Monotonicity-preserving rational bi-cubic spline surface interpolation

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

ABSTRACT: We discuss the problem of monotonicity preservation of surfaces through 3D monotone data. This can be done using a rational bi-cubic blended function that is an extension of a rational cubic function in the form of a cubic numerator and quadratic denominator. The function involves twelve shape parameters in each rectangular patch. Data-dependent constraints are derived on four of these shape parameters to conserve the shape of the data while the other eight are left free to modify the monotone surface as desired. Several numerical examples are presented to show the effectiveness and capability of the scheme. The present scheme is C¹, flexible, simple, local, and economical.

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^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

Monotonicity-preserving rational bi-cubic spline surface interpolation

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