Android自定义View进阶 - 贝塞尔曲线

Path之贝塞尔曲线

作者微博: @GcsSloop

【本系列相关文章】

在上一篇文章Path之基本图形中我们了解了Path的基本使用方法，本次了解Path中非常非常非常重要的内容-贝塞尔曲线。

---

一.Path常用方法表

为了兼容性(偷懒) 本表格中去除了在API21(即安卓版本5.0)以上才添加的方法。忍不住吐槽一下，为啥看起来有些顺手就能写的重载方法要等到API21才添加上啊。宝宝此刻内心也是崩溃的。

作用相关方法备注移动起点moveTo移动下一次操作的起点位置设置终点setLastPoint重置当前path中最后一个点位置，如果在绘制之前调用，效果和moveTo相同连接直线lineTo添加上一个点到当前点之间的直线到Path闭合路径close连接第一个点连接到最后一个点，形成一个闭合区域添加内容addRect, addRoundRect, addOval, addCircle, addPath, addArc, arcTo添加(矩形， 圆角矩形， 椭圆， 圆， 路径， 圆弧) 到当前Path (注意addArc和arcTo的区别)是否为空isEmpty判断Path是否为空是否为矩形isRect判断path是否是一个矩形替换路径set用新的路径替换到当前路径所有内容偏移路径offset对当前路径之前的操作进行偏移(不会影响之后的操作)贝塞尔曲线quadTo, cubicTo分别为二次和三次贝塞尔曲线的方法rXxx方法rMoveTo, rLineTo, rQuadTo, rCubicTo不带r的方法是基于原点的坐标系(偏移量)，rXxx方法是基于当前点坐标系(偏移量)填充模式setFillType, getFillType, isInverseFillType, toggleInverseFillType设置,获取,判断和切换填充模式提示方法incReserve提示Path还有多少个点等待加入(这个方法貌似会让Path优化存储结构)布尔操作(API19)op对两个Path进行布尔运算(即取交集、并集等操作)计算边界computeBounds计算Path的边界重置路径reset, rewind清除Path中的内容(reset相当于重置到new Path阶段，rewind会保留Path的数据结构)矩阵操作transform矩阵变换

二.Path详解

上一次除了一些常用函数之外，讲解的基本上都是直线，本次需要了解其中的曲线部分,说到曲线，就不得不提大名鼎鼎的贝塞尔曲线。它的发明者是下面这个人(法国数学家PierreBézier)。

贝塞尔曲线能干什么？

贝塞尔曲线的运用是十分广泛的，可以说贝塞尔曲线奠定了计算机绘图的基础(因为它可以将任何复杂的图形用精确的数学语言进行描述)，在你不经意间就已经使用过它了。

你会使用Photoshop的话，你可能会注意到里面有一个钢笔工具，这个钢笔工具核心就是贝塞尔曲线。

你说你不会PS？ 没关系，你如果看过前面的文章或者用过2D绘图，肯定绘制过圆，圆弧，圆角矩形等这些东西。这里面的圆弧部分全部都是贝塞尔曲线的运用。

贝塞尔曲线作用十分广泛，简单举几个的栗子:

• QQ小红点拖拽效果
• 一些炫酷的下拉刷新控件
• 阅读软件的翻书效果
• 一些平滑的折线图的制作
• 很多炫酷的动画效果

如何轻松入门贝塞尔曲线？

虽然贝塞尔曲线用途非常广泛，然而目前貌似并没有适合的中文教程，能够搜索出来Android关于贝塞尔曲线的中文文章基本可以分为以下几种： 
* 科普型(只是让人了解贝塞尔，并没有实质性的内容) 
* 装逼型(摆出来一大堆公式，引用一堆英文原文) 
* 基础型(仅仅是讲解贝塞尔曲线的两个函数用法) 
* 实战型(根据实例讲解其中贝塞尔曲线的运用)

以上几种类型中比较有用的就是基础型和实战型，但两者各有不足，本文会综合两者内容，从零开始学习贝塞尔曲线。

第一步.理解贝塞尔曲线的原理

此处理解贝塞尔曲线并非是学会公式的推倒过程，而是要了解贝塞尔曲线是如何生成的。贝塞尔曲线是用一系列点来控制曲线状态的，我将这些点简单分为两类：

类型作用数据点确定曲线的起始和结束位置控制点确定曲线的弯曲程度

此处暂时仅作了解概念，接下来就会讲解其中详细的含义。

一阶曲线原理：

一阶曲线是没有控制点的，仅有两个数据点(A 和 B)，最终效果一个线段。

上图表示的是一阶曲线生成过程中的某一个阶段，动态过程可以参照下图。

PS：一阶曲线其实就是前面讲解过的lineTo。

二阶曲线原理：

二阶曲线由两个数据点(A 和 C)，一个控制点(B)来描述曲线状态，大致如下：

上图中红色曲线部分就是传说中的二阶贝塞尔曲线，那么这条红色曲线是如何生成的呢？接下来我们就以其中的一个状态分析一下：

连接AB BC，并在AB上取点D，BC上取点E，使其满足条件： 

连接DE，取点F，使得: 

这样获取到的点F就是贝塞尔曲线上的一个点，动态过程如下：

PS: 二阶曲线对应的方法是quadTo

三阶曲线原理：

三阶曲线由两个数据点(A 和 D)，两个控制点(B 和 C)来描述曲线状态，如下：

三阶曲线计算过程与二阶类似，具体可以见下图动态效果：

PS: 三阶曲线对应的方法是cubicTo

贝塞尔曲线速查表

强烈推荐点击这里练习贝塞尔曲线，可以加深对贝塞尔曲线的理解程度。

第二步.了解贝塞尔曲线相关函数使用方法

一阶曲线：

一阶曲线是一条线段，非常简单，可以参见上一篇文章Path之基本操作，此处就不详细讲解了。

二阶曲线：

通过上面对二阶曲线的简单了解，我们知道二阶曲线是由两个数据点，一个控制点构成，接下来我们就用一个实例来演示二阶曲线是如何运用的。

首先，两个数据点是控制贝塞尔曲线开始和结束的位置，比较容易理解，而控制点则是控制贝塞尔的弯曲状态，相对来说比较难以理解，所以本示例重点在于理解贝塞尔曲线弯曲状态与控制点的关系，废话不多说，先上效果图：

为了更加容易看出控制点与曲线弯曲程度的关系，上图中绘制出了辅助点和辅助线，从上面的动态图可以看出，贝塞尔曲线在动态变化过程中有类似于橡皮筋一样的弹性效果，因此在制作一些弹性效果的时候很常用。

主要代码如下：

<code class="language-java hljs  has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">class</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Bezier</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">extends</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">View</span> {</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> Paint mPaint;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> centerX, centerY;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> PointF start, end, control;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-title" style="box-sizing: border-box;">Bessel1</span>(Context context) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>(context);        mPaint = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Paint();        mPaint.setColor(Color.BLACK);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>);        mPaint.setStyle(Paint.Style.STROKE);        mPaint.setTextSize(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">60</span>);        start = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        end = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        control = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">protected</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">onSizeChanged</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> w, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> h, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> oldw, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> oldh) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>.onSizeChanged(w, h, oldw, oldh);        centerX = w/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;        centerY = h/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 初始化数据点和控制点的位置</span>        start.x = centerX-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">200</span>;        start.y = centerY;        end.x = centerX+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">200</span>;        end.y = centerY;        control.x = centerX;        control.y = centerY-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">100</span>;    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">boolean</span> <span class="hljs-title" style="box-sizing: border-box;">onTouchEvent</span>(MotionEvent event) {        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 根据触摸位置更新控制点，并提示重绘</span>        control.x = event.getX();        control.y = event.getY();        invalidate();        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">protected</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">onDraw</span>(Canvas canvas) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>.onDraw(canvas);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制数据点和控制点</span>        mPaint.setColor(Color.GRAY);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20</span>);        canvas.drawPoint(start.x,start.y,mPaint);        canvas.drawPoint(end.x,end.y,mPaint);        canvas.drawPoint(control.x,control.y,mPaint);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制辅助线</span>        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>);        canvas.drawLine(start.x,start.y,control.x,control.y,mPaint);        canvas.drawLine(end.x,end.y,control.x,control.y,mPaint);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制贝塞尔曲线</span>        mPaint.setColor(Color.RED);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>);        Path path = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Path();        path.moveTo(start.x,start.y);        path.quadTo(control.x,control.y,end.x,end.y);        canvas.drawPath(path, mPaint);    }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li></ul>

三阶曲线：

三阶曲线由两个数据点和两个控制点来控制曲线状态。

代码:

<code class="language-java hljs  has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">class</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Bezier2</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">extends</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">View</span> {</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> Paint mPaint;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> centerX, centerY;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> PointF start, end, control1, control2;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">boolean</span> mode = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-title" style="box-sizing: border-box;">Bezier2</span>(Context context) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">this</span>(context, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">null</span>);    }    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-title" style="box-sizing: border-box;">Bezier2</span>(Context context, AttributeSet attrs) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>(context, attrs);        mPaint = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Paint();        mPaint.setColor(Color.BLACK);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>);        mPaint.setStyle(Paint.Style.STROKE);        mPaint.setTextSize(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">60</span>);        start = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        end = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        control1 = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        control2 = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);    }    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">setMode</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">boolean</span> mode) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">this</span>.mode = mode;    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">protected</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">onSizeChanged</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> w, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> h, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> oldw, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> oldh) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>.onSizeChanged(w, h, oldw, oldh);        centerX = w / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;        centerY = h / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 初始化数据点和控制点的位置</span>        start.x = centerX - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">200</span>;        start.y = centerY;        end.x = centerX + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">200</span>;        end.y = centerY;        control1.x = centerX;        control1.y = centerY - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">100</span>;        control2.x = centerX;        control2.y = centerY - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">100</span>;    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">boolean</span> <span class="hljs-title" style="box-sizing: border-box;">onTouchEvent</span>(MotionEvent event) {        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 根据触摸位置更新控制点，并提示重绘</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (mode) {            control1.x = event.getX();            control1.y = event.getY();        } <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span> {            control2.x = event.getX();            control2.y = event.getY();        }        invalidate();        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">protected</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">onDraw</span>(Canvas canvas) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>.onDraw(canvas);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//drawCoordinateSystem(canvas);</span>        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制数据点和控制点</span>        mPaint.setColor(Color.GRAY);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20</span>);        canvas.drawPoint(start.x, start.y, mPaint);        canvas.drawPoint(end.x, end.y, mPaint);        canvas.drawPoint(control1.x, control1.y, mPaint);        canvas.drawPoint(control2.x, control2.y, mPaint);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制辅助线</span>        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>);        canvas.drawLine(start.x, start.y, control1.x, control1.y, mPaint);        canvas.drawLine(control1.x, control1.y,control2.x, control2.y, mPaint);        canvas.drawLine(control2.x, control2.y,end.x, end.y, mPaint);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制贝塞尔曲线</span>        mPaint.setColor(Color.RED);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>);        Path path = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Path();        path.moveTo(start.x, start.y);        path.cubicTo(control1.x, control1.y, control2.x,control2.y, end.x, end.y);        canvas.drawPath(path, mPaint);    }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li></ul>

三阶曲线相比于二阶曲线可以制作更加复杂的形状，但是对于高阶的曲线，用低阶的曲线组合也可达到相同的效果，就是传说中的降阶。因此我们对贝塞尔曲线的封装方法一般最高只到三阶曲线。

降阶与升阶

类型释义变化降阶在保持曲线形状与方向不变的情况下，减少控制点数量，即降低曲线阶数方法变得简单，数据点变多，控制点可能减少，灵活性变弱升阶在保持曲线形状与方向不变的情况下，增加控制点数量，即升高曲线阶数方法更加复杂，数据点不变，控制点增加，灵活性变强

第三步.贝塞尔曲线使用实例

在制作这个实例之前，首先要明确一个内容，就是在什么情况下需要使用贝塞尔曲线？

需要绘制不规则图形时？ 当然不是！目前来说，我觉得使用贝塞尔曲线主要有以下几个方面(仅个人拙见，可能存在错误，欢迎指正)

序号内容用例1事先不知道曲线状态，需要实时计算时天气预报气温变化的平滑折线图2显示状态会根据用户操作改变时QQ小红点，仿真翻书效果3一些比较复杂的运动状态(配合PathMeasure使用)复杂运动状态的动画效果

至于只需要一个静态的曲线图形的情况，用图片岂不是更好，大量的计算会很不划算。

如果是显示SVG矢量图的话，已经有相关的解析工具了(内部依旧运用的有贝塞尔曲线)，不需要手动计算。

贝塞尔曲线的主要优点是可以实时控制曲线状态，并可以通过改变控制点的状态实时让曲线进行平滑的状态变化。

接下来我们就用一个简单的示例让一个圆渐变成为心形：

效果图：

思路分析：

我们最终的需要的效果是将一个圆转变成一个心形，通过分析可知，圆可以由四段三阶贝塞尔曲线组合而成，如下：

心形也可以由四段的三阶的贝塞尔曲线组成，如下：

两者的差别仅仅在于数据点和控制点位置不同，因此只需要调整数据点和控制点的位置，就能将圆形变为心形。

核心难点：

1.如何得到数据点和控制点的位置？

关于使用绘制圆形的数据点与控制点早就已经有人详细的计算好了，可以参考stackoverflow的一个回答How to create circle with Bézier curves?其中的数据只需要拿来用即可。

而对于心形的数据点和控制点，可以由圆形的部分数据点和控制点平移后得到，具体参数可以自己慢慢调整到一个满意的效果。

2.如何达到渐变效果？

渐变其实就是每次对数据点和控制点稍微移动一点，然后重绘界面，在短时间多次的调整数据点与控制点，使其逐渐接近目标值，通过不断的重绘界面达到一种渐变的效果。过程可以参照下图动态效果：

代码：

<code class="language-java hljs  has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">class</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Bezier3</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">extends</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">View</span> {</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">static</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">final</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span> C = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.551915024494</span>f;     <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 一个常量，用来计算绘制圆形贝塞尔曲线控制点的位置</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> Paint mPaint;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> mCenterX, mCenterY;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> PointF mCenter = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> PointF(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span> mCircleRadius = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">200</span>;                  <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 圆的半径</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span> mDifference = mCircleRadius*C;        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 圆形的控制点与数据点的差值</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span>[] mData = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span>[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>];               <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 顺时针记录绘制圆形的四个数据点</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span>[] mCtrl = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span>[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">16</span>];              <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 顺时针记录绘制圆形的八个控制点</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span> mDuration = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1000</span>;                     <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 变化总时长</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span> mCurrent = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;                         <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 当前已进行时长</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span> mCount = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">100</span>;                         <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 将时长总共划分多少份</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">float</span> mPiece = mDuration/mCount;            <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 每一份的时长</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-title" style="box-sizing: border-box;">Bezier3</span>(Context context) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">this</span>(context, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">null</span>);    }    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-title" style="box-sizing: border-box;">Bezier3</span>(Context context, AttributeSet attrs) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>(context, attrs);        mPaint = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Paint();        mPaint.setColor(Color.BLACK);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>);        mPaint.setStyle(Paint.Style.STROKE);        mPaint.setTextSize(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">60</span>);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 初始化数据点</span>        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] = mCircleRadius;        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>] = mCircleRadius;        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>] = -mCircleRadius;        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>] = -mCircleRadius;        mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 初始化控制点</span>        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>]+mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>];        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>];        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>]+mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>];        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>]-mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>]+mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>];        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>]-mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>]  = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>];        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">10</span>] = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>];        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">11</span>] = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>]-mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>] = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>];        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">13</span>] = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>]+mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">14</span>] = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>]-mDifference;        mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">15</span>] = mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>];    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">protected</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">onSizeChanged</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> w, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> h, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> oldw, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> oldh) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>.onSizeChanged(w, h, oldw, oldh);        mCenterX = w / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;        mCenterY = h / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;    }    <span class="hljs-annotation" style="color: rgb(155, 133, 157); box-sizing: border-box;">@Override</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">protected</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">onDraw</span>(Canvas canvas) {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">super</span>.onDraw(canvas);         drawCoordinateSystem(canvas);       <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制坐标系</span>        canvas.translate(mCenterX, mCenterY); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 将坐标系移动到画布中央</span>        canvas.scale(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);                 <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 翻转Y轴</span>        drawAuxiliaryLine(canvas);        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制贝塞尔曲线</span>        mPaint.setColor(Color.RED);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>);        Path path = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Path();        path.moveTo(mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>],mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]);        path.cubicTo(mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>],     mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>], mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>]);        path.cubicTo(mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>],     mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>], mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>]);        path.cubicTo(mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>],  mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">10</span>], mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">11</span>],    mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>], mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>]);        path.cubicTo(mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>], mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">13</span>], mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">14</span>], mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">15</span>],    mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>], mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]);        canvas.drawPath(path, mPaint);        mCurrent += mPiece;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (mCurrent < mDuration){            mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] -= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">120</span>/mCount;            mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7</span>] += <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">80</span>/mCount;            mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>] += <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">80</span>/mCount;            mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>] -= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20</span>/mCount;            mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">10</span>] += <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20</span>/mCount;        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//    postInvalidateDelayed((long) mPiece);</span>        }    }    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制辅助线</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">drawAuxiliaryLine</span>(Canvas canvas) {        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制数据点和控制点</span>        mPaint.setColor(Color.GRAY);        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20</span>);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i<<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>; i+=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>){            canvas.drawPoint(mData[i],mData[i+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>], mPaint);        }        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i<<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">16</span>; i+=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>){            canvas.drawPoint(mCtrl[i], mCtrl[i+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>], mPaint);        }        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制辅助线</span>        mPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>, j=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>; i<<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8</span>; i+=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>, j+=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>){            canvas.drawLine(mData[i],mData[i+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>],mCtrl[j],mCtrl[j+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>],mPaint);            canvas.drawLine(mData[i],mData[i+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>],mCtrl[j+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>],mCtrl[j+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>],mPaint);        }        canvas.drawLine(mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>],mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>],mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>],mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>],mPaint);        canvas.drawLine(mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>],mData[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>],mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">14</span>],mCtrl[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">15</span>],mPaint);    }    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制坐标系</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">drawCoordinateSystem</span>(Canvas canvas) {        canvas.save();                      <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 绘制做坐标系</span>        canvas.translate(mCenterX, mCenterY); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 将坐标系移动到画布中央</span>        canvas.scale(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);                 <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 翻转Y轴</span>        Paint fuzhuPaint = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Paint();        fuzhuPaint.setColor(Color.RED);        fuzhuPaint.setStrokeWidth(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>);        fuzhuPaint.setStyle(Paint.Style.STROKE);        canvas.drawLine(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2000</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2000</span>, fuzhuPaint);        canvas.drawLine(-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2000</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2000</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, fuzhuPaint);        canvas.restore();    }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li><li style="box-sizing: border-box; padding: 0px 5px;">127</li><li style="box-sizing: border-box; padding: 0px 5px;">128</li><li style="box-sizing: border-box; padding: 0px 5px;">129</li><li style="box-sizing: border-box; padding: 0px 5px;">130</li><li style="box-sizing: border-box; padding: 0px 5px;">131</li><li style="box-sizing: border-box; padding: 0px 5px;">132</li><li style="box-sizing: border-box; padding: 0px 5px;">133</li><li style="box-sizing: border-box; padding: 0px 5px;">134</li><li style="box-sizing: border-box; padding: 0px 5px;">135</li><li style="box-sizing: border-box; padding: 0px 5px;">136</li><li style="box-sizing: border-box; padding: 0px 5px;">137</li><li style="box-sizing: border-box; padding: 0px 5px;">138</li><li style="box-sizing: border-box; padding: 0px 5px;">139</li><li style="box-sizing: border-box; padding: 0px 5px;">140</li><li style="box-sizing: border-box; padding: 0px 5px;">141</li><li style="box-sizing: border-box; padding: 0px 5px;">142</li><li style="box-sizing: border-box; padding: 0px 5px;">143</li><li style="box-sizing: border-box; padding: 0px 5px;">144</li><li style="box-sizing: border-box; padding: 0px 5px;">145</li><li style="box-sizing: border-box; padding: 0px 5px;">146</li><li style="box-sizing: border-box; padding: 0px 5px;">147</li><li style="box-sizing: border-box; padding: 0px 5px;">148</li><li style="box-sizing: border-box; padding: 0px 5px;">149</li><li style="box-sizing: border-box; padding: 0px 5px;">150</li><li style="box-sizing: border-box; padding: 0px 5px;">151</li><li style="box-sizing: border-box; padding: 0px 5px;">152</li><li style="box-sizing: border-box; padding: 0px 5px;">153</li><li style="box-sizing: border-box; padding: 0px 5px;">154</li><li style="box-sizing: border-box; padding: 0px 5px;">155</li><li style="box-sizing: border-box; padding: 0px 5px;">156</li><li style="box-sizing: border-box; padding: 0px 5px;">157</li><li style="box-sizing: border-box; padding: 0px 5px;">158</li><li style="box-sizing: border-box; padding: 0px 5px;">159</li><li style="box-sizing: border-box; padding: 0px 5px;">160</li><li style="box-sizing: border-box; padding: 0px 5px;">161</li><li style="box-sizing: border-box; padding: 0px 5px;">162</li><li style="box-sizing: border-box; padding: 0px 5px;">163</li><li style="box-sizing: border-box; padding: 0px 5px;">164</li><li style="box-sizing: border-box; padding: 0px 5px;">165</li><li style="box-sizing: border-box; padding: 0px 5px;">166</li><li style="box-sizing: border-box; padding: 0px 5px;">167</li><li style="box-sizing: border-box; padding: 0px 5px;">168</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li><li style="box-sizing: border-box; padding: 0px 5px;">127</li><li style="box-sizing: border-box; padding: 0px 5px;">128</li><li style="box-sizing: border-box; padding: 0px 5px;">129</li><li style="box-sizing: border-box; padding: 0px 5px;">130</li><li style="box-sizing: border-box; padding: 0px 5px;">131</li><li style="box-sizing: border-box; padding: 0px 5px;">132</li><li style="box-sizing: border-box; padding: 0px 5px;">133</li><li style="box-sizing: border-box; padding: 0px 5px;">134</li><li style="box-sizing: border-box; padding: 0px 5px;">135</li><li style="box-sizing: border-box; padding: 0px 5px;">136</li><li style="box-sizing: border-box; padding: 0px 5px;">137</li><li style="box-sizing: border-box; padding: 0px 5px;">138</li><li style="box-sizing: border-box; padding: 0px 5px;">139</li><li style="box-sizing: border-box; padding: 0px 5px;">140</li><li style="box-sizing: border-box; padding: 0px 5px;">141</li><li style="box-sizing: border-box; padding: 0px 5px;">142</li><li style="box-sizing: border-box; padding: 0px 5px;">143</li><li style="box-sizing: border-box; padding: 0px 5px;">144</li><li style="box-sizing: border-box; padding: 0px 5px;">145</li><li style="box-sizing: border-box; padding: 0px 5px;">146</li><li style="box-sizing: border-box; padding: 0px 5px;">147</li><li style="box-sizing: border-box; padding: 0px 5px;">148</li><li style="box-sizing: border-box; padding: 0px 5px;">149</li><li style="box-sizing: border-box; padding: 0px 5px;">150</li><li style="box-sizing: border-box; padding: 0px 5px;">151</li><li style="box-sizing: border-box; padding: 0px 5px;">152</li><li style="box-sizing: border-box; padding: 0px 5px;">153</li><li style="box-sizing: border-box; padding: 0px 5px;">154</li><li style="box-sizing: border-box; padding: 0px 5px;">155</li><li style="box-sizing: border-box; padding: 0px 5px;">156</li><li style="box-sizing: border-box; padding: 0px 5px;">157</li><li style="box-sizing: border-box; padding: 0px 5px;">158</li><li style="box-sizing: border-box; padding: 0px 5px;">159</li><li style="box-sizing: border-box; padding: 0px 5px;">160</li><li style="box-sizing: border-box; padding: 0px 5px;">161</li><li style="box-sizing: border-box; padding: 0px 5px;">162</li><li style="box-sizing: border-box; padding: 0px 5px;">163</li><li style="box-sizing: border-box; padding: 0px 5px;">164</li><li style="box-sizing: border-box; padding: 0px 5px;">165</li><li style="box-sizing: border-box; padding: 0px 5px;">166</li><li style="box-sizing: border-box; padding: 0px 5px;">167</li><li style="box-sizing: border-box; padding: 0px 5px;">168</li></ul>

三.总结

其实关于贝塞尔曲线最重要的是核心理解贝塞尔曲线的生成方式，只有理解了贝塞尔曲线的生成方式，才能更好的运用贝塞尔曲线。在上一篇末尾说本篇要涉及一点自相交图形渲染问题，不幸的是，本篇没有了，请期待下一篇(可能会在下一篇中出现o(￣︶￣)o)，下一篇依旧Path相关内容，教给大家一些更好玩的东西。

解锁新的境界之【绘制一个弹性的圆】：

(,,• ₃ •,,)

PS: 由于本人水平有限，某些地方可能存在误解或不准确，如果你对此有疑问可以提交Issues进行反馈。

About Me

作者微博: @GcsSloop

参考资料

Path

Canvas

贝塞尔曲线扫盲

贝塞尔曲线-维基百科

How to create circle with Bézier curves?

三次贝塞尔曲线练习之弹性的圆