Surface Interpolation Using Partial Differentiation Equation with Positivity Preserving Cubic Bezier Curves Boundary Condition

This paper proposed the sufficient conditions for positivity preserving cubic boundary curves defined on rectangular grid using a polynomial solution of fourth order linear PDEs in order to improve the positivity preserving of the interpolating surface. We derive a sufficient condition on boundary curves for each edges of bicubic rectangular Bezier patches where the lower bound of edge Bezier ordinates are adjusted independently. From the results of using two well-known test functions show that our proposed method are well performed in term of preserving the positivity of the boundary curves and improve the positivity preserving of overall interpolating surfaces.