fix tiling shapes js
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908f0c65d5
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383958ae19
@ -103,300 +103,4 @@ This procedure can be applied recursively on larger values of $n$ as well, so
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this concludes a proof of tiling an equilateral triangle divided into $4^n$
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equilateral triangles using trapezoidal tiles after removing a single piece.
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<script>
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(function() {
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var tilingTriangle = document.getElementById('tiling-triangle');
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var c = tilingTriangle.getContext('2d');
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function TriangleCanvas(id) {
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this.element = document.getElementById(id);
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this.context = this.element.getContext('2d');
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}
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function modifyColor(c, p) {
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var e = document.createElement('i');
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e.style.background = c;
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var r = getComputedStyle(e).backgroundColor.slice(4, -1).split(',').map(parseFloat);
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return 'rgb(' + [r[0] + p, r[1] + p, r[2] + p].join(',') + ')';
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}
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function dedup(list) {
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return list.reduce(function(newList, item) {
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if (!newList.some(function(a) { return deepCompare(a, item) })) {
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return newList.concat(item);
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}
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return newList;
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}, []);
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}
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function deepCompare () {
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var i, l, leftChain, rightChain;
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function compare2Objects (x, y) {
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var p;
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// remember that NaN === NaN returns false
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// and isNaN(undefined) returns true
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if (isNaN(x) && isNaN(y) && typeof x === 'number' && typeof y === 'number') {
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return true;
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}
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// Compare primitives and functions.
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// Check if both arguments link to the same object.
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// Especially useful on the step where we compare prototypes
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if (x === y) {
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return true;
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}
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// Works in case when functions are created in constructor.
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// Comparing dates is a common scenario. Another built-ins?
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// We can even handle functions passed across iframes
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if ((typeof x === 'function' && typeof y === 'function') ||
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(x instanceof Date && y instanceof Date) ||
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(x instanceof RegExp && y instanceof RegExp) ||
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(x instanceof String && y instanceof String) ||
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(x instanceof Number && y instanceof Number)) {
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return x.toString() === y.toString();
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}
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// At last checking prototypes as good as we can
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if (!(x instanceof Object && y instanceof Object)) {
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return false;
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}
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if (x.isPrototypeOf(y) || y.isPrototypeOf(x)) {
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return false;
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}
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if (x.constructor !== y.constructor) {
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return false;
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}
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if (x.prototype !== y.prototype) {
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return false;
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}
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// Check for infinitive linking loops
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if (leftChain.indexOf(x) > -1 || rightChain.indexOf(y) > -1) {
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return false;
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}
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// Quick checking of one object being a subset of another.
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// todo: cache the structure of arguments[0] for performance
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for (p in y) {
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if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
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return false;
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}
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else if (typeof y[p] !== typeof x[p]) {
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return false;
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}
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}
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for (p in x) {
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if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
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return false;
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}
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else if (typeof y[p] !== typeof x[p]) {
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return false;
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}
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switch (typeof (x[p])) {
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case 'object':
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case 'function':
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leftChain.push(x);
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rightChain.push(y);
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if (!compare2Objects (x[p], y[p])) {
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return false;
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}
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leftChain.pop();
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rightChain.pop();
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break;
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default:
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if (x[p] !== y[p]) {
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return false;
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}
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break;
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}
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}
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return true;
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}
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if (arguments.length < 1) {
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return true; //Die silently? Don't know how to handle such case, please help...
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// throw "Need two or more arguments to compare";
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}
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for (i = 1, l = arguments.length; i < l; i++) {
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leftChain = []; //Todo: this can be cached
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rightChain = [];
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if (!compare2Objects(arguments[0], arguments[i])) {
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return false;
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}
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}
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return true;
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}
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TriangleCanvas.prototype.drawTriangle = function(x, y, size, fill, reversed) {
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var c = this.context;
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var corners = [{
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x: x,
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y: y,
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}, {
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x: x - size / 2,
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y: y + size,
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}, {
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x: x + size / 2,
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y: y + size,
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}];
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if (reversed) {
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corners = [{
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x: x + size / 2,
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y: y,
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}, {
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x: x - size / 2,
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y: y,
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}, {
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x: x,
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y: y + size
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}];
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}
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if (fill) {
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this.drawShape(corners, modifyColor(fill, 20), fill);
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} else {
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this.drawShape(corners);
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}
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}
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TriangleCanvas.prototype.drawTrapezoid = function(tiles, size, strokeStyle, fillStyle) {
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var corners = tiles
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.map(function(o) {
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return { x: o[0] * size, y: o[1] * size };
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});
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console.log(corners);
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this.drawShape(corners, strokeStyle, fillStyle);
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}
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TriangleCanvas.prototype.drawShape = function(corners, strokeStyle, fillStyle) {
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var c = this.context;
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c.beginPath();
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c.moveTo(corners[0].x, corners[0].y);
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corners.slice(1).concat([corners[0]]).forEach(function(object, index) {
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c.lineTo(object.x, object.y);
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});
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c.closePath();
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if (fillStyle) {
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c.fillStyle = fillStyle;
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c.fill();
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}
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if (strokeStyle) c.strokeStyle = strokeStyle;
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c.stroke();
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}
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TriangleCanvas.prototype.drawSplittedTriangle = function(x, y, size, split, blocks, rest) {
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var c = this.context;
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var rows = Math.sqrt(split);
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var rowHeight = size / rows;
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var triangleSize = size / rows;
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for (var i = 0; i < rows * 2; i += 2) {
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var row = Math.floor(i / 2);
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for (var j = 0; j < i + 1; j++) {
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var position = {
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x: x + triangleSize * j / 2 - (row * triangleSize / 2),
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y: y + row * rowHeight,
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};
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var block = blocks.reduce(function(c, a) {
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return (a[0] === row && a[1] === j) ? (a[2] || 'black') : c;
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}, null);
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this.drawTriangle(position.x, position.y, triangleSize, block || rest, j % 2 == 1);
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}
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}
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}
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var c1 = new TriangleCanvas('tiling-triangle');
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c1.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
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var c2 = new TriangleCanvas('base-case');
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c2.drawSplittedTriangle(50, 0, 100, 4, [[0, 0, '#435062']], '#92afd7');
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var c3 = new TriangleCanvas('n-2');
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c3.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
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var c4 = new TriangleCanvas('n-2-grouped');
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var groups = [
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[0, 0, '#809bce'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'],
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[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
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[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
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[2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
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];
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c4.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
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var c5 = new TriangleCanvas('n-2-grouped-removed');
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var groups = [
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[0, 0, 'rgb(90, 90, 90)'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'],
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[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
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[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
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[2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
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];
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c5.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
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c5.context.strokeStyle = '#ff7777';
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c5.context.lineWidth = 3;
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c5.drawTriangle(100, 0, 100);
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var c6 = new TriangleCanvas('n-2-grouped-neighbours');
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var groups = [
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[0, 0, '#e7ecf6'], [1, 0, '#e7ecf6'], [1, 1, '#e7ecf6'], [1, 2, '#e7ecf6'],
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[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#6d8699'],
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[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#657b73'],
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[2, 4, '#d6eadf'], [3, 4, '#89958e'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
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];
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c6.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
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var trapezoids = [
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[[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
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[[1, 2], [1.5, 3], [1, 4], [0, 4]],
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[[3, 2], [4, 4], [3, 4], [2.5, 3]],
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];
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c6.drawTrapezoid(trapezoids[0], 200 / 4, '#ff7777');
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c6.drawTrapezoid(trapezoids[1], 200 / 4, '#ff7777');
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c6.drawTrapezoid(trapezoids[2], 200 / 4, '#ff7777');
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var c7 = new TriangleCanvas('final');
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var groups = [
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[0, 0, '#435062'], [1, 0, '#92afd7'], [1, 1, '#92afd7'], [1, 2, '#92afd7'],
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[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
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[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
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[2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
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];
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c7.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
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var trapezoids = [
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[[1.5, 1], [2.5, 1], [3, 2], [1, 2]],
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[[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
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[[1, 2], [1.5, 3], [1, 4], [0, 4]],
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[[3, 2], [4, 4], [3, 4], [2.5, 3]],
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[[1.5, 3], [1, 4], [3, 4], [2.5, 3]],
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];
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trapezoids.forEach(function(el) {
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c7.drawTrapezoid(el, 200 / 4, '#ff7777');
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});
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}());
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</script>
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<script src="/js/tiling-shapes.js"></script>
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295
js/tiling-shapes.js
Normal file
295
js/tiling-shapes.js
Normal file
@ -0,0 +1,295 @@
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(function() {
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var tilingTriangle = document.getElementById('tiling-triangle');
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var c = tilingTriangle.getContext('2d');
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function TriangleCanvas(id) {
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this.element = document.getElementById(id);
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this.context = this.element.getContext('2d');
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}
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function modifyColor(c, p) {
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var e = document.createElement('i');
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e.style.background = c;
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var r = getComputedStyle(e).backgroundColor.slice(4, -1).split(',').map(parseFloat);
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return 'rgb(' + [r[0] + p, r[1] + p, r[2] + p].join(',') + ')';
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}
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function dedup(list) {
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return list.reduce(function(newList, item) {
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if (!newList.some(function(a) { return deepCompare(a, item) })) {
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return newList.concat(item);
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}
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return newList;
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}, []);
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}
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function deepCompare () {
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var i, l, leftChain, rightChain;
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function compare2Objects (x, y) {
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var p;
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// remember that NaN === NaN returns false
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// and isNaN(undefined) returns true
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if (isNaN(x) && isNaN(y) && typeof x === 'number' && typeof y === 'number') {
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return true;
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}
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// Compare primitives and functions.
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// Check if both arguments link to the same object.
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// Especially useful on the step where we compare prototypes
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if (x === y) {
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return true;
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}
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// Works in case when functions are created in constructor.
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// Comparing dates is a common scenario. Another built-ins?
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// We can even handle functions passed across iframes
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if ((typeof x === 'function' && typeof y === 'function') ||
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(x instanceof Date && y instanceof Date) ||
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(x instanceof RegExp && y instanceof RegExp) ||
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(x instanceof String && y instanceof String) ||
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(x instanceof Number && y instanceof Number)) {
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return x.toString() === y.toString();
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}
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// At last checking prototypes as good as we can
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if (!(x instanceof Object && y instanceof Object)) {
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return false;
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}
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if (x.isPrototypeOf(y) || y.isPrototypeOf(x)) {
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return false;
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}
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if (x.constructor !== y.constructor) {
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return false;
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}
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if (x.prototype !== y.prototype) {
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return false;
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}
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// Check for infinitive linking loops
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if (leftChain.indexOf(x) > -1 || rightChain.indexOf(y) > -1) {
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return false;
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}
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// Quick checking of one object being a subset of another.
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// todo: cache the structure of arguments[0] for performance
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for (p in y) {
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if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
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return false;
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}
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else if (typeof y[p] !== typeof x[p]) {
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return false;
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}
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}
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for (p in x) {
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if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
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return false;
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}
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else if (typeof y[p] !== typeof x[p]) {
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return false;
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}
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switch (typeof (x[p])) {
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case 'object':
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case 'function':
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leftChain.push(x);
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rightChain.push(y);
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if (!compare2Objects (x[p], y[p])) {
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return false;
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}
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leftChain.pop();
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rightChain.pop();
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break;
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default:
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if (x[p] !== y[p]) {
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return false;
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}
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break;
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}
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}
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return true;
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}
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if (arguments.length < 1) {
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return true; //Die silently? Don't know how to handle such case, please help...
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// throw "Need two or more arguments to compare";
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}
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for (i = 1, l = arguments.length; i < l; i++) {
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leftChain = []; //Todo: this can be cached
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rightChain = [];
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if (!compare2Objects(arguments[0], arguments[i])) {
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return false;
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}
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}
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return true;
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}
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TriangleCanvas.prototype.drawTriangle = function(x, y, size, fill, reversed) {
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var c = this.context;
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var corners = [{
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x: x,
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y: y,
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}, {
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x: x - size / 2,
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y: y + size,
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}, {
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x: x + size / 2,
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y: y + size,
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}];
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if (reversed) {
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corners = [{
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x: x + size / 2,
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y: y,
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}, {
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x: x - size / 2,
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y: y,
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}, {
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x: x,
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y: y + size
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}];
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}
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if (fill) {
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this.drawShape(corners, modifyColor(fill, 20), fill);
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} else {
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this.drawShape(corners);
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}
|
||||
}
|
||||
|
||||
TriangleCanvas.prototype.drawTrapezoid = function(tiles, size, strokeStyle, fillStyle) {
|
||||
var corners = tiles
|
||||
.map(function(o) {
|
||||
return { x: o[0] * size, y: o[1] * size };
|
||||
});
|
||||
|
||||
console.log(corners);
|
||||
|
||||
this.drawShape(corners, strokeStyle, fillStyle);
|
||||
}
|
||||
|
||||
TriangleCanvas.prototype.drawShape = function(corners, strokeStyle, fillStyle) {
|
||||
var c = this.context;
|
||||
c.beginPath();
|
||||
|
||||
c.moveTo(corners[0].x, corners[0].y);
|
||||
corners.slice(1).concat([corners[0]]).forEach(function(object, index) {
|
||||
c.lineTo(object.x, object.y);
|
||||
});
|
||||
|
||||
c.closePath();
|
||||
if (fillStyle) {
|
||||
c.fillStyle = fillStyle;
|
||||
c.fill();
|
||||
}
|
||||
if (strokeStyle) c.strokeStyle = strokeStyle;
|
||||
c.stroke();
|
||||
}
|
||||
|
||||
TriangleCanvas.prototype.drawSplittedTriangle = function(x, y, size, split, blocks, rest) {
|
||||
var c = this.context;
|
||||
|
||||
var rows = Math.sqrt(split);
|
||||
var rowHeight = size / rows;
|
||||
var triangleSize = size / rows;
|
||||
|
||||
for (var i = 0; i < rows * 2; i += 2) {
|
||||
var row = Math.floor(i / 2);
|
||||
|
||||
for (var j = 0; j < i + 1; j++) {
|
||||
var position = {
|
||||
x: x + triangleSize * j / 2 - (row * triangleSize / 2),
|
||||
y: y + row * rowHeight,
|
||||
};
|
||||
|
||||
var block = blocks.reduce(function(c, a) {
|
||||
return (a[0] === row && a[1] === j) ? (a[2] || 'black') : c;
|
||||
}, null);
|
||||
|
||||
this.drawTriangle(position.x, position.y, triangleSize, block || rest, j % 2 == 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
var c1 = new TriangleCanvas('tiling-triangle');
|
||||
c1.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
|
||||
|
||||
var c2 = new TriangleCanvas('base-case');
|
||||
c2.drawSplittedTriangle(50, 0, 100, 4, [[0, 0, '#435062']], '#92afd7');
|
||||
|
||||
var c3 = new TriangleCanvas('n-2');
|
||||
c3.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
|
||||
|
||||
var c4 = new TriangleCanvas('n-2-grouped');
|
||||
var groups = [
|
||||
[0, 0, '#809bce'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'],
|
||||
[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
|
||||
[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
|
||||
[2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
|
||||
];
|
||||
c4.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
|
||||
|
||||
var c5 = new TriangleCanvas('n-2-grouped-removed');
|
||||
var groups = [
|
||||
[0, 0, 'rgb(90, 90, 90)'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'],
|
||||
[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
|
||||
[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
|
||||
[2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
|
||||
];
|
||||
c5.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
|
||||
c5.context.strokeStyle = '#ff7777';
|
||||
c5.context.lineWidth = 3;
|
||||
c5.drawTriangle(100, 0, 100);
|
||||
|
||||
var c6 = new TriangleCanvas('n-2-grouped-neighbours');
|
||||
var groups = [
|
||||
[0, 0, '#e7ecf6'], [1, 0, '#e7ecf6'], [1, 1, '#e7ecf6'], [1, 2, '#e7ecf6'],
|
||||
[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#6d8699'],
|
||||
[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#657b73'],
|
||||
[2, 4, '#d6eadf'], [3, 4, '#89958e'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
|
||||
];
|
||||
c6.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
|
||||
|
||||
var trapezoids = [
|
||||
[[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
|
||||
[[1, 2], [1.5, 3], [1, 4], [0, 4]],
|
||||
[[3, 2], [4, 4], [3, 4], [2.5, 3]],
|
||||
];
|
||||
c6.drawTrapezoid(trapezoids[0], 200 / 4, '#ff7777');
|
||||
c6.drawTrapezoid(trapezoids[1], 200 / 4, '#ff7777');
|
||||
c6.drawTrapezoid(trapezoids[2], 200 / 4, '#ff7777');
|
||||
|
||||
var c7 = new TriangleCanvas('final');
|
||||
var groups = [
|
||||
[0, 0, '#435062'], [1, 0, '#92afd7'], [1, 1, '#92afd7'], [1, 2, '#92afd7'],
|
||||
[2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
|
||||
[2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
|
||||
[2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
|
||||
];
|
||||
c7.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
|
||||
|
||||
var trapezoids = [
|
||||
[[1.5, 1], [2.5, 1], [3, 2], [1, 2]],
|
||||
[[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
|
||||
[[1, 2], [1.5, 3], [1, 4], [0, 4]],
|
||||
[[3, 2], [4, 4], [3, 4], [2.5, 3]],
|
||||
[[1.5, 3], [1, 4], [3, 4], [2.5, 3]],
|
||||
];
|
||||
trapezoids.forEach(function(el) {
|
||||
c7.drawTrapezoid(el, 200 / 4, '#ff7777');
|
||||
});
|
||||
}());
|
||||
Loading…
Reference in New Issue
Block a user