Herbert Edelsbrunner: The intrinsic volumes of a space filling diagram and their derivatives скачать в хорошем качестве

Herbert Edelsbrunner: The intrinsic volumes of a space filling diagram and their derivatives

The morphological approach to modeling the free energy in molecular dynamics by Roth and Mecke suggests to write it as a linear combination of weighted versions of the four intrinsic volumes of a space filling diagram: the volume, the area, the total mean curvature, and the total Gaussian curvature. Based on the Alpha shape representation of a union of solid spheres, we derive formulas for the weighted intrinsic volumes as well as for their derivatives. Acknowledgements. The formulas for the weighted volume and the area derivatives go back to joint work with Robert Bryant, Patrice Koehl, and Michael Levitt more that a decade ago, while the formulas for the weighted mean and Gaussian curvature derivatives have been obtained recently in collaboration with Arseniy Akopyan.