球面上にN個の点を均等に配置したい。その5（フィボナッチ数個）そしてマウスのドラッグで回転もできる

JavaScript

もちろんこれは、夏に向けての花火の種となる

<!DOCTYPE html>
<meta charset="UTF-8">
<title>N個の点を持つ球体を描画する</title>
<style>
  body,canvas { background : black; }
</style>

<body>
<canvas width="1000" height="1000"></canvas>


<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;

}) ();



(function () {

// フィボナッチ関数
  var round = Math.round;
  var pow = Math.pow;
  var sqrt = Math.sqrt;
  var sqrt5 = sqrt (5);
  var goldR = (1 + sqrt5) / 2;
  var pi = Math.PI;


  function fibonacci (n) {
    return (n < 0)
    ? round (pow (goldR, -n) / sqrt5) * ((n&1) ? 1: -1)
    : round (pow (goldR, n) / sqrt5);
  }


  function create (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] = [
        Math.cos (pi2y) * sqx2r,
        Math.sin (pi2y) * sqx2r,
        (1 - 2 * x) * r
      ];

    }
    return rst;
  }

  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(0,0,0,.25)';
    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 - 600) / z;
      var alpha = Math.min (Math.max (0, op), 1);
      ctx.fillStyle = 'rgba(255,0,0,' + alpha + ')';
      ctx.fillRect (cx + px * zz, cy - py * zz, 2, 2);
    }
  };
}


  var loop = (function () {
    var target = document.querySelector ('canvas');
    var ctl = RotationController.create (target);
    var ps = createSpherePoint (17, 300);
    var draw = canvasDrawCreate (target);

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

  setInterval (loop, 1000/60); //タイマーで呼び出す
</script>