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+{{18.7553606,21.0894159}, {20.5067044,22.676722}, {21.4650431,26.4450934}},
+{{21.4650431,26.4450934}, {22.5692754,31.7464864}, {26.4671516,34.648351}},
+{{26.4671516,34.648351}, {30.3650278,37.5502156}, {41.873704,30.8489321}},
+{{41.873704,30.8489321}, {53.3823801,24.1476487}, {77.3190123,0.63959742}},
+</div>
+
+</div>
+
+<script type="text/javascript">
+
+var testDivs = [
+ cubic18,
+ cubic17,
+ cubic16,
+ cubic15,
+ quad13,
+ quad12,
+ cubic14,
+ cubic13,
+ cubic12,
+ cubic11,
+ cubic10,
+ cubic9,
+ quad11,
+ quad10,
+ quad9,
+ quad8,
+ quad7,
+ cubic8,
+ quad6,
+ quad5,
+ quad4,
+ quad3,
+ cubic7,
+ quad2,
+ cubic6,
+ quad1,
+ cubic5,
+ cubic4,
+ cubic1x0,
+ cubic1x0x,
+ cubic1x1,
+ cubic1x1x,
+ cubic1x2,
+ cubic1x2x,
+ cubic1x3,
+ cubic1x3x,
+ cubic1x4,
+ cubic1x4x,
+ cubic1x5,
+ cubic1x5x,
+ cubic1x6,
+ cubic1x6x,
+ cubic1x7,
+ cubic1x7x,
+ cubic1x8,
+ cubic1x8x,
+ cubic1x9,
+ cubic1x9x,
+ cubic2x0,
+ cubic2x0x,
+ cubic2x1,
+ cubic2x1x,
+ cubic2x2,
+ cubic2x2x,
+ cubic2x3,
+ cubic2x3x,
+ cubic2x4,
+ cubic2x4x,
+ cubic2x5,
+ cubic2x5x,
+ cubic2x6,
+ cubic2x6x,
+ cubic2x7,
+ cubic2x7x,
+ cubic2x8,
+ cubic2x8x,
+ cubic2x9,
+ cubic2x9x,
+ cubic3x0,
+ cubic3x0x,
+ cubic3x1,
+ cubic3x1x,
+ cubic3x2,
+ cubic3x2x,
+ cubic3x3,
+ cubic3x3x,
+ cubic3x4,
+ cubic3x4x,
+ cubic3x5,
+ cubic3x5x,
+ cubic3x6,
+ cubic3x6x,
+ cubic3x7,
+ cubic3x7x,
+ cubic3x8,
+ cubic3x8x,
+ cubic3x9,
+ cubic3x9x,
+ cubic4x0,
+ cubic4x0x,
+ cubic4x1,
+ cubic4x1x,
+ cubic4x2,
+ cubic4x2x,
+ cubic4x3,
+ cubic4x3x,
+ cubic4x4,
+ cubic4x4x,
+ cubic4x5,
+ cubic4x5x,
+ cubic4x6,
+ cubic4x6x,
+ cubic4x7,
+ cubic4x7x,
+ cubic4x8,
+ cubic4x8x,
+ cubic4x9,
+ cubic4x9x,
+ cubic5x0,
+ cubic5x0x,
+ cubic5x1,
+ cubic5x1x,
+ cubic5x2,
+ cubic5x2x,
+ cubic5x3,
+ cubic5x3x,
+ cubic5x4,
+ cubic5x4x,
+ cubic5x5,
+ cubic5x5x,
+ cubic5x6,
+ cubic5x6x,
+ cubic5x7,
+ cubic5x7x,
+ cubic5x8,
+ cubic5x8x,
+ cubic5x9,
+ cubic5x9x,
+ cubic6x0,
+ cubic6x0x,
+ cubic6x1,
+ cubic6x1x,
+ cubic6x2,
+ cubic6x2x,
+ cubic6x3,
+ cubic6x3x,
+ cubic6x4,
+ cubic6x4x,
+ cubic6x5,
+ cubic6x5x,
+ cubic6x6,
+ cubic6x6x,
+ cubic6x7,
+ cubic6x7x,
+ cubic6x8,
+ cubic6x8x,
+ cubic6x9,
+ cubic6x9x,
+ cubic7x0,
+ cubic7x0x,
+ cubic7x1,
+ cubic7x1x,
+ cubic7x2,
+ cubic7x2x,
+ cubic7x3,
+ cubic7x3x,
+ cubic7x4,
+ cubic7x4x,
+ cubic7x5,
+ cubic7x5x,
+ cubic7x6,
+ cubic7x6x,
+ cubic7x7,
+ cubic7x7x,
+ cubic7x8,
+ cubic7x8x,
+ cubic7x9,
+ cubic7x9x,
+ cubic8x0,
+ cubic8x0x,
+ cubic8x1,
+ cubic8x1x,
+ cubic8x2,
+ cubic8x2x,
+ cubic8x3,
+ cubic8x3x,
+ cubic8x4,
+ cubic8x4x,
+ cubic8x5,
+ cubic8x5x,
+ cubic8x6,
+ cubic8x6x,
+ cubic8x7,
+ cubic8x7x,
+ cubic8x8,
+ cubic8x8x,
+ cubic8x9,
+ cubic8x9x,
+ cubic3,
+ cubic2,
+ cubic1,
+];
+
+var scale, columns, rows, xStart, yStart;
+
+var ticks = 10;
+var at_x = 13 + 0.5;
+var at_y = 23 + 0.5;
+var init_decimal_places = 1; // make this 3 to show more precision
+var decimal_places;
+var tests = [];
+var testTitles = [];
+var testIndex = 0;
+var ctx;
+var minScale = 1;
+var subscale = 1;
+var curveT = -1;
+var drawCubics = true;
+var drawQuads = true;
+var drawControlLines = true;
+
+function parse(test, title) {
+ var curveStrs = test.split("{{");
+ if (curveStrs.length == 1)
+ curveStrs = test.split("=(");
+ var pattern = /[a-z$=]?-?\d+\.*\d*/g;
+ var curves = [];
+ for (var c in curveStrs) {
+ var curveStr = curveStrs[c];
+ var points = curveStr.match(pattern);
+ var pts = [];
+ for (var wd in points) {
+ var num = parseFloat(points[wd]);
+ if (isNaN(num)) continue;
+ pts.push(num);
+ }
+ if (pts.length > 2)
+ curves.push(pts);
+ }
+ if (curves.length >= 1) {
+ tests.push(curves);
+ testTitles.push(title);
+ }
+}
+
+function init(test) {
+ var canvas = document.getElementById('canvas');
+ if (!canvas.getContext) return;
+ canvas.width = window.innerWidth - at_x;
+ canvas.height = window.innerHeight - at_y;
+ ctx = canvas.getContext('2d');
+ var xmin = Infinity;
+ var xmax = -Infinity;
+ var ymin = Infinity;
+ var ymax = -Infinity;
+ for (var curves in test) {
+ var curve = test[curves];
+ var last = curve.length;
+ for (var idx = 0; idx < last; idx += 2) {
+ xmin = Math.min(xmin, curve[idx]);
+ xmax = Math.max(xmax, curve[idx]);
+ ymin = Math.min(ymin, curve[idx + 1]);
+ ymax = Math.max(ymax, curve[idx + 1]);
+ }
+ }
+ var testW = xmax - xmin;
+ var testH = ymax - ymin;
+ subscale = 1;
+ while (testW * subscale < 0.1 && testH * subscale < 0.1) {
+ subscale *= 10;
+ }
+ while (testW * subscale > 10 && testH * subscale > 10) {
+ subscale /= 10;
+ }
+ xStart = Math.floor(xmin * subscale) / subscale;
+ yStart = Math.floor(ymin * subscale) / subscale;
+ var xEnd = Math.ceil(xmin * subscale) / subscale;
+ var yEnd = Math.ceil(ymin * subscale) / subscale;
+ var cCelsW = Math.floor(ctx.canvas.width / 10);
+ var cCelsH = Math.floor(ctx.canvas.height / 10);
+ testW = xEnd - xStart;
+ testH = yEnd - yStart;
+ var scaleWH = 1;
+ while (cCelsW > testW * scaleWH * 10 && cCelsH > testH * scaleWH * 10) {
+ scaleWH *= 10;
+ }
+ while (cCelsW * 10 < testW * scaleWH && cCelsH * 10 < testH * scaleWH) {
+ scaleWH /= 10;
+ }
+
+ columns = Math.ceil(xmax * subscale) - Math.floor(xmin * subscale) + 1;
+ rows = Math.ceil(ymax * subscale) - Math.floor(ymin * subscale) + 1;
+
+ var hscale = ctx.canvas.width / columns / ticks;
+ var vscale = ctx.canvas.height / rows / ticks;
+ minScale = Math.floor(Math.min(hscale, vscale));
+ scale = minScale * subscale;
+}
+
+function drawPoint(px, py, xoffset, yoffset, unit) {
+ var label = px.toFixed(decimal_places) + ", " + py.toFixed(decimal_places);
+ var _px = px * unit + xoffset;
+ var _py = py * unit + yoffset;
+ ctx.beginPath();
+ ctx.arc(_px, _py, 3, 0, Math.PI*2, true);
+ ctx.closePath();
+ ctx.fill();
+ ctx.fillText(label, _px + 5, _py);
+}
+
+function draw(test, title, scale) {
+ ctx.fillStyle = "rgba(0,0,0, 0.1)";
+ ctx.font = "normal 50px Arial";
+ ctx.fillText(title, 50, 50);
+ ctx.font = "normal 10px Arial";
+
+ var unit = scale * ticks;
+ ctx.lineWidth = 1;
+ var i;
+ for (i = 0; i <= rows * ticks; ++i) {
+ ctx.strokeStyle = (i % ticks) != 0 ? "rgb(200,200,200)" : "black";
+ ctx.beginPath();
+ ctx.moveTo(at_x + 0, at_y + i * minScale);
+ ctx.lineTo(at_x + ticks * columns * minScale, at_y + i * minScale);
+ ctx.stroke();
+ }
+ for (i = 0; i <= columns * ticks; ++i) {
+ ctx.strokeStyle = (i % ticks) != 0 ? "rgb(200,200,200)" : "black";
+ ctx.beginPath();
+ ctx.moveTo(at_x + i * minScale, at_y + 0);
+ ctx.lineTo(at_x + i * minScale, at_y + ticks * rows * minScale);
+ ctx.stroke();
+ }
+
+ var xoffset = xStart * -unit + at_x;
+ var yoffset = yStart * -unit + at_y;
+
+ ctx.fillStyle = "rgb(40,80,60)"
+ for (i = 0; i <= columns; i += 1)
+ {
+ num = xStart + i / subscale;
+ ctx.fillText(num.toFixed(decimal_places), xoffset + num * unit - 5, 10);
+ }
+ for (i = 0; i <= rows; i += 1)
+ {
+ num = yStart + i / subscale;
+ ctx.fillText(num.toFixed(decimal_places), 0, yoffset + num * unit + 0);
+ }
+ var curves, pts;
+ for (curves in test) {
+ var curve = test[curves];
+ if (curve.length == 6 && !drawQuads) {
+ continue;
+ }
+ if (curve.length == 8 && !drawCubics) {
+ continue;
+ }
+ ctx.beginPath();
+ ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit);
+ switch (curve.length) {
+ case 6:
+ ctx.quadraticCurveTo(
+ xoffset + curve[2] * unit, yoffset + curve[3] * unit,
+ xoffset + curve[4] * unit, yoffset + curve[5] * unit);
+ break;
+ case 8:
+ ctx.bezierCurveTo(
+ xoffset + curve[2] * unit, yoffset + curve[3] * unit,
+ xoffset + curve[4] * unit, yoffset + curve[5] * unit,
+ xoffset + curve[6] * unit, yoffset + curve[7] * unit);
+ break;
+ }
+ if (curves == 2) ctx.strokeStyle = curves ? "red" : "blue";
+ ctx.stroke();
+ if (drawControlLines) {
+ ctx.strokeStyle = "rgba(0,0,0, 0.3)";
+ ctx.beginPath();
+ ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit);
+ ctx.lineTo(xoffset + curve[2] * unit, yoffset + curve[3] * unit);
+ ctx.lineTo(xoffset + curve[4] * unit, yoffset + curve[5] * unit);
+ if (curve.length == 8)
+ ctx.lineTo(xoffset + curve[6] * unit, yoffset + curve[7] * unit);
+ ctx.stroke();
+ }
+ if (curveT >= 0 && curveT <= 1) {
+ var x, y;
+ var t = curveT;
+ switch (curve.length) {
+ case 6:
+ var one_t = 1 - t;
+ var a = one_t * one_t;
+ var b = 2 * one_t * t;
+ var c = t * t;
+ x = a * curve[0] + b * curve[2] + c * curve[4];
+ y = a * curve[1] + b * curve[3] + c * curve[5];
+ break;
+ case 8:
+ var one_t = 1 - t;
+ var one_t2 = one_t * one_t;
+ var a = one_t2 * one_t;
+ var b = 3 * one_t2 * t;
+ var t2 = t * t;
+ var c = 3 * one_t * t2;
+ var d = t2 * t;
+ x = a * curve[0] + b * curve[2] + c * curve[4] + d * curve[6];
+ y = a * curve[1] + b * curve[3] + c * curve[5] + d * curve[7];
+ break;
+ }
+ drawPoint(x, y, xoffset, yoffset, unit);
+ var num = curveT.toFixed(3);
+ ctx.beginPath();
+ ctx.rect(200,10,200,10);
+ ctx.fillStyle="white";
+ ctx.fill();
+ ctx.fillStyle="black";
+ ctx.fillText(num, 230, 18);
+ if (curve.length == 8) {
+ var one_t = 1 - t;
+ var a = curve[0];
+ var b = curve[2];
+ var c = curve[4];
+ var d = curve[6];
+ var dx = (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
+ a = curve[1];
+ b = curve[3];
+ c = curve[5];
+ d = curve[7];
+ var dy = (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
+ ctx.beginPath();
+ ctx.moveTo(xoffset + (x - dx) * unit, yoffset + (y - dy) * unit);
+ ctx.lineTo(xoffset + (x + dx) * unit, yoffset + (y + dy) * unit);
+ ctx.stroke();
+ }
+ }
+ }
+}
+
+function drawTop() {
+ init(tests[testIndex]);
+ redraw();
+}
+
+function redraw() {
+ ctx.beginPath();
+ ctx.rect(0, 0, ctx.canvas.width, ctx.canvas.height);
+ ctx.fillStyle="white";
+ ctx.fill();
+ draw(tests[testIndex], testTitles[testIndex], scale);
+}
+
+function doKeyPress(evt) {
+ var char = String.fromCharCode(evt.charCode);
+ switch (char) {
+ case 'c':
+ drawCubics ^= true;
+ redraw();
+ break;
+ case 'l':
+ drawControlLines ^= true;
+ redraw();
+ break;
+ case 'N':
+ testIndex += 9;
+ case 'n':
+ if (++testIndex >= tests.length)
+ testIndex = 0;
+ mouseX = Infinity;
+ drawTop();
+ break;
+ case 'P':
+ testIndex -= 9;
+ case 'p':
+ if (--testIndex < 0)
+ testIndex = tests.length - 1;
+ mouseX = Infinity;
+ drawTop();
+ break;
+ case 'q':
+ drawQuads ^= true;
+ redraw();
+ break;
+ case 'x':
+ drawCubics ^= true;
+ drawQuads ^= true;
+ redraw();
+ break;
+ }
+}
+
+function handleMouseClick() {
+ var e = window.event;
+ var tgt = e.target || e.srcElement;
+ var min = tgt.offsetTop + Math.ceil(at_y);
+ var max = min + ticks * rows * minScale;
+ curveT = (e.clientY - min) / (max - min);
+ redraw();
+}
+
+function calcXY() {
+ var e = window.event;
+ var tgt = e.target || e.srcElement;
+ var left = tgt.offsetLeft;
+ var top = tgt.offsetTop;
+ var unit = scale * ticks;
+ mouseX = (e.clientX - left - Math.ceil(at_x) + 1) / unit + xStart;
+ mouseY = (e.clientY - top - Math.ceil(at_y)) / unit + yStart;
+}
+
+function handleMouseOver() {
+ calcXY();
+ var num = mouseX.toFixed(3) + ", " + mouseY.toFixed(3);
+ ctx.beginPath();
+ ctx.rect(30,10,200,10);
+ ctx.fillStyle="white";
+ ctx.fill();
+ ctx.fillStyle="black";
+ ctx.fillText(num, 30, 18);
+}
+
+function start() {
+ for (i = 0; i < testDivs.length; ++i) {
+ var title = testDivs[i].id.toString();
+ var str = testDivs[i].firstChild.data;
+ parse(str, title);
+ }
+ drawTop();
+ window.addEventListener('keypress', doKeyPress, true);
+ window.onresize = function() {
+ drawTop();
+ }
+}
+
+</script>
+</head>
+
+<body onLoad="start();">
+<canvas id="canvas" width="750" height="500"
+ onmousemove="handleMouseOver()"
+ onclick="handleMouseClick()"
+ ></canvas >
+</body>
+</html>