Bernstein Polynomial and Magic Surfaces

The so called magic surfaces are some Bernstein-Bezier surfaces with certain magic square as their control matrixes.This kind of surfaces presents some intrinsic invariant of energe conservation of surface,and their potential applications are explored.Some geometrical properties of magic surfaces are illustrated.It is proved that any magic surface of second degree has non-positive Gaussian curvature. Approach to smooth connection of magic surfaces is discussed.