Finding the Meshgrid provided a surface.

Hi All, given a surface, is there anyway to find the underlying meshgrid of the surface. For example, I have a surface given by function Z that has been created in the following manner:

x = -4:0.4:4; y = -8:0.4:8; [X,Y] = meshgrid(x,y);
Z = comp_z(X,Y);
    %Given just the surface, Z , is there a way to find the meshgrid that created it?

[Stephen23]

"Given just the surface, Z , is there a way to find the meshgrid that created it?"

In general this is not possible. Consider a simple 2D example: if I give you:

Y = [0,-0.70711,-1,-0.70711,0,0.70711,1,0.70711,0]

can you tell me which X values I used the generate those Y values?:

Y = sin(X)

Unless you have other information (e.g. about the shape of the curve, sample spacing, a range, a domain and some other restrictions, etc) then the general answer is this is not possible.

Answer 1

[Cris LaPierre]

How are you given the surface? As a fig file? You could extract the X and Y indices of the surface:

x = -4:0.4:4; 
y = -8:0.4:8; 
[X,Y] = meshgrid(x,y);
Z = (X.*Y);
surf(X,Y,Z)

h = findobj('Type','Surface');
surfX = h.XData;
surfY = h.YData;

all(all(surfX==X))
ans = 
   1

all(all(surfY==Y))
ans = 
   1

[Carlos Pedro]

Hi Cris, thanks for your assistance,

Basically, its part if a bigger function, I want to be able to input a surface,Z ( a function of x and y), into the function and be able to interpolate values of Z (using cubic interpolation) at different points. This is what I have so far:

function [z0] = myinterp_function(Z,x0,y0)

X =?

Y = ?

fun_interp = griddedInterpolant(X',Y',Z','cubic');

z0 = fun_interp(x0,y0);

end

Essentialy I want Z to be defined outside of the function but for this to work I will need a way to get X and Y from Z.

[Cris LaPierre]

So it's not a surface in MATLAB yet. You have a matrix of numbers and want to somehow reverse engineer it to get what the values of X and Y were to compute the Z values?

Can you not also pass in your X and Y values?

The only other option I can think of is to use your equation and the z values you have. Create a defined interpolated grid of x values and solve for the corresponding y values.

[Carlos Pedro]

Yes exactly, I just want to pass Z in and retrieve X and Y inside the function so I can perform the interpolation.

No I need to define Z outside of the function.

The Z function I have is: z = cos(x/2).* cos(y) + (y/10) - (x/5);

[Cris LaPierre]

I didn't say define Z inside the function. I said use the values of Z and your interpolated X to solve for Y. You might be able to use the solve function in MATLAB

[Carlos Pedro]

I've had a look and a think and I don't think what I want is possible.

Thankyou regardless.