【摘要】 Bezier曲线是计算机辅助几何设计(CAGD)领域中广泛运用的一种曲线。首先引入三个基本算子:移位算子、恒等算子和向前差分算子,然后将Bernstein-Bezier形式的Bezier曲线表示为更为简洁和直观的算子表示形式,并进一步讨论算子表示下Bezier曲线的各种性质,给出相关证明过程。实践表明,算子表示形式从与传统表示方法不同的另一角度揭示了Bezier曲线基本几何性质,简化了相关结论的推导。更多还原

【Abstract】 Bezier curve is one of the most widely used curves in Computer Aided Geometry Design (CAGD). Three operators, the transpositional, identical and forward differential, are introduced firstly. Then the Bezier curve in conventional Bernstein-Bezier (B-B) form is transformed to its operator form. Several properties of the curve 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 geometry properties of Bezier curve from a completely different angle of view and simplifies the deductions of relative theorems.更多还原