Determination of a curve with a given curvature

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Alessandro Masullo
Alessandro Masullo 2012-10-9
Hello! I have a set of points and I have to calculate the curvature. To find the curvature I made this simple code, which solves a linear system:
curv = zeros(1, length(x));
rad = zeros(1, length(x));
circ = zeros(length(x), 3);
for i = 2:length(x)-1;
M = [x(i-1) y(i-1) 1; ...
x(i) y(i) 1; ...
x(i+1) y(i+1) 1];
V = [x(i-1)^2 + y(i-1)^2; ...
x(i)^2 + y(i)^2; ...
x(i+1)^2 + y(i+1)^2]; ...
circ(i, :) = (- M^-1 * V)';
rad(i) = sqrt(circ(i, 1)^2/4 + circ(i, 2)^2/4 - circ(i, 3));
curv(i) = 1/rad(i);
end
Now, how do I get back the x and y starting from the curvature? I tried with a simple cumtrapz, but it doesn't seem to work...
Thank you!

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