Closest Point to Segment

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

.circle {
  fill: none;
  stroke: red;
  stroke-width: 2px;
}

.circle.intersects {
  stroke: green;
}

.line {
  stroke: #000;
  stroke-dasharray: 3,3;
}

.segment {
  stroke: #000;
  stroke-width: 1.5px;
}

text {
  text-anchor: middle;
}

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

var width = 960,
    height = 500;

var svg = d3.select("body").append("svg")
    .attr("width", width)
    .attr("height", height)
    .on("mousemove", function() { move(d3.mouse(this)); });

var p0 = [width * .2, height * .8],
    p1 = [width * .8, height * .2];

svg.append("path")
    .attr("class", "line")
    .attr("d", "M" + [0, height] + "L" + [width, 0]);

svg.append("path")
    .attr("class", "segment")
    .attr("d", "M" + p0 + "L" + p1);

svg.selectAll(".endpoint")
    .data([p0, p1])
  .enter().append("circle")
    .attr("class", "endpoint")
    .attr("transform", function(d) { return "translate(" + d + ")"; })
    .attr("r", 4.5);

svg.selectAll(".tick")
    .data(d3.range(.1, 1, .1))
  .enter().append("circle")
    .attr("class", "tick")
    .attr("transform", function(d) { return "translate(" + d3.interpolate(p0, p1)(d) + ")"; })
    .attr("r", 2.5);

var projection = svg.append("path")
    .attr("class", "line");

var closest = svg.append("circle")
    .attr("class", "circle intersects")
    .attr("r", 4.5);

var label = svg.append("text")
    .attr("y", -6);

move([Math.random() * width, Math.random() * height]);

function move(p2) {
  var t = pointLineSegmentParameter(p2, p0, p1),
      x10 = p1[0] - p0[0],
      y10 = p1[1] - p0[1],
      p3 = [p0[0] + t * x10, p0[1] + t * y10];

label.attr("transform", "translate(" + p3 + ")rotate(" + Math.atan2(y10, x10) / Math.PI * 180 + ")").text(t.toFixed(3));
  closest.attr("transform", "translate(" + p3 + ")").classed("intersects", Math.abs(t - .5) < .5);
  projection.attr("d", "M" + p2 + "L" + p3);
}

function pointLineSegmentParameter(p2, p0, p1) {
  var x10 = p1[0] - p0[0], y10 = p1[1] - p0[1],
      x20 = p2[0] - p0[0], y20 = p2[1] - p0[1];
  return (x20 * x10 + y20 * y10) / (x10 * x10 + y10 * y10);
}

</script>

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