In this study, shape preserving data driven rational cubic schemes are developed. A piecewise function (quadratic denominator and numerator) with two parameters was transformed to C1 function. Constraints were derived on free by means of some mathematical derivations train demonstrate convex curve. The scheme, then, advanced partially blended bi-cubic eight which controlled ascertain surface. n...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

This paper deals with the shape preserving C rational cubic interpolation. The developed rational cubic interpolating function has only one free parameter. The approximation order of rational cubic function is investigated and range of optimal error constant is determined. Moreover, positive, constrained and monotone data preserving schemes are developed. 2000 Mathematics Subject Classification...

We explore a class of polynomial tensor-product spline surfaces on 3-6 polyhedra, whose vertices have valence n = 3 or n = 6. This restriction makes it possible to exclusively use rational linear transition maps between the pieces: transitions between the bi-cubic tensor-product spline pieces are either C1 or they are G1 (tangent continuous) based on one single rational linear reparameterizatio...

Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these...

A smooth surface interpolation scheme for positive and convex data has been developed. This scheme has been extended from the rational quadratic spline function of Sarfraz [11] to a rational bi-quadratic spline function. Simple data dependent constraints are derived on the free parameters in the description of rational bi-quadratic spline function to preserve the shape of 3D positive and convex...

Abstract. In this paper, first free parameters are constrained in the description of rational cubic function [6] to preserve the shape of data that lies above the straight line. Then, rational cubic function is extended to rational bicubic partially blended function (Coons patches). A local positivity preserving scheme is developed for positive data by making constraints on free parameters in t...

Geometric modelling of several intricate and complex structures such as trees, mountains, clouds, ferns, geographic topography, coastlines is challenging in computer graphics. Traditional splines astrigonometric, polynomial, exponential, rational fail to simulate this significant class structures, which are highly irregular nature. For purpose, research develops a novel cutting-edgemethod for s...