球面上にN個の点を均等に配置したい。その６　／ 「多数の点を球面上に一様に分布させるソフトウェア」（山路敦）を JavaScriptに移植（コアな部分だけ）してみる

JavaScript

理論とか面倒なことは理解できないのだが、それにしても Pascal言語が理解しづらい。
そしてこんな理論を考えられる人が、なんで配列の操作を0からではなく1から始めたのかわからない
なので、Javascriptらしく書き直す予定。
iPad でも動くよ。下の5種類は、個別に回転操作ができます。
オブジェクト指向って、すばらしい！

<!DOCTYPE html>
<meta charset="UTF-8">
<title>N個の点を持つ球体を描画する</title>
<style>
</style>

<body>
<canvas width="600" height="600"></canvas>


<script>

//http://d.hatena.ne.jp/MikuHatsune/20160714/1468397633
//https://www.jstage.jst.go.jp/article/geoinformatics/12/1/12_1_3/_pdf


(function () {
  var pi = Math.PI;
  var asin = Math.asin;
  var acos = Math.acos;
  var atan2 = Math.atan2;
  var sqrt = Math.sqrt;
  var sin = Math.sin;
  var cos = Math.cos;

  var sq2 = sqrt (2);

  //const
  var Max_Number_of_point = 5000;
  var Min_Number_of_point =   20;
  var Relocates1 = null;
  var RelocatedN = null;
  var GSS = [ ];
  var Number_of_point = null;
  var NP_on_hemisphere = null;


  //Tfrom_Mauin_Edit_NPKeyUp
  function create (n, r) {
    var k, hk;
    var gss = [{ lon: 0, col: pi }];

    if ((n < Min_Number_of_point) ||
        (n > Max_Number_of_point)) {
      throw new Error ([
        Min_Number_of_point,
        ' < N < ',
        Max_Number_of_point
      ].join (''));
    }

    Number_of_point = n;
    Generate_GSS ();
    TFrom_Main_RelocateFirstPoint ();


    return GSS.map (Spherical2Cartesian).map (function (p){return [p.x*r,p.y*r,p.z*r];});

  }


  function Generate_GSS () {
    var k, hk;
    GSS = [ ];

    GSS[1] = { };
    GSS[1].lon = 0;
    GSS[1].col = pi;

    for (k = 2; k <= Number_of_point - 1; k += 1) {
      hk = -1 + 2 * (k - 1) / (Number_of_point - 1);
      GSS[k] = { };
      GSS[k].col = acos (hk);
      GSS[k].lon = GSS[k - 1].lon
                  + 3.6 / sqrt (Number_of_point) / sqrt (1 - hk * hk);

    }
    GSS[Number_of_point] = { };
    GSS[Number_of_point].lon = 0;
    GSS[Number_of_point].col = 0;
  }


  function Spherical2Cartesian (p) {
    return {
      x: sin (p.col) * cos (p.lon),
      y: sin (p.col) * sin (p.lon),
      z: cos (p.col)
    };
  }


  function Cartesian2Spherical (p) {
    return {
      col: acos (p.z / sqrt (p.x * p.x + p.y * p.y + p.z * p.z)),
      lon: atan2 (p.y, p.x)
    };
  }


  function Equal_area_projection_of_lower_hemisph (p) {
    var r = sq2 * sin (pi / 4 - (p.col - pi / 2) / 2);
    return {
      x: r * cos (p.lon),
      y: r * sin (p.lon)
    };
  }


  function TFrom_Main_RelocateFirstPoint () {
    var five_points = new Array (5);
    var mean = { };
    var i;

    five_points[1] = 2;
    five_points[2] = 3;
    five_points[3] = 5;
    five_points[4] = 6;
    five_points[5] = 7;

    mean.x = 0; mean.y = 0; mean.z = 0;
    for (i = 1; i <= 5; i += 1) {
      mean = vector_sum (mean, Spherical2Cartesian (GSS[five_points[i]]));

    }

    Relocates1 = Cartesian2Spherical (mean);

    mean.x = 0; mean.y = 0; mean.z = 0;
    for (i = 1; i <= 5; i += 1) {
      mean = vector_sum (mean, Spherical2Cartesian (GSS[Number_of_point - five_points[i] + 1]));
    }
    RelocatedN = Cartesian2Spherical (mean);


    GSS[0] = Relocates1;
    GSS[Number_of_point] = RelocatedN;
  }


  function vector_sum (a, b) {
    return {
      x: a.x + b.x,
      y: a.y + b.y,
      z: a.z + b.z
    };
  }



  this.create = create;

}) ();


//___________________________________

(function () {

  var INIT_QUATERNION = [1, 0, 0, 0];

  function RotationController (element) {
    this.target = element;
    this.mouseX = null;//マウス座標の基点
    this.mouseY = null;//マウス座標の基点
    this.touchF = false; //ドラッグ中か？
    this.Qnow = INIT_QUATERNION; //今回のマウスのドラッグ中のクォータニオン
    this.Qbef = INIT_QUATERNION; //前回のクォータニオン
    this.rots = INIT_QUATERNION; //今回と前回のクォータニオンの積（これが重要）
    this.gain = 1 / element.offsetWidth ; // mouse移動の感度
    this.dx = 0;//マウスの慣性移動量
    this.dy = 0;//マウスの慣性移動量
    this.timerId = null;//慣性移動中のタイマーID
    this.miniInertia = 1e-7;//慣性移動量の最小値
  }


  //画面の２次元移動量から３次元の回転量を求める
  function rotation (dx, dy) {
    var a, b, a0, a1, a2, a3, b0, b1, b2, b3, r, t, as;

    if (t = dx * dx + dy * dy) {
      r = Math.sqrt (t);
      as = Math.sin (r) / r;
      a = this.Qnow;
      a0 = a[0]; a1 = a[1]; a2 = a[2]; a3 = a[3];
      b0 = dy * as; b1 = dx * as; b3 = Math.cos (r);

      // クオータニオンによる回転
      a = this.Qbef;
      b = this.Qnow = [
        a0 * b3 - a3 * b0           - a2 * b1,
        a1 * b3 + a3 * b1 - a2 * b0,
        a2 * b3           + a0 * b1 + a1 * b0,
        a3 * b3 + a0 * b0 - a1 * b1
      ];

      //前回(a)と今回(b)のクォータニオンの積
      a0 = a[0]; a1 = a[1]; a2 = a[2]; a3 = a[3];
      b0 = b[0]; b1 = b[1]; b2 = b[2]; b3 = b[3];

      this.rots = [
        a0 * b0 - a1 * b1 - a2 * b2 - a3 * b3,
        a0 * b1 + a1 * b0 + a2 * b3 - a3 * b2,
        a0 * b2 - a1 * b3 + a2 * b0 + a3 * b1,
        a0 * b3 + a1 * b2 - a2 * b1 + a3 * b0
      ];
      this.dx = dx;
      this.dy = dy;
    }
    return t;
  }


  //慣性
  function inertia () {
    var distance = rotation.call (
      this,
      this.dx - this.dx / 40,
      this.dy - this.dy / 40
    );

    if (this.miniInertia < distance)
      this.timerId = setTimeout (inertia.bind (this), 33);
  }


  //クォータニオンによる座標群の回転
  function quaternionRotation (point) {

    var i, j, x, y, z;
    var p, vertex;
    var q = this.rots;
    var q0 = q[0], q1 = q[1], q2 = q[2], q3 = q[3];
    var a0, a1, a2, a3;
    var s = [], rst = [];

    for (i = 0; p = point[i]; i++) {
        x = p[0], y = p[1], z = p[2];
        a0 =  q3 * x + q1 * z - q2 * y;
        a1 =  q3 * y + q2 * x - q0 * z;
        a2 =  q3 * z + q0 * y - q1 * x;
        a3 = -q0 * x - q1 * y - q2 * z;
        s = [
          a0 * q3 - a3 * q0 - a1 * q2 + a2 * q1,
          a1 * q3 - a3 * q1 - a2 * q0 + a0 * q2,
          a2 * q3 - a3 * q2 - a0 * q1 + a1 * q0
        ];
      rst[i] = s;
    }
    return rst;
  }


  //各イベント処理
  function handleEvent (event) {
    var e, x, y, dx, dy, a, b, c, e, r, t;
    var a0, a1, a2, a3, b0, b1, b2, b3, as;

    switch (event.type) {

    // 制御終了
    case 'mouseup' :
    case 'mouseout' :
    case 'touchend' :
      this.touchF = false;
      inertia.call (this);//制御を慣性にする
      break;

    // 制御開始
    case 'mousedown' :
    case 'touchstart' :
      if (this.timerId) {//慣性を解除
        clearTimeout (this.timerId);
        this.timerId = null;
      }
      this.touchF = true;
      this.Qnow = INIT_QUATERNION;
      this.Qbef = this.rots;
      e = event.target.getBoundingClientRect ();
      this.mouseX = event.pageX - e.left;
      this.mouseY = event.pageY - e.top;
      break;

    // 回転制御中
    case 'mousemove' :
    case 'touchmove' :
      event.preventDefault ();//ipadなどでスクロールさせないため
      e = event.target.getBoundingClientRect ();
      x = event.pageX - e.left;
      y = event.pageY - e.top;

      if (this.touchF){
        dx = (x - this.mouseX) * this.gain;
        dy = (y - this.mouseY) * this.gain;
        rotation.call (this, dx, dy);
      }

      this.mouseX = x;
      this.mouseY = y;
      break;
    }

  }


  // 要素にイベントを追加する
  function addEvent (event_type) {
    this.target.addEventListener (event_type, this, false);
  }


  // オブジェクトの生成
  function create (target) {
    if (1 > arguments.length)
      throw new Error ('引数がない');

    var obj = new RotationController (target);
    var event_list = window.TouchEvent //touchイベントがあるなら優先
      ? ['touchstart', 'touchend', 'touchmove']
      : ['mousedown', 'mouseup', 'mousemove', 'mouseout'];

    canvas = null;// メモリーリークパターンを断ち切る
    event_list.forEach (addEvent, obj);

    return obj;
  }

  //__

  RotationController.prototype.handleEvent = handleEvent;
  RotationController.prototype.quaternionRotation = quaternionRotation;
  //__
  RotationController.create = create;

  this.RotationController = RotationController;

}) ();


function canvasDrawCreate (canvas) {
  var ctx = canvas.getContext ('2d');
  var w = canvas.width;
  var h = canvas.height;
  var cx = w / 2;
  var cy = h / 2;
  var z = 1000;
  var opmax = 255;

  return function (ary) {
    ctx.fillStyle = 'RGBA(255,255,255,1)';
    ctx.fillRect (0,0, w, h);

    for (var i = 0; i < ary.length; i++) {
      var px = ary[i][0];
      var py = ary[i][1];
      var pz = ary[i][2];
      var zz = (z - pz) / z;
      var op = -(pz - 400) / z;
      var alpha = Math.min (Math.max (0, op), 1);
      ctx.fillStyle = 'rgba(0,0,255,' + alpha + ')';
      ctx.fillRect (cx + px * zz, cy - py * zz, 3, 3);
    }
  };
}


  var loop = (function () {
    var target = document.querySelector ('canvas');
    var ctl = RotationController.create (target);
    var ps = create (500, 200); //球面の点の数と半径
    var draw = canvasDrawCreate (target);

    return function () {
      var ps_ = ctl.quaternionRotation (ps);
      draw (ps_);
    };
  })();

  setInterval (loop, 1000/30); //タイマーで呼び出す

</script>

「多数の点を球面上に一様に分布させるソフトウェア」（山路敦）を JavaScriptに移植

https://www.jstage.jst.go.jp/article/geoinformatics/12/1/12_1_3/_pdf
専門用語はわからないが、2つの座標系があり、その両方に行ったりきたりで複雑化していた。
なのでばっさりカット。極の座標の平均は、今風に。

<!DOCTYPE html>
<meta charset="UTF-8">
<title>N個の点を持つ球体を描画する</title>
<style>
</style>

<body>
<canvas width="600" height="600"></canvas>


<script>

//https://www.jstage.jst.go.jp/article/geoinformatics/12/1/12_1_3/_pdf

(function () {
  var pi = Math.PI;

  var acos = Math.acos;
  var atan2 = Math.atan2;
  var sqrt = Math.sqrt;
  var sin = Math.sin;
  var cos = Math.cos;


  function sum_ag3 (a, b) {
    return [a[0] + b[0], a[1] + b[1], a[2] + b[2]];
  }


  function create (n, r) {
    var five_points = [0, 1, 3, 4, 5];
    var rst = [ ];
    var sqn = sqrt (n);
    var i, t, t0, t1, t2;
    var s, e;
    var p = 0;

    for (i = 0; i < n - 1; i += 1) {
      t = -1 + 2 * (i + 1) / (n - 1);
      t0 = acos (t);
      t2 = sin (t0) * r;
      p = p + 3.6 / sqn / sqrt (1 - t * t);
      rst.push ([
        t2 * cos (p),
        t2 * sin (p),
        cos (t0) * r
      ]);
    }

    s = five_points
       .map (function (i) { return rst[i]; })
       .reduce (sum_ag3);
    e = five_points
       .map (function (i) { return rst[n - i - 2]; })
       .reduce (sum_ag3);

    return Array.prototype.concat.call ([s], rst, [e]);
  }


  this.create = create;

}) ();


//___________________________________

(function () {

  var INIT_QUATERNION = [1, 0, 0, 0];

  function RotationController (element) {
    this.target = element;
    this.mouseX = null;//マウス座標の基点
    this.mouseY = null;//マウス座標の基点
    this.touchF = false; //ドラッグ中か？
    this.Qnow = INIT_QUATERNION; //今回のマウスのドラッグ中のクォータニオン
    this.Qbef = INIT_QUATERNION; //前回のクォータニオン
    this.rots = INIT_QUATERNION; //今回と前回のクォータニオンの積（これが重要）
    this.gain = 1 / element.offsetWidth ; // mouse移動の感度
    this.dx = 0;//マウスの慣性移動量
    this.dy = 0;//マウスの慣性移動量
    this.timerId = null;//慣性移動中のタイマーID
    this.miniInertia = 1e-7;//慣性移動量の最小値
  }


  //画面の２次元移動量から３次元の回転量を求める
  function rotation (dx, dy) {
    var a, b, a0, a1, a2, a3, b0, b1, b2, b3, r, t, as;

    if (t = dx * dx + dy * dy) {
      r = Math.sqrt (t);
      as = Math.sin (r) / r;
      a = this.Qnow;
      a0 = a[0]; a1 = a[1]; a2 = a[2]; a3 = a[3];
      b0 = dy * as; b1 = dx * as; b3 = Math.cos (r);

      // クオータニオンによる回転
      a = this.Qbef;
      b = this.Qnow = [
        a0 * b3 - a3 * b0           - a2 * b1,
        a1 * b3 + a3 * b1 - a2 * b0,
        a2 * b3           + a0 * b1 + a1 * b0,
        a3 * b3 + a0 * b0 - a1 * b1
      ];

      //前回(a)と今回(b)のクォータニオンの積
      a0 = a[0]; a1 = a[1]; a2 = a[2]; a3 = a[3];
      b0 = b[0]; b1 = b[1]; b2 = b[2]; b3 = b[3];

      this.rots = [
        a0 * b0 - a1 * b1 - a2 * b2 - a3 * b3,
        a0 * b1 + a1 * b0 + a2 * b3 - a3 * b2,
        a0 * b2 - a1 * b3 + a2 * b0 + a3 * b1,
        a0 * b3 + a1 * b2 - a2 * b1 + a3 * b0
      ];
      this.dx = dx;
      this.dy = dy;
    }
    return t;
  }


  //慣性
  function inertia () {
    var distance = rotation.call (
      this,
      this.dx - this.dx / 40,
      this.dy - this.dy / 40
    );

    if (this.miniInertia < distance)
      this.timerId = setTimeout (inertia.bind (this), 33);
  }


  //クォータニオンによる座標群の回転
  function quaternionRotation (point) {

    var i, j, x, y, z;
    var p, vertex;
    var q = this.rots;
    var q0 = q[0], q1 = q[1], q2 = q[2], q3 = q[3];
    var a0, a1, a2, a3;
    var s = [], rst = [];

    for (i = 0; p = point[i]; i++) {
        x = p[0], y = p[1], z = p[2];
        a0 =  q3 * x + q1 * z - q2 * y;
        a1 =  q3 * y + q2 * x - q0 * z;
        a2 =  q3 * z + q0 * y - q1 * x;
        a3 = -q0 * x - q1 * y - q2 * z;
        s = [
          a0 * q3 - a3 * q0 - a1 * q2 + a2 * q1,
          a1 * q3 - a3 * q1 - a2 * q0 + a0 * q2,
          a2 * q3 - a3 * q2 - a0 * q1 + a1 * q0
        ];
      rst[i] = s;
    }
    return rst;
  }


  //各イベント処理
  function handleEvent (event) {
    var e, x, y, dx, dy, a, b, c, e, r, t;
    var a0, a1, a2, a3, b0, b1, b2, b3, as;

    switch (event.type) {

    // 制御終了
    case 'mouseup' :
    case 'mouseout' :
    case 'touchend' :
      this.touchF = false;
      inertia.call (this);//制御を慣性にする
      break;

    // 制御開始
    case 'mousedown' :
    case 'touchstart' :
      if (this.timerId) {//慣性を解除
        clearTimeout (this.timerId);
        this.timerId = null;
      }
      this.touchF = true;
      this.Qnow = INIT_QUATERNION;
      this.Qbef = this.rots;
      e = event.target.getBoundingClientRect ();
      this.mouseX = event.pageX - e.left;
      this.mouseY = event.pageY - e.top;
      break;

    // 回転制御中
    case 'mousemove' :
    case 'touchmove' :
      event.preventDefault ();//ipadなどでスクロールさせないため
      e = event.target.getBoundingClientRect ();
      x = event.pageX - e.left;
      y = event.pageY - e.top;

      if (this.touchF){
        dx = (x - this.mouseX) * this.gain;
        dy = (y - this.mouseY) * this.gain;
        rotation.call (this, dx, dy);
      }

      this.mouseX = x;
      this.mouseY = y;
      break;
    }

  }


  // 要素にイベントを追加する
  function addEvent (event_type) {
    this.target.addEventListener (event_type, this, false);
  }


  // オブジェクトの生成
  function create (target) {
    if (1 > arguments.length)
      throw new Error ('引数がない');

    var obj = new RotationController (target);
    var event_list = window.TouchEvent //touchイベントがあるなら優先
      ? ['touchstart', 'touchend', 'touchmove']
      : ['mousedown', 'mouseup', 'mousemove', 'mouseout'];

    canvas = null;// メモリーリークパターンを断ち切る
    event_list.forEach (addEvent, obj);

    return obj;
  }

  //__

  RotationController.prototype.handleEvent = handleEvent;
  RotationController.prototype.quaternionRotation = quaternionRotation;
  //__
  RotationController.create = create;

  this.RotationController = RotationController;

}) ();


function canvasDrawCreate (canvas) {
  var ctx = canvas.getContext ('2d');
  var w = canvas.width;
  var h = canvas.height;
  var cx = w / 2;
  var cy = h / 2;
  var z = 1000;
  var opmax = 255;

  return function (ary) {
    ctx.fillStyle = 'RGBA(255,255,255,1)';
    ctx.fillRect (0,0, w, h);

    for (var i = 0; i < ary.length; i++) {
      var px = ary[i][0];
      var py = ary[i][1];
      var pz = ary[i][2];
      var zz = (z - pz) / z;
      var op = -(pz - 400) / z;
      var alpha = Math.min (Math.max (0, op), 1);
      ctx.fillStyle = 'rgba(0,0,255,' + alpha + ')';
      ctx.fillRect (cx + px * zz, cy - py * zz, 3, 3);
    }
  };
}


  var loop = (function () {
    var target = document.querySelector ('canvas');
    var ctl = RotationController.create (target);
    var ps = create (1000, 200); //球面の点の数と半径
    var draw = canvasDrawCreate (target);

    return function () {
      var ps_ = ctl.quaternionRotation (ps);
      draw (ps_);
    };
  })();

  setInterval (loop, 1000/30); //タイマーで呼び出す

</script>

五種類の方法を表示させてみる

<!DOCTYPE html>
<meta charset="UTF-8">
<title>N個の点を持つ球体を描画する</title>
<style>
ol li {
  display: inline-block;
  width: 460px;
  height: 460px;
  border: 2px red solid;
  margin: 2px;
}
h2 {
  margin: 0;
  font-size: large;
}
</style>

<body>
<ol>
 <li>
  <h2>Type A</h2>
  <canvas width="400" height="400"></canvas>

 <li>
  <h2>Type B</h2>
  <canvas width="400" height="400"></canvas>

 <li>
  <h2>Type C</h2>
  <canvas width="400" height="400"></canvas>

 <li>
  <h2>Type D</h2>
  <canvas width="400" height="400"></canvas>

 <li>
  <h2>Type E</h2>
  <canvas width="400" height="400"></canvas>
</ol>


<script>

(function () {

  var INIT_QUATERNION = [1, 0, 0, 0];

  function RotationController (element) {
    this.target = element;
    this.mouseX = null;//マウス座標の基点
    this.mouseY = null;//マウス座標の基点
    this.touchF = false; //ドラッグ中か？
    this.Qnow = INIT_QUATERNION; //今回のマウスのドラッグ中のクォータニオン
    this.Qbef = INIT_QUATERNION; //前回のクォータニオン
    this.rots = INIT_QUATERNION; //今回と前回のクォータニオンの積（これが重要）
    this.gain = 1 / element.offsetWidth ; // mouse移動の感度
    this.dx = 0;//マウスの慣性移動量
    this.dy = 0;//マウスの慣性移動量
    this.timerId = null;//慣性移動中のタイマーID
    this.miniInertia = 1e-7;//慣性移動量の最小値
  }


  //画面の２次元移動量から３次元の回転量を求める
  function rotation (dx, dy) {
    var a, b, a0, a1, a2, a3, b0, b1, b2, b3, r, t, as;

    if (t = dx * dx + dy * dy) {
      r = Math.sqrt (t);
      as = Math.sin (r) / r;
      a = this.Qnow;
      a0 = a[0]; a1 = a[1]; a2 = a[2]; a3 = a[3];
      b0 = dy * as; b1 = dx * as; b3 = Math.cos (r);

      // クオータニオンによる回転
      a = this.Qbef;
      b = this.Qnow = [
        a0 * b3 - a3 * b0           - a2 * b1,
        a1 * b3 + a3 * b1 - a2 * b0,
        a2 * b3           + a0 * b1 + a1 * b0,
        a3 * b3 + a0 * b0 - a1 * b1
      ];

      //前回(a)と今回(b)のクォータニオンの積
      a0 = a[0]; a1 = a[1]; a2 = a[2]; a3 = a[3];
      b0 = b[0]; b1 = b[1]; b2 = b[2]; b3 = b[3];

      this.rots = [
        a0 * b0 - a1 * b1 - a2 * b2 - a3 * b3,
        a0 * b1 + a1 * b0 + a2 * b3 - a3 * b2,
        a0 * b2 - a1 * b3 + a2 * b0 + a3 * b1,
        a0 * b3 + a1 * b2 - a2 * b1 + a3 * b0
      ];
      this.dx = dx;
      this.dy = dy;
    }
    return t;
  }


  //慣性
  function inertia () {
    var distance = rotation.call (
      this,
      this.dx - this.dx / 40,
      this.dy - this.dy / 40
    );

    if (this.miniInertia < distance)
      this.timerId = setTimeout (inertia.bind (this), 33);
  }


  //クォータニオンによる座標群の回転
  function quaternionRotation (point) {

    var i, j, x, y, z;
    var p, vertex;
    var q = this.rots;
    var q0 = q[0], q1 = q[1], q2 = q[2], q3 = q[3];
    var a0, a1, a2, a3;
    var s = [], rst = [];

    for (i = 0; p = point[i]; i++) {
        x = p[0], y = p[1], z = p[2];
        a0 =  q3 * x + q1 * z - q2 * y;
        a1 =  q3 * y + q2 * x - q0 * z;
        a2 =  q3 * z + q0 * y - q1 * x;
        a3 = -q0 * x - q1 * y - q2 * z;
        s = [
          a0 * q3 - a3 * q0 - a1 * q2 + a2 * q1,
          a1 * q3 - a3 * q1 - a2 * q0 + a0 * q2,
          a2 * q3 - a3 * q2 - a0 * q1 + a1 * q0
        ];
      rst[i] = s;
    }
    return rst;
  }


  //各イベント処理
  function handleEvent (event) {
    var e, x, y, dx, dy, a, b, c, e, r, t;
    var a0, a1, a2, a3, b0, b1, b2, b3, as;

    switch (event.type) {

    // 制御終了
    case 'mouseup' :
    case 'mouseout' :
    case 'touchend' :
      this.touchF = false;
      inertia.call (this);//制御を慣性にする
      break;

    // 制御開始
    case 'mousedown' :
    case 'touchstart' :
      if (this.timerId) {//慣性を解除
        clearTimeout (this.timerId);
        this.timerId = null;
      }
      this.touchF = true;
      this.Qnow = INIT_QUATERNION;
      this.Qbef = this.rots;
      e = event.target.getBoundingClientRect ();
      this.mouseX = event.pageX - e.left;
      this.mouseY = event.pageY - e.top;
      break;

    // 回転制御中
    case 'mousemove' :
    case 'touchmove' :
      event.preventDefault ();//ipadなどでスクロールさせないため
      e = event.target.getBoundingClientRect ();
      x = event.pageX - e.left;
      y = event.pageY - e.top;

      if (this.touchF){
        dx = (x - this.mouseX) * this.gain;
        dy = (y - this.mouseY) * this.gain;
        rotation.call (this, dx, dy);
      }

      this.mouseX = x;
      this.mouseY = y;
      break;
    }

  }


  // 要素にイベントを追加する
  function addEvent (event_type) {
    this.target.addEventListener (event_type, this, false);
  }


  // オブジェクトの生成
  function create (target) {
    if (1 > arguments.length)
      throw new Error ('引数がない');

    var obj = new RotationController (target);
    var event_list = window.TouchEvent //touchイベントがあるなら優先
      ? ['touchstart', 'touchend', 'touchmove']
      : ['mousedown', 'mouseup', 'mousemove', 'mouseout'];

    canvas = null;// メモリーリークパターンを断ち切る
    event_list.forEach (addEvent, obj);

    return obj;
  }

  //__

  RotationController.prototype.handleEvent = handleEvent;
  RotationController.prototype.quaternionRotation = quaternionRotation;
  //__
  RotationController.create = create;

  this.RotationController = RotationController;

}) ();

//http://d.hatena.ne.jp/ryamada/20130910/1378959553


//フィボナッチ格子を球面に展開
//http://d.hatena.ne.jp/MikuHatsune/20160714/1468397633
(function () {


  var round = Math.round;
  var pow = Math.pow;
  var sin = Math.sin;
  var cos = Math.cos;
  var asin = Math.asin;
  var acos = Math.acos;
  var sqrt = Math.sqrt;
  var sqrt5 = sqrt (5);
  var goldR = (1 + sqrt5) / 2;
  var pi = Math.PI;
  var phi_ = 2 * pi * (goldR - 1);


  // フィボナッチ関数
  function fibonacci (n) {
    return (n < 0)
    ? round (pow (goldR, -n) / sqrt5) * ((n&1) ? 1: -1)
    : round (pow (goldR, n) / sqrt5);
  }

  //フィボナッチ格子を球面に展開(有限法)
  //http://d.hatena.ne.jp/ryamada/20130910/1378959553
  function create_type_A (n, r) {
    var kn = fibonacci (n);
    var rst = [ ];
    var k, x, y, sqx2r, pi2y;

    for (k = 0; k < kn; k += 1) {
      x = k / fibonacci (n);
      y = (k * fibonacci (n-1) / fibonacci (n)) % 1;
      sqx2r = sqrt (x - x * x) * 2 * r;
      pi2y = 2 * pi * y;

      rst[k] = [
        cos (pi2y) * sqx2r,
        sin (pi2y) * sqx2r,
        (1 - 2 * x) * r
      ];

    }
    return rst;
  }


  //フィボナッチ格子を球面に展開(球面らせん法)
  //http://d.hatena.ne.jp/ryamada/20130910/1378959553
  function create_type_B (n, r) {
    var rst = [ ];
    var i, theta, phi;
    var n = fibonacci (n);
    var n2 = n / 2;
    var n3 = n + 1;
    var ctr;

    for (i = -n2; i <= n2; i += 1) {
      theta = asin (2 * i / n3);
      phi = phi_ * i;
      ctr = cos (theta) * r;
      rst.push ([
        ctr * cos (phi),
        ctr * sin (phi),
        sin (theta) * r
      ]);
    }
    return rst;
  }


  //だいたいN個の点を半径１の球面上に「ほぼ均一に配置する」
  //http://d.hatena.ne.jp/ryamada22/20080831
  function create_type_D (n, r) {
    var rst = [ ];
    var t = pi * (goldR - 2);
    var i, a, b, c;

    for (i = -n; i < n; i += 2) {
      a = asin (i / n);
      b = cos (a) * r;
      c = t * i;

      rst.push ([
        b * cos (c),
        b * sin (c),
        sin (a) * r
      ]);
    }
    return rst;
  }


  //球面上にランダムで置いたプロットをなるべく分散させたい
  //http://qiita.com/clomie/items/e5dd35dcfcba082b2a7f
  var random = Math.random;
  var sqrt = Math.sqrt;

  function create_type_C (n, r) {
    var rst = [ ];
    var i, x, y, z, rdt, t;

    for (i = 0; i <= n; i += 1) {
      z = random () * 2 - 1;
      rdt = random () * 360;
      t = sqrt (1 - z * z) * r;
      rst[i] = [
        t * cos (rdt),
        t * sin (rdt),
        r * z
      ];
    }
    return rst;
  }


  function sum_ag3 (a, b) {
    return [a[0] + b[0], a[1] + b[1], a[2] + b[2]];
  }



  function create_type_E (n, r) {
    var five_points = [0, 1, 3, 4, 5];
    var rst = [ ];
    var sqn = sqrt (n);
    var i, t, t0, t1, t2;
    var s, e;
    var p = 0;

    for (i = 0; i < n - 1; i += 1) {
      t = -1 + 2 * (i + 1) / (n - 1);
      t0 = acos (t);
      t2 = sin (t0) * r;
      p = p + 3.6 / sqn / sqrt (1 - t * t);
      rst.push ([
        t2 * cos (p),
        t2 * sin (p),
        cos (t0) * r
      ]);
    }

    s = five_points
       .map (function (i) { return rst[i]; })
       .reduce (sum_ag3);
    e = five_points
       .map (function (i) { return rst[n - i - 2]; })
       .reduce (sum_ag3);

    return Array.prototype.concat.call ([s], rst, [e]);
  }


  function create (type, n, r) {
    var rst = null;

    switch (type) {
    case 'a' :
      rst = create_type_A;
      break;

    case 'b' :
      rst = create_type_B;
      break;

    case 'c' :
      rst = create_type_C;
      break;

    case 'd' :
      rst = create_type_D;
      break;

    case 'e' :
      rst = create_type_E;
      break;
    }

    return rst (n, r);
  }


  this.createSpherePoint = create;
}) ();




function canvasDrawCreate (canvas) {
  var ctx = canvas.getContext ('2d');
  var w = canvas.width;
  var h = canvas.height;
  var cx = w / 2;
  var cy = h / 2;
  var z = 1000;
  var opmax = 255;

  return function (ary) {
    ctx.fillStyle = 'RGBA(255,255,255,1)';
    ctx.fillRect (0,0, w, h);

    for (var i = 0; i < ary.length; i++) {
      var px = ary[i][0];
      var py = ary[i][1];
      var pz = ary[i][2];
      var zz = (z - pz) / z;
      var op = -(pz - 400) / z;
      var alpha = Math.min (Math.max (0, op), 1);
      ctx.fillStyle = 'rgba(0,0,255,' + alpha + ')';
      ctx.fillRect (cx + px * zz, cy - py * zz, 3, 3);
    }
  };
}


  var loop = (function () {
    var cv = document.querySelectorAll ('canvas');
    A:
      var ac = RotationController.create (cv[0]);
      var ap = createSpherePoint ('a', 17, 180);
      var ad = canvasDrawCreate (cv[0]);
    B:
      var bc = RotationController.create (cv[1]);
      var bp = createSpherePoint ('b', 17, 180);
      var bd = canvasDrawCreate (cv[1]);
    C:
      var cc = RotationController.create (cv[2]);
      var cp = createSpherePoint ('c', 1597, 180);
      var cd = canvasDrawCreate (cv[2]);
    D:
      var dc = RotationController.create (cv[3]);
      var dp = createSpherePoint ('d', 1597, 180);
      var dd = canvasDrawCreate (cv[3]);
    E:
      var ec = RotationController.create (cv[4]);
      var ep = createSpherePoint ('e', 1597, 180);
      var ed = canvasDrawCreate (cv[4]);


    return function () {
      ad (ac.quaternionRotation (ap));
      bd (bc.quaternionRotation (bp));
      cd (cc.quaternionRotation (cp));
      dd (dc.quaternionRotation (dp));
      ed (ec.quaternionRotation (ep));
    };
  })();

  setInterval (loop, 1000/30); //タイマーで呼び出す
</script>