算子表示的矩形域Bernstein-Bézier曲面

Operator Representation of Rectangular Bernstein-Bézier Surface

通过引入3个算子:移位算子、向前差分算子和恒等算子,将矩形域上Bernstein-Bézier曲面(B-B曲面)表示为更简洁直观的算子表示形式,并讨论了用算子表示的B-B曲面的各种性质,给出了相关的证明.结果表明,算子表示形式从另一角度揭示了矩形域B-B曲面的基本几何性质,也大大简化了相关结论的推导过程.

Three operators, the translation（operator）, forward difference and identical, are introduced firstly. Then the rectangular Bernstein-Bézier surface in conventional form is transformed to its operator form. Several properties of the surface are discussed in its operator form. Related proofs are given to show that the operator representation is more intuitional and compact than the conventional one. The operator representation reveals the basic geometrical properties of B-B surface from another angle of view and simplifies the deductions of related theorems.