Getting the piecewise polynomial function of a 3D plot

Is there a method to get the piecewise function of the 3D plot below? My requirement is to get a value for X as the output when Y and Z are given as inputs. The plot is created using the curve fitting tool (linear interpolation)

Inputs should be - z , y

Output should be - x

[Senal Perera]

Note that the curve fitting tool does not show the equation. It only says ' Piecewise polynomial'. The data cursor shows the coordinates upon clicking on the plot. But that is not what I want. I want to save the output in to the workspace which i have to feed it into a servo motor.

[ANKUR KUMAR]

Why are you using fitting tool GUI? You can do the same using interpolation code in a script.

[DGM]

Unless I'm missing something, this is a more fundamental problem. If your goal is to get x from y and z, you need to note that your function is overdefined. In other words, there are multiple x values that may satisfy a given y,z pair. The conceptual consequences of that fact may vary depending on your usage.

Answer 1

[ANKUR KUMAR]

You can use interp2 to calculate values programmatically.

clc
clear
[X,Y] = meshgrid(-5:1:5);
Z = Y.*sin(X) - 5*X.*cos(2*Y);
s = surf(X,Y,Z,'FaceAlpha',0.5);

[XX,YY] = meshgrid(-5:0.05:5);
ZZ=interp2(X,Y,Z,XX,YY);
figure
s = surf(XX,YY,ZZ,'FaceAlpha',0.5);
s.EdgeColor = 'none';


x_reqired=randi(50,1,10)/10;
y_reqired=randi(50,1,10)/10;
z_reqired=interp2(X,Y,Z,x_reqired,y_reqired)

[Senal Perera]

I appreciate your effort Ankur. I guess interp2 is okay if z is needed as the output. But i need x as the output where z and y are inputs.