Convex data modelling using rational bi-cubic spline function

Muhammad Abbas^a,b,*, Ahmad Abd Majid^b, Mohd Nain Hj Awang^c, Jamaludin Md Ali^b

ABSTRACT: A piecewise rational cubic function in the form of a cubic/quadratic has been extended to a rational bi-cubic blended function to visualize 3D convex data. It involves twelve shape parameters in each rectangular mesh for its representation. Simple data-dependent constraints are imposed on four shape parameters to conserve convexity of convex data. The remaining shape parameters are left up to the user for modification of convex surfaces. Several numerical examples are presented to show the visually pleasing convexity preserving surfaces as compared to existing interpolants.

Download PDF

7 Downloads 1608 Views

^a	Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
^b	School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
^c	School of Distance Education, Universiti Sains Malaysia, 11800 USM Penang, Malaysia

* Corresponding author, E-mail: m.abbas@uos.edu.pk

Received 13 Feb 2014, Accepted 0 0000

Convex data modelling using rational bi-cubic spline function

Muhammad Abbasa,b,*, Ahmad Abd Majidb, Mohd Nain Hj Awangc, Jamaludin Md Alib

Muhammad Abbas^a,b,*, Ahmad Abd Majid^b, Mohd Nain Hj Awang^c, Jamaludin Md Ali^b