矩形域上张量积 Bézier 曲面的分段定理

Subdivision theorem for rectangular Bеzier surfaces

利用计算机辅助几何设计（ＣＡＧＤ）中使用最广泛的参数曲面之一Ｂｚｉｅｒ曲面的算子表示与重新参数化技巧，给出定义在矩形域内任一四边形上的子曲面片的张量积Ｂｚｉｅｒ表示，其Ｂｚｉｅｒ控制顶点可从原曲面的控制顶点由显式的公式计算。Ｂｚｉｅｒ曲面传统的离散方法与广义离散方法均为该文的特例。

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.