Shape-preserving interpolation by G1 and G2 PH quintic splines

Abstract

The interpolation of a planar sequence of points p 0 ,..., p N by shape-preserving G 1 or G 2 PH quintic splines with specified end conditions is considered. The shape-preservation property is secured by adjusting 'tension' parameters that arise upon relaxing parametric continuity to geometric continuity. In the G 2 case, the PH spline construction is based on applying Newton-Raphson iterations to a global system of equations, commencing with a suitable initialization strategy-this generalizes the construction described previously in Numerical Algorithms 27, 35-60 (2001). As a simpler and cheaper alternative, a shape-preserving G 1 PH quintic spline scheme is also introduced. Although the order of continuity is lower, this has the advantage of allowing construction through purely local equations.