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{h1 bézier cubic curve}
{canvas {@ id="bez_canvas" height="400" width="600" style="border:1px solid grey;"}}
{pre {@ id="bezier"} code}
{input {@ type="submit" value="click to init" onclick="°°

(function() {
  var canvas, ctx, code, point, style, drag = null, dPoint;

// define initial points
  function Init(quadratic) {
    point = {
      p1: { x:100, y:250 },
      p2: { x:400, y:250 }
    };
    if (quadratic) {
      point.cp1 = { x: 250, y: 100 };
    }
    else {
      point.cp1 = { x: 150, y: 100 };
      point.cp2 = { x: 350, y: 100 };
    }
    // default styles
    style = {
      curve:	{ width: 6, color: '#333' },
      cpline:	{ width: 1, color: '#C00' },
      point: { radius: 10, width: 2, color: '#900', 
               fill: 'rgba(200,200,200,0.5)', arc1: 0, arc2: 2 * Math.PI }
    }
    // line style defaults
    ctx.lineCap = 'round';
    ctx.lineJoin = 'round';
    // event handlers
    canvas.onmousedown = DragStart;
    canvas.onmousemove = Dragging;
    canvas.onmouseup = canvas.onmouseout = DragEnd;
    //	canvas.addEventListener('mousedown', DragStart, false);
    //	canvas.addEventListener('mousemove', Dragging, false);
    //	canvas.addEventListener('mouseup', DragEnd, false);
    DrawCanvas();
  }

// draw canvas
  function DrawCanvas() {
    ctx.clearRect(0, 0, canvas.width, canvas.height);
    // control lines
    ctx.lineWidth = style.cpline.width;
    ctx.strokeStyle = style.cpline.color;
    ctx.beginPath();
    ctx.moveTo(point.p1.x, point.p1.y);
    ctx.lineTo(point.cp1.x, point.cp1.y);
    if (point.cp2) {
      ctx.moveTo(point.p2.x, point.p2.y);
      ctx.lineTo(point.cp2.x, point.cp2.y);
    }
    else {
      ctx.lineTo(point.p2.x, point.p2.y);
    }
    ctx.stroke();

// curve
    ctx.lineWidth = style.curve.width;
    ctx.strokeStyle = style.curve.color;
    ctx.beginPath();
    ctx.moveTo(point.p1.x, point.p1.y);
    if (point.cp2) {
      ctx.bezierCurveTo(point.cp1.x, point.cp1.y, point.cp2.x, point.cp2.y, point.p2.x, point.p2.y);
    }
    else {
      ctx.quadraticCurveTo(point.cp1.x, point.cp1.y, point.p2.x, point.p2.y);
    }
    ctx.stroke();

// control points
    for (var p in point) {
      ctx.lineWidth = style.point.width;
      ctx.strokeStyle = style.point.color;
      ctx.fillStyle = style.point.fill;
      ctx.beginPath();
      ctx.arc(point[p].x, point[p].y, style.point.radius, style.point.arc1, style.point.arc2, true);
      ctx.fill();
      ctx.stroke();
    }

ShowCode();
  }

// show canvas code
  function ShowCode() {
    if (code) {
      //code.firstChild.nodeValue = 
      code.innerHTML = 
        'canvas = getId(\'canvas\');\n'+ 'ctx = canvas.getContext(\'2d\')\n'+
        'ctx.lineWidth = ' + style.curve.width +
        ';\nctx.strokeStyle = \'' + style.curve.color + '\';\nctx.beginPath();\n' +
        'ctx.moveTo(' + point.p1.x + ', ' + point.p1.y +');\n' + (point.cp2 ? 
	      'ctx.bezierCurveTo('+point.cp1.x+', '+point.cp1.y+', '+point.cp2.x+', '+point.cp2.y+', '+point.p2.x+', '+point.p2.y+');' :
        'ctx.quadraticCurveTo('+point.cp1.x+', '+point.cp1.y+', '+point.p2.x+', '+point.p2.y+');'
        ) + '\nctx.stroke();' ;
    }
  }

// start dragging
  function DragStart(e) {
    e = MousePos(e);
    var dx, dy;
    for (var p in point) {
      dx = point[p].x - e.x;
      dy = point[p].y - e.y;
      if ((dx * dx) + (dy * dy) < style.point.radius * style.point.radius) {
        drag = p;
        dPoint = e;
        canvas.style.cursor = 'move';
        return;
      }
    }
  }

// dragging
  function Dragging(e) {
    if (drag) {
      e = MousePos(e);
      point[drag].x += e.x - dPoint.x;
      point[drag].y += e.y - dPoint.y;
      dPoint = e;
      DrawCanvas();
    }
  }

// end dragging
  function DragEnd(e) {
    drag = null;
    canvas.style.cursor = 'default';
    DrawCanvas();
  }

// event parser (with thanks to ryan-artecona)
    function relMouseCoords(event){
      var totalOffsetX = 0, totalOffsetY = 0, canvasX = 0, canvasY = 0;   
      var currentElement = this;
      do {
        totalOffsetX += currentElement.offsetLeft;
        totalOffsetY += currentElement.offsetTop;
      }
      while(currentElement = currentElement.offsetParent)
      canvasX = event.pageX - totalOffsetX;
      canvasY = event.pageY - totalOffsetY;
      return { x:canvasX, y:canvasY }
   }

HTMLCanvasElement.prototype.relMouseCoords = relMouseCoords;

function MousePos(event) {
     coords = canvas.relMouseCoords(event);
     return {x:coords.x, y:coords.y }
   }

// start
  canvas = getId('bez_canvas'); 
  code = getId('bezier');
  if (canvas.getContext) {
    ctx = canvas.getContext('2d');
    Init(canvas.className == 'quadratic');
  }

})();

°°"}} , then play with control points

{pre
/* 
* Canvas curves example
*
* By Craig Buckler,		http://twitter.com/craigbuckler
* of OptimalWorks.net		http://optimalworks.net/
* for SitePoint.com		http://sitepoint.com/
* 
* Refer to:
* http://blogs.sitepoint.com/html5-canvas-draw-quadratic-curves/
* http://blogs.sitepoint.com/html5-canvas-draw-bezier-curves/
*
* This code can be used without restriction.

* with thanks to Ryan Artecona for the function relMouseCoords(event)
* (http://stackoverflow.com/users/671915/ryan-artecona)       
*/
}