Algorithm for Computing the Medial Axis of Arbitrary Simple Polygons

This article presents a MATLAB implementation of the medial axis algorithm for arbitrary simple polygons. The medial axis, also known as the skeleton, represents the central spine of a polygon by identifying the set of points equidistant from at least two boundary edges. This algorithm proves valuable for shape analysis and structural optimization in applications such as computational geometry, path planning, and image processing. Key implementation aspects include Voronoi diagram computation, boundary distance calculations, and branch pruning techniques to handle polygon complexity.

By implementing this algorithm in MATLAB, developers gain insight into its computational mechanics through practical code examination. We provide complete MATLAB source code accompanied by sample inputs and outputs, demonstrating functions like polygon_medial_axis() for core computation and boundary_processing() for edge normalization. This facilitates debugging and performance testing while highlighting algorithmic nuances like handling concave vertices and degenerate cases.

Rather than treating the code as a black box, we emphasize understanding each computational step—from polygon input validation using validate_polygon() to skeleton refinement via prune_branches(). This approach ensures proper adaptation for specific use cases, such as optimizing mesh generation or collision detection systems, by modifying parameters like distance thresholds and angular constraints in the algorithm configuration.