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In many geodetic applications and tasks it is necessary to describe a 3D-point cloud by continuous mathematical functions in order to utilise them for further processing steps, especially for deformation analysis. Depending on the complexity of the object, captured by the 3D-point cloud, and the desired quality of the approximation, different functions can be used. This paper describes the most important mathematical (free-form) surfaces from polynomial functions to Bézier and B-Spline functions to Non-uniform rational B-Splines (NURBS) in this context. Beside the mathematical basics of the functions, the approximation process for curves and surfaces and the crucial modification parameters, especially the model selection, are described.