使用JavaScript如何实现贝塞尔曲线算法（详细教程）

<p style="position:absolute;left:0;top:0;width:500px;height:300px;overflow:hidden;">
<svg id="root" width="500" height="300" viewBox="0 0 500 300" xmlns="http://www.w3.org/2000/svg">
<title>svg</title>
<path d="M20,100 c80 -200 280 200 380 0 h-400" fill="none" stroke-width="1" stroke="gray" stroke-dasharray="3,3" />
</svg>
</p>
<p id="dotMove" style="position:absolute;width:6px;height:6px;overflow:hidden;background-color:#FF0000;"></p>
<script type="text/javascript">
/*
参考维基百科
http://zh.wikipedia.org/wiki/%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A
*/
function Point2D(x,y){
 this.x=x||0.0;
 this.y=y||0.0;
}
/*
 cp在此是四個元素的陣列:
 cp[0]為起始點，或上圖中的P0
 cp[1]為第一個控制點，或上圖中的P1
 cp[2]為第二個控制點，或上圖中的P2
 cp[3]為結束點，或上圖中的P3
 t為參數值，0 <= t <= 1
*/
function PointOnCubicBezier( cp, t )
{
 var ax, bx, cx;
 var ay, by, cy;
 var tSquared, tCubed;
 var result = new Point2D ;
 /*計算多項式係數*/
 cx = 3.0 * (cp[1].x - cp[0].x);
 bx = 3.0 * (cp[2].x - cp[1].x) - cx;
 ax = cp[3].x - cp[0].x - cx - bx;
 cy = 3.0 * (cp[1].y - cp[0].y);
 by = 3.0 * (cp[2].y - cp[1].y) - cy;
 ay = cp[3].y - cp[0].y - cy - by;
 /*計算位於參數值t的曲線點*/
 tSquared = t * t;
 tCubed = tSquared * t;
 result.x = (ax * tCubed) + (bx * tSquared) + (cx * t) + cp[0].x;
 result.y = (ay * tCubed) + (by * tSquared) + (cy * t) + cp[0].y;
 return result;
}
/*
 ComputeBezier以控制點cp所產生的曲線點，填入Point2D結構的陣列。
 呼叫者必須分配足夠的記憶體以供輸出結果，其為<sizeof(Point2D) numberOfPoints>
*/
function ComputeBezier( cp, numberOfPoints, curve )
{
 var dt;
 var i;
 dt = 1.0 / ( numberOfPoints - 1 );
 for( i = 0; i < numberOfPoints; i++)
 curve[i] = PointOnCubicBezier( cp, i*dt );
}
var cp=[
 new Point2D(20, 0), new Point2D(100, 200), new Point2D(300, -200), new Point2D(400, 0)
];
var numberOfPoints=100;
var curve=[];
ComputeBezier( cp, numberOfPoints, curve );
var i=0, dot=document.getElementById("dotMove");
setInterval(function (){
 var j = (i<100)?i:(199-i);
 dot.style.left=curve[j].x+'px';
 dot.style.top=100-curve[j].y+'px';
 if(++i==200)i=0;
}, 50);
</script>