An Improved B-spline Approach for the Surfaces Reconstruction from Data Measured by Cmm

The aim of this paper is the reconstruction of a surface starting from a cloud of points. In particular we tackle with a special kind of surfaces: kinematic surfaces. A coordinate measuring machine (CMM) measures the coordinates of the curve points. Contact probing devices, as CMM, provide an accurate, sensitive and reproducible indication, but there are still uncertainties associated with them. In this work measurement uncertainty and process errors are not estimated a priori but are considered as problem variables. The starting point is a set of measured data and to approximate this data we will use a λ-spline which is an integral B-spline depending on a parameter λ; the value of this parameter affects the control points. From the computational point of view the construction of the λ-spline reduces to the computation of a linear combination of a classical Bspline and an integral B-spline. The weights of this linear combination are (1-λ) and λ hence a suitable choice of λ is crucial to obtain a good approximation. An automatic optimization algorithm has been implemented to find the optimum value of λ to get the best approximating surface. The algorithm is deeply discussed and some examples are presented to prove the effectiveness of the proposed method.