The paper introduces the concept of α-shapes, a formal definition of the "shape" of a finite point set in three-dimensional space. An α-shape is a polytope derived from the Delaunay triangulation of the point set, with a parameter α controlling the level of detail. The authors present an algorithm to construct the entire family of α-shapes for a given set of n points in O(n²) time. The paper discusses the implementation of the algorithm, its robustness, and several applications in scientific computing. Key concepts include α-hulls, α-diagrams, Delaunay triangulations, and Voronoi diagrams. The relationship between these geometric concepts and α-shapes is explored, providing a comprehensive understanding of the topic.The paper introduces the concept of α-shapes, a formal definition of the "shape" of a finite point set in three-dimensional space. An α-shape is a polytope derived from the Delaunay triangulation of the point set, with a parameter α controlling the level of detail. The authors present an algorithm to construct the entire family of α-shapes for a given set of n points in O(n²) time. The paper discusses the implementation of the algorithm, its robustness, and several applications in scientific computing. Key concepts include α-hulls, α-diagrams, Delaunay triangulations, and Voronoi diagrams. The relationship between these geometric concepts and α-shapes is explored, providing a comprehensive understanding of the topic.