Closest Point on Path II by mbostock

As an alternative to the search algorithm, another approximate method for finding the closest point on any given SVG path is to sample points on that path and then compute the Voronoi tessellation. Use the range slider to control the distance between samples; denser samples produce more accurate results, but is more expensive to compute.

(Sampling paths can also be useful for path tweening.)

index.html

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

.line {
  fill: none;
  stroke: #000;
  stroke-width: 1.5px;
}

.voronoi path {
  fill: none;
  pointer-events: all;
  stroke: #000;
  stroke-opacity: .15;
}

.voronoi circle {
  fill: red;
  display: none;
}

.voronoi :hover circle {
  display: inline;
}

.voronoi :hover path {
  stroke: red;
  stroke-opacity: 1;
}

#subdivision {
  position: absolute;
  top: 20px;
  left: 20px;
}

#subdivision input {
  width: 200px;
}

</style>
<div id="subdivision">
  <input type="range" min="1.5" max="100">
  <output name="subdivision"></output>
</div>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var points = [[474,276],[586,393],[378,388],[338,323],[341,138],[547,252],[589,148],[346,227],[365,108],[562,62]];

var width = 960,
    height = 500;

var x = d3.scale.pow()
    .exponent(3);

var formatPrecision = d3.format(".2f");

var voronoi = d3.geom.voronoi()
    .clipExtent([[-2, -2], [width + 2, height + 2]]);

var line = d3.svg.line()
    .interpolate("cardinal");

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

var path = svg.append("path")
    .datum(points)
    .attr("class", "line")
    .attr("d", line);

var cell = svg.append("g")
    .attr("class", "voronoi")
  .selectAll("g");

var output = d3.select("output");

var input = d3.select("input")
    .each(function() { var d = [+this.min, +this.max]; x.domain(d).range(d); resample(x(this.value = x.invert(8))); })
    .on("input", function() { resample(x(+this.value)); });

function resample(precision) {
  output.text(formatPrecision(precision));
  cell = cell.data(voronoi(sample(path.node(), precision)));
  cell.exit().remove();
  var cellEnter = cell.enter().append("g");
  cellEnter.append("circle").attr("r", 3.5);
  cellEnter.append("path");
  cell.select("circle").attr("transform", function(d) { return "translate(" + d.point + ")"; });
  cell.select("path").attr("d", function(d) { return "M" + d.join("L") + "Z"; });
}

function sample(pathNode, precision) {
  var pathLength = pathNode.getTotalLength(),
      samples = [];
  for (var sample, sampleLength = 0; sampleLength <= pathLength; sampleLength += precision) {
    sample = pathNode.getPointAtLength(sampleLength);
    samples.push([sample.x, sample.y]);
  }
  return samples;
}

</script>