Form Convex Hull to Concavity: Surface Contraction Around a Point Set

Abstract

This paper investigates the transformation of a convex hull, derived from a d-dimensional point cloud, into a concave surface. Our primary focus is on the development of a methodology that ensures all points in the point cloud are encapsulated within a closed, non-intersecting concave surface. The study begins with the initial convex hull and employs an iterative process of facet replacement and expansion to evolve the surface into Scc, which accurately conforms to the complex geometry of the point cloud.