如何使用javascript HTML5画布通过N个点绘制平滑的曲线？

将后续采样点与不相交的“curveTo”类型函数连接在一起的问题在于曲线相遇的位置不平滑。这是因为两条曲线共享一个终点，但受到完全不相交的控制点的影响。一种解决方案是将“曲线”弯曲到“接下来的2个后续采样点之间的中点。使用这些新的插值点连接曲线可在端点处实现平滑过渡（一次迭代的终点将成为下一次迭代的控制点）。换句话说，两条不相交的曲线现在有更多的共同点。

此解决方案摘自《Foundation ActionScript 3.0 Animation： Making Things Move》一书。p.95 - 渲染技术：创建多条曲线。

注意：这个解决方案实际上并没有通过每个点进行绘制，这是我问题的标题（而是通过采样点近似曲线，但从未穿过采样点），但是对于我的目的（绘图应用程序），它对我来说已经足够好了，从视觉上看，你无法分辨出区别。有一个解决方案可以遍历所有采样点，但它要复杂得多（请参阅 http://www.cartogrammar.com/blog/actionscript-curves-update/)

以下是近似方法的绘制代码：

// move to the first point
   ctx.moveTo(points[0].x, points[0].y);


   for (i = 1; i < points.length - 2; i ++)
   {
      var xc = (points[i].x + points[i + 1].x) / 2;
      var yc = (points[i].y + points[i + 1].y) / 2;
      ctx.quadraticCurveTo(points[i].x, points[i].y, xc, yc);
   }
 // curve through the last two points
 ctx.quadraticCurveTo(points[i].x, points[i].y, points[i+1].x,points[i+1].y);

有点晚了，但为了记录。

通过使用基本样条（也称为规范样条）绘制穿过点的平滑曲线，可以实现平滑线。

我为画布制作了这个函数 - 它分为三个函数以增加多功能性。主包装器函数如下所示：

function drawCurve(ctx, ptsa, tension, isClosed, numOfSegments, showPoints) {

    showPoints  = showPoints ? showPoints : false;

    ctx.beginPath();

    drawLines(ctx, getCurvePoints(ptsa, tension, isClosed, numOfSegments));

    if (showPoints) {
        ctx.stroke();
        ctx.beginPath();
        for(var i=0;i<ptsa.length-1;i+=2) 
                ctx.rect(ptsa[i] - 2, ptsa[i+1] - 2, 4, 4);
    }
}

要绘制曲线，则有一个数组，其 x，y 点的顺序为：。x1,y1, x2,y2, ...xn,yn

像这样使用它：

var myPoints = [10,10, 40,30, 100,10]; //minimum two points
var tension = 1;

drawCurve(ctx, myPoints); //default tension=0.5
drawCurve(ctx, myPoints, tension);

上面的函数调用两个子函数，一个用于计算平滑点。这将返回一个包含新点的数组 - 这是计算平滑点的核心函数：

function getCurvePoints(pts, tension, isClosed, numOfSegments) {

    // use input value if provided, or use a default value   
    tension = (typeof tension != 'undefined') ? tension : 0.5;
    isClosed = isClosed ? isClosed : false;
    numOfSegments = numOfSegments ? numOfSegments : 16;

    var _pts = [], res = [],    // clone array
        x, y,           // our x,y coords
        t1x, t2x, t1y, t2y, // tension vectors
        c1, c2, c3, c4,     // cardinal points
        st, t, i;       // steps based on num. of segments

    // clone array so we don't change the original
    //
    _pts = pts.slice(0);

    // The algorithm require a previous and next point to the actual point array.
    // Check if we will draw closed or open curve.
    // If closed, copy end points to beginning and first points to end
    // If open, duplicate first points to befinning, end points to end
    if (isClosed) {
        _pts.unshift(pts[pts.length - 1]);
        _pts.unshift(pts[pts.length - 2]);
        _pts.unshift(pts[pts.length - 1]);
        _pts.unshift(pts[pts.length - 2]);
        _pts.push(pts[0]);
        _pts.push(pts[1]);
    }
    else {
        _pts.unshift(pts[1]);   //copy 1. point and insert at beginning
        _pts.unshift(pts[0]);
        _pts.push(pts[pts.length - 2]); //copy last point and append
        _pts.push(pts[pts.length - 1]);
    }

    // ok, lets start..

    // 1. loop goes through point array
    // 2. loop goes through each segment between the 2 pts + 1e point before and after
    for (i=2; i < (_pts.length - 4); i+=2) {
        for (t=0; t <= numOfSegments; t++) {

            // calc tension vectors
            t1x = (_pts[i+2] - _pts[i-2]) * tension;
            t2x = (_pts[i+4] - _pts[i]) * tension;

            t1y = (_pts[i+3] - _pts[i-1]) * tension;
            t2y = (_pts[i+5] - _pts[i+1]) * tension;

            // calc step
            st = t / numOfSegments;

            // calc cardinals
            c1 =   2 * Math.pow(st, 3)  - 3 * Math.pow(st, 2) + 1; 
            c2 = -(2 * Math.pow(st, 3)) + 3 * Math.pow(st, 2); 
            c3 =       Math.pow(st, 3)  - 2 * Math.pow(st, 2) + st; 
            c4 =       Math.pow(st, 3)  -     Math.pow(st, 2);

            // calc x and y cords with common control vectors
            x = c1 * _pts[i]    + c2 * _pts[i+2] + c3 * t1x + c4 * t2x;
            y = c1 * _pts[i+1]  + c2 * _pts[i+3] + c3 * t1y + c4 * t2y;

            //store points in array
            res.push(x);
            res.push(y);

        }
    }

    return res;
}

并且实际上将点绘制为平滑曲线（或任何其他分割线，只要您有一个x，y数组）：

function drawLines(ctx, pts) {
    ctx.moveTo(pts[0], pts[1]);
    for(i=2;i<pts.length-1;i+=2) ctx.lineTo(pts[i], pts[i+1]);
}

var ctx = document.getElementById("c").getContext("2d");


function drawCurve(ctx, ptsa, tension, isClosed, numOfSegments, showPoints) {

  ctx.beginPath();

  drawLines(ctx, getCurvePoints(ptsa, tension, isClosed, numOfSegments));
  
  if (showPoints) {
    ctx.beginPath();
    for(var i=0;i<ptsa.length-1;i+=2) 
      ctx.rect(ptsa[i] - 2, ptsa[i+1] - 2, 4, 4);
  }

  ctx.stroke();
}


var myPoints = [10,10, 40,30, 100,10, 200, 100, 200, 50, 250, 120]; //minimum two points
var tension = 1;

drawCurve(ctx, myPoints); //default tension=0.5
drawCurve(ctx, myPoints, tension);


function getCurvePoints(pts, tension, isClosed, numOfSegments) {

  // use input value if provided, or use a default value	 
  tension = (typeof tension != 'undefined') ? tension : 0.5;
  isClosed = isClosed ? isClosed : false;
  numOfSegments = numOfSegments ? numOfSegments : 16;

  var _pts = [], res = [],	// clone array
      x, y,			// our x,y coords
      t1x, t2x, t1y, t2y,	// tension vectors
      c1, c2, c3, c4,		// cardinal points
      st, t, i;		// steps based on num. of segments

  // clone array so we don't change the original
  //
  _pts = pts.slice(0);

  // The algorithm require a previous and next point to the actual point array.
  // Check if we will draw closed or open curve.
  // If closed, copy end points to beginning and first points to end
  // If open, duplicate first points to befinning, end points to end
  if (isClosed) {
    _pts.unshift(pts[pts.length - 1]);
    _pts.unshift(pts[pts.length - 2]);
    _pts.unshift(pts[pts.length - 1]);
    _pts.unshift(pts[pts.length - 2]);
    _pts.push(pts[0]);
    _pts.push(pts[1]);
  }
  else {
    _pts.unshift(pts[1]);	//copy 1. point and insert at beginning
    _pts.unshift(pts[0]);
    _pts.push(pts[pts.length - 2]);	//copy last point and append
    _pts.push(pts[pts.length - 1]);
  }

  // ok, lets start..

  // 1. loop goes through point array
  // 2. loop goes through each segment between the 2 pts + 1e point before and after
  for (i=2; i < (_pts.length - 4); i+=2) {
    for (t=0; t <= numOfSegments; t++) {

      // calc tension vectors
      t1x = (_pts[i+2] - _pts[i-2]) * tension;
      t2x = (_pts[i+4] - _pts[i]) * tension;

      t1y = (_pts[i+3] - _pts[i-1]) * tension;
      t2y = (_pts[i+5] - _pts[i+1]) * tension;

      // calc step
      st = t / numOfSegments;

      // calc cardinals
      c1 =   2 * Math.pow(st, 3) 	- 3 * Math.pow(st, 2) + 1; 
      c2 = -(2 * Math.pow(st, 3)) + 3 * Math.pow(st, 2); 
      c3 = 	   Math.pow(st, 3)	- 2 * Math.pow(st, 2) + st; 
      c4 = 	   Math.pow(st, 3)	- 	  Math.pow(st, 2);

      // calc x and y cords with common control vectors
      x = c1 * _pts[i]	+ c2 * _pts[i+2] + c3 * t1x + c4 * t2x;
      y = c1 * _pts[i+1]	+ c2 * _pts[i+3] + c3 * t1y + c4 * t2y;

      //store points in array
      res.push(x);
      res.push(y);

    }
  }

  return res;
}

function drawLines(ctx, pts) {
  ctx.moveTo(pts[0], pts[1]);
  for(i=2;i<pts.length-1;i+=2) ctx.lineTo(pts[i], pts[i+1]);
}

canvas { border: 1px solid red; }

<canvas id="c"><canvas>

这将导致：

您可以轻松扩展画布，以便可以这样称呼它：

ctx.drawCurve(myPoints);

将以下内容添加到 javascript 中：

if (CanvasRenderingContext2D != 'undefined') {
    CanvasRenderingContext2D.prototype.drawCurve = 
        function(pts, tension, isClosed, numOfSegments, showPoints) {
       drawCurve(this, pts, tension, isClosed, numOfSegments, showPoints)}
}

你可以在 NPM （） 或 GitLab 上找到更优化的版本。npm i cardinal-spline-js