Point-Along-Path Interpolation

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

path {
  fill: none;
  stroke: #000;
  stroke-width: 3px;
}

circle {
  fill: steelblue;
  stroke: #fff;
  stroke-width: 3px;
}

</style>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var points = [
  [480, 200],
  [580, 400],
  [680, 100],
  [780, 300],
  [180, 300],
  [280, 100],
  [380, 400]
];

var svg = d3.select("body").append("svg")
    .attr("width", 960)
    .attr("height", 500);

var path = svg.append("path")
    .data([points])
    .attr("d", d3.svg.line()
    .tension(0) // Catmull–Rom
    .interpolate("cardinal-closed"));

svg.selectAll(".point")
    .data(points)
  .enter().append("circle")
    .attr("r", 4)
    .attr("transform", function(d) { return "translate(" + d + ")"; });

var circle = svg.append("circle")
    .attr("r", 13)
    .attr("transform", "translate(" + points[0] + ")");

transition();

function transition() {
  circle.transition()
      .duration(10000)
      .attrTween("transform", translateAlong(path.node()))
      .each("end", transition);
}

// Returns an attrTween for translating along the specified path element.
function translateAlong(path) {
  var l = path.getTotalLength();
  return function(d, i, a) {
    return function(t) {
      var p = path.getPointAtLength(t * l);
      return "translate(" + p.x + "," + p.y + ")";
    };
  };
}

</script>

https://d3js.org/d3.v3.min.js