Cartogram Experiments

readme.md

Automatic continuous area cartogram deformation of topojson layers in d3.carto.map using Shawn Allen's d3.cartogram.

This is available (as long as you call cartogram.js) with map.continuousCartogram(topojsonLayer, attributeAccessor). You can change the mode by clicking the buttons and re-run the cartogram by clicking cartogram.

The cartogram doesn't seem to work so well in mercator projection and if anyone knows why, I'd love to hear a reason.

This example uses yet another variation on d3.svg.legend.

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

      // project the arcs into screen space
      var tf = transformer(topology.transform),x,y,len1,i1,out1,len2=topology.arcs.length,i2=0,
          projectedArcs = new Array(len2);
          while(i2<len2){
            x = 0;
            y = 0;
            len1 = topology.arcs[i2].length;
            i1 = 0;
            out1 = new Array(len1);
            while(i1<len1){
              topology.arcs[i2][i1][0] = (x += topology.arcs[i2][i1][0]);
              topology.arcs[i2][i1][1] = (y += topology.arcs[i2][i1][1]);
              out1[i1] = projection(tf(topology.arcs[i2][i1]));
              i1++;
            }
            projectedArcs[i2++]=out1;
            
          }

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

      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 = d3.sum(values);

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

     var i = 0;
      while (i++ < iterations) {
        var areas = objects.map(path.area);
            var totalArea = d3.sum(areas),
            sizeErrorsTot =0,
            sizeErrorsNum=0,
            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);
              sizeErrorsTot+=sizeError;
              sizeErrorsNum++;
              // 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 = sizeErrorsTot/sizeErrorsNum,
            forceReductionFactor = 1 / (1 + sizeError);

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

        var len1,i1,delta,len2=projectedArcs.length,i2=0,delta,len3,i3,centroid,mass,radius,rSquared,dx,dy,distSquared,dist,Fij;
        while(i2<len2){
            len1=projectedArcs[i2].length;
            i1=0;
            while(i1<len1){
              // create an array of vectors: [x, y]
              delta = [0,0];
              len3 = meta.length;
              i3=0;
              while(i3<len3) {
                centroid =  meta[i3].centroid;
                mass =      meta[i3].mass;
                radius =    meta[i3].radius;
                rSquared = (radius*radius);
                dx = projectedArcs[i2][i1][0] - centroid[0];
                dy = projectedArcs[i2][i1][1] - centroid[1];
                distSquared = dx * dx + dy * dy;
                dist=Math.sqrt(distSquared);
                Fij = (dist > radius)
                  ? mass * radius / dist
                  : mass *
                    (distSquared / rSquared) *
                    (4 - 3 * dist / radius);
                delta[0]+=(Fij * cosArctan(dy,dx));
                delta[1]+=(Fij * sinArctan(dy,dx));
                i3++;
              }
            projectedArcs[i2][i1][0] += (delta[0]*forceReductionFactor);
            projectedArcs[i2][i1][1] += (delta[1]*forceReductionFactor);
            i1++;
          }
          i2++;
        }

        // break if we hit the target size error
        if (sizeError <= 1) 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(null);

    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 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);
    };
  }
  function cosArctan(dx,dy){
    var div = dx/dy;
    return (dy>0)?
      (1/Math.sqrt(1+(div*div))):
      (-1/Math.sqrt(1+(div*div)));
  }
  function sinArctan(dx,dy){
    var div = dx/dy;
    return (dy>0)?
      (div/Math.sqrt(1+(div*div))):
      (-div/Math.sqrt(1+(div*div)));
  }
  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);

d3map.css

path,circle,rect,polygon,ellipse,line {
    vector-effect: non-scaling-stroke;
}
svg, canvas {
    top: 0;
}
#d3MapZoomBox {
    position: absolute;
    z-index: 10;
    height: 100px;
    width: 25px;
    top: 10px;
    right: 50px;
}

#d3MapZoomBox > button {
    height:25px;
    width: 25px;
    line-height: 25px;
}


.d3MapControlsBox > button {
  font-size:22px;
  font-weight:900;
  border: none;
  height:25px;
  width:25px;
  background: rgba(35,31,32,.85);
  color: white;
  padding: 0;
  cursor: pointer;
}

.d3MapControlsBox > button:hover {
  background: black;
}

#d3MapPanBox {
    position: absolute;
    z-index: 10;
    height: 100px;
    width: 25px;
    top: 60px;
    right: 50px;
}
#d3MapPanBox > button {
    height:25px;
    width: 25px;
    line-height: 25px;
}

#d3MapPanBox > button#left {
  position: absolute;
  left: -25px;
  top: 10px;
}

#d3MapPanBox > button#right {
  position: absolute;
  right: -25px;
  top: 10px;
}

#d3MapLayerBox {
    position: relative;
    z-index: 10;
    height: 100px;
    width: 120px;
    top: 10px;
    left: 10px;
    overflow: auto;
    color: white;
    background: rgba(35,31,32,.85);
}

#d3MapLayerBox > div {
    margin: 5px;
    border: none;
}

#d3MapLayerBox ul {
    list-style: none;
    padding: 0;
    margin: 0;
    cursor: pointer;
}
#d3MapLayerBox li {
    list-style: none;
    padding: 0;
}

#d3MapLayerBox li:hover {
    font-weight:700;
}

#d3MapLayerBox li input {
    cursor: pointer;
}

div.d3MapModal {
    position: absolute;
    z-index: 11;
    background: rgba(35,31,32,.90);
    top: 50px;
    left: 50px;
    color: white;
    max-width: 400px;
}

div.d3MapModalContent {
    width:100%;
    height: 100%;
    overflow: auto;
}

div.d3MapModalContent > p {
    padding: 0px 20px;
    margin: 5px 0;
}

div.d3MapModalContent > h1 {
    padding: 0px 20px;
    font-size: 20px;
}

div.d3MapModalArrow {
    content: "";
	width: 0; 
	height: 0; 
	border-left: 20px solid transparent;
	border-right: 20px solid transparent;
	border-top: 20px solid rgba(35,31,32,.90);
        position: absolute;
        bottom: -20px;
        left: 33px;
}


#d3MapSVG {

}

rect.minimap-extent {
    fill: rgba(200,255,255,0.35);
    stroke: black;
    stroke-width: 2px;
    stroke-dasharray: 5 5;
}

circle.newpoints {
    fill: black;
    stroke: red;
    stroke-width: 2px;
}

path.newfeatures {
    fill: steelblue;
    fill-opacity: .5;
    stroke: pink;
    stroke-width: 2px;
}

index.html

<html xmlns="http://www.w3.org/1999/xhtml">
<head>
  <title>d3.carto - Automatic Continuous Area Cartogram</title>
  <meta charset="utf-8" />
    <link type="text/css" rel="stylesheet" href="d3map.css" />
</head>
<style>
  html,body {
    height: 100%;
    width: 100%;
    margin: 0;
  }

  #map {
    height: 100%;
    width: 100%;
    position: absolute;
  }
  
  .country {
    stroke: lightgray;
    stroke-width: 1px;
  }
  
  .smallmap {
    width: 33%;
    float: left;
    border: 1px lightgray solid;
  }

    #legend {
    position: absolute;
    left: 20px;
    bottom: 20px;
    width: 400px;
    height: 95px;
    background: white;
    z-index: 99;
  }
      #buttondiv {
    position: absolute;
    left: 120px;
    top: 20px;
    background: white;
    z-index: 99;
  }
</style>
<script>
    function makeSomeMaps() {

    colorScale = d3.scale.linear().domain([0,1,100,1000,10000,16000]).range(["gray","blue","green","yellow","red","darkred"])
    
    legend = d3.svg.legend().unitLabel("billion")
    .unitTranslate([10,0])
    .formatter(d3.format(".0f"))
    .title("GDP")
    .scale(colorScale);
    
    d3.select("#legend").append("svg").style("width", "100%").style("height", "100%").append("g").attr("transform", "translate(20,35)").attr("class", "legend").call(legend);

    map = d3.carto.map();
    d3.select("#map").call(map);

    map.mode("projection");

    countryLayer = d3.carto.layer.topojson();
    
    countryLayer.path("world.topojson")
    .label("Countries")
    .renderMode("svg")
    .cssClass("country")
    .on("load", runCarto);

    map.addCartoLayer(countryLayer);
    
    function runCarto() {
      d3.selectAll("path").style("fill", function(d) {return colorScale(parseFloat(d.properties.gdp))})
      map.continuousCartogram(countryLayer, function(d) {return d.properties.gdp});
    }
    
    d3.select("#buttondiv").append("button").html("cartogram").on("click", runCarto);
    d3.select("#buttondiv").append("button").html("globe").on("click", function() {map.mode("globe")});
    d3.select("#buttondiv").append("button").html("mercator").on("click", function() {map.mode("transform")});
    d3.select("#buttondiv").append("button").html("equidistant").on("click", function() {map.mode("projection")});
  }
</script>
<body onload="makeSomeMaps()">
<div id="map"></div>
<div id="legend"></div>
<div id="buttondiv"></div>
<footer>
<script src="http://d3js.org/d3.v3.min.js" charset="utf-8" type="text/javascript"></script>
<script src="http://d3js.org/colorbrewer.v1.min.js" charset="utf-8" type="text/javascript"></script>
<script src="https://rawgit.com/emeeks/d3-carto-map/master/d3.carto.map.js" type="text/javascript">
</script>
<script src="http://d3js.org/topojson.v1.min.js" type="text/javascript">
</script>
<script src="cartogram.js" type="text/javascript">
</script>
<script src="legend.js" type="text/javascript">
</script>
</footer>
</body>
</html>

legend.js

d3.svg.legend = function() {
      var data = [];
      var size = [300,20];
      var xScale = d3.scale.linear();
      var scale;
      var title = "Legend";
      var numberFormat = d3.format(".4n");
      var units = "Units";
      var unitTranslate =[0,0];

    function legend(gSelection) {
      
      createLegendData(scale);
      
      var xMin = d3.min(data, function(d) {return d.domain[0]});
      var xMax = d3.max(data, function(d) {return d.domain[1]});
      xScale.domain([xMin,xMax]).range([0,size[0]])

      console.log(data)
      gSelection.selectAll("rect")
      .data(data)
      .enter()
      .append("rect")
      .attr("height", size[1])
//      .attr("width", function (d) {return xScale(d.domain[1]) -  xScale(d.domain[0])})
      .attr("width", size[0] / scale.domain().length)
//      .attr("x", function (d) {return xScale(d.domain[0])})
      .attr("x", function(d,i) {return i * (size[0] / scale.domain().length)})
      .style("fill", function(d) {return d.color})

      gSelection.selectAll("line")
      .data(data)
      .enter()
      .append("line")
//      .attr("x1", function (d) {return xScale(d.domain[0])})
//      .attr("x2", function (d) {return xScale(d.domain[0])})
      .attr("x1", function(d,i) {return (i + .5) * (size[0] / scale.domain().length)})
      .attr("x2", function(d,i) {return (i + .5) * (size[0] / scale.domain().length)})
      .attr("y1", 0)
      .attr("y2", size[1] + 5)
      .style("stroke", "black")
      .style("stroke-width", "2px")

      gSelection.selectAll("text")
      .data(data)
      .enter()
      .append("g")
//      .attr("transform", function (d) {return "translate(" + (xScale(d.domain[0])) +"," + (size[1] + 20) + ")"})
      .attr("transform", function (d,i) {return "translate(" + ((i + .5) * (size[0] / scale.domain().length)) +"," + (size[1] + 20) + ")"})
      .style("text-anchor", "middle")
      .append("text")
      .text(function(d) {return numberFormat(d.domain[0])})

      gSelection.append("text")
      .attr("transform", function (d) {return "translate(" + (xScale(xMin)) +"," + (size[1] - 30) + ")"})
      .text(title)

      gSelection.append("text")
      .attr("transform", function (d) {return "translate(" + (xScale(xMax) + unitTranslate[0]) +"," + (size[1] + 20  + unitTranslate[1]) + ")"})
      .text(units)

      return legend;
    }
    
    function createLegendData(incScale) {
      var rangeArray = incScale.range();
      data = [];
      
      for (x in rangeArray) {
        var colorValue = rangeArray[x];
        if (incScale.invertExtent) {
              var domainValues = incScale.invertExtent(colorValue);
        }
        else {
            if (x == incScale.domain().length) {
            var domainValues = [incScale.domain()[x],incScale.domain()[x]];                  
            }
            else {
            var domainValues = [incScale.domain()[x],incScale.domain()[parseInt(x) + 1]];
            }
        }
        data.push({color: colorValue, domain: domainValues})
      }
    }

    
    legend.scale = function(newScale) {
      if (!arguments.length) return scale;
      scale = newScale;
      return this;
    }

    legend.title = function(newTitle) {
      if (!arguments.length) return title;
      title = newTitle;
      return this;
    }

    legend.unitLabel = function(newUnits) {
      if (!arguments.length) return units;
      units = newUnits;
      return this;
    }

    legend.unitTranslate = function(newTranslate) {
      if (!arguments.length) return unitTranslate;
      unitTranslate = newTranslate;
      return this;
    }
    
    legend.formatter = function(newFormatter) {
      if (!arguments.length) return numberFormat;
      numberFormat = newFormatter;
      return this;
    }

    return legend;
  }

thumbnail.png

world.topojson