How do I perform an integration on a two-dimensional surface of scatttered data?

I have measured data in two dimensions, not on a uniform grid. I want to perform the surface integral over the two dimensions, to get a smooth 2D surface function that I can evaluate at any input (x, y), which may be beyond the original measurement space, so smoothness and sensible extrapolation are desirable features of the integrated surface.

I have used 'scatteredInterpolant' function to obtain the surface of the original data, and then used 1-dimensional numerical integration in each dimension to create the appearance of a surface, but this is not a function F(x,y).

Answer 1

[Yogesh Khurana]

Hi,

I am assuming that you already got the interpolated data by using scatteredInterpolant. Now for integrating the data you can use MATLAB’s integral functions like:

trapz, documentation: https://www.mathworks.com/help/matlab/ref/trapz.html

integral2, documentation: https://www.mathworks.com/help/matlab/ref/integral2.html

Following are some links that are some of the cases similar to this case:

https://www.mathworks.com/matlabcentral/answers/352186-partial-integral-of-a-2d-interpolation

https://www.mathworks.com/matlabcentral/answers/73319-how-to-use-trapz-on-a-double-integral

https://www.mathworks.com/matlabcentral/answers/129371-how-to-perform-surface-integral-using-an-interpolation-function

Please refer to links above for more information.

Hope this helps!

[John Wood]

The first link that you provided is very similar to what I am doing already, so perhaps I am on the right track and need some help with the details.

I have used scatteredInterpolant function on measured data, but the resulting surface is still quite noisy, particularly at the edges of the data set. None of the parameters 'linear', 'nearest' seem to make any diffrence, so if there is anything else I could try that may help.

I choose an integration starting point (in each direction) that is 'inside' the data in a relatively smooth region. The choice of starting point affects the result, in terms of the smoothness and shape of the integrated surface.

I also get different results depending on which axis I use for the first line integration, in other words, the integral isn't conservative, which it is supposed to be.