pm5/LICENSE

## README.md

      
    Raw
  

              README.md
            
          
    Experimental Bézier curve control


## index.html
<!DOCTYPE html>
<html>
  <head>
    <title>Approximating arcs with Bézier curves</title>
    <script src="https://d3js.org/d3-selection.v1.min.js"></script>
    <script src="https://d3js.org/d3-path.v1.min.js"></script>
    <script src="https://d3js.org/d3-shape.v1.min.js"></script>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/immutable/3.8.1/immutable.min.js"></script>
    <style>
      html, body {
        padding: 0;
      }
      .canvas .curve {
        stroke: black;
        stroke-width: 2px;
        fill: none;
      }
      .canvas .controlPoint,
      .canvas .center {
        stroke: #999;
        stroke-width: 1px;
        fill: white;
      }
      .canvas .controlPoint.focused,
      .canvas .center.focused {
        fill: #f4cc00;
      }
      .canvas .controlLine {
        stroke: #900;
        stroke-width: 1px;
        fill: none;
      }
      .canvas .tangentLine,
      .canvas .radiusLine {
        stroke: #ccc;
        stroke-width: 1px;
        stroke-dasharray: 5 5;
        fill: none;
      }
      .canvas .tip {
        display: none;
        stroke: #ccc;
        stroke-width: 1px;
        fill: white;
      }
    </style>
  </head>
  <body>
    <svg class="canvas"></svg>
    <script>
      var margin = {
        top: 0,
        right: 0,
        bottom: 0,
        left: 0
      };
      var width = 960;
      var height = 500;
      var canvas = d3.select(".canvas")
        .attr("width", width + margin.left + margin.right)
        .attr("height", height + margin.top + margin.bottom);

      var Point = Immutable.Record({ index: 0, x: 0, y: 0 });
      var Monad = Immutable.Record({ x: 0, y: 0, P: Point() });

      var controlPoints = Immutable.List.of(
        Point({ index: 0, x: 300, y: 100 }),
        Point({ index: 1, x: 190, y: 100 }),
        Point({ index: 2, x: 100, y: 190 }),
        Point({ index: 3, x: 100, y: 300 })
      );
      var userState = false;

      init();

      function controlLines(controlPoints) {
        return [
          controlPoints.slice(0, 2), controlPoints.slice(2)
        ];
      }

      function tangentLines(controlPoints) {
        const multiply = 10
        const p0 = controlPoints.get(0);
        const p1 = controlPoints.get(1);
        const p2 = controlPoints.get(2);
        const p3 = controlPoints.get(3);
        return [
          Immutable.List.of(
            M(p0).sub(p1).scale(multiply).add(p0).P,
            M(p1).sub(p0).scale(multiply).add(p1).P
          ),
          Immutable.List.of(
            M(p2).sub(p3).scale(multiply).add(p2).P,
            M(p3).sub(p2).scale(multiply).add(p3).P
          ),
        ];
      }

      function radiusLines(controlPoints) {
        if (!center(controlPoints)) {
          return [];
        }
        return [
          Immutable.List.of(
            controlPoints.get(0),
            center(controlPoints)
          ),
          Immutable.List.of(
            center(controlPoints),
            controlPoints.get(3)
          )
        ];
      }

      function tip(controlPoints) {
        const p0 = controlPoints.get(0);
        const p1 = controlPoints.get(1);
        const p2 = controlPoints.get(2);
        const p3 = controlPoints.get(3);
        const t = -((p2.y - p3.y) * (p0.x - p3.x) - (p2.x - p3.x) * (p0.y - p3.y))
          / ((p2.y - p3.y) * (p1.x - p0.x) - (p2.x - p3.x) * (p1.y - p0.y));
        return M(p1).sub(p0).scale(t).add(p0).P;
      }

      function tips(controlPoints) {
        const t = tip(controlPoints);
        if (!t || isNaN(t.x) || isNaN(t.y)) {
          return [];
        }
        return [t];
      }

      function center(controlPoints) {
        const p0 = controlPoints.get(0);
        const p1 = controlPoints.get(1);
        const p2 = controlPoints.get(2);
        const p3 = controlPoints.get(3);
        const p0p1 = M(p1).sub(p0);
        const p0p3 = M(p3).sub(p0);
        const p3p2 = M(p2).sub(p3);
        const p3p0 = M(p0).sub(p3);
        const p0c = p0p3.sub(proj(p0p3, p0p1));
        const p3c = p3p0.sub(proj(p3p0, p3p2));
        const t = tip(controlPoints);
        if (!t || isNaN(t.x) || isNaN(t.y)) {
          return;
        }
        const c = tip(Immutable.List.of(p0, p0c.add(p0).P, p3c.add(p3).P, p3));
        if (dist(c, p0) !== dist(c, p3)) {
          return;
        }
        return c;
      }

      function centers(controlPoints) {
        c = center(controlPoints);
        if (!c) {
          return [];
        }
        return [c];
      }

      function M(p) {
        var m = Monad({
          x: p.x,
          y: p.y,
          P: Point(p)
        });
        m.sub = q => M({ x: p.x - q.x, y: p.y - q.y }),
        m.add = q => M({ x: p.x + q.x, y: p.y + q.y }),
        m.round = () => M({ x: Math.round(p.x), y: Math.round(p.y) }),
        m.scale = r => M({ x: p.x * r, y: p.y * r }),
        m.length = () => Math.sqrt(p.x * p.x + p.y * p.y),
        m.unit = () => M(p).scale(1/M(p).length())
        return m;
      }

      function length(p) {
        return Math.sqrt(p.x * p.x + p.y * p.y);
      }

      function dist(p, q) {
        return length(M(p).sub(q));
      }

      function dot(p, q) {
        return p.x * q.x + p.y * q.y;
      }

      function proj(v, w) {
        return w.unit().scale(dot(v, w.unit()));
      }

      function mouseOver(d) {
        d3.select(this)
          .classed("focused", true);
      }

      function mouseOut(d) {
        if (userState) return;
        d3.select(this)
          .classed("focused", false);
      }

      function mouseDownOnCenter(d) {
        userState = "dragging";
        const c = center(controlPoints);
        const t = tip(controlPoints);
        const p0 = controlPoints.get(0);
        const p1 = controlPoints.get(1);
        const p2 = controlPoints.get(2);
        const p3 = controlPoints.get(3);
        const p0p1ratio = dist(t, p1) / dist(t, p0);
        const p3p2ratio = dist(t, p2) / dist(t, p3);

        canvas.on("mousemove", () => {
          const m = Point({
            x: d3.mouse(this)[0],
            y: d3.mouse(this)[1]
          });
          const p0p1 = M(p1).sub(p0).unit();
          const p3p2 = M(p2).sub(p3).unit();
          const axis = p0p1.add(p3p2).scale(1/1.414);
          const move = proj(M(m).sub(c), axis);
          controlPoints = Immutable.List.of(
            M(p0).add(proj(move, p0p1)).P.merge({ index: 0 }),
            M(p1).add(proj(move, p0p1).scale(p0p1ratio)).P.merge({ index: 1 }),
            M(p2).add(proj(move, p3p2).scale(p3p2ratio)).P.merge({ index: 2 }),
            M(p3).add(proj(move, p3p2)).P.merge({ index: 3 })
          );
          update();
        });
      }

      function mouseDownOnControlPoint(d) {
        userState = "dragging";
        const p0 = controlPoints.get(0);
        const p1 = controlPoints.get(1);
        const p2 = controlPoints.get(2);
        const p3 = controlPoints.get(3);
        canvas.on("mousemove", () => {
          var m = Point({
            x: d3.mouse(this)[0],
            y: d3.mouse(this)[1]
          });
          controlPoints = controlPoints.set(d.index, m.merge({ index: d.index }));
          if (d.index === 0) {
            controlPoints = controlPoints.set(1, M(p1).add(m).sub(p0).round().P.merge({ index: 1 }));
          } else if (d.index === 3) {
            controlPoints = controlPoints.set(2, M(p2).add(m).sub(p3).round().P.merge({ index: 2 }));
          }
          update();
        });
      }

      function init() {
        canvas.on("mouseup", function () {
          canvas.on("mousemove", null);
          userState = false;
          d3.select(".focused")
            .classed("focused", false);
        });

        canvas.selectAll("path.curve")
          .data([controlPoints])
        .enter().append("path")
          .classed("curve", true)
          .attr("d", d => `M${d.get(0).x},${d.get(0).y}C${d.slice(1).map(p => p.x + ',' + p.y).join(",")}`);

        canvas.selectAll("line.controlLine")
          .data(controlLines(controlPoints))
        .enter().append("line")
          .classed("controlLine", true)
          .attr("x1", d => d.get(0).x)
          .attr("y1", d => d.get(0).y)
          .attr("x2", d => d.get(1).x)
          .attr("y2", d => d.get(1).y);

        canvas.selectAll("line.tangentLine")
          .data(tangentLines(controlPoints))
        .enter().append("line")
          .classed("tangentLine", true)
          .attr("x1", d => d.get(0).x)
          .attr("y1", d => d.get(0).y)
          .attr("x2", d => d.get(1).x)
          .attr("y2", d => d.get(1).y);

        canvas.selectAll("line.radiusLine")
          .data(radiusLines(controlPoints))
        .enter().append("line")
          .classed("radiusLine", true)
          .attr("x1", d => d.get(0).x)
          .attr("y1", d => d.get(0).y)
          .attr("x2", d => d.get(1).x)
          .attr("y2", d => d.get(1).y);

        canvas.selectAll("circle.tip")
          .data(tips(controlPoints))
        .enter().append("circle")
          .classed("tip", true)
          .attr("cx", d => d.x)
          .attr("cy", d => d.y)
          .attr("r", 4);

        canvas.selectAll("circle.center")
          .data(centers(controlPoints))
        .enter().append("circle")
          .classed("center", true)
          .attr("cx", d => d.x)
          .attr("cy", d => d.y)
          .attr("r", 4)
          .on("mousedown", mouseDownOnCenter)
          .on("mouseover", mouseOver)
          .on("mouseout", mouseOut);

        canvas.selectAll("circle.controlPoint")
          .data(controlPoints.toArray(), d => d.index)
        .enter().append("circle")
          .classed("controlPoint", true)
          .attr("cx", d => d.x)
          .attr("cy", d => d.y)
          .attr("r", 4)
          .on("mousedown", mouseDownOnControlPoint)
          .on("mouseover", mouseOver)
          .on("mouseout", mouseOut);
      }

      function update() {
        canvas.selectAll("path.curve")
          .data([controlPoints])
          .attr("d", d => `M${d.get(0).x},${d.get(0).y}C${d.slice(1).map(p => p.x + ',' + p.y).join(",")}`);

        canvas.selectAll("line.controlLine")
          .data(controlLines(controlPoints))
          .attr("x1", d => d.get(0).x)
          .attr("y1", d => d.get(0).y)
          .attr("x2", d => d.get(1).x)
          .attr("y2", d => d.get(1).y);

        canvas.selectAll("line.tangentLine")
          .data(tangentLines(controlPoints))
          .attr("x1", d => d.get(0).x)
          .attr("y1", d => d.get(0).y)
          .attr("x2", d => d.get(1).x)
          .attr("y2", d => d.get(1).y);

        radiusLineElements = canvas.selectAll("line.radiusLine")
          .data(radiusLines(controlPoints))
          .attr("x1", d => d.get(0).x)
          .attr("y1", d => d.get(0).y)
          .attr("x2", d => d.get(1).x)
          .attr("y2", d => d.get(1).y);
        radiusLineElements.enter().append("line")
          .classed("radiusLine", true)
          .attr("x1", d => d.get(0).x)
          .attr("y1", d => d.get(0).y)
          .attr("x2", d => d.get(1).x)
          .attr("y2", d => d.get(1).y);
        radiusLineElements.exit()
          .remove();

        canvas.selectAll("circle.tip")
          .data(tips(controlPoints))
          .attr("cx", d => d.x)
          .attr("cy", d => d.y);

        centerElements = canvas.selectAll("circle.center")
          .data(centers(controlPoints))
          .attr("cx", d => d.x)
          .attr("cy", d => d.y);
        centerElements.enter().append("circle")
          .classed("center", true)
          .attr("cx", d => d.x)
          .attr("cy", d => d.y)
          .attr("r", 4)
          .on("mousedown", mouseDownOnCenter)
          .on("mouseover", mouseOver)
          .on("mouseout", mouseOut);
        centerElements.exit()
          .remove();

        canvas.selectAll("circle.controlPoint")
          .data(controlPoints.toArray(), d => d.index)
          .attr("cx", d => d.x)
          .attr("cy", d => d.y);
      }
    </script>
  </body>
</html>

## LICENSE
The MIT License (MIT)

Copyright © 2016 Pomin Wu

Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the “Software”), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

Fork this project to create your own MIT license that you can always link to.
	<!DOCTYPE html>
	<html>
	<head>
	<title>Approximating arcs with Bézier curves</title>
	<script src="https://d3js.org/d3-selection.v1.min.js"></script>
	<script src="https://d3js.org/d3-path.v1.min.js"></script>
	<script src="https://d3js.org/d3-shape.v1.min.js"></script>
	<script src="https://cdnjs.cloudflare.com/ajax/libs/immutable/3.8.1/immutable.min.js"></script>
	<style>
	html, body {
	padding: 0;
	}
	.canvas .curve {
	stroke: black;
	stroke-width: 2px;
	fill: none;
	}
	.canvas .controlPoint,
	.canvas .center {
	stroke: #999;
	stroke-width: 1px;
	fill: white;
	}
	.canvas .controlPoint.focused,
	.canvas .center.focused {
	fill: #f4cc00;
	}
	.canvas .controlLine {
	stroke: #900;
	stroke-width: 1px;
	fill: none;
	}
	.canvas .tangentLine,
	.canvas .radiusLine {
	stroke: #ccc;
	stroke-width: 1px;
	stroke-dasharray: 5 5;
	fill: none;
	}
	.canvas .tip {
	display: none;
	stroke: #ccc;
	stroke-width: 1px;
	fill: white;
	}
	</style>
	</head>
	<body>
	<svg class="canvas"></svg>
	<script>
	var margin = {
	top: 0,
	right: 0,
	bottom: 0,
	left: 0
	};
	var width = 960;
	var height = 500;
	var canvas = d3.select(".canvas")
	.attr("width", width + margin.left + margin.right)
	.attr("height", height + margin.top + margin.bottom);

	var Point = Immutable.Record({ index: 0, x: 0, y: 0 });
	var Monad = Immutable.Record({ x: 0, y: 0, P: Point() });

	var controlPoints = Immutable.List.of(
	Point({ index: 0, x: 300, y: 100 }),
	Point({ index: 1, x: 190, y: 100 }),
	Point({ index: 2, x: 100, y: 190 }),
	Point({ index: 3, x: 100, y: 300 })
	);
	var userState = false;

	init();

	function controlLines(controlPoints) {
	return [
	controlPoints.slice(0, 2), controlPoints.slice(2)
	];
	}

	function tangentLines(controlPoints) {
	const multiply = 10
	const p0 = controlPoints.get(0);
	const p1 = controlPoints.get(1);
	const p2 = controlPoints.get(2);
	const p3 = controlPoints.get(3);
	return [
	Immutable.List.of(
	M(p0).sub(p1).scale(multiply).add(p0).P,
	M(p1).sub(p0).scale(multiply).add(p1).P
	),
	Immutable.List.of(
	M(p2).sub(p3).scale(multiply).add(p2).P,
	M(p3).sub(p2).scale(multiply).add(p3).P
	),
	];
	}

	function radiusLines(controlPoints) {
	if (!center(controlPoints)) {
	return [];
	}
	return [
	Immutable.List.of(
	controlPoints.get(0),
	center(controlPoints)
	),
	Immutable.List.of(
	center(controlPoints),
	controlPoints.get(3)
	)
	];
	}

	function tip(controlPoints) {
	const p0 = controlPoints.get(0);
	const p1 = controlPoints.get(1);
	const p2 = controlPoints.get(2);
	const p3 = controlPoints.get(3);
	const t = -((p2.y - p3.y) * (p0.x - p3.x) - (p2.x - p3.x) * (p0.y - p3.y))
	/ ((p2.y - p3.y) * (p1.x - p0.x) - (p2.x - p3.x) * (p1.y - p0.y));
	return M(p1).sub(p0).scale(t).add(p0).P;
	}

	function tips(controlPoints) {
	const t = tip(controlPoints);
	if (!t \|\| isNaN(t.x) \|\| isNaN(t.y)) {
	return [];
	}
	return [t];
	}

	function center(controlPoints) {
	const p0 = controlPoints.get(0);
	const p1 = controlPoints.get(1);
	const p2 = controlPoints.get(2);
	const p3 = controlPoints.get(3);
	const p0p1 = M(p1).sub(p0);
	const p0p3 = M(p3).sub(p0);
	const p3p2 = M(p2).sub(p3);
	const p3p0 = M(p0).sub(p3);
	const p0c = p0p3.sub(proj(p0p3, p0p1));
	const p3c = p3p0.sub(proj(p3p0, p3p2));
	const t = tip(controlPoints);
	if (!t \|\| isNaN(t.x) \|\| isNaN(t.y)) {
	return;
	}
	const c = tip(Immutable.List.of(p0, p0c.add(p0).P, p3c.add(p3).P, p3));
	if (dist(c, p0) !== dist(c, p3)) {
	return;
	}
	return c;
	}

	function centers(controlPoints) {
	c = center(controlPoints);
	if (!c) {
	return [];
	}
	return [c];
	}

	function M(p) {
	var m = Monad({
	x: p.x,
	y: p.y,
	P: Point(p)
	});
	m.sub = q => M({ x: p.x - q.x, y: p.y - q.y }),
	m.add = q => M({ x: p.x + q.x, y: p.y + q.y }),
	m.round = () => M({ x: Math.round(p.x), y: Math.round(p.y) }),
	m.scale = r => M({ x: p.x * r, y: p.y * r }),
	m.length = () => Math.sqrt(p.x * p.x + p.y * p.y),
	m.unit = () => M(p).scale(1/M(p).length())
	return m;
	}

	function length(p) {
	return Math.sqrt(p.x * p.x + p.y * p.y);
	}

	function dist(p, q) {
	return length(M(p).sub(q));
	}

	function dot(p, q) {
	return p.x * q.x + p.y * q.y;
	}

	function proj(v, w) {
	return w.unit().scale(dot(v, w.unit()));
	}

	function mouseOver(d) {
	d3.select(this)
	.classed("focused", true);
	}

	function mouseOut(d) {
	if (userState) return;
	d3.select(this)
	.classed("focused", false);
	}

	function mouseDownOnCenter(d) {
	userState = "dragging";
	const c = center(controlPoints);
	const t = tip(controlPoints);
	const p0 = controlPoints.get(0);
	const p1 = controlPoints.get(1);
	const p2 = controlPoints.get(2);
	const p3 = controlPoints.get(3);
	const p0p1ratio = dist(t, p1) / dist(t, p0);
	const p3p2ratio = dist(t, p2) / dist(t, p3);

	canvas.on("mousemove", () => {
	const m = Point({
	x: d3.mouse(this)[0],
	y: d3.mouse(this)[1]
	});
	const p0p1 = M(p1).sub(p0).unit();
	const p3p2 = M(p2).sub(p3).unit();
	const axis = p0p1.add(p3p2).scale(1/1.414);
	const move = proj(M(m).sub(c), axis);
	controlPoints = Immutable.List.of(
	M(p0).add(proj(move, p0p1)).P.merge({ index: 0 }),
	M(p1).add(proj(move, p0p1).scale(p0p1ratio)).P.merge({ index: 1 }),
	M(p2).add(proj(move, p3p2).scale(p3p2ratio)).P.merge({ index: 2 }),
	M(p3).add(proj(move, p3p2)).P.merge({ index: 3 })
	);
	update();
	});
	}

	function mouseDownOnControlPoint(d) {
	userState = "dragging";
	const p0 = controlPoints.get(0);
	const p1 = controlPoints.get(1);
	const p2 = controlPoints.get(2);
	const p3 = controlPoints.get(3);
	canvas.on("mousemove", () => {
	var m = Point({
	x: d3.mouse(this)[0],
	y: d3.mouse(this)[1]
	});
	controlPoints = controlPoints.set(d.index, m.merge({ index: d.index }));
	if (d.index === 0) {
	controlPoints = controlPoints.set(1, M(p1).add(m).sub(p0).round().P.merge({ index: 1 }));
	} else if (d.index === 3) {
	controlPoints = controlPoints.set(2, M(p2).add(m).sub(p3).round().P.merge({ index: 2 }));
	}
	update();
	});
	}

	function init() {
	canvas.on("mouseup", function () {
	canvas.on("mousemove", null);
	userState = false;
	d3.select(".focused")
	.classed("focused", false);
	});

	canvas.selectAll("path.curve")
	.data([controlPoints])
	.enter().append("path")
	.classed("curve", true)
	.attr("d", d => `M${d.get(0).x},${d.get(0).y}C${d.slice(1).map(p => p.x + ',' + p.y).join(",")}`);

	canvas.selectAll("line.controlLine")
	.data(controlLines(controlPoints))
	.enter().append("line")
	.classed("controlLine", true)
	.attr("x1", d => d.get(0).x)
	.attr("y1", d => d.get(0).y)
	.attr("x2", d => d.get(1).x)
	.attr("y2", d => d.get(1).y);

	canvas.selectAll("line.tangentLine")
	.data(tangentLines(controlPoints))
	.enter().append("line")
	.classed("tangentLine", true)
	.attr("x1", d => d.get(0).x)
	.attr("y1", d => d.get(0).y)
	.attr("x2", d => d.get(1).x)
	.attr("y2", d => d.get(1).y);

	canvas.selectAll("line.radiusLine")
	.data(radiusLines(controlPoints))
	.enter().append("line")
	.classed("radiusLine", true)
	.attr("x1", d => d.get(0).x)
	.attr("y1", d => d.get(0).y)
	.attr("x2", d => d.get(1).x)
	.attr("y2", d => d.get(1).y);

	canvas.selectAll("circle.tip")
	.data(tips(controlPoints))
	.enter().append("circle")
	.classed("tip", true)
	.attr("cx", d => d.x)
	.attr("cy", d => d.y)
	.attr("r", 4);

	canvas.selectAll("circle.center")
	.data(centers(controlPoints))
	.enter().append("circle")
	.classed("center", true)
	.attr("cx", d => d.x)
	.attr("cy", d => d.y)
	.attr("r", 4)
	.on("mousedown", mouseDownOnCenter)
	.on("mouseover", mouseOver)
	.on("mouseout", mouseOut);

	canvas.selectAll("circle.controlPoint")
	.data(controlPoints.toArray(), d => d.index)
	.enter().append("circle")
	.classed("controlPoint", true)
	.attr("cx", d => d.x)
	.attr("cy", d => d.y)
	.attr("r", 4)
	.on("mousedown", mouseDownOnControlPoint)
	.on("mouseover", mouseOver)
	.on("mouseout", mouseOut);
	}

	function update() {
	canvas.selectAll("path.curve")
	.data([controlPoints])
	.attr("d", d => `M${d.get(0).x},${d.get(0).y}C${d.slice(1).map(p => p.x + ',' + p.y).join(",")}`);

	canvas.selectAll("line.controlLine")
	.data(controlLines(controlPoints))
	.attr("x1", d => d.get(0).x)
	.attr("y1", d => d.get(0).y)
	.attr("x2", d => d.get(1).x)
	.attr("y2", d => d.get(1).y);

	canvas.selectAll("line.tangentLine")
	.data(tangentLines(controlPoints))
	.attr("x1", d => d.get(0).x)
	.attr("y1", d => d.get(0).y)
	.attr("x2", d => d.get(1).x)
	.attr("y2", d => d.get(1).y);

	radiusLineElements = canvas.selectAll("line.radiusLine")
	.data(radiusLines(controlPoints))
	.attr("x1", d => d.get(0).x)
	.attr("y1", d => d.get(0).y)
	.attr("x2", d => d.get(1).x)
	.attr("y2", d => d.get(1).y);
	radiusLineElements.enter().append("line")
	.classed("radiusLine", true)
	.attr("x1", d => d.get(0).x)
	.attr("y1", d => d.get(0).y)
	.attr("x2", d => d.get(1).x)
	.attr("y2", d => d.get(1).y);
	radiusLineElements.exit()
	.remove();

	canvas.selectAll("circle.tip")
	.data(tips(controlPoints))
	.attr("cx", d => d.x)
	.attr("cy", d => d.y);

	centerElements = canvas.selectAll("circle.center")
	.data(centers(controlPoints))
	.attr("cx", d => d.x)
	.attr("cy", d => d.y);
	centerElements.enter().append("circle")
	.classed("center", true)
	.attr("cx", d => d.x)
	.attr("cy", d => d.y)
	.attr("r", 4)
	.on("mousedown", mouseDownOnCenter)
	.on("mouseover", mouseOver)
	.on("mouseout", mouseOut);
	centerElements.exit()
	.remove();

	canvas.selectAll("circle.controlPoint")
	.data(controlPoints.toArray(), d => d.index)
	.attr("cx", d => d.x)
	.attr("cy", d => d.y);
	}
	</script>
	</body>
	</html>
	The MIT License (MIT)

	Copyright © 2016 Pomin Wu

	Permission is hereby granted, free of charge, to any person obtaining a copy of
	this software and associated documentation files (the “Software”), to deal in
	the Software without restriction, including without limitation the rights to
	use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
	of the Software, and to permit persons to whom the Software is furnished to do
	so, subject to the following conditions:

	The above copyright notice and this permission notice shall be included in all
	copies or substantial portions of the Software.

	THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
	AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
	LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
	OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
	SOFTWARE.

	Fork this project to create your own MIT license that you can always link to.