Adaptive fitting with THB-splines: Error analysis and industrial applications

Automatic fitting techniques are required in many industrial applications, as for example, instrument calibration, data analysis, geometric modeling or reverse engineering. We present an error analysis of advanced techniques for scattered data approximation based on truncated hierarchical B-spline (THB-spline) constructions. The adaptive fitting framework is validated on data of industrial complexity related to geometric models of different aircraft engine parts. We demonstrate that the twofold adaptive nature of the method, which takes into account both the shape and the distribution of the data, is crucial to define an effective fully automatic scheme with suitable local refinement capabilities.