I want to plot the approximation of a surface by polynomials. The surface is given by (x,y,f(x,y)) where f(x,y) is given by the following expression
proc (x) options operator, arrow; (sum(i*cos((i+1)*(-2+4*x)+i), i = 1 .. 5))*(sum(i*cos((i+1)*(-2+4*x)+i), i = 1 .. 5)) end proc
with both variables varying in the interval [0,1]. Then, by using the Bernstein polynomials of two variables (see, for instance, this paper for details https://www.sciencedirect.com/science/article/pii/0021904589900956), the graph of the resulting (plot3d) surface (x,y,p(x,y)) it is not even like to the original surfaces.
Please, see this PDF of what I have done: plots.pdf
Some idea or suggestion?