Voronoi Circles

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<canvas width="960" height="500"></canvas>
<script>

/* https://github.com/d3/d3-voronoi Copyright 2015 Mike Bostock */
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/* https://github.com/d3/d3-timer Copyright 2015 Mike Bostock */
"undefined"==typeof requestAnimationFrame&&(requestAnimationFrame="undefined"!=typeof window&&(window.msRequestAnimationFrame||window.mozRequestAnimationFrame||window.webkitRequestAnimationFrame||window.oRequestAnimationFrame)||function(e){return setTimeout(e,17)}),function(e,n){"object"==typeof exports&&"undefined"!=typeof module?n(exports):"function"==typeof define&&define.amd?define(["exports"],n):n(e.timer={})}(this,function(e){"use strict";function n(){r=m=0,c=1/0,t(u())}function t(e){if(!r){var t=e-Date.now();t>24?c>e&&(m&&clearTimeout(m),m=setTimeout(n,t),c=e):(m&&(m=clearTimeout(m),c=1/0),r=requestAnimationFrame(n))}}function i(e,n,i){i=null==i?Date.now():+i,null!=n&&(i+=+n);var o={callback:e,time:i,flush:!1,next:null};a?a.next=o:f=o,a=o,t(i)}function o(e,n,t){t=null==t?Date.now():+t,null!=n&&(t+=+n),l.callback=e,l.time=t}function u(e){e=null==e?Date.now():+e;var n=l;for(l=f;l;)e>=l.time&&(l.flush=l.callback(e-l.time,e)),l=l.next;l=n,e=1/0;for(var t,i=f;i;)i.flush?i=t?t.next=i.next:f=i.next:(i.time<e&&(e=i.time),i=(t=i).next);return a=t,e}var a,m,r,f,l,c=1/0;e.timer=i,e.timerReplace=o,e.timerFlush=u});

var canvas = document.querySelector("canvas"),
    width = canvas.width,
    height = canvas.height,
    context = canvas.getContext("2d"),
    voro = voronoi.voronoi().extent([[0.5, 0.5], [width - 0.5, height - 0.5]]);

var n = 100,
    particles = new Array(n);

for (var i = 0; i < n; ++i) particles[i] = {0: Math.random() * width, 1: Math.random() * height, vx: 0, vy: 0};

timer.timer(function(elapsed) {
  for (var i = 0; i < n; ++i) {
    var p = particles[i];
    p[0] += p.vx; if (p[0] < 0) p[0] = p.vx *= -1; else if (p[0] > width) p[0] = width + (p.vx *= -1);
    p[1] += p.vy; if (p[1] < 0) p[1] = p.vy *= -1; else if (p[1] > height) p[1] = height + (p.vy *= -1);
    p.vx += 0.1 * (Math.random() - .5) - 0.01 * p.vx;
    p.vy += 0.1 * (Math.random() - .5) - 0.01 * p.vy;
  }

var cells = voro(particles);
  context.clearRect(0, 0, width, height);

context.beginPath();
  cells.forEach(function(cell) { drawPolygonIncircle(cell, -2.5); });
  context.fillStyle = "#ddd";
  context.fill();

context.beginPath();
  cells.forEach(function(cell) { drawPolygon(cell); });
  context.lineWidth = 1;
  context.strokeStyle = "#aaa";
  context.stroke();

context.beginPath();
  particles.forEach(function(particle) { drawPoint(particle); });
  context.fillStyle = "#000";
  context.fill();
});

function drawPoint(point) {
  context.moveTo(point[0] + 1.5, point[1]);
  context.arc(point[0], point[1], 1.5, 0, 2 * Math.PI);
}

function drawPolygon(points) {
  context.moveTo(points[0][0], points[0][1]);
  for (var i = 1, n = points.length; i < n; ++i) context.lineTo(points[i][0], points[i][1]);
  context.closePath();
}

function drawPolygonIncircle(points, offsetRadius) {
  var circle = polygonIncircle(points),
      radius = circle.radius + offsetRadius;
  if (radius > 0) {
    context.moveTo(circle[0] + radius, circle[1]);
    context.arc(circle[0], circle[1], radius, 0, 2 * Math.PI);
  }
}

// A horrible brute-force algorithm for determining the largest circle that can
// fit inside a convex polygon. For each distinct set of three sides of the
// polygon, compute the tangent circle. Then reduce the circle’s radius against
// the remaining sides of the polygon.
function polygonIncircle(points) {
  var circle = {radius: 0};

for (var i = 0, n = points.length; i < n; ++i) {
    var pi0 = points[i],
        pi1 = points[(i + 1) % n];
    for (var j = i + 1; j < n; ++j) {
      var pj0 = points[j],
          pj1 = points[(j + 1) % n],
          pij = j === i + 1 ? pj0 : lineLineIntersection(pi0[0], pi0[1], pi1[0], pi1[1], pj0[0], pj0[1], pj1[0], pj1[1]);
      search: for (var k = j + 1; k < n; ++k) {
        var pk0 = points[k],
            pk1 = points[(k + 1) % n],
            pik = lineLineIntersection(pi0[0], pi0[1], pi1[0], pi1[1], pk0[0], pk0[1], pk1[0], pk1[1]),
            pjk = k === j + 1 ? pk0 : lineLineIntersection(pj0[0], pj0[1], pj1[0], pj1[1], pk0[0], pk0[1], pk1[0], pk1[1]),
            candidate = triangleIncircle(pij[0], pij[1], pik[0], pik[1], pjk[0], pjk[1]),
            radius = candidate.radius;

for (var l = 0; l < n; ++l) {
          var pl0 = points[l],
              pl1 = points[(l + 1) % n],
              r = pointLineDistance(candidate[0], candidate[1], pl0[0], pl0[1], pl1[0], pl1[1]);
          if (r < circle.radius) continue search;
          if (r < radius) radius = r;
        }

circle = candidate;
        circle.radius = radius;
      }
    }
  }

return circle;
}

// Returns the incircle of the triangle 012.
function triangleIncircle(x0, y0, x1, y1, x2, y2) {
  var x01 = x0 - x1, y01 = y0 - y1,
      x02 = x0 - x2, y02 = y0 - y2,
      x12 = x1 - x2, y12 = y1 - y2,
      l01 = Math.sqrt(x01 * x01 + y01 * y01),
      l02 = Math.sqrt(x02 * x02 + y02 * y02),
      l12 = Math.sqrt(x12 * x12 + y12 * y12),
      k0 = l01 / (l01 + l02),
      k1 = l12 / (l12 + l01),
      center = lineLineIntersection(x0, y0, x1 - k0 * x12, y1 - k0 * y12, x1, y1, x2 + k1 * x02, y2 + k1 * y02);
  center.radius = Math.sqrt((l02 + l12 - l01) * (l12 + l01 - l02) * (l01 + l02 - l12) / (l01 + l02 + l12)) / 2;
  return center;
}

// Returns the intersection of the infinite lines 01 and 23.
function lineLineIntersection(x0, y0, x1, y1, x2, y2, x3, y3) {
  var x02 = x0 - x2, y02 = y0 - y2,
      x10 = x1 - x0, y10 = y1 - y0,
      x32 = x3 - x2, y32 = y3 - y2,
      t = (x32 * y02 - y32 * x02) / (y32 * x10 - x32 * y10);
  return [x0 + t * x10, y0 + t * y10];
}

// Returns the signed distance from point 0 to the infinite line 12.
function pointLineDistance(x0, y0, x1, y1, x2, y2) {
  var x21 = x2 - x1, y21 = y2 - y1;
  return (y21 * x0 - x21 * y0 + x2 * y1 - y2 * x1) / Math.sqrt(y21 * y21 + x21 * x21);
}

</script>