Quaternionic NURBS curves and tensor product surface patches

In the first chapter of this study titled as Quaternionic NURBS Curves and Tensor Product Surface Patches, a summary of the literature on Hermite, Bezier, B-Spline and NURBS curves and quaternion geometry is given. In addition, application areas are mentioned. In the second chapter, fundamental definitions and theorems related to the properties of Hermite, Bezier, B-Spline, NURBS curves and surfaces used in the thesis are given. In addition, some important properties of quaternion geometry, rotational surfaces and tensor product surface patches are mentioned. In the third chapter, rotational surfaces are generated with cubic Hermite and cubic Bezier curves and some characterizations are mentioned. In addition, tensor product surface designs of general type trigonometric basis functions with Bezier, B-Spline, NURBS curves of certain orders are created. Afterwards, a comparison is made between the surfaces formed by the higher order curves. In the fourth and last chapter, quaternionic Bezier, B-Spline, NURBS curves and surface patches are obtained by using general type trigonometric basis functions in quaternionic structure. In addition, the necessary conditions related to these surfaces are investigated and samples are made.