sharp interface and curvature
 

i want to calculate the curvature of the circle(radius, r) in cartesian grid.

First, I set the circle by using the color function, c (c=1 inside fluid A, c=0 inside fluid B).However, it is not exact circle because of using the cartesian grid. So, my calculation result (curvature) doesn't equal to 1/r.

How should I set the circle in the cartesian grid and calculate the curvature of the circle?