How to retrieve x, y values from surf given z?

I got surf by using

s = surf(X, Y, Z);

I know I can use xq, yq, and inter2 to retrieve zq from the surf, like following

zq = interp2(X, Y, Z, xq, yq);

but how to get all the x,y on the surf where z is a certain value.

Answer 1

[Stephen23]

You could use contour or contourc or contour3 for what you want, but this is much more challenging than you think. Consider a 3D plane or 3D curve without any discontinuities: for some Z on that plane/curve, there could be infinite X and Y values that have the same Z value: these are the contours of that plane/curve. In some degenerate cases there may be only one X or Y value.

So which if those infinite/one X and Y values do you want? Think about contours, and then think about how such results could possibly be encoded or returned. Read the contour and contourc help. Read about the contour matrix:

https://www.mathworks.com/help/matlab/ref/matlab.graphics.chart.primitive.contour-properties.html#budgut_-ContourMatrix

Here is a simple example of how it works:

[X,Y,Z] = peaks(25);
surf(X,Y,Z)
Xg = X(1,:);
Yg = Y(:,1);
hold on
M = contour3(Xg,Yg,Z,[5,5],'*-r');
%
fun = @(s,v)fprintf('%s %s\n',s,sprintf(' %5.2f',v));
% display grid:
fun('Xg',Xg)
fun('Yg',Yg)
% display contour:
fun('Xc',M(1,2:end))
fun('Yc',M(2,2:end))

Original grid:

Xv  -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25  0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00
Yv  -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25  0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00

Contour matrix for Z==5:

Xc  -0.48 -0.25  0.00  0.25  0.50  0.50  0.70  0.66  0.50  0.38  0.25  0.00 -0.25 -0.38 -0.50 -0.64 -0.66 -0.50 -0.48
Yc   1.25  1.14  1.12  1.16  1.25  1.25  1.50  1.75  1.92  2.00  2.06  2.10  2.06  2.00  1.92  1.75  1.50  1.27  1.25

The contour for Z==5 is plotted in red:

[jonas]

Good idea. If you already know the level you are interested in, then you can just draw a single contour. For example, if you are interested in z = 0.5:

[xy]=contour(peaks,'levellist',0.5)

+1

[Kyle Gao]

Thank you so much for both of you! Actually, I want to get the [xy] within the area where zq-tol < zq < zq+tol. If I got the area, I can randomly pick [xy] so I don't need to worry about interpolation or continues problem. I wonder if this can make things easier?

[Stephen23]

"I have thought about this, I think like interp2, the output is given based on the grid"

That is basically what the contour family does. But you need to consider that where any specific Z value is probably won't correspond to both gridded X and Y values at the same time. Generally speaking, it is very unlikely that both the X and Y values that correspond to your specific Z value will both be on their grid. So what the contour family does is find the gridded X values for that Z values, and the gridded Y values for that Z value, and gives you that combined set.

See the example in my answer: I tried to make it clear that the contour matrix includes either X or Y gridded values, by printing the values aligned in columns. Not that if you have multiple distinct contours then the contour matrix is more complex: read the link I gave you very carefully!

[Kyle Gao]

Thank you so much! I think this is what I want, I still need to try this on my dataset. Hope it works! Thanks a lot!

Answer 2

[jonas]

Well, you can use

xq(zq==v)
xq(zq==v)

to find the points ( xq & yq ) where zq is equal to some specific value, v, but you're going to run into problems with comparing floats. A better approach would be to specify some tolerance, tol

xq(abs(zq-v)<tol)
yq(abs(zq-v)<tol)

[Kyle Gao]

Thanks for your help. Do you mean

xq = inter2(abs(zq-v)<tol)

I tried this but it gives me an error which is

Interpolation requires at least two sample points in each dimension.

[jonas]

No, that is not what I mean. You interpolate first, then you find the coordinates.

xc=xq(abs(zq-v)<tol)
yc=yq(abs(zq-v)<tol)

It is the syntax for logical indexing. Basically you find the indices in zq where some condition is satisfied, in this case abs(zq-v)<tol, and then you put those indices directly into xq and yq.

[jonas]

I don't want to hijack Stephens answer, so I'll just leave another reply here.

" Actually, I want to get the [xy] within the area where zq-tol < zq < zq+tol "

This is exactly what

 abs(zq-v)<tol

does... you obtain all values for zq +- tol. But honestly, the other answer is better, as it does not require any tolerance. The interpolation is kinda of integrated with the contour plot.

[Kyle Gao]

Thank you jonas! Stephen's approach suits my problem better. But your idea definitely also helped me a lot!