FITTING MONOTONE SURFACES TO SCATTERED DATA USING C-1 PIECEWISE CUBICS

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.