TABLE OF CONTENTS Herbert Edelsbrunner, University of Illinois, Urbana, Illinois, USA
Space filling diagrams are geometric models of molecular conformations in three-dimensional space. Each atom is a location is space and a quantitative expression of influence on the immediate surrounding. This paper surveys the basic types of space filling diagrams with a focus on the dual alpha shape. Properties of those diagrams that relate to questions of connectivity, size, shape and symmetry, and metamorphosis are discussed.
The concept of a molecule seems to be an essential and stable ingredient in scientific studies of microscopic events. Still, people's understanding and image of what molecules are has changed with time. Even today the question whether there are atoms can still be asked, Bader [3]. We rephrase and ask whether it is useful to postulate the existence of atoms, and if yes, what model of an atom is most productive. This is the utilitarian viewpoint which is adopted in this paper, but the question is directed towards molecules. Since even the utilitarian goal is rather ambitious, we claim without justification that some of the most useful models are geometric. We then go ahead and survey a class of geometric models known as space filling diagrams.
Geometry in biology. There is in fact a large body of evidence in favor of the thesis that geometry plays an important role in life on the microscopic level. One of the most striking insights generated by decades of research is that geometric shape decides how biomolecules...
