Let's say that you had an edge connecting two points (the black line in the example below.) For which of the two curved edges (the dotted line or the dashed line) do you want to compute the arc length and why?
plot([-1 1], [0 0], 'k-');
hold on
x = -1:0.01:1;
edge1 = polyfit([-1 0 1], [0 1 0], 2);
plot(x, polyval(edge1, x), ':')
edge2 = polyfit([-1 0 1], [0 2 0], 2);
plot(x, polyval(edge2, x), '--')
axis([-1, 1, -1, 2])
