msbarry · September 13, 2023 18:34
diff --git a/readme-douglaspeucker.js b/readme-douglaspeucker.js
 // Douglas Peucker polyline simplification algorithm
 // Adapted from http://onthegomap.com
 (function () {
  // utilities  
  var sqr = function (x) { return x * x; };
  var distSquared = function (p1, p2) {
    return sqr(p1[0] - p2[0]) + sqr(p1[1] - p2[1]);
  };

  // Representation of a line segment, used to determine distance to a point
  var Line = function(p1, p2) {
    this.p1 = p1;
    this.p2 = p2;
    this.lengthSquared = distSquared(p1, p2);
  };
  Line.prototype = {
    getRatio: function (point) {
      var p1 = this.p1, p2 = this.p2;
      var segmentLength = this.lengthSquared;
      if (segmentLength === 0) {
        return distSquared(point, p1);
      }
      return ((point[0] - p1[0]) * (p2[0] - p1[0]) +
        (point[1] - p1[1]) * (p2[1] - p1[1])) / segmentLength;
    },
    distanceToSquared: function (point) {
      var p1 = this.p1, p2 = this.p2;
      var t = this.getRatio(point);
      if (t < 0) { return distSquared(point, p1); }
      if (t > 1) { return distSquared(point, p2); }
      return distSquared(point, [
        p1[0] + t * (p2[0] - p1[0]),
        p1[1] + t * (p2[1] - p1[1])
      ]);
    },
    distanceTo: function (point) {
      return Math.sqrt(this.distanceToSquared(point));
    }
  };

  window.simplifyDouglasPeucker = function (points, pointsToKeep) {
    var start = new Date().getTime();
    var weights = [];
    var len = points.length;
    function douglasPeucker (start, end) {
      if (end > start + 1) {
        var line = new Line(points[start], points[end]);
        var maxDist = -1;
        var maxDistIndex = 0;
        var dist;
        // find point furthest off the line from start to end
        for (var i = start + 1; i < end; i += 1) {
          dist = line.distanceToSquared(points[i]);
          if (dist > maxDist) {
            maxDist = dist;
            maxDistIndex = i;
          }
        }
        // record the weight of this point
        weights[maxDistIndex] = maxDist;
        // split the segment at that furthest point, and recursively invoke
        // this method to assign weights to each point in the subsegments
        douglasPeucker(start, maxDistIndex);
        douglasPeucker(maxDistIndex, end);
      }
    }

    douglasPeucker(0, len - 1);
    weights[0] = Infinity;
    weights[len - 1] = Infinity;

    // create descending weight array so to get n most important weights,
    // just find all points with weights >= weightsDescending[n]
    var weightsDescending = weights.slice();
    weightsDescending.sort(function (a, b) {
      return b - a;
    });

    var maxTolerance = weightsDescending[pointsToKeep -1];
    var result = points.filter(function (d, i) {
      return weights[i] >= maxTolerance;
    });
    var end = new Date().getTime();
    window.simplifyDouglasPeucker.stats[pointsToKeep] = end - start;
    return result;
  };

  window.simplifyDouglasPeucker.stats = {};
 })();
diff --git a/readme-visvalingam.js b/readme-visvalingam.js
 // Visvalingam polyline simplification algorithm, adapted from
 // http://bost.ocks.org/mike/simplify/simplify.js
 (function () {

  window.simplifyVisvalingam = function (points, pointsToKeep) {
    var start = new Date().getTime(),
        heap = minHeap(),
        maxArea = 0,
        triangle,
        triangles = [];
    points = points.map(function (d) { return d.slice(0,2); });
    for (var i = 1, n = points.length - 1; i < n; ++i) {
      triangle = points.slice(i - 1, i + 2);
      if (triangle[1][2] = area(triangle)) {
        triangles.push(triangle);
        heap.push(triangle);
      }
    }

    for (var i = 0, n = triangles.length; i < n; ++i) {
      triangle = triangles[i];
      triangle.previous = triangles[i - 1];
      triangle.next = triangles[i + 1];
    }

    while (triangle = heap.pop()) {
      // If the area of the current point is less than that of the previous point
      // to be eliminated, use the latters area instead. This ensures that the
      // current point cannot be eliminated without eliminating previously-
      // eliminated points.
      if (triangle[1][2] < maxArea) triangle[1][2] = maxArea;
      else maxArea = triangle[1][2];

      if (triangle.previous) {
        triangle.previous.next = triangle.next;
        triangle.previous[2] = triangle[2];
        update(triangle.previous);
      } else {
        triangle[0][2] = triangle[1][2];
      }

      if (triangle.next) {
        triangle.next.previous = triangle.previous;
        triangle.next[0] = triangle[0];
        update(triangle.next);
      } else {
        triangle[2][2] = triangle[1][2];
      }
    }

    function update(triangle) {
      heap.remove(triangle);
      triangle[1][2] = area(triangle);
      heap.push(triangle);
    }

    var weights = points.map(function (d) { return d.length < 3 ? Infinity : d[2] += Math.random(); /* break ties */ });
    weights.sort(function (a, b) {
      return b - a;
    });

    var result = points.filter(function (d) {
      return d[2] > weights[pointsToKeep];
    });
    var end = new Date().getTime();
    window.simplifyVisvalingam.stats[pointsToKeep] = end - start;
    return result;
  };

  window.simplifyVisvalingam.stats = {};


  function compare(a, b) {
    return a[1][2] - b[1][2];
  }

  function area(t) {
    return Math.abs((t[0][0] - t[2][0]) * (t[1][1] - t[0][1]) - (t[0][0] - t[1][0]) * (t[2][1] - t[0][1]));
  }

  function minHeap() {
    var heap = {},
        array = [];

    heap.push = function() {
      for (var i = 0, n = arguments.length; i < n; ++i) {
        var object = arguments[i];
        up(object.index = array.push(object) - 1);
      }
      return array.length;
    };

    heap.pop = function() {
      var removed = array[0],
          object = array.pop();
      if (array.length) {
        array[object.index = 0] = object;
        down(0);
      }
      return removed;
    };

    heap.size = function () {
      return array.length;
    };

    heap.remove = function(removed) {
      var i = removed.index,
          object = array.pop();
      if (i !== array.length) {
        array[object.index = i] = object;
        (compare(object, removed) < 0 ? up : down)(i);
      }
      return i;
    };

    function up(i) {
      var object = array[i];
      while (i > 0) {
        var up = ((i + 1) >> 1) - 1,
            parent = array[up];
        if (compare(object, parent) >= 0) break;
        array[parent.index = i] = parent;
        array[object.index = i = up] = object;
      }
    }

    function down(i) {
      var object = array[i];
      while (true) {
        var right = (i + 1) * 2,
            left = right - 1,
            down = i,
            child = array[down];
        if (left < array.length && compare(array[left], child) < 0) child = array[down = left];
        if (right < array.length && compare(array[right], child) < 0) child = array[down = right];
        if (down === i) break;
        array[child.index = i] = child;
        array[object.index = i = down] = object;
      }
    }

    return heap;
  }
 })();
diff --git a/README.md b/README.md
diff --git a/index.html b/index.html
 <!DOCTYPE html>
 <style type="text/css">
 body {
  font-size: 12px;
  font-family: Arial;
  width: 960px;
  margin: 1em auto 0.3em auto;
 }

 .path {
  fill: none;
  stroke: #ccc;
  stroke-width: 1px;
 }

 .simpler {
  stroke: black;
  fill: red;
  fill-opacity: 20%;
 }

 text {
  fill: #888;
 }

 .numpoints {
  fill: black;
  font-size: 30px;
 }

 .arrow {
  fill: lightGray;
 }

 .arrow:hover {
  fill: steelBlue;
 }
 </style>
 <body>
 <script src="http://d3js.org/d3.v3.min.js" charset="utf-8"></script>
 <script src="readme-visvalingam.js"></script>
 <script src="readme-douglaspeucker.js"></script>
 <script>

 var margin = { top: 10, right: 100, bottom: 10, left: 10 },
    width = 960 - margin.left - margin.right,
    height = 400 - margin.top - margin.bottom,
    padding = 40,
    numPoints = 10,
    rows = 2,
    smallWidth = width / 2,
    smallHeight = height,
    verticalSpacing = 25;


 var svg = d3.select("body").append("svg")
    .attr("width", 960)
    .attr("height", 400);

 // read in the route, pre-projected using mercator projection
 d3.json("seven-climbs-mercator.json", function(fullResPoints) {
  var path = d3.svg.line();

  // draw small multiples
  var left = svg.append('g')
    .attr('transform', 'translate(' + margin.left + ',' + margin.top + ')');
  var right = svg.append('g')
    .attr('transform', 'translate(' + (margin.left + smallWidth) + ',' + (margin.top) + ')');
  var sections = svg.selectAll('g');

  // labels
  left.append('text')
    .text('Visvalingam')
    .attr('dy', 30);
  right.append('text')
    .text('Douglas Peucker')
    .attr('dy', 30);

  // draw the polylines simplified using visvalingam algorithm
  var visSimplified = left.append('path')
      .attr('class', 'simpler');

  // draw the polylines simplified using douglas peucker algorithm
  var dpSimplified = right.append('path')
      .attr('class', 'simpler');

  // draw reference polylines
  sections.append('path')
      .datum(fullResPoints)
      .attr('class', 'path')
      .call(drawPath);

  var pointsDisplay = svg.append('text')
      .attr('class', 'numpoints')
      .attr('x', width + margin.left + margin.right / 2)
      .attr('y', height / 2)
      .attr('text-anchor', 'middle');
  var line = d3.svg.line();
  function arrow (dir) {
    return svg.append('path')
        .datum([[0, dir * 40], [40, 0], [-40, 0]])
        .attr('class', 'arrow')
        .attr('transform', 'translate(' + (width + margin.left + margin.right / 2) + ',' + (height / 2 - 8 + dir * 30) + ')')
        .attr('d', line);
  }
  var up = arrow(-1);
  var down = arrow(1);
  var pts = 10;
  function incr() { pts = Math.min(pts + 1, fullResPoints.length); update(pts); }
  function decr() { pts = Math.max(pts - 1, 4); update(pts); }
  up.on('click', incr);
  down.on('click', decr);
  d3.select('body').on('keydown', function () {
    if (d3.event.keyCode === 40) { decr(); d3.event.preventDefault(); }
    else if (d3.event.keyCode === 38) { incr(); d3.event.preventDefault(); }
  });

  function update(numPoints) {
    pts = numPoints;
    visSimplified
      .datum(fullResPoints.concat(simplifyVisvalingam(fullResPoints, numPoints).reverse()))
      .call(drawPath);
    dpSimplified
      .datum(fullResPoints.concat(simplifyDouglasPeucker(fullResPoints, numPoints).reverse()))
      .call(drawPath);
    pointsDisplay.text(numPoints);
  }

  update(10);

  function drawPath(selection) {
    return selection
        .attr("d", path)
        .attr('transform', 'translate(' + padding + ',' + verticalSpacing + ')');
  }
 });

 d3.select(self.frameElement).style("height", "400px");
 </script>
diff --git a/seven-climbs-mercator.json b/seven-climbs-mercator.json
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 ]
diff --git a/thumbnail.png b/thumbnail.png
	// Douglas Peucker polyline simplification algorithm
	// Adapted from http://onthegomap.com
	(function () {
	// utilities
	var sqr = function (x) { return x * x; };
	var distSquared = function (p1, p2) {
	return sqr(p1[0] - p2[0]) + sqr(p1[1] - p2[1]);
	};

	// Representation of a line segment, used to determine distance to a point
	var Line = function(p1, p2) {
	this.p1 = p1;
	this.p2 = p2;
	this.lengthSquared = distSquared(p1, p2);
	};
	Line.prototype = {
	getRatio: function (point) {
	var p1 = this.p1, p2 = this.p2;
	var segmentLength = this.lengthSquared;
	if (segmentLength === 0) {
	return distSquared(point, p1);
	}
	return ((point[0] - p1[0]) * (p2[0] - p1[0]) +
	(point[1] - p1[1]) * (p2[1] - p1[1])) / segmentLength;
	},
	distanceToSquared: function (point) {
	var p1 = this.p1, p2 = this.p2;
	var t = this.getRatio(point);
	if (t < 0) { return distSquared(point, p1); }
	if (t > 1) { return distSquared(point, p2); }
	return distSquared(point, [
	p1[0] + t * (p2[0] - p1[0]),
	p1[1] + t * (p2[1] - p1[1])
	]);
	},
	distanceTo: function (point) {
	return Math.sqrt(this.distanceToSquared(point));
	}
	};

	window.simplifyDouglasPeucker = function (points, pointsToKeep) {
	var start = new Date().getTime();
	var weights = [];
	var len = points.length;
	function douglasPeucker (start, end) {
	if (end > start + 1) {
	var line = new Line(points[start], points[end]);
	var maxDist = -1;
	var maxDistIndex = 0;
	var dist;
	// find point furthest off the line from start to end
	for (var i = start + 1; i < end; i += 1) {
	dist = line.distanceToSquared(points[i]);
	if (dist > maxDist) {
	maxDist = dist;
	maxDistIndex = i;
	}
	}
	// record the weight of this point
	weights[maxDistIndex] = maxDist;
	// split the segment at that furthest point, and recursively invoke
	// this method to assign weights to each point in the subsegments
	douglasPeucker(start, maxDistIndex);
	douglasPeucker(maxDistIndex, end);
	}
	}

	douglasPeucker(0, len - 1);
	weights[0] = Infinity;
	weights[len - 1] = Infinity;

	// create descending weight array so to get n most important weights,
	// just find all points with weights >= weightsDescending[n]
	var weightsDescending = weights.slice();
	weightsDescending.sort(function (a, b) {
	return b - a;
	});

	var maxTolerance = weightsDescending[pointsToKeep -1];
	var result = points.filter(function (d, i) {
	return weights[i] >= maxTolerance;
	});
	var end = new Date().getTime();
	window.simplifyDouglasPeucker.stats[pointsToKeep] = end - start;
	return result;
	};

	window.simplifyDouglasPeucker.stats = {};
	})();
	// Visvalingam polyline simplification algorithm, adapted from
	// http://bost.ocks.org/mike/simplify/simplify.js
	(function () {

	window.simplifyVisvalingam = function (points, pointsToKeep) {
	var start = new Date().getTime(),
	heap = minHeap(),
	maxArea = 0,
	triangle,
	triangles = [];
	points = points.map(function (d) { return d.slice(0,2); });
	for (var i = 1, n = points.length - 1; i < n; ++i) {
	triangle = points.slice(i - 1, i + 2);
	if (triangle[1][2] = area(triangle)) {
	triangles.push(triangle);
	heap.push(triangle);
	}
	}

	for (var i = 0, n = triangles.length; i < n; ++i) {
	triangle = triangles[i];
	triangle.previous = triangles[i - 1];
	triangle.next = triangles[i + 1];
	}

	while (triangle = heap.pop()) {
	// If the area of the current point is less than that of the previous point
	// to be eliminated, use the latters area instead. This ensures that the
	// current point cannot be eliminated without eliminating previously-
	// eliminated points.
	if (triangle[1][2] < maxArea) triangle[1][2] = maxArea;
	else maxArea = triangle[1][2];

	if (triangle.previous) {
	triangle.previous.next = triangle.next;
	triangle.previous[2] = triangle[2];
	update(triangle.previous);
	} else {
	triangle[0][2] = triangle[1][2];
	}

	if (triangle.next) {
	triangle.next.previous = triangle.previous;
	triangle.next[0] = triangle[0];
	update(triangle.next);
	} else {
	triangle[2][2] = triangle[1][2];
	}
	}

	function update(triangle) {
	heap.remove(triangle);
	triangle[1][2] = area(triangle);
	heap.push(triangle);
	}

	var weights = points.map(function (d) { return d.length < 3 ? Infinity : d[2] += Math.random(); /* break ties */ });
	weights.sort(function (a, b) {
	return b - a;
	});

	var result = points.filter(function (d) {
	return d[2] > weights[pointsToKeep];
	});
	var end = new Date().getTime();
	window.simplifyVisvalingam.stats[pointsToKeep] = end - start;
	return result;
	};

	window.simplifyVisvalingam.stats = {};


	function compare(a, b) {
	return a[1][2] - b[1][2];
	}

	function area(t) {
	return Math.abs((t[0][0] - t[2][0]) * (t[1][1] - t[0][1]) - (t[0][0] - t[1][0]) * (t[2][1] - t[0][1]));
	}

	function minHeap() {
	var heap = {},
	array = [];

	heap.push = function() {
	for (var i = 0, n = arguments.length; i < n; ++i) {
	var object = arguments[i];
	up(object.index = array.push(object) - 1);
	}
	return array.length;
	};

	heap.pop = function() {
	var removed = array[0],
	object = array.pop();
	if (array.length) {
	array[object.index = 0] = object;
	down(0);
	}
	return removed;
	};

	heap.size = function () {
	return array.length;
	};

	heap.remove = function(removed) {
	var i = removed.index,
	object = array.pop();
	if (i !== array.length) {
	array[object.index = i] = object;
	(compare(object, removed) < 0 ? up : down)(i);
	}
	return i;
	};

	function up(i) {
	var object = array[i];
	while (i > 0) {
	var up = ((i + 1) >> 1) - 1,
	parent = array[up];
	if (compare(object, parent) >= 0) break;
	array[parent.index = i] = parent;
	array[object.index = i = up] = object;
	}
	}

	function down(i) {
	var object = array[i];
	while (true) {
	var right = (i + 1) * 2,
	left = right - 1,
	down = i,
	child = array[down];
	if (left < array.length && compare(array[left], child) < 0) child = array[down = left];
	if (right < array.length && compare(array[right], child) < 0) child = array[down = right];
	if (down === i) break;
	array[child.index = i] = child;
	array[object.index = i = down] = object;
	}
	}

	return heap;
	}
	})();
	<!DOCTYPE html>
	<style type="text/css">
	body {
	font-size: 12px;
	font-family: Arial;
	width: 960px;
	margin: 1em auto 0.3em auto;
	}

	.path {
	fill: none;
	stroke: #ccc;
	stroke-width: 1px;
	}

	.simpler {
	stroke: black;
	fill: red;
	fill-opacity: 20%;
	}

	text {
	fill: #888;
	}

	.numpoints {
	fill: black;
	font-size: 30px;
	}

	.arrow {
	fill: lightGray;
	}

	.arrow:hover {
	fill: steelBlue;
	}
	</style>
	<body>
	<script src="http://d3js.org/d3.v3.min.js" charset="utf-8"></script>
	<script src="readme-visvalingam.js"></script>
	<script src="readme-douglaspeucker.js"></script>
	<script>

	var margin = { top: 10, right: 100, bottom: 10, left: 10 },
	width = 960 - margin.left - margin.right,
	height = 400 - margin.top - margin.bottom,
	padding = 40,
	numPoints = 10,
	rows = 2,
	smallWidth = width / 2,
	smallHeight = height,
	verticalSpacing = 25;


	var svg = d3.select("body").append("svg")
	.attr("width", 960)
	.attr("height", 400);

	// read in the route, pre-projected using mercator projection
	d3.json("seven-climbs-mercator.json", function(fullResPoints) {
	var path = d3.svg.line();

	// draw small multiples
	var left = svg.append('g')
	.attr('transform', 'translate(' + margin.left + ',' + margin.top + ')');
	var right = svg.append('g')
	.attr('transform', 'translate(' + (margin.left + smallWidth) + ',' + (margin.top) + ')');
	var sections = svg.selectAll('g');

	// labels
	left.append('text')
	.text('Visvalingam')
	.attr('dy', 30);
	right.append('text')
	.text('Douglas Peucker')
	.attr('dy', 30);

	// draw the polylines simplified using visvalingam algorithm
	var visSimplified = left.append('path')
	.attr('class', 'simpler');

	// draw the polylines simplified using douglas peucker algorithm
	var dpSimplified = right.append('path')
	.attr('class', 'simpler');

	// draw reference polylines
	sections.append('path')
	.datum(fullResPoints)
	.attr('class', 'path')
	.call(drawPath);

	var pointsDisplay = svg.append('text')
	.attr('class', 'numpoints')
	.attr('x', width + margin.left + margin.right / 2)
	.attr('y', height / 2)
	.attr('text-anchor', 'middle');
	var line = d3.svg.line();
	function arrow (dir) {
	return svg.append('path')
	.datum([[0, dir * 40], [40, 0], [-40, 0]])
	.attr('class', 'arrow')
	.attr('transform', 'translate(' + (width + margin.left + margin.right / 2) + ',' + (height / 2 - 8 + dir * 30) + ')')
	.attr('d', line);
	}
	var up = arrow(-1);
	var down = arrow(1);
	var pts = 10;
	function incr() { pts = Math.min(pts + 1, fullResPoints.length); update(pts); }
	function decr() { pts = Math.max(pts - 1, 4); update(pts); }
	up.on('click', incr);
	down.on('click', decr);
	d3.select('body').on('keydown', function () {
	if (d3.event.keyCode === 40) { decr(); d3.event.preventDefault(); }
	else if (d3.event.keyCode === 38) { incr(); d3.event.preventDefault(); }
	});

	function update(numPoints) {
	pts = numPoints;
	visSimplified
	.datum(fullResPoints.concat(simplifyVisvalingam(fullResPoints, numPoints).reverse()))
	.call(drawPath);
	dpSimplified
	.datum(fullResPoints.concat(simplifyDouglasPeucker(fullResPoints, numPoints).reverse()))
	.call(drawPath);
	pointsDisplay.text(numPoints);
	}

	update(10);

	function drawPath(selection) {
	return selection
	.attr("d", path)
	.attr('transform', 'translate(' + padding + ',' + verticalSpacing + ')');
	}
	});

	d3.select(self.frameElement).style("height", "400px");
	</script>