An improved positivity preserving odd degree-n Said-Ball boundary curves on rectangular grid using partial differential equation - Kherd, Ahmed; Saaban, Azizan; Man, Noraziah (Science Publications, 2016)
This paper discusses the sufficient conditions for positivity preserving odd degree-n Said-Ball boundary curves defined on a rectangular grid.We derive a sufficient condition on boundary curves of rectangular Said-Ball patches where the lower bound ordinates are adjusted independently.To construct the boundary curves for each rectangular patch, the Said-Ball polynomial solution of fourth order PDE will be considered where its coefficients can be calculated using edge Said-Ball ordinates which fulfill the positivity preserving conditions.Graphical examples are presented using well-known test functions.