Open Access Open Access  Restricted Access Subscription or Fee Access

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

Wan Nurhadani Wan Jaafar, Muhammad Abbas, Abd Rahni Mt Piah, Tahir Nazir

Abstract



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.

Keywords


Rational cubic and bi-cubic ball functions, interpolation, positive curves and surfaces, positive data.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.