We describe a new method for creating rectangular Bezier surface patches on an implicit cubic surface. Traditional techniques for representing surfaces have relied on parametric representations of surfaces, that, in general, generate surfaces of implicit degree eight in case of rectangular Bezier surfaces with rational biquadratic parametrization. Thus we have achieved low-degree algebraic surface patch construction by reducing the implicit degree from eight to three. The construction uses a rectangular biquadratic Bezier control polyhedron, embedded within a tetrahedron and satisfying a projective constraint. The control polyhedron and the resulting cubic surface patch satisfy all of the standard properties of parametric Bezier surfaces, including interpolation of the corners of the control polyhedron and the convex hull property.
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