In no other field of computer science has the hardware been evolved more quickly than in computer graphics. Therefore the GPU offers, aside from the pure rendering of triangles, a bunch of further pipeline steps that allows visualisation of other graphics objects, like freeform surfaces. This bachelor’s thesis is about the rendering of freeform surfaces, in particular bezier surfaces. For that reason an implementation for management and visualisation of bézier surfaces was created for the rendering framework of the university Koblenz (CVK). For this purpose first a triangulation was implemented and finally a tesselation of bezier surfaces with normals and texture coordinates, as well as the handling of trim curves.