Knowledge diffusion from GIScience to other fields: the example of the usage of weighted surface networks in nanotechnology

Abstract

This article demonstrates how the generalisation of topographic surfaces has been formalised by means of graph theory and how this formalised approach has been integrated into an ISO standard that is employed within nanotechnology. By applying concepts from higher-dimensional calculus and topology, it is shown that Morse functions are those mappings that are ideally suited for the formal characterisation of topographic surfaces. Based on this result, a data structure termed weighted surface network is defined that may be applied for both the characterisation and the generalisation of the topological structure of a topographic surface. Hereafter, the focus is laid on specific issues of the standard ISO 25178-2; within this standard change trees, a data structure similar to weighted surface networks, are applied to portray the topological information of topographic surfaces. Furthermore, an approach termed Wolf pruning is used to simplify the change tree, with this pruning method being equivalent to the graph-theoretic contractions by which weighted surface networks can be simplified. Finally, some practical applications of the standard ISO 25178-2 within nanotechnology are discussed.

Keywords:

• generalisation of topographic surfaces
• weighted surface networks
• ISO 25178-2
• Wolf pruning
• nanotechnology

Acknowledgements

The assistance of F. Blateyron from Digital Surf and of P.J. Scott from the University of Huddersfield for providing the respective graphics is gratefully acknowledged.