Double integration in Matlab on given data set

[ALYAZAN]

Homework Statement

Hello,

I have a problem

I have a strand (pathway) defined in Matlab as X and Y and s where X and Y are the coordinates and s is an indexing (1, 2, 3, .....), and I can have this X and Y in high resultion, namely very small distance between them

I need to achieve this double integral

∫₀ ^L ∫₀ ^L < ( r (s1) - r (s2) )² > ds1 ds2


where L is known (the length of the strand) and r is the representation of the curve, namely a contour function of the strand !

I have no idea how to achieve such an integral !

hope you can help me

Alyazan

Homework Equations

The Attempt at a Solution

1- I thought about turning this integral into a sum ! but I am not sure how to do that

2- I thought also about extrapolating a contour function r (s) from my X and Y data set but still I have very different shapes of strands everynow and then which look just like worms !