The Largest Empty Sphere Problem in 3D Hollowed Point Clouds

Abstract

We introduce a new approach for the adaptation of the Maximal Internal Envelope method, extended to address the Largest Empty Sphere problem within unstructured 3D point clouds. We explore the identification of the Largest Empty Sphere by computing Convex Hull vertices and employing a Voidness Score based on Minimal Distance Scoring for optimal segment selection. The integration of Delaunay triangulation and Voronoi diagrams facilitates the initial identification of potential Largest Empty Sphere candidates. Our analysis reveals the method's efficacy and efficiency, often locating the Largest Empty Sphere in initial computational stages, suggesting a lower complexity than initially projected.