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
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 !