The Intrinsic Volumes of Space Filling Diagrams and their Derivatives

1^st May 2025, 14:00
Herbert Edelsbrunner
IST Austria

Abstract

The free energy of a protein in solution was conjectured to be proportional to the area of the solvent accessible surface, but there was also evidence that it might relate to the volume. The morphological approach to the question supposes that it is a linear combination of all four intrinsic volumes: the volume, area, total mean curvature, and total Gaussian curvature. We use this is the motivation to produce fast formulas for these intrinsic volumes as well as to their derivatives. Code implementing the formulas is available from Patrice Koehl at UC Davis.