The T-hull approach to transformations of discrete point sets to continua and shape transformations between discontinuous objects using alpha-hulls

In molecular shape analysis and in the analysis of various molecular functi ons used in modeling chemical reactions and biochemical interactions, it is often useful to generate transformations that interconvert various molecul ar models into one another. Some of these models are continua whereas some others have disconnected parts or even separated discrete points. The inter conversion between such very different descriptors is a nontrivial task. Th e associated mathematical and computational problems are even more complex if relations and possible interconversions between models describing differ ent molecules are considered. In this contribution two conceptually simple techniques are described. These approaches are based on alpha-hulls and T-h ulls, leading to shape transformations between discontinuous objects and tr ansformations between discrete point sets and continua. Applications of the se methods are not restricted to chemistry, however, some of the special fe atures discussed are designed for molecular modeling applications.