Selection of Parameterization Method for Fitting of Freeform Curves Using Uniformly Spaced Data

The term “parameterization” refers to the mapping of measured data points in Cartesian space into parametric space for the fitting of freeform curves and surfaces, etc. Among the conventional parameterization methods, the chord length and centripetal parameterization methods are generally considered adequate for most of the applications. However, the choice between these two parameterization methods is not obvious. The present work attempts to analyze the measured data points in order to select between the chord length and centripetal parameterization methods for achieving better results while fitting the freeform curves. The chord length between two adjacent measured data points and the discrete curvature at each point have been used to develop an approach to select between the two parameterization methods considered. For validation purposes, the measured data points with uniform spacing have been taken from some assumed example freeform curves of varying complexities. The proposed approach has been found to correctly select the appropriate parameterization method in all examples considered.