In this paper, the topic of parametric surfaces and their application to the 3D point cloud is dealt with. An insight into the theoretical background is given and basic concepts according to which these surfaces behave are explained. A complete process, from converting a 3D point cloud to a triangulated surface, through the formulation of the control point matrix to the generation of the BSpline surface itself, based on the given data. Furthermore, the quality of the generated BSpline surface is assessed with respect to its compatibility with the original object. Optimization methods, by using which the compatibility can be improved, are presented and finally, optimization of the control point matrix with Nelder – Mead simplex method is conducted. The optimization is executed in the MATLAB program package using the fminsearch() command. Control points which are optimized are selected based on the variance ratio of the set of points, positioned in a certain control point's area of influence. That criterion is appropriate because the variance ratio indicates which geometric feature is in the observed area. A higher variance ratio, thus, implies that it is an area optimizing which is, in terms of improving the compatibility of the BSpline surface with the original object, more profitable because in that case, the geometric feature in question is either a corner or an edge. During the optimization, the results, contingent on the surface degree and the minimum value of variance ratio which a set of points on the control point's area of influence must measure up to in order for the aforementioned control point to be optimized, are obtained. And lastly, the obtained results are compared and a commentary on the feasibility of certain parameter choices is given.