caa a22 4500 60620055X CHVBK 20210128100944.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00025-015-0445-3 doi (NATIONALLICENCE)springer-10.1007/s00025-015-0445-3 The Exchange Variations of Offset Curves and Surfaces [Elektronische Daten] [Vahide Bulut, Ali Caliskan] 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. Springer Basel, 2015 Generalized offset curve nationallicence generalized offset surface nationallicence first variation of arc length nationallicence variation of floor space nationallicence Bulut Vahide Department of Mathematics, Ege University, 35100, Izmir, Turkey aut Caliskan Ali Department of Mathematics, Ege University, 35100, Izmir, Turkey aut Results in Mathematics Springer Basel 67/3-4(2015-06-01), 303-332 1422-6383 67:3-4<303 2015 67 25 https://doi.org/10.1007/s00025-015-0445-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-015-0445-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bulut Vahide Department of Mathematics, Ege University, 35100, Izmir, Turkey aut NATIONALLICENCE 700 1- Caliskan Ali Department of Mathematics, Ege University, 35100, Izmir, Turkey aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 67/3-4(2015-06-01), 303-332 1422-6383 67:3-4<303 2015 67 25