Medial axis of a planar region by offset self-intersections

The medial axis (MA) of a planar region is the locus of those maximal disks contained within its boundary. This entity has many CAD/CAM applications. Approximations based on the Voronoi diagram are efficient for linear-arc boundaries, but such constructions are more difficult if the boundary is free. This paper proposes an algorithm for free-form boundaries that uses the relation between MA and offsets. It takes the curvature information from the boundary in order to find the self-intersections of successive offset curves. These self-intersection points belong to the MA and can be interpolated to obtain an approximation in Bézier form. This method also approximates the medial axis transform by using the offset distance to each self-intersection.