Technological desing of curves and surfaces

Curves and surfaces play an important role not only in theoretical mathematics but also in applied fields such as technology, engineering, and computer aided design. From a theoretical perspective, curves and surfaces enable the understanding of geometric structures and the development of abstract mathematical models, while in applied fields, they provide tools for modelling complex shapes. With this understanding, our study examines generalized offset curves and their variations within the framework of curve and surface theory in Euclidean and Minkowski spaces. Within the scope of the thesis, the definition and geometric properties of generalized offset curves in Euclidean and Minkowski spaces are provided, while the variations of the fundamental functions related to these curves are analysed and supported by applied examples. Furthermore, surfaces, like curves, are defined as generalized offset surfaces in Minkowski space, and different floor space variations are analysed. In addition to the generalization and variation investigations, approaches have been developed for the construction of timelike developable surfaces along the common curvature line of surfaces. Our study aims to contribute to the subject of offset curves and surfaces and to create a new perspective in this field by providing theoretical models and applied mathematical analyses.