Kinematic constant distance hypersurfaces and curves from the edge of regression with the computer applications

The theory of surfaces and curves is a common field of study. Different surfaces have been investigated in differential geometry and many studies have been carried out. Defining surfaces at a constant distance from the edge of regression, Tarakçı and Hacısalihoğlu (2004) gave differential geometric properties of them. In her doctoral study, Kemer (2015) investigated the basic differential geometric properties of the M^v screw surface. In this thesis, the kinematic surface with fixed ridge distance M^g is obtained by applying the rigid body motion expressed as quaternions to the points of a surface M taken in E^3 space in the most general way. Differential geometric properties of M^g (i.e.shape operator, Gaussian and mean curvatures, asymptotic and conjugate directions expressions based on the same expressions on the M surface) are found. Then we take parameter curves of M as curvature line α of surface. \beta image curve of this curve is found on M^g. Darboux and Frenet frame, and curvature, torsion, normal curvature, geodesic curvature, geodesic torsion of curve \beta are calculated based on the same expressions of curve α. All calculations of the surfaces and curves on these surfaces are visualized by coding in Python programming language.