How to get polynomial function of a 3d plane of data?

Hi,

I have a 3d array of coordinates x,y and z. For each of these coordinates I have assigned a magnetic flux density value B. I want to get a polynomial function of x and y for the front and back face of my 3D array? Does anyone know how I could do this? I tried to surface fitting tool but I have problems with my z input as it is 2d not 1d.

Cheers,

Philip

Answer 1

[Walter Roberson]

[x(:) y(:) ones(numel(x),1)] \ z(:)

would return a vector [m n c] best fitting z = m * x + n * y + c

[Philip]

Hi, Thank you for your response. There seems to be an error when I attempt to input this into matlab. The dimensions of the variables seem to be conflicting. What output should I get from this code?

[Walter Roberson]

Example:

>> x = rand(17,1); y = rand(17,1); z = rand(17,1); 
>> [x, y, ones(17,1)] \ z

ans =

           0.220332829994951
          -0.336337071783378
           0.567484042153482

That indicates that for this data, z = 0.22 * x - 0.34 * y + 0.57

If this is not appropriate then you should show a small example of your data structure.

Ah... did you miss something in your question? Did you mean to ask about getting finding B as a polynomial function of x and y along those two faces? You didn't specify it was B whose value was to be related.

[Philip]

Yes apologies, that is what I am trying to get. A function of the b values for x and y coordinates. I have got a 4th order polynomial of the distribution in the x and y direction so far for each face and obtained coefficients for each. But this function does not describe distribution of B across the x, y plane. So my ideal function is B=f(x,y)=a1x^n +a2x^n-1....+cy^n.... +cxy (constant relating the x and y values)

[Walter Roberson]

Would "n" be 3 for the above, as you mention 4th order? And can you confirm that you have no cross-terms between the two variables, e.g., no a3*x*y

[Philip]

I have only worked out polynomials for x and y individually so far and tried to sum them which I know is not the correct method. My polynomial equation I have at the minute is 4th order.

[Walter Roberson]

Which are the "front" and "back" face of your 3D array? Which coordinate is being held constant?

Are you indicating that you would like to include cross-terms between the x and y, or that we should exclude those?

[Philip]

Hi,

Thank you very much for your help. I've managed to solve my problem. I have sucessfully imported the data into the surface fitting tool so I should be able to do whatever I want now. I originally had a text file of data representing a cube of b values which exported in a long list of data. I converted that data to a 3d Array of B values but the original format was perfect for importing into the surface fitting tool. Thanks again for you help.

Philip