Theα, β, γ- Hull and theT-hull of a point set: Tools for the analysis of shapes and relative orientations of objects in 3d-space

Abstract Two new generalizations of the concept of convexity are introduced, suitable for detailed shape characterizations of point sets. The generalizations are also applicable for direct shape comparisons between point sets and for discrimination based on relative orientations. The methods ofα, β, γ-hull andT-hull are applicable for the description of molecular shapes in external electromagnetic fields or within enzyme cavities. These methods are suggested for the study of the similarity of shapes of interacting molecules, and for the analysis of certain biochemical interactions.