The Exchange Variations of Offset Curves and Surfaces

Abstract

This paper proposes a novel definition of generalized and standard offset curves and surfaces that was inspired by the needs in many engineering design practices. We also give some analytic properties of generalized offset curves and surfaces using this new definition. In addition, we present the first variation of standard offset curves, the first and second variation of floor space of standard offset surfaces, and the first variation of Gauss and mean curvatures between the standard offset surface and the progenitor surface and we describe some special conditions.