B-spline data interpolation and approximation require parameterization at the first step. For this purpose, many algorithms have been developed, such as the uniform, centripetal, chord length, Foley and universal methods. The uniform method works well if the input data points are distributed regularly. The chord length method produces large deflections if long chords exist in the data polygon. To remove this effect, the centripetal method was developed. The traditional centripetal method uses a fixed power for chord lengths for parameter distribution. In this paper, we propose an improved version of the centripetal parameterization method for B-spline data interpolation. Our experiments show that individual dynamic power calculation can be possible for each chord length. This new parameterization method produces better behavior when compared to the traditional centripetal method and is more robust against fast changes in chord lengths since it uses the natural logarithm of chord lengths to calculate the parameters. INDEX TERMS B-spline curves, parameterization, interpolation.

In this work we deal with the enterpolation of B-spline curves to fiven data points. B-spline curves are generated and compared with the given data points by various parameterization methods. To perform B-spline curve interpolation on the input data, the parameterization and the node vector must be generated using the input data. For parameterization purposes, uniform, chord length, centripetal, Foley, universal and similar methods have been developed. The uniform method gives good results if the data points are regular. Chord-to-beam parameterization can produce undesirable oscillations in long chords. Therefore, the centripetal method has been developed which operates according to the square root of the chord distance. In this study, these methods were compared with different data sets.