L. Han et Ll. Schumaker, FITTING MONOTONE SURFACES TO SCATTERED DATA USING C-1 PIECEWISE CUBICS, SIAM journal on numerical analysis, 34(2), 1997, pp. 569-585
We derive sufficient conditions on the Bezier net of a Bernstein-Bezie
r polynomial defined on a triangle in the plane to insure that the cor
responding surface is monotone. We then apply these conditions to cons
truct a new algorithm for fitting a monotone surface to gridded data.
The method uses C-1 cubic splines defined on the triangulation obtaine
d by drawing both diagonals of each subrectangle. In addition, we pres
ent an algorithm for the monotone scattered data interpolation problem
which is based on a method for creating gridded data from the scatter
ed data. Numerical results for several test examples are presented.