Interpolate pairs of values from matrix

I have a coarse 2D-matrix with [X,Y,Z]-values.

I want to input a Z-value and would like to interpolate possible values for the [X,Y]-pairs. These [X,Y]-pairs are then used for a fit. This means that for a given value of Z, if I choose any X value, Y can be calcualted and the other way arround.

I have tried the interp2 already, but it seems that I can only input X and Y values to get the interpolated Z value and not the other way around, where I input a Z-value and get a list of [X,Y]-pairs for that.

All the best

Chris

[Rik]

So essentially you want to find the coordinates on a fine sample grid where Z is close to some target value?

Can you provide example data? that will make it easier to play around with a realistic example.

[Chris Pruefert]

Esaclty, the value for Z most likely is not listed in the original coarse matrix. This means, that the corresponding X and Y value most likely will have to be interpolated from the coarse grid of Z. Would that be possible?

[Chris Pruefert]

To grab this example matrix, in the first colum if X=125, 0.3 is inbetween Z = 0.247 and 0.389, with Y = 4.459 4.526 respectively. Eliminating the NaN, interp1(Z(:,1),Y,0.3) would then give 4.4838. Is that the way to do it?

Answer 1

[Mathieu NOE]

hello

you can surely get the required x , y data for a given z value ; use contour for that purpose as shown in code example below :

Z = peaks(50)/10;
level = 0.3;

surf(Z)
hold on

% extract all isoclines  for a given level
[C,h] = contour(Z,level*[1 1]);
[m,n] = size(C);
ind = find(C(1,:)==level); % index of beginning of each isocline data in C
ind = [ind n+1]; % add end (+1) 
for k = 1:numel(ind)-1
    xc = C(1,ind(k)+1:ind(k+1)-1);
    yc = C(2,ind(k)+1:ind(k+1)-1);
    zc = level*ones(size(xc));
    plot3(xc,yc,zc,'linewidth',5);
end
hold off

[Chris Pruefert]

This worked fine, yet as you mentioned, I should add some example the data.

The solution you provided gave me the indices of the respective "X" or "Y" values. In this, for exmaple one of the given indices was 4.1111, does that mean that it is X=0.9999*X(4)+0.1111*X(5)?

The value for Z most likely is not listed in the original coarse matrix. This means, that the corresponding X and Y value most likely will have to be interpolated from the coarse grid of Z. Would that be possible too?

[Chris Pruefert]

To grab this example matrix, in the first colum if X=125, 0.3 is inbetween Z = 0.247 and 0.389, with Y = 4.459 4.526 respectively. Eliminating the NaN, interp1(Z(:,1),Y,0.3) would then give 4.4838. Is that the way to do it?

[Mathieu NOE]

hello again

not sure to understand what you are doing

I slightly changed the code to match with your data

so basically you end up with a 2D curve defined by xc and yc coordinates (see second plot)

you can select then any valid value for x and use interp1 to find the corresponding y value on this 2D curve

load('XYZ_test.mat')
% extract all isoclines  for a given level
level = 0.3;

surf(X,Y,Z)
hold on

[C,h] = contour(X,Y,Z,level*[1 1]);
[m,n] = size(C);

ind = find(C(1,:)==level); % index of beginning of each isocline data in C
ind = [ind n+1]; % add end (+1) 
for k = 1:numel(ind)-1
    xc = C(1,ind(k)+1:ind(k+1)-1);
    yc = C(2,ind(k)+1:ind(k+1)-1);
    zc = level*ones(size(xc));
    plot3(xc,yc,zc,'*-r','markersize',15);
end
hold off

% plot the xc,yc curve
figure 
plot(xc,yc,'-r');
xlabel('x');
ylabel('y');

[Chris Pruefert]

Yes, that is exactly what I tried to achieve. Thanks

[Mathieu NOE]

my pleasure !!