Circle-Polygon Intersection

Drag the control points of the polygon to see whether the polygon intersects with the circle.

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

.circle {
  fill: red;
  fill-opacity: .3;
}

.circle.intersects {
  fill: green;
}

.polygon path {
  fill: #000;
  fill-opacity: .3;
}

.polygon circle {
  fill: #000;
  stroke: #fff;
  cursor: move;
}

</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);

var circle = svg.append("circle")
    .attr("class", "circle intersects")
    .datum([width / 2, height / 2, 120])
    .call(positionCircle)
    .attr("r", function(d) { return d[2]; });

var polygon = svg.append("g")
    .attr("class", "polygon")
    .datum([[500, 300], [600, 300], [600, 400], [500, 400]]);

polygon.append("path")
    .call(positionPath);

polygon.selectAll("circle")
    .data(function(d) { return d; })
  .enter().append("circle")
    .call(positionCircle)
    .attr("r", 4.5)
    .call(d3.behavior.drag()
      .origin(function(d) { return {x: d[0], y: d[1]}; })
      .on("drag", function(d) {
        d[0] = d3.event.x, d[1] = d3.event.y;
        d3.select(this).call(positionCircle);
        polygon.select("path").call(positionPath);
        circle.classed("intersects", intersects(circle.datum(), polygon.datum()));
      }));

function positionCircle(circle) {
  circle
      .attr("cx", function(d) { return d[0]; })
      .attr("cy", function(d) { return d[1]; });
}

function positionPath(path) {
  path
      .attr("d", function(d) { return "M" + d.join("L") + "Z"; });
}

function intersects(circle, polygon) {
  return pointInPolygon(circle, polygon)
      || polygonEdges(polygon).some(function(line) { return pointLineSegmentDistance(circle, line) < circle[2]; });
}

function polygonEdges(polygon) {
  return polygon.map(function(p, i) {
    return i ? [polygon[i - 1], p] : [polygon[polygon.length - 1], p];
  });
}

function pointInPolygon(point, polygon) {
  for (var n = polygon.length, i = 0, j = n - 1, x = point[0], y = point[1], inside = false; i < n; j = i++) {
    var xi = polygon[i][0], yi = polygon[i][1],
        xj = polygon[j][0], yj = polygon[j][1];
    if ((yi > y ^ yj > y) && (x < (xj - xi) * (y - yi) / (yj - yi) + xi)) inside = !inside;
  }
  return inside;
}

function pointLineSegmentDistance(point, line) {
  var v = line[0], w = line[1], d, t;
  return Math.sqrt(pointPointSquaredDistance(point, (d = pointPointSquaredDistance(v, w))
      ? ((t = ((point[0] - v[0]) * (w[0] - v[0]) + (point[1] - v[1]) * (w[1] - v[1])) / d) < 0 ? v
      : t > 1 ? w
      : [v[0] + t * (w[0] - v[0]), v[1] + t * (w[1] - v[1])])
      : v));
}

function pointPointSquaredDistance(v, w) {
  var dx = v[0] - w[0], dy = v[1] - w[1];
  return dx * dx + dy * dy;
}

</script>

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