I'll refine the mesh.

The last thing now is, instead of setting to zero the values, I would like to interpolate them, so the colormap gradually changes. Any idea how to do it?

[Sara]

Try looking at the interp functions in matlab. Otherwise you can write your own bilinear interpolator

[Thales]

Ok, thank you.

Answer 1

[Image Analyst]

Try scatteredInterpolant() to make a solid 2D array out of the individual scattered points, then display with imshow() or image().

[Thales]

How do I do that? Never used imshow or image to plot something...

[Image Analyst]

imshow(yourImageArray, []); % Requires Image Processing Toolbox.
image(yourImageArray); % Does not require Image Processing Toolbox.