Canada Character Distribution

README.md

Chrome users: If the animation doesn't work for you, try viewing the cartogram in its own window by clicking: "Open in new window".

This cartogram scales the area of Canada's provinces and territories by the number of characters used in the name of the province or territory.

Built with D3js and Cartogram.js. Province and territory data obtained from the Government of Canada's Open Data Portal.

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);

index.html

<!DOCTYPE html>
<html>
  <head>
    <script src="http://d3js.org/d3.v2.js"></script>
    <script src="topojson-v0.0.10.js"></script>
    <script src="cartogram.js"></script>

    <style type="text/css">
      html, body { margin: 0; padding: 0; height: 100%; }
      #map {
        display: block;
        position: absolute;
        background: #fff;
        width: 100%;
        height: 100%;
        margin: 0;
      }
      path.province {
        fill: steelblue;
        stroke: white;
      }
      path.province:hover {
        fill: orange;
      }
    </style>
  </head>
  <body>
    <div id="map-container" data-provinces="prov_4326_simple.topo.json"></div>
    <script type="text/javascript">
      (function () {
        var container = d3.select('#map-container').node(),
            data = container.dataset;

        var width = 960,
            height = 500;

            var proj = d3.geo.albers(),
                path = d3.geo.path().projection(proj);

        var svg = d3.select(container).append("svg")
                .attr("width", width)
                .attr("height", height);

        d3.json(data.provinces, ready);

        function ready(canada) {

            var carto = d3.cartogram()
                .projection(proj)
                .properties(function (geom, topo) {
                    return geom.properties;
                })
                // Morph on the number of characters in province's name.
                .value(get_id_length);

            var provinces = svg.append("g")
                .attr("class", "provinces")
                .selectAll("path")
                .data(topojson.object(canada, canada.objects.provinces).geometries)
                // .data(features)
                .enter().append("path")
                .attr("class", "province")
                .attr("d", path)
                // .attr("d", carto.path)
                .attr("transform", "translate(0,350)" +
                      "scale(0.75,0.75)");

            var title = provinces.append("title")
                    .text(function(d) { return get_id_length(d) + ": " + d.id; });

            var features = carto(canada, canada.objects.provinces.geometries).features;

            provinces.data(features)
                .transition()
                .duration(2000)
                .ease("sin-in-out")
                .attr("d", carto.path);

            console.log(provinces.length);
        }

        function get_id_length (d) {
          return d.id.length;
        }
      }());
    </script>
  </body>
</html>

prov_4326_simple.topo.json

{"type":"Topology","transform":{"scale":[0.008840750540454047,0.004142862466646652],"translate":[-141.01807315799994,41.71096215800009]},"objects":{"provinces":{"type":"GeometryCollection","geometries":[{"type":"MultiPolygon","id":"Yukon","arcs":[[[0,1]],[[2]],[[3]],[[4]],[[5,6,7,8]]],"properties":{"PRUID":"60","PRNAME":"Yukon","PRENAME":"Yukon","PRFNAME":"Yukon","PREABBR":"Y.T.","PRFABBR":"Yn"}},{"type":"Polygon","id":"Saskatchewan","arcs":[[9,10,11,12,13]],"properties":{"PRUID":"47","PRNAME":"Saskatchewan","PRENAME":"Saskatchewan","PRFNAME":"Saskatchewan","PREABBR":"Sask.","PRFABBR":"Sask."}},{"type":"Polygon","id":"Manitoba","arcs":[[14,15,-13,16,17]],"properties":{"PRUID":"46","PRNAME":"Manitoba","PRENAME":"Manitoba","PRFNAME":"Manitoba","PREABBR":"Man.","PRFABBR":"Man."}},{"type":"MultiPolygon","id":"Nova Scotia","arcs":[[[18]],[[19]],[[20]],[[21]],[[22]],[[23]],[[24]],[[25]],[[26]],[[27]],[[28]],[[29]],[[30]],[[31]],[[32,33,34,35,36,37,38,39]],[[40]],[[41,42,43],[44],[45],[46]],[[47]]],"properties":{"PRUID":"12","PRNAME":"Nova Scotia / Nouvelle-Écosse","PRENAME":"Nova Scotia","PRFNAME":"Nouvelle-Écosse","PREABBR":"N.S.","PRFABBR":"N.-É."}},{"type":"Polygon","id":"Alberta","arcs":[[48,49,50,-10,51]],"properties":{"PRUID":"48","PRNAME":"Alberta","PRENAME":"Alberta","PRFNAME":"Alberta","PREABBR":"Alta.","PRFABBR":"Alb."}},{"type":"MultiPolygon","id":"British Columbia","arcs":[[[52]],[[53]],[[54]],[[55]],[[56]],[[57]],[[58]],[[59]],[[60]],[[61]],[[62]],[[63]],[[64]],[[65]],[[66]],[[67]],[[68]],[[69]],[[70]],[[71]],[[72]],[[73]],[[74]],[[75]],[[76]],[[77]],[[78]],[[79]],[[80]],[[81]],[[82]],[[83]],[[84]],[[85]],[[86]],[[87]],[[88]],[[89]],[[90]],[[91]],[[92]],[[93]],[[94]],[[95]],[[96]],[[97]],[[98]],[[99]],[[100]],[[101]],[[102]],[[103]],[[104]],[[105]],[[106]],[[107]],[[108]],[[109]],[[110]],[[111]],[[112]],[[113]],[[114,-49,115]]],"properties":{"PRUID":"59","PRNAME":"British Columbia / Colombie-Britannique","PRENAME":"British Columbia","PRFNAME":"Colombie-Britannique","PREABBR":"B.C.","PRFABBR":"C.-B."}},{"type":"MultiPolygon","id":"Ontario","arcs":[[[116]],[[117]],[[118]],[[119]],[[120]],[[120]],[[121]],[[122]],[[123,124]],[[125,-125,126]],[[127,128]],[[-128,127,129]],[[130,131]],[[132]],[[133]],[[134]],[[135]],[[136]],[[137]],[[138]],[[139]],[[140]],[[141]],[[142]],[[143]],[[144]],[[145]],[[146]],[[147]],[[148]],[[149]],[[150]],[[151]],[[152]],[[153]],[[154]],[[155]],[[156]],[[157]],[[158]],[[159]],[[160]],[[161]],[[162]],[[163]],[[164]],[[164]],[[165]],[[166]],[[167]],[[168]],[[169]],[[170]],[[171]],[[172]],[[173]],[[174]],[[175]],[[176]],[[177]],[[178]],[[179]],[[180]],[[181]],[[182]],[[183,184]],[[185]],[[186]],[[187]],[[188]],[[189]],[[190]],[[191]],[[192]],[[193,194]],[[195]],[[196]],[[197]],[[198]],[[199]],[[200]],[[201]],[[202]],[[203]],[[204,205]],[[206,207]],[[208]],[[209]],[[210]],[[211]],[[212]],[[213]],[[214,215,216,-15,217,218,219,220,221,222,223,224,225,226,227,228,229,-184,230,231]]],"properties":{"PRUID":"35","PRNAME":"Ontario","PRENAME":"Ontario","PRFNAME":"Ontario","PREABBR":"Ont.","PRFABBR":"Ont."}},{"type":"MultiPolygon","id":"Quebec","arcs":[[[232]],[[233]],[[234]],[[235]],[[236]],[[237]],[[238]],[[239]],[[240]],[[241]],[[242]],[[243]],[[244]],[[245]],[[246]],[[247]],[[248]],[[249]],[[250]],[[251]],[[252]],[[253]],[[254]],[[255]],[[256]],[[257]],[[258]],[[259,260,261,262,263]],[[264]],[[265]],[[266]],[[267]],[[268]],[[269]],[[270]],[[271]],[[272]],[[273]],[[274]],[[275]],[[276]],[[277]],[[278]],[[279]],[[280]],[[281]],[[282]],[[-229,283,-227,284,-225,285,-223,286,-221,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310]]],"properties":{"PRUID":"24","PRNAME":"Quebec / Québec","PRENAME":"Quebec","PRFNAME":"Québec","PREABBR":"Que.","PRFABBR":"Qc"}},{"type":"MultiPolygon","id":"Prince Edward Island","arcs":[[[311]],[[312]],[[313]],[[314]],[[315]],[[316]],[[317,318,319]],[[320]],[[321]],[[322]],[[323]]],"properties":{"PRUID":"11","PRNAME":"Prince Edward Island / Île-du-Prince-Édouard","PRENAME":"Prince Edward Island","PRFNAME":"Île-du-Prince-Édouard","PREABBR":"P.E.I.","PRFABBR":"Î.-P.-É."}},{"type":"MultiPolygon","id":"Nunavut","arcs":[[[324]],[[325]],[[326]],[[327]],[[328]],[[329]],[[330]],[[331]],[[332]],[[333]],[[334]],[[335]],[[336]],[[337]],[[338]],[[339]],[[340]],[[341]],[[342]],[[343]],[[344]],[[345]],[[346]],[[347]],[[348]],[[349]],[[350]],[[351]],[[352]],[[353]],[[354]],[[355]],[[356]],[[357]],[[358]],[[359]],[[360]],[[361]],[[362]],[[363]],[[364]],[[365]],[[366]],[[367]],[[368]],[[369]],[[370]],[[371]],[[372]],[[373]],[[374]],[[375]],[[376]],[[377]],[[378]],[[379]],[[380]],[[381]],[[382]],[[383,384]],[[385]],[[386]],[[387]],[[388]],[[389]],[[390]],[[391]],[[392]],[[393]],[[394]],[[395]],[[396]],[[397]],[[398]],[[399]],[[400]],[[401]],[[402]],[[403]],[[404]],[[405]],[[406]],[[407]],[[408]],[[409]],[[410]],[[411]],[[412]],[[413]],[[414]],[[415]],[[416]],[[417]],[[418]],[[419]],[[420]],[[421]],[[422]],[[423]],[[424]],[[425]],[[426]],[[427]],[[428]],[[429]],[[430]],[[431]],[[432]],[[433]],[[434]],[[435]],[[436]],[[437]],[[438]],[[439]],[[440]],[[441]],[[442]],[[443]],[[444]],[[445]],[[446]],[[447]],[[448]],[[449]],[[450]],[[451]],[[452]],[[453]],[[454]],[[455]],[[456]],[[457]],[[458]],[[459]],[[460]],[[461]],[[462]],[[463]],[[464,465]],[[466]],[[467]],[[468]],[[469]],[[470]],[[471]],[[472]],[[473]],[[474]],[[475]],[[476]],[[477]],[[478]],[[479]],[[480]],[[481]],[[482]],[[483]],[[484]],[[485]],[[486]],[[487]],[[488]],[[489]],[[490]],[[491]],[[492]],[[493]],[[494]],[[495]],[[496]],[[497]],[[498]],[[499]],[[500]],[[501]],[[502]],[[503]],[[504]],[[505]],[[506]],[[507]],[[508]],[[509]],[[510]],[[511]],[[512]],[[513]],[[514]],[[515]],[[516]],[[517]],[[518]],[[519]],[[520]],[[521]],[[522]],[[523]],[[524]],[[525]],[[526]],[[527]],[[528]],[[529]],[[530]],[[531]],[[532]],[[533]],[[534]],[[535]],[[536]],[[537]],[[538]],[[539]],[[540]],[[541]],[[542]],[[543]],[[544]],[[545]],[[546]],[[547]],[[548]],[[549]],[[550]],[[551]],[[552]],[[553]],[[554]],[[555]],[[556]],[[557]],[[558]],[[559]],[[560]],[[561]],[[562]],[[563]],[[564]],[[565]],[[566]],[[567]],[[568]],[[569]],[[570]],[[571]],[[572]],[[573]],[[574]],[[575]],[[576]],[[577]],[[578]],[[579]],[[580]],[[581]],[[582]],[[583]],[[584]],[[585]],[[586]],[[587]],[[588]],[[589]],[[590]],[[591]],[[592]],[[593]],[[594]],[[595]],[[596]],[[597]],[[598]],[[599]],[[600]],[[601]],[[602]],[[603]],[[604]],[[605]],[[606]],[[607]],[[608]],[[609]],[[610]],[[611]],[[612]],[[613]],[[614]],[[615]],[[616]],[[617]],[[618]],[[619]],[[620]],[[-17,621,622,623,624,625,626]],[[627]],[[628]],[[629]],[[630]],[[631]],[[632]],[[633]],[[634]],[[635]],[[636]],[[637]],[[638]],[[639]],[[640]],[[641]],[[642]],[[643]],[[644]],[[645]],[[646]],[[647]],[[648]],[[649]],[[650]],[[651]],[[652]],[[653]],[[654]],[[655]],[[656]],[[657]],[[658]],[[659]],[[660]],[[661]],[[662]],[[663]],[[664]],[[665,666,667]],[[668]],[[669,670],[671],[672],[673,674]],[[675]],[[676]],[[677]],[[678]],[[679]],[[680]],[[681]],[[682]],[[683]],[[684]],[[685]],[[686]],[[687]],[[688]],[[689]],[[690]],[[691]],[[692]],[[693]],[[694]],[[695]],[[696]],[[697]],[[698]],[[699]],[[700]],[[701]],[[702]],[[703]],[[704]],[[705]],[[706]],[[707]],[[708]],[[709]],[[710]],[[711]],[[712]],[[713]],[[714]],[[715]],[[716]],[[717]],[[718]],[[719]],[[720]],[[721]],[[722]],[[723]],[[724]],[[725]],[[726]],[[727]],[[728]],[[729]],[[730]],[[731]],[[732]],[[733]],[[734]],[[735]],[[736]],[[737]],[[738]],[[739]],[[740]],[[741]],[[742]],[[743]],[[744]],[[745]],[[746]],[[747]],[[748]],[[749,750,751,752,753]],[[754]],[[755]],[[756]],[[757]],[[758]],[[759]],[[760]],[[761]],[[762]],[[763]],[[764]],[[765]],[[766]],[[767]],[[768]],[[769]],[[770]],[[771]],[[772,773]],[[774]],[[775]],[[776]],[[777]],[[778]],[[779]],[[780]],[[781]],[[782]],[[783]],[[784]],[[785]],[[786]],[[787]],[[788]],[[789]],[[790]],[[791]],[[792]],[[793]],[[794]],[[795]],[[796]],[[797]],[[798]],[[799]],[[800]],[[801]],[[802]]],"properties":{"PRUID":"62","PRNAME":"Nunavut","PRENAME":"Nunavut","PRFNAME":"Nunavut","PREABBR":"Nvt.","PRFABBR":"Nt"}},{"type":"MultiPolygon","id":"Northwest Territories","arcs":[[[803]],[[804]],[[805]],[[806]],[[807]],[[808]],[[809]],[[810]],[[811]],[[812]],[[813]],[[814]],[[815]],[[816]],[[817]],[[818]],[[819]],[[820]],[[821]],[[822]],[[-622,-12,823,824,-7,825,826]],[[827,-667,828]],[[829]],[[830]],[[831]],[[832]],[[833]],[[834]],[[835]],[[836]],[[837]],[[-753,838]],[[839]],[[-750,840]],[[841]],[[842]],[[843]],[[844]],[[845]],[[846]],[[847]],[[848]],[[849]],[[850]],[[851]],[[-773,852]],[[853]],[[854]],[[855]],[[856]]],"properties":{"PRUID":"61","PRNAME":"Northwest Territories / Territoires du Nord-Ouest","PRENAME":"Northwest Territories","PRFNAME":"Territoires du Nord-Ouest","PREABBR":"N.W.T.","PRFABBR":"T.N.-O."}},{"type":"MultiPolygon","id":"Newfoundland and 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thumbnail.png

topojson-v0.0.10.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);

      geomsByArc.forEach(arguments.length < 3
          ? function(geoms, i) { arcs.push([i]); }
          : function(geoms, i) { if (filter(geoms[0], geoms[geoms.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 point(coordinates) {
      return [coordinates[0] * kx + dx, coordinates[1] * ky + dy];
    }

    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);
      return o;
    }

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

  function bisect(a, x) {
    var lo = 0, hi = a.length;
    while (lo < hi) {
      var mid = lo + hi >>> 1;
      if (a[mid] < x) lo = mid + 1;
      else hi = mid;
    }
    return lo;
  }

  function neighbors(topology, objects) {
    var objectsByArc = [],
        neighbors = objects.map(function() { return []; });

    function line(arcs, i) {
      arcs.forEach(function(a) {
        if (a < 0) a = ~a;
        var o = objectsByArc[a] || (objectsByArc[a] = []);
        if (!o[i]) o.forEach(function(j) {
          var n, k;
          k = bisect(n = neighbors[i], j); if (n[k] !== j) n.splice(k, 0, j);
          k = bisect(n = neighbors[j], i); if (n[k] !== i) n.splice(k, 0, i);
        }), o[i] = i;
      });
    }

    function polygon(arcs, i) {
      arcs.forEach(function(arc) { line(arc, i); });
    }

    function geometry(o, i) {
      geometryType[o.type](o.arcs, i);
    }

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

    objects.forEach(geometry);
    return neighbors;
  }

  return {
    version: "0.0.10",
    mesh: mesh,
    object: object,
    neighbors: neighbors
  };
})();