目录
一、概述.........................................................................................................................................1
二、发展历史.................................................................................................................................1
三、Bézier 曲线的推导..................................................................................................................2
3.1 Bézier 曲线的数学表示....................................................................................................2
3.2 Bézier 曲线的性质............................................................................................................3
3.2.1 端点的性质............................................................................................................3
3.2.2 对称性....................................................................................................................4
3.2.3 凸包性....................................................................................................................4
3.2.4 几何不变性............................................................................................................5
3.2.5 变差缩减性............................................................................................................5
3.2.6 多值性....................................................................................................................5
3.2.7 交互能力................................................................................................................5
3.3 常用的 Bézier 曲线...........................................................................................................5
3.3.1 二次 Bézier 曲线....................................................................................................5
3.3.2 三次 Bézier 曲线....................................................................................................6
3.4 Bézier 曲线的拼接............................................................................................................8
3.5 de Casteljau 算法的递推过程..........................................................................................9
3.6 反求 Bézier 曲线控制点.................................................................................................10
3.7 有理 Bézier 曲线.............................................................................................................11
四、Bézier 曲线的特点及用途....................................................................................................11
4.1 Bézier 曲线的特点..........................................................................................................11
4.2 Bézier 曲线的用途..........................................................................................................12
4.3 Bézier 曲线缺点..............................................................................................................12
五、代码实现...............................................................................................................................12
5.1 二次 Bézier 曲线源代码：.............................................................................................12
5.2 三次 Bézier 曲线源代码：.............................................................................................15
六、总结.......................................................................................................................................18
