Sankey Particles

readme.md

Using particles to indicate flow between reservoirs in a sankey diagram. Original sankey diagram and layout done by Mike Bostock.

This method takes advantage of a couple of really useful built-in SVG functions: svg:path.getTotalLength() and svg:path.getPointAtLength() that allows you to calculate where a particle would need to be along a path. Because this is animation and the individual particles don't need to be interacted with, the particles are drawn with canvas, though you can drag the nodes around to see the particles change routes.

d3.sankey.js

d3.sankey = function() {
  var sankey = {},
      nodeWidth = 24,
      nodePadding = 8,
      size = [1, 1],
      nodes = [],
      links = [];

  sankey.nodeWidth = function(_) {
    if (!arguments.length) return nodeWidth;
    nodeWidth = +_;
    return sankey;
  };

  sankey.nodePadding = function(_) {
    if (!arguments.length) return nodePadding;
    nodePadding = +_;
    return sankey;
  };

  sankey.nodes = function(_) {
    if (!arguments.length) return nodes;
    nodes = _;
    return sankey;
  };

  sankey.links = function(_) {
    if (!arguments.length) return links;
    links = _;
    return sankey;
  };

  sankey.size = function(_) {
    if (!arguments.length) return size;
    size = _;
    return sankey;
  };

  sankey.layout = function(iterations) {
    computeNodeLinks();
    computeNodeValues();
    computeNodeBreadths();
    computeNodeDepths(iterations);
    computeLinkDepths();
    return sankey;
  };

  sankey.relayout = function() {
    computeLinkDepths();
    return sankey;
  };

  sankey.link = function() {
    var curvature = .5;

    function link(d) {
      var x0 = d.source.x + d.source.dx,
          x1 = d.target.x,
          xi = d3.interpolateNumber(x0, x1),
          x2 = xi(curvature),
          x3 = xi(1 - curvature),
          y0 = d.source.y + d.sy + d.dy / 2,
          y1 = d.target.y + d.ty + d.dy / 2;
      return "M" + x0 + "," + y0
           + "C" + x2 + "," + y0
           + " " + x3 + "," + y1
           + " " + x1 + "," + y1;
    }

    link.curvature = function(_) {
      if (!arguments.length) return curvature;
      curvature = +_;
      return link;
    };

    return link;
  };

  // Populate the sourceLinks and targetLinks for each node.
  // Also, if the source and target are not objects, assume they are indices.
  function computeNodeLinks() {
    nodes.forEach(function(node) {
      node.sourceLinks = [];
      node.targetLinks = [];
    });
    links.forEach(function(link) {
      var source = link.source,
          target = link.target;
      if (typeof source === "number") source = link.source = nodes[link.source];
      if (typeof target === "number") target = link.target = nodes[link.target];
      source.sourceLinks.push(link);
      target.targetLinks.push(link);
    });
  }

  // Compute the value (size) of each node by summing the associated links.
  function computeNodeValues() {
    nodes.forEach(function(node) {
      node.value = Math.max(
        d3.sum(node.sourceLinks, value),
        d3.sum(node.targetLinks, value)
      );
    });
  }

  // Iteratively assign the breadth (x-position) for each node.
  // Nodes are assigned the maximum breadth of incoming neighbors plus one;
  // nodes with no incoming links are assigned breadth zero, while
  // nodes with no outgoing links are assigned the maximum breadth.
  function computeNodeBreadths() {
    var remainingNodes = nodes,
        nextNodes,
        x = 0;

    while (remainingNodes.length) {
      nextNodes = [];
      remainingNodes.forEach(function(node) {
        node.x = x;
        node.dx = nodeWidth;
        node.sourceLinks.forEach(function(link) {
          if (nextNodes.indexOf(link.target) < 0) {
            nextNodes.push(link.target);
          }
        });
      });
      remainingNodes = nextNodes;
      ++x;
    }

    //
    moveSinksRight(x);
    scaleNodeBreadths((size[0] - nodeWidth) / (x - 1));
  }

  function moveSourcesRight() {
    nodes.forEach(function(node) {
      if (!node.targetLinks.length) {
        node.x = d3.min(node.sourceLinks, function(d) { return d.target.x; }) - 1;
      }
    });
  }

  function moveSinksRight(x) {
    nodes.forEach(function(node) {
      if (!node.sourceLinks.length) {
        node.x = x - 1;
      }
    });
  }

  function scaleNodeBreadths(kx) {
    nodes.forEach(function(node) {
      node.x *= kx;
    });
  }

  function computeNodeDepths(iterations) {
    var nodesByBreadth = d3.nest()
        .key(function(d) { return d.x; })
        .sortKeys(d3.ascending)
        .entries(nodes)
        .map(function(d) { return d.values; });

    //
    initializeNodeDepth();
    resolveCollisions();
    for (var alpha = 1; iterations > 0; --iterations) {
      relaxRightToLeft(alpha *= .99);
      resolveCollisions();
      relaxLeftToRight(alpha);
      resolveCollisions();
    }

    function initializeNodeDepth() {
      var ky = d3.min(nodesByBreadth, function(nodes) {
        return (size[1] - (nodes.length - 1) * nodePadding) / d3.sum(nodes, value);
      });

      nodesByBreadth.forEach(function(nodes) {
        nodes.forEach(function(node, i) {
          node.y = i;
          node.dy = node.value * ky;
        });
      });

      links.forEach(function(link) {
        link.dy = link.value * ky;
      });
    }

    function relaxLeftToRight(alpha) {
      nodesByBreadth.forEach(function(nodes, breadth) {
        nodes.forEach(function(node) {
          if (node.targetLinks.length) {
            var y = d3.sum(node.targetLinks, weightedSource) / d3.sum(node.targetLinks, value);
            node.y += (y - center(node)) * alpha;
          }
        });
      });

      function weightedSource(link) {
        return center(link.source) * link.value;
      }
    }

    function relaxRightToLeft(alpha) {
      nodesByBreadth.slice().reverse().forEach(function(nodes) {
        nodes.forEach(function(node) {
          if (node.sourceLinks.length) {
            var y = d3.sum(node.sourceLinks, weightedTarget) / d3.sum(node.sourceLinks, value);
            node.y += (y - center(node)) * alpha;
          }
        });
      });

      function weightedTarget(link) {
        return center(link.target) * link.value;
      }
    }

    function resolveCollisions() {
      nodesByBreadth.forEach(function(nodes) {
        var node,
            dy,
            y0 = 0,
            n = nodes.length,
            i;

        // Push any overlapping nodes down.
        nodes.sort(ascendingDepth);
        for (i = 0; i < n; ++i) {
          node = nodes[i];
          dy = y0 - node.y;
          if (dy > 0) node.y += dy;
          y0 = node.y + node.dy + nodePadding;
        }

        // If the bottommost node goes outside the bounds, push it back up.
        dy = y0 - nodePadding - size[1];
        if (dy > 0) {
          y0 = node.y -= dy;

          // Push any overlapping nodes back up.
          for (i = n - 2; i >= 0; --i) {
            node = nodes[i];
            dy = node.y + node.dy + nodePadding - y0;
            if (dy > 0) node.y -= dy;
            y0 = node.y;
          }
        }
      });
    }

    function ascendingDepth(a, b) {
      return a.y - b.y;
    }
  }

  function computeLinkDepths() {
    nodes.forEach(function(node) {
      node.sourceLinks.sort(ascendingTargetDepth);
      node.targetLinks.sort(ascendingSourceDepth);
    });
    nodes.forEach(function(node) {
      var sy = 0, ty = 0;
      node.sourceLinks.forEach(function(link) {
        link.sy = sy;
        sy += link.dy;
      });
      node.targetLinks.forEach(function(link) {
        link.ty = ty;
        ty += link.dy;
      });
    });

    function ascendingSourceDepth(a, b) {
      return a.source.y - b.source.y;
    }

    function ascendingTargetDepth(a, b) {
      return a.target.y - b.target.y;
    }
  }

  function center(node) {
    return node.y + node.dy / 2;
  }

  function value(link) {
    return link.value;
  }

  return sankey;
};

energy.json

{"nodes":[
{"name":"Agricultural 'waste'"},
{"name":"Bio-conversion"},
{"name":"Liquid"},
{"name":"Losses"},
{"name":"Solid"},
{"name":"Gas"},
{"name":"Biofuel imports"},
{"name":"Biomass imports"},
{"name":"Coal imports"},
{"name":"Coal"},
{"name":"Coal reserves"},
{"name":"District heating"},
{"name":"Industry"},
{"name":"Heating and cooling - commercial"},
{"name":"Heating and cooling - homes"},
{"name":"Electricity grid"},
{"name":"Over generation / exports"},
{"name":"H2 conversion"},
{"name":"Road transport"},
{"name":"Agriculture"},
{"name":"Rail transport"},
{"name":"Lighting & appliances - commercial"},
{"name":"Lighting & appliances - homes"},
{"name":"Gas imports"},
{"name":"Ngas"},
{"name":"Gas reserves"},
{"name":"Thermal generation"},
{"name":"Geothermal"},
{"name":"H2"},
{"name":"Hydro"},
{"name":"International shipping"},
{"name":"Domestic aviation"},
{"name":"International aviation"},
{"name":"National navigation"},
{"name":"Marine algae"},
{"name":"Nuclear"},
{"name":"Oil imports"},
{"name":"Oil"},
{"name":"Oil reserves"},
{"name":"Other waste"},
{"name":"Pumped heat"},
{"name":"Solar PV"},
{"name":"Solar Thermal"},
{"name":"Solar"},
{"name":"Tidal"},
{"name":"UK land based bioenergy"},
{"name":"Wave"},
{"name":"Wind"}
],
"links":[
{"source":0,"target":1,"value":124.729},
{"source":1,"target":2,"value":0.597},
{"source":1,"target":3,"value":26.862},
{"source":1,"target":4,"value":280.322},
{"source":1,"target":5,"value":81.144},
{"source":6,"target":2,"value":35},
{"source":7,"target":4,"value":35},
{"source":8,"target":9,"value":11.606},
{"source":10,"target":9,"value":63.965},
{"source":9,"target":4,"value":75.571},
{"source":11,"target":12,"value":10.639},
{"source":11,"target":13,"value":22.505},
{"source":11,"target":14,"value":46.184},
{"source":15,"target":16,"value":104.453},
{"source":15,"target":14,"value":113.726},
{"source":15,"target":17,"value":27.14},
{"source":15,"target":12,"value":342.165},
{"source":15,"target":18,"value":37.797},
{"source":15,"target":19,"value":4.412},
{"source":15,"target":13,"value":40.858},
{"source":15,"target":3,"value":56.691},
{"source":15,"target":20,"value":7.863},
{"source":15,"target":21,"value":90.008},
{"source":15,"target":22,"value":93.494},
{"source":23,"target":24,"value":40.719},
{"source":25,"target":24,"value":82.233},
{"source":5,"target":13,"value":0.129},
{"source":5,"target":3,"value":1.401},
{"source":5,"target":26,"value":151.891},
{"source":5,"target":19,"value":2.096},
{"source":5,"target":12,"value":48.58},
{"source":27,"target":15,"value":7.013},
{"source":17,"target":28,"value":20.897},
{"source":17,"target":3,"value":6.242},
{"source":28,"target":18,"value":20.897},
{"source":29,"target":15,"value":6.995},
{"source":2,"target":12,"value":121.066},
{"source":2,"target":30,"value":128.69},
{"source":2,"target":18,"value":135.835},
{"source":2,"target":31,"value":14.458},
{"source":2,"target":32,"value":206.267},
{"source":2,"target":19,"value":3.64},
{"source":2,"target":33,"value":33.218},
{"source":2,"target":20,"value":4.413},
{"source":34,"target":1,"value":4.375},
{"source":24,"target":5,"value":122.952},
{"source":35,"target":26,"value":839.978},
{"source":36,"target":37,"value":504.287},
{"source":38,"target":37,"value":107.703},
{"source":37,"target":2,"value":611.99},
{"source":39,"target":4,"value":56.587},
{"source":39,"target":1,"value":77.81},
{"source":40,"target":14,"value":193.026},
{"source":40,"target":13,"value":70.672},
{"source":41,"target":15,"value":59.901},
{"source":42,"target":14,"value":19.263},
{"source":43,"target":42,"value":19.263},
{"source":43,"target":41,"value":59.901},
{"source":4,"target":19,"value":0.882},
{"source":4,"target":26,"value":400.12},
{"source":4,"target":12,"value":46.477},
{"source":26,"target":15,"value":525.531},
{"source":26,"target":3,"value":787.129},
{"source":26,"target":11,"value":79.329},
{"source":44,"target":15,"value":9.452},
{"source":45,"target":1,"value":182.01},
{"source":46,"target":15,"value":19.013},
{"source":47,"target":15,"value":289.366}
]}

index.html

<!DOCTYPE html>

<html lang="en">
<head>
<meta charset="utf-8" />
<title>Sankey Particles</title>
<style>
.node rect {
  cursor: move;
  fill-opacity: .9;
  shape-rendering: crispEdges;
}

.node text {
  pointer-events: none;
  text-shadow: 0 1px 0 #fff;
}

.link {
  fill: none;
  stroke: #000;
  stroke-opacity: .05;
}

.link:hover {
  stroke-opacity: .25;
}

svg {
  position: absolute;
}

canvas {
  position: absolute;
}


</style>
</head>
<body>
<canvas width="1000" height="1000" ></canvas>
<svg width="1000" height="1000" ></svg>

<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.16/d3.min.js" charset="utf-8" type="text/javascript"></script>
<script src="d3.sankey.js" charset="utf-8" type="text/javascript"></script>

    <script type="text/javascript">

var margin = {top: 1, right: 1, bottom: 6, left: 1},
    width = 960 - margin.left - margin.right,
    height = 500 - margin.top - margin.bottom;

var formatNumber = d3.format(",.0f"),
    format = function(d) { return formatNumber(d) + " TWh"; },
    color = d3.scale.category20();

var svg = d3.select("svg")
    .attr("width", width + margin.left + margin.right)
    .attr("height", height + margin.top + margin.bottom)
  .append("g")
    .attr("transform", "translate(" + margin.left + "," + margin.top + ")");

var sankey = d3.sankey()
    .nodeWidth(15)
    .nodePadding(10)
    .size([width, height]);

var path = sankey.link();

var freqCounter = 1;


d3.json("energy.json", function(energy) {

  sankey
      .nodes(energy.nodes)
      .links(energy.links)
      .layout(32);

  var link = svg.append("g").selectAll(".link")
      .data(energy.links)
    .enter().append("path")
      .attr("class", "link")
      .attr("d", path)
      .style("stroke-width", function(d) { return Math.max(1, d.dy); })
      .sort(function(a, b) { return b.dy - a.dy; });

  link.append("title")
      .text(function(d) { return d.source.name + " → " + d.target.name + "\n" + format(d.value); });

  var node = svg.append("g").selectAll(".node")
      .data(energy.nodes)
    .enter().append("g")
      .attr("class", "node")
      .attr("transform", function(d) { return "translate(" + d.x + "," + d.y + ")"; })
    .call(d3.behavior.drag()
      .origin(function(d) { return d; })
      .on("dragstart", function() { this.parentNode.appendChild(this); })
      .on("drag", dragmove));

  node.append("rect")
      .attr("height", function(d) { return d.dy; })
      .attr("width", sankey.nodeWidth())
      .style("fill", function(d) { return d.color = color(d.name.replace(/ .*/, "")); })
      .style("stroke", "none")
    .append("title")
      .text(function(d) { return d.name + "\n" + format(d.value); });

  node.append("text")
      .attr("x", -6)
      .attr("y", function(d) { return d.dy / 2; })
      .attr("dy", ".35em")
      .attr("text-anchor", "end")
      .attr("transform", null)
      .text(function(d) { return d.name; })
    .filter(function(d) { return d.x < width / 2; })
      .attr("x", 6 + sankey.nodeWidth())
      .attr("text-anchor", "start");

  function dragmove(d) {
    d3.select(this).attr("transform", "translate(" + d.x + "," + (d.y = Math.max(0, Math.min(height - d.dy, d3.event.y))) + ")");
    sankey.relayout();
    link.attr("d", path);
  }

  var linkExtent = d3.extent(energy.links, function (d) {return d.value});
  var frequencyScale = d3.scale.linear().domain(linkExtent).range([1,100]);
  var particleSize = d3.scale.linear().domain(linkExtent).range([1,5]);


  energy.links.forEach(function (link) {
    link.freq = frequencyScale(link.value);
    link.particleSize = particleSize(link.value);
    link.particleColor = d3.scale.linear().domain([1,1000]).range([link.source.color, link.target.color]);
  })

  var t = d3.timer(tick, 1000);
  var particles = [];

  function tick(elapsed, time) {

    particles = particles.filter(function (d) {return d.time > (elapsed - 1000)});

    if (freqCounter > 100) {
      freqCounter = 1;
    }

    d3.selectAll("path.link")
    .each(
      function (d) {
        if (d.freq >= freqCounter) {
          var offset = (Math.random() - .5) * d.dy;
          particles.push({link: d, time: elapsed, offset: offset, path: this})
        }
      });

    particleEdgeCanvasPath(elapsed);
    freqCounter++;

  }

  function particleEdgeCanvasPath(elapsed) {
    var context = d3.select("canvas").node().getContext("2d")

    context.clearRect(0,0,1000,1000);

      context.fillStyle = "gray";
      context.lineWidth = "1px";
    for (var x in particles) {
        var currentTime = elapsed - particles[x].time;
        var currentPercent = currentTime / 1000 * particles[x].path.getTotalLength();
        var currentPos = particles[x].path.getPointAtLength(currentPercent)
        context.beginPath();
      context.fillStyle = particles[x].link.particleColor(currentTime);
        context.arc(currentPos.x,currentPos.y + particles[x].offset,particles[x].link.particleSize,0,2*Math.PI);
        context.fill();
    }
  }


});

    </script>
</body>
</html>

thumbnail.png