  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.
