Positive Data Modelling using Rational Cubic Ball Spline Function with Cubic Numerator and Denominator

Shape preserving interpolation is an essential scheme in Computer Aided Geometric Design (CAGD) for generating curves and surfaces in the plane and space, respectively. The present study concerns the problem of shape preserving data visualization through regular positive data in the form of positive curves and surfaces. A new rational cubic ball function (cubic/cubic) with shape parameters is presented to generate positive curves through positive data. It is extended to a rational bi-cubic Ball function with eight shape parameters to preserve the positivity of surfaces through 3D positive data. Shape parameters provide a guarantee to preserve the shape of the data with suitable and simple data dependent constraints which are derived in the scheme. The scheme also contains parameters which are free for designers to improve and modify the shape of the curve or surface. The proposed scheme is C1, computationally economical, local and provides independent choices for parameters as compared to existing rational schemes.