Figure 3.

The local geometry of a point on the medial manifold. The ball represents a medial node m(u¹,u²), and the vectors ∂m/∂u¹ and ∂m/∂u² span the tangent plane to m. The vector ∇_mR lies in the tangent plane and points in the direction of maximal change of the radial thickness field R on m. The points of tangency between a ball centered at m(u¹,u²) with radius R and the boundary of the object are b⁺ and b⁻. Unit vectors U⁺ and U⁻ point from m(u¹,u²) toward b⁺ and b⁻ and are perpendicular to the object boundary at these points.