A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.
"Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface." J. Appl. Math. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/987076