球面上にN個の点を均等に配置したい。その7(正二十面体を細かく分割)
正二十面体を細かく分割して球体にしてみる
分割処理は正三角形を一度に4等分割するので、3回行うと 20 * 4^3 = 1280 個の三角形ができるのだが(頂点はダブっているぞ!)、5回の分割だと Core i7 でもぎりぎり。
プログラム的には命名がおかしいけど、後で見直すこと。
もしかして立方体からできるんじゃね?
その前に、三角形を4つに分割した時にできる3点は、必ずまた使われるのだから
バッファーに蓄えておくべきだよな。
その分割点が再度利用されるのは1回だけだろうか。
なにか良いアイディアはないものか。
<!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 Point (x, y, z) { this.x = x || 0; this.y = y || 0; this.z = z || 0; } function Surface (/* p0, p1, p.., pn */) { this.vertex = Array.prototype.slice.call (arguments, 0); } //http://www.h6.dion.ne.jp/~ooya/Suugaku/Seitamentai.pdf var gr = (1 + sqrt (5)) / 2; var p = [ new Point (0, -1, -gr), new Point (0, 1, -gr), new Point (0, -1, gr), new Point (0, 1, gr), new Point (-gr, 0, -1), new Point (-gr, 0, 1), new Point (gr, 0, -1), new Point (gr, 0, 1), new Point (-1, -gr, 0), new Point (1, -gr, 0), new Point (-1, gr, 0), new Point (1, gr, 0) ]; var RegularIcosahedron = [ new Surface (p[0], p[1], p[6]), new Surface (p[1], p[0], p[4]), new Surface (p[2], p[3], p[5]), new Surface (p[3], p[2], p[7]), new Surface (p[4], p[5], p[10]), new Surface (p[5], p[4], p[8]), new Surface (p[6], p[7], p[9]), new Surface (p[7], p[6], p[11]), new Surface (p[8], p[9], p[2]), new Surface (p[9], p[8], p[0]), new Surface (p[10],p[11],p[1]), new Surface (p[11],p[10],p[3]), new Surface (p[0], p[6], p[9]), new Surface (p[0], p[8], p[4]), new Surface (p[1], p[4], p[10]), new Surface (p[1], p[11],p[6]), new Surface (p[2], p[5], p[8]), new Surface (p[2], p[9], p[7]), new Surface (p[3], p[7], p[11]), new Surface (p[3], p[10],p[5]) ]; function splitOfTriangle (s) { var ax = s.vertex[0].x, bx = s.vertex[1].x, cx = s.vertex[2].x, ay = s.vertex[0].y, by = s.vertex[1].y, cy = s.vertex[2].y, az = s.vertex[0].z, bz = s.vertex[1].z, cz = s.vertex[2].z; var abx = (ax + bx) / 2, bcx = (bx + cx) / 2, cax = (cx + ax) / 2, aby = (ay + by) / 2, bcy = (by + cy) / 2, cay = (cy + ay) / 2, abz = (az + bz) / 2, bcz = (bz + cz) / 2, caz = (cz + az) / 2; var p0 = new Point (abx, aby, abz), p1 = new Point (bcx, bcy, bcz), p2 = new Point (cax, cay, caz); return [ new Surface (s.vertex[0], p0, p2), new Surface (p0, p1, p2), new Surface (p0, s.vertex[1], p1), new Surface (p2, p1, s.vertex[2]) ]; } function getVertex (s) { return s.vertex; } function getPoint (p) { var rr = this * this; var a = p.x * p.x + p.y * p.y + p.z * p.z, b = 0, c = -rr; var t = .5*Math.sqrt(-4*a*c)/a; return [p.x * t, p.y * t, p.z * t]; } function calcLength (x, y, z, rr) { var a = x * x + y * y + z * z, b = 0, c = -rr; var t = .5*Math.sqrt(-4*a*c)/a; return [x * t, y * t, z * t]; } function create (n, r) { var surface = RegularIcosahedron.slice (0); //copy var i, a = [ ], p = [ ], t = surface; for (i = 0; i < n; i += 1) t = Array.prototype.concat.apply ([], t.map (splitOfTriangle)); p = Array.prototype.concat.apply ([], t.map (getVertex, p)).map (getPoint, r); return p; } 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 - 300) / 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, 2.5, 2.5); } }; } var loop = (function () { var target = document.querySelector ('canvas'); var ctl = RotationController.create (target); var ps = create (3, 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>