center of curvature

The point on the positive ray of the normal vector at a distance ρ(s), where ρ is the radius of curvature. It is given by z | = | x + ρ N | = | x + ρ^2 (d T)/(d s), where N is the normal vector and T is the tangent vector. It can be written in terms of x explicitly as z = x + (x'' (x'·x')^2 - x'(x'·x')(x'·x''))/((x'·x')(x''·x'') - (x'·x'')^2).

curvature | osculating circle