Positivity Preserving for Curve and Surface Interpolation using Rational Cubic Bézier

Abstract

In [2] the authors have asserted that their proposed partially blended rational bi-cubic spline is shape preserving only for monotone and convex data. In this paper, we prove that the scheme of [2] also positive shape preserving interpolation for positive data. We begin with positive interpolating for curve. Then the sufficient condition for positive surface interpolation is derived on all four boundary curves to form positive interpolating surface. Several numerical results are presented including comparison with some existing scheme.