Find Z-value corresponding to X and Y points

I'm plotting something using pcolor in Matlab. I am using the code pcolor(X,Y,Z), where X and Y are 2-D matrices of equal size to Z.

My question is that, given a value of X and Y, how can I find the value of Z at this point. For example, the value of Z when X = 10.32 and Y = -12.5. I know how to find the location in the the X and Y matrices where these values occur, but I'm not sure how get the Z value from this.

The Z matrix isn't simply an analytical function of X and Y, rather I was just given value of Z and their corresponding X and Y points.

X and Y are NOT monotonically increasing.

The values of X and Y that I want to find Z at will always be present in the original X and Y matrices. For example, I want to find the value of Z corresponding to the X value at X(10,20) and Y value at Y(15,25).

Thanks!

Answer 1

[Mike Garrity]

If the X & Y are in the input matrices, then you can do the following:

[x,y,z] = peaks;
h = surf(x,y,z);
[r,c] = find((h.XData==2.625) & (h.YData==2.625));
disp(h.ZData(r,c))

A couple of things to watch out for.

• That == is an exact comparison. You might need to do a comparison with a tolerance.
• Because your XData & YData are not monotone, you might get more than one match. In that case, r & c will be vectors.

[Walter Roberson]

2.625 is 2+5/8 which is a value that is exactly representable in binary floating point. If you know that your values were "cleanly" created then you can meaningfully compare to 2.625.

But 10.32 is not exactly representable in binary floating point. The precise sequence of steps that were used in creating the value that is nominally 10.32 would determine whether the number actually stored is 10.3199999999999985078602549037896096706390380859375 or 10.32000000000000028421709430404007434844970703125 or 10.3200000000000020605739337042905390262603759765625

Therefore you should never compare a constant to a calculated floating point number: you should compare within a tolerance instead. The only time you should compare with "==" for floating point numbers is if one of the numbers is extracted from the array to be compared against. For example,

A = rand(1,1000);
B = min(A);
find(A == B)

in such a case where an exact bit pattern has been transferred, it is meaningful to compare for the exact bit pattern.

[Akbar Raza]

Hi Mike. I found your reply very useful. But now what I need is that I want to trisurf the extracted points again and see only the area that is in the selected variables then how can i do that?

tri = delaunay(x(:),y(:));
  %z=repmat(z,1,1,3);
  %plot3(x,y,1,'.')
  %zc=ones(1,3337);
  %[r,c] = size(tri);

   % pcolor(x,y,z')
  h = trisurf(tri, x(:), y(:), z(:));
    h.XData;
    %h.ZData
    %Slice=slice(z,x,y,zc);
  [r,c]=find((h.XData<=5E-3 & h.XData>=-5E-3) & h.YData==-0.0090); %& (h.YData==-0.01))
   ReconSurfaceY= (h.YData(r,c));
   ReconSurfaceX= (h.XData(r,c));
   ReconSurfaceZ= (h.ZData(r,c));
   length(ReconSurface)
    axis on

    shading interp;
    colorbar

[Walter Roberson]

-0.0090 and -0.01 are not exactly representable in binary. You should not be doing exact comparison of floating point numbers, as I explained above.

[Akbar Raza]

Hi Walter I used "round" to limit the number of decimal points to 3 in the main function and I am able to generate a matrix of numbers that are expected to be the range that I want. But how to plot them now? can I use trisurf or should I go for pcolor?

[Walter Roberson]

Once you have your [r, c] results of find(), I would suggest,

   ReconSurfaceZ = nan(size(h.ZData));
   ind = sub2ind(size(h.YData, r, c));
   ReconSurfaceZ(ind) = h.ZData(ind);
   surf( h.XData, h.YData, ReconSurfaceZ);

[Akbar Raza]

Thanks Walter. Now what I need to do is to stack multiple copies of this data in the z-dimension which will result effectively in a 4D plot. Currently, if we assume that the same data is being used multiple times in the z-dimension, then how can I have a volumetric structure such that it becomes a continuous form of scatter3 plot. Need your help with this problem

[Akbar Raza]

what I want eventually is stacking all the slices to make the attached volumetric structure. How can I do that? Please ignore the axis in this figure