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@feng3d/bezier

v0.8.2

Published

解决n次Bézier曲线拟合与求解问题

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8

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Links

Git

Maintainers

feng3dfeng3d

Keywords

bezierfeng3d

Readme

Bézier曲线

https://wardenfeng.github.io/bezier

创建该库的原始目的是为了解决feng3d引擎粒子中时间与常量的变化曲线问题。

制作Bézier曲线这个库忙了整整3天了，感觉要跳进高等代数的坑了，得赶紧爬出这个坑，这坑太深了，以后再来跳。

说了不陷入，结果又制作了 EquationSolving.ts 提供了方程求解功能。

核心文件

  1. Bezier.ts Bézier曲线
Bezier.ts

解决任意Bézier曲线的求值求导获取极值等问题。

  1. 1次Bézier曲线
    • 求值 bezier.linear
    • 导数 bezier.linearDerivative
    • 二阶导数 bezier.linearSecondDerivative
  2. 2次Bézier曲线
    • 求值 bezier.quadratic
    • 导数 bezier.quadraticDerivative
    • 二阶导数 bezier.quadraticSecondDerivative
  3. 3次Bézier曲线
    • 求值 bezier.cubic
    • 导数 bezier.cubicDerivative
    • 二阶导数 bezier.cubicSecondDerivative
  4. n次Bézier曲线的值 n > 0
    • 求值 bezier.getValue
    • 导数 bezier.getDerivative
    • 二阶导数 bezier.getSecondDerivative
    • N阶导数 bezier.bnND
  5. n次Bézier曲线的极值列表 bezier.getExtremums
  6. n次Bézier曲线的区间列表 bezier.getMonotoneIntervals
  7. 查找区间内极值列表 bezier.getExtremums
  8. 获取目标值所在的插值度T bezier.getTFromValue
  9. 分割曲线，在曲线插值度t位置分割为两条连接起来与原曲线完全重合的曲线 bezier.split
  10. 合并曲线，合并两条连接的曲线为一条曲线并且可以还原为分割前的曲线 bezier.merge
EquationSolving.ts

解决任意一元函数求导以及方程求解等问题。

  1. 获取近似导函数 f'(x) equationSolving.getDerivative
  2. 二分法 求解 f(x) == 0 equationSolving.binary
  3. 连线法 求解 f(x) == 0 equationSolving.line
  4. 切线法 求解 f(x) == 0 equationSolving.tangent
  5. 割线法（弦截法） 求解 f(x) == 0 equationSolving.secant

示例

使用BezierCurve进行模拟canvas提供的 bezierCurveTo方法

quickstart website

随机生成n阶Bézier曲线并且播放插值动画

quickstart website

Bézier曲线编辑器

quickstart website

连续三阶Bézier曲线编辑

quickstart website

基于时间轴的连续三阶Bézier曲线编辑

该示例已经满足feng3d中曲线编辑器的需求。

quickstart website

单元测试

quickstart website

参考资料

  1. https://en.wikipedia.org/wiki/B%C3%A9zier_curve
  2. https://baike.baidu.com/item/%E8%B4%9D%E5%A1%9E%E5%B0%94%E6%9B%B2%E7%BA%BF/1091769
  3. https://blog.csdn.net/venshine/article/details/51750906
  4. https://github.com/venshine/BezierMaker
  5. https://github.com/gre/bezier-easing
  6. https://github.com/vrk/beziertool
  7. https://github.com/gre/bezier-easing-editor
  8. 高等数学 第七版上册 第三章第八节 方程的近似解

关于作者

网站：http://feng3d.com/

github：https://github.com/wardenfeng

github：https://github.com/feng3d-labs

getee：https://gitee.com/feng3d

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