Contiguous Cartogram I

.block

height: 530
license: gpl-3.0

README.md

An implementation of d3-cartogram in D3.js version 2. Based on Maggie Lee's block of Georgia counties, which was based on Jeff Fletcher's tutorial. The algorithm used to construct the cartogram is by James A. Dougenik, Nicholas R. Chrisman, and Duane R. Niemeyer.

cartogram.js

(function(exports) {

  /*
   * d3.cartogram is a d3-friendly implementation of An Algorithm to Construct
   * Continuous Area Cartograms:
   *
   * <http://chrisman.scg.ulaval.ca/G360/dougenik.pdf>
   *
   * It requires topojson to decode TopoJSON-encoded topologies:
   *
   * <http://github.com/mbostock/topojson/>
   *
   * Usage:
   *
   * var cartogram = d3.cartogram()
   *  .projection(d3.geo.albersUsa())
   *  .value(function(d) {
   *    return Math.random() * 100;
   *  });
   * d3.json("path/to/topology.json", function(topology) {
   *  var features = cartogram(topology);
   *  d3.select("svg").selectAll("path")
   *    .data(features)
   *    .enter()
   *    .append("path")
   *      .attr("d", cartogram.path);
   * });
   */
  d3.cartogram = function() {

    function carto(topology, geometries) {
      // copy it first
      topology = copy(topology);

      // objects are projected into screen coordinates
      var projectGeometry = projector(projection);

      // project the arcs into screen space
      var tf = transformer(topology.transform),
          projectedArcs = topology.arcs.map(function(arc) {
            var x = 0, y = 0;
            return arc.map(function(coord) {
              coord[0] = (x += coord[0]);
              coord[1] = (y += coord[1]);
              return projection(tf(coord));
            });
          });

      // path with identity projection
      var path = d3.geo.path()
        .projection(ident);

      var objects = object(projectedArcs, {type: "GeometryCollection", geometries: geometries})
          .geometries.map(function(geom) {
            return {
              type: "Feature",
              id: geom.id,
              properties: properties.call(null, geom, topology),
              geometry: geom
            };
          });

      var values = objects.map(value),
          totalValue = sum(values);

      // no iterations; just return the features
      if (iterations <= 0) {
        return objects;
      }

      var i = 0,
          targetSizeError = 1;
      while (i++ < iterations) {
        var areas = objects.map(path.area),
            totalArea = sum(areas),
            sizeErrors = [],
            meta = objects.map(function(o, j) {
              var area = Math.abs(areas[j]), // XXX: why do we have negative areas?
                  v = +values[j],
                  desired = totalArea * v / totalValue,
                  radius = Math.sqrt(area / Math.PI),
                  mass = Math.sqrt(desired / Math.PI) - radius,
                  sizeError = Math.max(area, desired) / Math.min(area, desired);
              sizeErrors.push(sizeError);
              // console.log(o.id, "@", j, "area:", area, "value:", v, "->", desired, radius, mass, sizeError);
              return {
                id:         o.id,
                area:       area,
                centroid:   path.centroid(o),
                value:      v,
                desired:    desired,
                radius:     radius,
                mass:       mass,
                sizeError:  sizeError
              };
            });

        var sizeError = mean(sizeErrors),
            forceReductionFactor = 1 / (1 + sizeError);

        // console.log("meta:", meta);
        // console.log("  total area:", totalArea);
        // console.log("  force reduction factor:", forceReductionFactor, "mean error:", sizeError);

        projectedArcs.forEach(function(arc) {
          arc.forEach(function(coord) {
            // create an array of vectors: [x, y]
            var vectors = meta.map(function(d) {
              var centroid =  d.centroid,
                  mass =      d.mass,
                  radius =    d.radius,
                  theta =     angle(centroid, coord),
                  dist =      distance(centroid, coord),
                  Fij = (dist > radius)
                    ? mass * radius / dist
                    : mass *
                      (Math.pow(dist, 2) / Math.pow(radius, 2)) *
                      (4 - 3 * dist / radius);
              return [
                Fij * Math.cos(theta),
                Fij * Math.sin(theta)
              ];
            });

            // using Fij and angles, calculate vector sum
            var delta = vectors.reduce(function(a, b) {
              return [
                a[0] + b[0],
                a[1] + b[1]
              ];
            }, [0, 0]);

            delta[0] *= forceReductionFactor;
            delta[1] *= forceReductionFactor;

            coord[0] += delta[0];
            coord[1] += delta[1];
          });
        });

        // break if we hit the target size error
        if (sizeError <= targetSizeError) break;
      }

      return {
        features: objects,
        arcs: projectedArcs
      };
    }

    var iterations = 8,
        projection = d3.geo.albers(),
        properties = function(id) {
          return {};
        },
        value = function(d) {
          return 1;
        };

    // for convenience
    carto.path = d3.geo.path()
      .projection(ident);

    carto.iterations = function(i) {
      if (arguments.length) {
        iterations = i;
        return carto;
      } else {
        return iterations;
      }
    };

    carto.value = function(v) {
      if (arguments.length) {
        value = d3.functor(v);
        return carto;
      } else {
        return value;
      }
    };

    carto.projection = function(p) {
      if (arguments.length) {
        projection = p;
        return carto;
      } else {
        return projection;
      }
    };

    carto.feature = function(topology, geom) {
      return {
        type: "Feature",
        id: geom.id,
        properties: properties.call(null, geom, topology),
        geometry: {
          type: geom.type,
          coordinates: topojson.object(topology, geom).coordinates
        }
      };
    };

    carto.features = function(topo, geometries) {
      return geometries.map(function(f) {
        return carto.feature(topo, f);
      });
    };

    carto.properties = function(props) {
      if (arguments.length) {
        properties = d3.functor(props);
        return carto;
      } else {
        return properties;
      }
    };

    return carto;
  };

  var transformer = d3.cartogram.transformer = function(tf) {
    var kx = tf.scale[0],
        ky = tf.scale[1],
        dx = tf.translate[0],
        dy = tf.translate[1];

    function transform(c) {
      return [c[0] * kx + dx, c[1] * ky + dy];
    }

    transform.invert = function(c) {
      return [(c[0] - dx) / kx, (c[1]- dy) / ky];
    };

    return transform;
  };

  function sum(numbers) {
    var total = 0;
    for (var i = numbers.length - 1; i-- > 0;) {
      total += numbers[i];
    }
    return total;
  }

  function mean(numbers) {
    return sum(numbers) / numbers.length;
  }

  function angle(a, b) {
    return Math.atan2(b[1] - a[1], b[0] - a[0]);
  }

  function distance(a, b) {
    var dx = b[0] - a[0],
        dy = b[1] - a[1];
    return Math.sqrt(dx * dx + dy * dy);
  }

  function projector(proj) {
    var types = {
      Point: proj,
      LineString: function(coords) {
        return coords.map(proj);
      },
      MultiLineString: function(arcs) {
        return arcs.map(types.LineString);
      },
      Polygon: function(rings) {
        return rings.map(types.LineString);
      },
      MultiPolygon: function(rings) {
        return rings.map(types.Polygon);
      }
    };
    return function(geom) {
      return types[geom.type](geom.coordinates);
    };
  }

  // identity projection
  function ident(c) {
    return c;
  }

  function copy(o) {
    return (o instanceof Array)
      ? o.map(copy)
      : (typeof o === "string" || typeof o === "number")
        ? o
        : copyObject(o);
  }
  
  function copyObject(o) {
    var obj = {};
    for (var k in o) obj[k] = copy(o[k]);
    return obj;
  }

  function object(arcs, o) {
    function arc(i, points) {
      if (points.length) points.pop();
      for (var a = arcs[i < 0 ? ~i : i], k = 0, n = a.length; k < n; ++k) {
        points.push(a[k]);
      }
      if (i < 0) reverse(points, n);
    }

    function line(arcs) {
      var points = [];
      for (var i = 0, n = arcs.length; i < n; ++i) arc(arcs[i], points);
      return points;
    }

    function polygon(arcs) {
      return arcs.map(line);
    }

    function geometry(o) {
      o = Object.create(o);
      o.coordinates = geometryType[o.type](o.arcs);
      return o;
    }

    var geometryType = {
      LineString: line,
      MultiLineString: polygon,
      Polygon: polygon,
      MultiPolygon: function(arcs) { return arcs.map(polygon); }
    };

    return o.type === "GeometryCollection"
        ? (o = Object.create(o), o.geometries = o.geometries.map(geometry), o)
        : geometry(o);
  }

  function reverse(array, n) {
    var t, j = array.length, i = j - n; while (i < --j) t = array[i], array[i++] = array[j], array[j] = t;
  }

})(this);

data.csv

geo.json

index.html

<!DOCTYPE html>
	<head>
		<meta charset="utf-8">
	</head>
	<body>

		<div id="legendholder">
		  <button id="click_to_run" onclick="do_update()">View by Population</button>
		  <button id="click_to_normal" onclick="do_normal()">View Normal</button>
		</div> 
		  
		<div id="map-wrapper"></div>

		<script src="https://d3js.org/d3.v2.min.js"></script>
		<script src="topojson.js"></script>
		<script src="cartogram.js"></script>

		<script src="scripts.js"></script> 

	</body>
</html>

scripts.js

var width = window.innerWidth,
  height = window.innerHeight,
  margin = {top: 0, bottom: 0, left: 0, right: 0};

var svg = d3.select("#map-wrapper").append("svg")
  .attr("width", width - margin.left - margin.right)
  .attr("height", height - margin.top - margin.bottom);

var states = svg.append("g")
  .attr("id", "states")
  .selectAll("path");

var projection = d3.geo.albers()
  .origin([79.375986, 23.368801])
  .scale(1000);

var topology,
  geometries,
  carto_features;

var pop_data = d3.map();

var carto = d3.cartogram()
    .projection(projection)
    .properties(function (d) {
      // this adds the "properties" properties to the geometries
      return d.properties;
    });

d3.csv("data.csv", function(data){
  data.forEach(function(d){
    pop_data.set(d.state_ut, [d.population_2011, d.sex_ratio])
  });
});

d3.json("geo.json", function(data){

  topology = data;
  geometries = topology.objects['india_state'].geometries;

  var features = carto.features(topology, geometries),
    path = d3.geo.path()
      .projection(projection);

  states = states.data(features)
      .enter()
      .append("path")
      .attr("class", "state")
      .attr("id", function (d) { return slugify(d.properties.ST_NM); })
      .attr("fill", "white")
      .attr("d", path)
      .attr("stroke", "black");

});

function do_update() {

  d3.select("#click_to_run").text("thinking...");
  setTimeout(function () {

    carto.value(function (d) {
      var ret = +pop_data.get(d.properties['ST_NM'])[0]
      return ret;
    });

    if (carto_features == undefined)
        carto_features = carto(topology, geometries).features;

    states.data(carto_features)
      .text(function (d) {  
        return d.properties.ST_NM;
      })

    states.transition()
        .duration(3750)
        .each("end", function () {
            d3.select("#click_to_run").text("View by Population")
        })
        .attr("d", carto.path);
  }, 10);

}

function do_normal() {
  d3.select("#click_to_normal").text("thinking...");
  setTimeout(function () {

  var features = carto.features(topology, geometries),
    path = d3.geo.path()
      .projection(projection);

  states.data(features)
      .transition()
        .duration(3750)
        .each("end", function () {
            d3.select("#click_to_normal").text("View Normal")
        })
       .attr("d", path);
  }, 10);

};

function slugify(text){
  return text.toString().toLowerCase()
    .replace(/\s+/g, '-')           // Replace spaces with -
    .replace(/[^\w\-]+/g, '')       // Remove all non-word chars
    .replace(/\-\-+/g, '-')         // Replace multiple - with single -
    .replace(/^-+/, '')             // Trim - from start of text
    .replace(/-+$/, '');            // Trim - from end of text
}

thumbnail.png

topojson.js

topojson = (function() {

  function merge(topology, arcs) {
    var arcsByEnd = {},
        fragmentByStart = {},
        fragmentByEnd = {};

    arcs.forEach(function(i) {
      var e = ends(i);
      (arcsByEnd[e[0]] || (arcsByEnd[e[0]] = [])).push(i);
      (arcsByEnd[e[1]] || (arcsByEnd[e[1]] = [])).push(~i);
    });

    arcs.forEach(function(i) {
      var e = ends(i),
          start = e[0],
          end = e[1],
          f, g;

      if (f = fragmentByEnd[start]) {
        delete fragmentByEnd[f.end];
        f.push(i);
        f.end = end;
        if (g = fragmentByStart[end]) {
          delete fragmentByStart[g.start];
          var fg = g === f ? f : f.concat(g);
          fragmentByStart[fg.start = f.start] = fragmentByEnd[fg.end = g.end] = fg;
        } else if (g = fragmentByEnd[end]) {
          delete fragmentByStart[g.start];
          delete fragmentByEnd[g.end];
          var fg = f.concat(g.map(function(i) { return ~i; }).reverse());
          fragmentByStart[fg.start = f.start] = fragmentByEnd[fg.end = g.start] = fg;
        } else {
          fragmentByStart[f.start] = fragmentByEnd[f.end] = f;
        }
      } else if (f = fragmentByStart[end]) {
        delete fragmentByStart[f.start];
        f.unshift(i);
        f.start = start;
        if (g = fragmentByEnd[start]) {
          delete fragmentByEnd[g.end];
          var gf = g === f ? f : g.concat(f);
          fragmentByStart[gf.start = g.start] = fragmentByEnd[gf.end = f.end] = gf;
        } else if (g = fragmentByStart[start]) {
          delete fragmentByStart[g.start];
          delete fragmentByEnd[g.end];
          var gf = g.map(function(i) { return ~i; }).reverse().concat(f);
          fragmentByStart[gf.start = g.end] = fragmentByEnd[gf.end = f.end] = gf;
        } else {
          fragmentByStart[f.start] = fragmentByEnd[f.end] = f;
        }
      } else if (f = fragmentByStart[start]) {
        delete fragmentByStart[f.start];
        f.unshift(~i);
        f.start = end;
        if (g = fragmentByEnd[end]) {
          delete fragmentByEnd[g.end];
          var gf = g === f ? f : g.concat(f);
          fragmentByStart[gf.start = g.start] = fragmentByEnd[gf.end = f.end] = gf;
        } else if (g = fragmentByStart[end]) {
          delete fragmentByStart[g.start];
          delete fragmentByEnd[g.end];
          var gf = g.map(function(i) { return ~i; }).reverse().concat(f);
          fragmentByStart[gf.start = g.end] = fragmentByEnd[gf.end = f.end] = gf;
        } else {
          fragmentByStart[f.start] = fragmentByEnd[f.end] = f;
        }
      } else if (f = fragmentByEnd[end]) {
        delete fragmentByEnd[f.end];
        f.push(~i);
        f.end = start;
        if (g = fragmentByEnd[start]) {
          delete fragmentByStart[g.start];
          var fg = g === f ? f : f.concat(g);
          fragmentByStart[fg.start = f.start] = fragmentByEnd[fg.end = g.end] = fg;
        } else if (g = fragmentByStart[start]) {
          delete fragmentByStart[g.start];
          delete fragmentByEnd[g.end];
          var fg = f.concat(g.map(function(i) { return ~i; }).reverse());
          fragmentByStart[fg.start = f.start] = fragmentByEnd[fg.end = g.start] = fg;
        } else {
          fragmentByStart[f.start] = fragmentByEnd[f.end] = f;
        }
      } else {
        f = [i];
        fragmentByStart[f.start = start] = fragmentByEnd[f.end = end] = f;
      }
    });

    function ends(i) {
      var arc = topology.arcs[i], p0 = arc[0], p1 = [0, 0];
      arc.forEach(function(dp) { p1[0] += dp[0], p1[1] += dp[1]; });
      return [p0, p1];
    }

    var fragments = [];
    for (var k in fragmentByEnd) fragments.push(fragmentByEnd[k]);
    return fragments;
  }

  function mesh(topology, o, filter) {
    var arcs = [];

    if (arguments.length > 1) {
      var geomsByArc = [],
          geom;

      function arc(i) {
        if (i < 0) i = ~i;
        (geomsByArc[i] || (geomsByArc[i] = [])).push(geom);
      }

      function line(arcs) {
        arcs.forEach(arc);
      }

      function polygon(arcs) {
        arcs.forEach(line);
      }

      function geometry(o) {
        geom = o;
        geometryType[o.type](o.arcs);
      }

      var geometryType = {
        LineString: line,
        MultiLineString: polygon,
        Polygon: polygon,
        MultiPolygon: function(arcs) { arcs.forEach(polygon); }
      };

      o.type === "GeometryCollection"
          ? o.geometries.forEach(geometry)
          : geometry(o);

      if (arguments.length < 3) for (var i in geomsByArc) arcs.push([i]);
      else for (var i in geomsByArc) if (filter((geom = geomsByArc[i])[0], geom[geom.length - 1])) arcs.push([i]);
    } else {
      for (var i = 0, n = topology.arcs.length; i < n; ++i) arcs.push([i]);
    }

    return object(topology, {type: "MultiLineString", arcs: merge(topology, arcs)});
  }

  function object(topology, o) {
    var tf = topology.transform,
        kx = tf.scale[0],
        ky = tf.scale[1],
        dx = tf.translate[0],
        dy = tf.translate[1],
        arcs = topology.arcs;

    function arc(i, points) {
      if (points.length) points.pop();
      for (var a = arcs[i < 0 ? ~i : i], k = 0, n = a.length, x = 0, y = 0, p; k < n; ++k) points.push([
        (x += (p = a[k])[0]) * kx + dx,
        (y += p[1]) * ky + dy
      ]);
      if (i < 0) reverse(points, n);
    }

    function line(arcs) {
      var points = [];
      for (var i = 0, n = arcs.length; i < n; ++i) arc(arcs[i], points);
      return points;
    }

    function polygon(arcs) {
      return arcs.map(line);
    }

    function geometry(o) {
      o = Object.create(o);
      o.coordinates = geometryType[o.type](o.arcs);
      return o;
    }

    var geometryType = {
      LineString: line,
      MultiLineString: polygon,
      Polygon: polygon,
      MultiPolygon: function(arcs) { return arcs.map(polygon); }
    };

    return o.type === "GeometryCollection"
        ? (o = Object.create(o), o.geometries = o.geometries.map(geometry), o)
        : geometry(o);
  }

  function reverse(array, n) {
    var t, j = array.length, i = j - n; while (i < --j) t = array[i], array[i++] = array[j], array[j] = t;
  }

  return {
    version: "0.0.3",
    mesh: mesh,
    object: object
  };
})();

Thank you for sharing this. This is super helpful.