Sampled medial loci and boundary differential geometry

We introduce a novel algorithm to compute a dense sample of points on the medial locus of a polyhedral object, with a guarantee that each medial point is within a specified tolerance ¿ from the medial surface. Motivated by Damon´s work on the relationship between the differential geometry of the smooth boundary of an object and its medial surface, we then develop a computational method by which boundary differential geometry can be recovered directly from this dense medial point cloud. Experimental results on models of varying complexity demonstrate the validity of the approach, with principal curvature values that are consistent with those provided by an alternative method that works directly on the boundary. As such, we demonstrate the richness of a dense medial point cloud as a shape descriptor for 3D data processing.