Subdivision theorem for rectangular Bеzier surfaces

Bеzier surfaces are among the most commonly used parametric surface in computer aided geometric design. By using operator representation of Bеzier surface and reparametrization techniques, this paper presents Bеzier representation of a subpatch which is defined on a quadrilateral in domain of a Bеzier surface; the new control points can be computed from the control points of original surface by an explicit formula. The traditional subdivision method and the generalized subdivision method are special cases of this theorem.