G2 Hermite interpolation with quartic regular linear normal curves

Abstract

In this paper, the properties of quartic linear normal (LN) curves are studied. In particular, we present necessary and sufficient conditions for quartic LN curves to be regular. Using these conditions, we obtain an approximation method for convex curves by quartic regular LN curves which are G2 Hermite interpolation of convex curves. We show that the approximation order of our approximation method is six. In the approximation method, a convex curve is approximated by a piecewise G2 quartic regular LN curve. Each of the pieces approximates the convex curve as long as possible within the tolerance. Consequently, the G2 spline curves consist of the minimum number of quartic regular LN curves that approximate the convex curve. The algorithm for our approximation method has been implemented and has been used to approximate convex curves.