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