In this paper a computational model called dynamic medial axis (DMA) is proposed to describe the internal evolution of planar shapes. To define the DMA, a symbolic representation called matching list is proposed to depict the topological structure of the medial axis. As shown in this paper with provable properties, the DMA exhibits an interesting dynamic skeleton structure for planar shapes. Fi...

The popularity of medial axis in shape modeling and analysis comes from several of its well known fundamental properties. For example, medial axis captures the connectivity of the domain, has a lower dimension than the space itself, and is closely related to the distance function constructed over the same domain. We propose the new concept of a medial zone of an n-dimensional semi-analytic doma...

Boundary approximation of planar shapes by circular arcs has quantitative and qualitative advantages compared to using straight-line segments. We demonstrate this by way of three basic and frequent computations on shapes – convex hull, decomposition, and medial axis. In particular, we propose a novel medial axis algorithm that beats existing methods in simplicity and practicality, and at the sa...

An adaptive algorithm to compute the medial axis transform of 2D polygonal domains with arbitrary genus is presented. The algorithm is based in the reenement of a coarse medial axis transform by subdividing the domain adaptively. The algorithm provides the medial axis represented by a set of triangles of a predeened size and the closest boundary element. Examples of results are also presented t...

We consider an algorithm, first presented in [13], that outputs regions intersected by the medial axis of a 3D solid. In practice, this algorithm is used to approximate the medial axis with a collection of points having a desired density. The quality of the medial axis approximation is supported by experimental results. Despite promising 2D results, the algorithm’s theoretical guarantees are no...