/* Quadrilateral Transform - (c) Ken Nilsen, CC3.0-Attr */
var img = new Image();  img.onload = go;
img.src = "https://i.imgur.com/EWoZkZm.jpg";

function go() {
  var me = this,
      stepEl = document.querySelector("input"),
      stepTxt = document.querySelector("span"),
      c = document.querySelector("canvas"),
      ctx = c.getContext("2d"),
      corners = [
        {x: 100, y: 20},           // ul
        {x: 520, y: 20},           // ur
        {x: 520, y: 380},          // br
        {x: 100, y: 380}           // bl
      ],
      radius = 10, cPoint, timer,  // for mouse handling
      step = 4;                    // resolution

  update();

  // render image to quad using current settings
  function render() {
		
    var p1, p2, p3, p4, y1c, y2c, y1n, y2n,
        w = img.width - 1,         // -1 to give room for the "next" points
        h = img.height - 1;

    ctx.clearRect(0, 0, c.width, c.height);

    for(y = 0; y < h; y += step) {
      for(x = 0; x < w; x += step) {
        y1c = lerp(corners[0], corners[3],  y / h);
        y2c = lerp(corners[1], corners[2],  y / h);
        y1n = lerp(corners[0], corners[3], (y + step) / h);
        y2n = lerp(corners[1], corners[2], (y + step) / h);

        // corners of the new sub-divided cell p1 (ul) -> p2 (ur) -> p3 (br) -> p4 (bl)
        p1 = lerp(y1c, y2c,  x / w);
        p2 = lerp(y1c, y2c, (x + step) / w);
        p3 = lerp(y1n, y2n, (x + step) / w);
        p4 = lerp(y1n, y2n,  x / w);

        ctx.drawImage(img, x, y, step, step,  p1.x, p1.y, // get most coverage for w/h:
            Math.ceil(Math.max(step, Math.abs(p2.x - p1.x), Math.abs(p4.x - p3.x))) + 1,
            Math.ceil(Math.max(step, Math.abs(p1.y - p4.y), Math.abs(p2.y - p3.y))) + 1)
      }
    }
  }
  
  function lerp(p1, p2, t) {
    return {
      x: p1.x + (p2.x - p1.x) * t, 
      y: p1.y + (p2.y - p1.y) * t}
  }

  /* Stuff for demo: -----------------*/
  function drawCorners() {
    ctx.strokeStyle = "#09f"; 
    ctx.lineWidth = 2;
    ctx.beginPath();
    // border
    for(var i = 0, p; p = corners[i++];) ctx[i ? "lineTo" : "moveTo"](p.x, p.y);
    ctx.closePath();
    // circular handles
    for(i = 0; p = corners[i++];) {
      ctx.moveTo(p.x + radius, p.y); 
      ctx.arc(p.x, p.y, radius, 0, 6.28);
    }
    ctx.stroke()
  }
	
  function getXY(e) {
    var r = c.getBoundingClientRect();
    return {x: e.clientX - r.left, y: e.clientY - r.top}
  }
	
  function inCircle(p, pos) {
    var dx = pos.x - p.x,
        dy = pos.y - p.y;
    return dx*dx + dy*dy <= radius * radius
  }

  // handle mouse
  c.onmousedown = function(e) {
    var pos = getXY(e);
    for(var i = 0, p; p = corners[i++];) {if (inCircle(p, pos)) {cPoint = p; break}}
  }
  window.onmousemove = function(e) {
    if (cPoint) {
      var pos = getXY(e);
      cPoint.x = pos.x; cPoint.y = pos.y;
      cancelAnimationFrame(timer);
      timer = requestAnimationFrame(update.bind(me))
    }
  }
  window.onmouseup = function() {cPoint = null}
  
  stepEl.oninput = function() {
    stepTxt.innerHTML = (step = Math.pow(2, +this.value));
    update();
  }
  
  function update() {render(); drawCorners()}
}

body {margin:20px;font:16px sans-serif}
canvas {border:1px solid #000;margin-top:10px}

<label>Step: <input type=range min=0 max=5 value=2></label><span>4</span><br>
<canvas width=620 height=400></canvas>