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Research articles

ScienceAsia 43 (2017): 186-194 |doi: 10.2306/scienceasia1513-1874.2017.43.186

C1 rational interpolation schemes for modelling positive and/or monotonic 3D data

Xiangbin Qina, Lei Qinb, Qingsong Xua,*

ABSTRACT:     By using the boolean sum of cubic interpolating operators to blend together kinds of rational quartic/linear interpolation splines as the boundary functions, a class of C1 bi-cubic partially blended rational quartic/linear interpolation splines with four families of local control parameters is constructed. By developing new constraints on the boundary functions, simple sufficient data-dependent conditions are derived for the local control parameters to generate C1 positivity- and/or monotonicity-preserving interpolation surfaces for positive and/or monotonic data on rectangular grids.

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a School of Mathematics and Statistics, Central South University, Changsha 410083, China
b College of Environmental Science and Engineering, Hunan University, Changsha 410082, China

* Corresponding author, E-mail: qsxu@csu.edu.cn

Received 13 Oct 2015, Accepted 26 Jul 2017