Interpolating sequences of 3D-data with C2 quintic PH B-spline curves

Abstract

The goal of this paper is to present an effective method for interpolating sequences of 3D-data by means of C2 quintic Pythagorean-Hodograph (PH) B-spline curves. The strategy we propose works successfully with both open and closed sequences of 3D-points. It relies on calculations that are mostly explicit thanks to the fact that the interpolation conditions can explicitly be solved in dependence of the coefficients of the pre-image PH B-spline curve. In order to select a more suitable interpolant a functional is minimized in two remaining free coefficients of the pre-image PH B-spline curve and some angular parameters