A new parameterisation method for NURBS surface interpolation

Abstract

A new method is proposed for the parameterisation of data points in NURBS surface global interpolation. In this method, the parameter value at the maximum of each rational B-spline basis function is defined as the parameter value of the associated data point. Some advantages of this method in geometric modelling are: 1. It selects the knot vectors freely regardless of the distribution of data points. 2. It is invariant under affine transformations of the data points. 3. It allows multiple data points.