On a new class of bézier type curves

The main purpose of this thesis is to calculate the Serret-Frenet frame and the curvature of Bézier type curves of order m in the space R^2. For this, firstly Bernstein type functions which are the basis of Bézier type curves analysed. The first and second derivatives of these functions are calculated. With the help of these derivatives, the first and second derivatives of Bézier type curves are obtained. Using these derivatives, the Serret-Frenet frame and curvature of Bézier type curves are calculated. The values of the Serret-Frenet frame and curvature of Bézier type curves in the space R^2 at the starting and ending points.