Determination of a curve with a given curvature

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!