Transition curves in computer aided geometric design

In the first chapter of this study titled as Transition Curves in Computer Aided Geometric Design a summary of the literature related to the Bezier curves and B-spline curves is given. Also, the application areas of these curves are presented. In the second chapter, some fundamental definitions and theorems with respect of differential geometry of the curves used in the thesis are given. Next, some important properties of the Bezier curves and B-spline curves are recalled. In the third chapter, the definition of the Beta-Bezier curve is given and the existence of the cusp and loop points of the cubic Beta-Bezier curve is researched. Next, the necessary conditions to join two cubic Beta-Bezier curves are investigated. Lastly, the conditions of the Pythogorean-Hodograph curve for the cubic Beta-Bezier curves are presented. In the fourth chapter, new cubic Bezier-like basis functions are defined and a new cubic Bezier-like curve is created by using this base functions. Further, the properties of these curves are investigated. In the fifth and last chapter, the quadratic B-spline curve is considered. Moreover, the necessary conditions are researched so that the curve is a spiral curve.