A Morse theoretic approach to the geometrical feature terms specified in ISO 25178-2 and ISO 16610-85

Abstract

Abstract Morse theoretic concepts are today widely employed for the formal characterisation of surfaces and surface features. Although nowhere explicitly mentioned, several core concepts of surface metrology, such as the geometrical feature terms being specified in ISO 25178-2 and ISO 16610-85, are also closely related to Morse theory. The current lack of adequate formal definitions, however, implies that several inconsistencies and ambiguities can actually be found within the two standards. As a consequence, in the present paper the focus is laid on (a) the investigation of the interrelationships between Morse theory and the geometrical feature terms and (b) the presentation of some modifications of the existing definitions in order to eliminate the addressed ambiguities. Apart from the benefit of a consistent topological framework with respect to the definitions of the geometrical feature terms, the application of Morse theory would have the additional advantage that a powerful mathematical tool could be exploited in order to gain new insights into surface structures.