A center of curvature is defined at each position s located a distance ρ (the radius of curvature) from the curve on a line along the normal u n (s). The required distance ρ (s) at arc length s is defined in terms of the rate of rotation of the tangent to the curve, which in turn is determined by the path itself. If the orientation of the tangent relative to some starting position is θ (s), then ρ (s) is defined by the derivative d θ /d s :