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HTML

              
                <canvas class='c'></canvas>
<canvas class='c'></canvas>
<canvas class='c'></canvas>

<section class='controls'>
  <section class='controls__basic'>
    <label for='r1'>fixed circle radius (R):</label>
    <input id='r1' type='range' 
           min='.2' max='.62' value='.5' 
           step='.01'/>

    <label for='r2'>rolling circle radius (r):</label>
    <input id='r2' type='range' 
           min='.25' max='.62' value='.18' 
           step='.01'/>

    <label for='d'>tracer distance (d):</label>
    <input id='d' type='range' 
           min='.5' max='2.62' value='1.87' 
           step='.05'/>

    <label for='v'>velocity (v):</label>
    <input id='v' type='range' 
           min='.2' max='1' value='.5' 
           step='.01'/>
  </section>

  <section class='controls__type'>
    <input type='radio' name='type' id='hypo' checked/>
    <label for='hypo'>hypotrochoid</label>
    <input type='radio' name='type' id='epi'/>
    <label for='epi'>epitrochoid</label>
  </section>

  <section class='controls__scheme'>
    <label for='hue'>hue:</label>
    <input id='hue' type='range' 
           min='0' max='360' value='90' 
           step='1'/>
  </section>

  <section class='controls__btns'>
    <button id='rand'>random</button>
    <button id='apply'>apply</button>
    <button id='cancel'>cancel</button>
  </section>

  <button id='toggle'>toggle controls</button>
</section>
              
            
!

CSS

              
                @import "compass/css3";

$grid-major-c: rgba(gainsboro, .15);
$grid-minor-c: rgba(silver, .1);
$grid-major-th: .25em;
$grid-minor-th: .125em;
$grid-major-s: 10em;
$grid-minor-s: $grid-major-s/5;
$axis-c: rgba(white, .4);
$axis-th: 1.25*$grid-major-th;
$bg: darken(#143d63, 10%);
$hue-grad-list: ();

@mixin track() {
  height: 1.5em;
  background: transparent;
}

@mixin h-track() {
  background: transparent;
}

@mixin thumb() {
  width: .5em; height: 1.5em;
  box-shadow: 0 0 1px 1px $bg;
  background: whitesmoke;
  cursor: ew-resize;
}

@for $i from 0 to 36 {
  $hue-grad-list: append(
    $hue-grad-list, 
    hsl($i*10, 100%, 50%), 
    comma
  );
}

html, body, .c { width: 100%; height: 100%; }

body {
  overflow: hidden;
  margin: 0;
  background: 
    radial-gradient(
      rgba($bg, .001), darken(rgba($bg, .99), 20)),
    
    linear-gradient(90deg, 
      $axis-c $axis-th, 
      transparent $axis-th) 
    calc(50vw - #{$axis-th/2}) 0, 

    linear-gradient(
      $axis-c $axis-th, 
      transparent $axis-th) 
    0 calc(50vh - #{$axis-th/2}), 
    
    linear-gradient(90deg, 
      $grid-major-c $grid-major-th, 
      transparent $grid-major-th) 
    calc(50vw - #{$grid-major-th/2}) 0, 

    linear-gradient(
      $grid-major-c $grid-major-th, 
      transparent $grid-major-th) 
    0 calc(50vh - #{$grid-major-th/2}), 

    linear-gradient(90deg, 
      $grid-minor-c $grid-minor-th, 
      transparent $grid-minor-th) 
    calc(50vw - #{$grid-minor-th/2}) 0, 

    linear-gradient(
      $grid-minor-c $grid-minor-th, 
      transparent $grid-minor-th) 
    0 calc(50vh - #{$grid-minor-th/2}) 
  
  darken(#143d63, 10%);
  background-size: 100% 100%, 
    100% 100%, 100% 100%, 
    $grid-major-s $grid-major-s, 
    $grid-major-s $grid-major-s, 
    $grid-minor-s $grid-minor-s, 
    $grid-minor-s $grid-minor-s;
  font: 1em verdana, sans-serif;
}

.c {
  position: absolute;
  z-index: -1;
}

.controls {
  position: absolute;
  bottom: 100%;
  padding: 0 .5em;
  background: #111;
  color: #eee;
  transition: .35s ease-out;
  
  &--open {
    transform: translateY(100%);
  }
  
  section {
    margin: .75em 0;
    padding: .5em;
    border-radius: .25em;
    box-shadow: 0 0 2px rgba(white, .25);
  }
  
  button, input, [type='radio'] + label {
    cursor: pointer;
  }
  
  button {
    border: none;
    font: 1em/2 verdana, sans-serif;
    transition: .3s;
    
    &:hover {
      color: greenyellow;
      background: #333;
    }
  }
  
  input[type='range'] {
    -webkit-appearance: none;
    display: block;
    margin: .5em 0 1em;
    padding: 0;
    width: 100%; height: 1.5em;
    background: grey;

    &[id='hue'] {
      background: 
        linear-gradient(90deg, $hue-grad-list);
      
      &::-webkit-slider-runnable-track {
        @include h-track();
      }
      
      &::-moz-range-track { @include h-track(); }
      
      &::-ms-track { @include h-track(); }
    }
    
    &::-webkit-slider-runnable-track {
      -webkit-appearance: none;
      @include track();
    }
    
    &::-webkit-slider-thumb {
      -webkit-appearance: none;
      @include thumb();
    }
    
    &::-moz-range-track { @include track(); }
    
    &::-moz-range-thumb {
      border-radius: 0;
      @include thumb();
    }
    
    &::-ms-track {
      @include track();
      padding: 0;
      color: transparent;
    }
    
    &::-ms-thumb {
      @include thumb();
    }
    
    &::-ms-fill-lower, &::-ms-fill-upper {
      background: transparent;
    }
    
    &::-ms-tooltip { display: none; }
    
    &:focus { outline: none; }
  }
  
  input[type='radio'] {
    display: none;
    
    & + label {
      display: inline-block;
      color: lightsalmon;
      
      &:last-child { margin-right: .5em; }

      &:before {
        display: inline-block;
        margin: 0 .25em;
        transform: translateY(.125em);
        font: 1.5em/1 verdana, sans-serif;
        content: '☒';
      }
    }
    
    &:checked + label {
      color: greenyellow;
      
      &:before {
        content: '☑';
      }
    }
  }
  
  input:checked + label { color: greenyellow; }
  
  & &__btns {
    text-align: center;
    box-shadow: none;
  }
  
  [id='toggle'] {
    position: absolute;
    top: 100%; left: 0;
    width: 100%;
  }
}
              
            
!

JS

              
                Object.getOwnPropertyNames(Math).map(function(p) {
  window[p] = Math[p];
});

var rand = function(min, max, isInt) {
  var max = ((max - 1) || 0) + 1, 
      min = min || 0, 
      gen = min + (max - min)*random();
    
  return (isInt)?(~~gen):gen;
};

var randsign = function() {
  return (random() < .5)?-1:1;
};

var c = document.querySelectorAll('.c'), 
    w, h, min_dim, ctx =[], 
    ctrls = document.querySelector('.controls'), 
    ctrl_c = 'hsl(84, 99%, 69%)', 
    r1_ctrl = document.getElementById('r1'), 
    r1, r1_f, r1_c = 'hsl(328, 100%, 75%)', 
    r2_ctrl = document.getElementById('r2'), 
    r2, r2_f, r2_c = 'hsl(60, 100%, 75%)', 
    sign, r2_rot, r2_r, 
    trace_ctrl = document.getElementById('d'), 
    d, d_f, 
    hue_ctrl = document.getElementById('hue'), 
    hue, 
    trace_c, 
    hypo_ctrl = document.getElementById('hypo'), 
    epi_ctrl = document.getElementById('epi'), 
    v_ctrl = document.getElementById('v'), 
    v_f, 
    rand_ctrl = document.getElementById('rand'), 
    ok_ctrl = document.getElementById('apply'), 
    no_ctrl = document.getElementById('cancel'), 
    toggle = document.getElementById('toggle'),
    prev_pos = null, 
    theta = 0, u = PI/180;
    t = 0, rID = null, running = false;

var setUpCanvas = function() {
  var s = getComputedStyle(c[0]);
  
  w = ~~s.width.split('px')[0];
  h = ~~s.height.split('px')[0];
  min_dim = min(w, h);
  
  for(var i = 0; i < 3; i++) {
    c[i].width = w;
    c[i].height = h;
    ctx[i] = c[i].getContext('2d');
    ctx[i].lineWidth = 3;
    ctx[i].translate(w/2, h/2);
  }
  
  initValues();
};

var initValues = function() {
  r1_f = 1*r1_ctrl.value;
  r2_f = 1*r2_ctrl.value;
  d_f = 1*trace_ctrl.value;
  v_f = 1*v_ctrl.value;
  
  sign = (hypo_ctrl.checked)?-1:1;
  hue = ~~hue_ctrl.value;
  trace_c = 'hsl(' + hue + ', 100%, 56%)'
  
  r1 = r1_f*min_dim/2;
  r2 = r2_f*r1;
  d = d_f*r2;
  
  r2_rot = r1 + sign*r2;
  r2_r = r2_rot/r2;
  
  if(rID) {
    cancelAnimationFrame(rID);
    t = 0;
    theta = 0;
    prev_pos = null;
    
    for(var i = 0; i < 3; i++) {
      ctx[i].clearRect(-w/2, -h/2, w, h);
    }
  }
  
  styleSlider(r1_ctrl);
  styleSlider(r2_ctrl);
  styleSlider(trace_ctrl);
  styleSlider(v_ctrl);
  
  drawFixed();
  ctx[2].strokeStyle = trace_c;
  ani();
};

var resetValues = function() {
  r1_ctrl.value = r1_f;
  r2_ctrl.value = r2_f;
  trace_ctrl.value = d_f;
  v_ctrl.value = v_f;
  
  hypo_ctrl.checked = (sign < 0)?true:false;
  epi_ctrl.checked = (sign > 0)?true:false;
  
  hue_ctrl.value = hue;
  
  styleSlider(r1_ctrl);
  styleSlider(r2_ctrl);
  styleSlider(trace_ctrl);
  styleSlider(v_ctrl);
};

var randValues = function() {
  var tmps = randsign();
  
  r1_ctrl.value = rand(1*r1_ctrl.max, 1*r1_ctrl.min).toFixed(2);
  r2_ctrl.value = rand(1*r2_ctrl.max, 1*r2_ctrl.min).toFixed(2);
  trace_ctrl.value = rand(1*trace_ctrl.max, 1*trace_ctrl.min).toFixed(2);
  v_ctrl.value = rand(1*v_ctrl.max, 1*v_ctrl.min).toFixed(2);
  
  hypo_ctrl.checked = (tmps < 0)?true:false;
  epi_ctrl.checked = (tmps > 0)?true:false;
  
  hue_ctrl.value = ~~rand(1*hue_ctrl.max, 1*hue_ctrl.min);
  
  styleSlider(r1_ctrl);
  styleSlider(r2_ctrl);
  styleSlider(trace_ctrl);
  styleSlider(v_ctrl);
};

var drawFixed = function() {
  ctx[0].strokeStyle = r1_c;
  ctx[0].beginPath();
  ctx[0].moveTo(r1, 0);
  ctx[0].arc(0, 0, r1, 0, 2*PI);
  ctx[0].closePath();
  ctx[0].stroke();
};

var drawRoller = function(pc, pt) {
  var pc = { 'x': round(pc.x), 'y': round(pc.y) };
  
  ctx[1].clearRect(-w/2, -h/2, w, h);
  ctx[1].strokeStyle = r2_c;
  ctx[1].beginPath();
  ctx[1].moveTo(pc.x + r2, pc.y);
  ctx[1].arc(pc.x, pc.y, r2, 0, 2*PI);
  ctx[1].moveTo(pc.x + 2, pc.y);
  ctx[1].arc(pc.x, pc.y, 2, 0, 2*PI);
  ctx[1].moveTo(pc.x, pc.y);
  ctx[1].lineTo(pt.x, pt.y);
  ctx[1].closePath();
  ctx[1].stroke();
  
  ctx[1].strokeStyle = trace_c;
  ctx[1].beginPath();
  ctx[1].moveTo(pt.x, pt.y);
  ctx[1].arc(pt.x, pt.y, 3, 0, 2*PI);
  ctx[1].closePath();
  ctx[1].stroke();
};

var drawTracer = function(pt) {  
  if(prev_pos) {
    ctx[2].beginPath();
    ctx[2].moveTo(prev_pos.x, prev_pos.y);
    ctx[2].lineTo(pt.x, pt.y);
    ctx[2].closePath();
    ctx[2].stroke();
  }
  
  prev_pos = {'x': pt.x, 'y': pt.y};
};

var ani = function() {
  var pc, pt, j, k;
  
  if(running) {
    theta = v_f*t/60*2*PI/((r2_rot + d)/128);

    pc = {
      'x': r2_rot*cos(theta), 
      'y': r2_rot*sin(theta)
    };

    pt = {
      'x': round(pc.x - sign*d*cos(theta*r2_r)), 
      'y': round(pc.y - d*sin(theta*r2_r))
    };

    drawRoller(pc, pt);
    drawTracer(pt);
  }
  
  t++;
  
  j = floor(theta/PI);
  k = theta - j*PI;
  
  if(running && abs(theta) > PI && 
     abs(k) < 5*u && t > 1 && 
     abs(r2_rot - sign*d - pt.x) < 8 && 
     abs(pt.y) < 8) {
    running = false;
    
    pc = { 'x': r2_rot, 'y': 0 };
    pt = { 'x': r2_rot - sign*d, 'y': 0 };
    
    drawRoller(pc, pt);
    drawTracer(pt);
    
    t = 0;
  }
  else { if(running) { running = true; } }
  
  if(!running && t > 30) {
    ctx[2].clearRect(-w/2, -h/2, w, h);
    running = true;
    t = 0;
  }
  
  rID = requestAnimationFrame(ani);
};

var styleSlider = function(me, pre) {
  var span = me.max - me.min, 
      rel_val = (me.value - me.min)/span, 
      perc = round(rel_val*100), 
      txt_val = 'linear-gradient(90deg, ' + 
        ctrl_c + ' ' + perc + '%, grey ' + perc + '%)';
  
  me.style.background = txt_val;
};

setTimeout(function() {
  setUpCanvas();
  
  addEventListener('resize', setUpCanvas, false);
  
  r1_ctrl.addEventListener('input', function() {
    styleSlider(this);
  }, false);
  
  r1_ctrl.addEventListener('change', function() {
    styleSlider(this);
  }, false);
  
  r2_ctrl.addEventListener('input', function() {
    styleSlider(this);
  }, false);
  
  r2_ctrl.addEventListener('change', function() {
    styleSlider(this);
  }, false);
  
  trace_ctrl.addEventListener('input', function() {
    styleSlider(this);
  }, false);
  
  trace_ctrl.addEventListener('change', function() {
    styleSlider(this);
  }, false);
  
  v_ctrl.addEventListener('input', function() {
    styleSlider(this);
  }, false);
  
  v_ctrl.addEventListener('change', function() {
    styleSlider(this);
  }, false);
  
  rand_ctrl.addEventListener('click', randValues, false);
  ok_ctrl.addEventListener('click', function() {
    initValues();
    ctrls.classList.remove('controls--open');
  }, false);
  no_ctrl.addEventListener('click', resetValues, false);
  
  toggle.addEventListener('click', function() {
    ctrls.classList.toggle('controls--open');
  }, false);
}, 15);
              
            
!
999px

Console