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@syntagmatic
Last active Aug 27, 2015
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1200
0 2
2 4
4 3
3 1
1 0
0 5
5 7
7 6
6 1
8 10
10 12
12 11
11 9
9 8
8 13
13 15
15 14
14 9
5 17
17 16
16 2
6 19
19 18
18 3
13 17
16 10
14 19
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12 4
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41 40
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42 47
48 56
56 43
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57 44
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61 60
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72 61
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62 67
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175 222
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50 210
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362 66
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283 394
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395 24
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8 490
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412 12
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36 561
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562 37
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18 566
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567 19
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494 571
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574 39
499 537
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433 593
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359 585
584 341
360 587
586 342
370 589
588 348
374 591
590 355
371 593
592 349
375 595
594 356
378 597
596 366
379 599
598 367
720
5 0 2 4 3 1
5 0 5 7 6 1
5 8 10 12 11 9
5 8 13 15 14 9
5 0 5 17 16 2
5 1 6 19 18 3
5 8 13 17 16 10
5 9 14 19 18 11
5 2 16 10 12 4
5 3 18 11 12 4
5 5 17 13 15 7
5 6 19 14 15 7
5 20 22 24 23 21
5 20 25 27 26 21
5 28 30 32 31 29
5 28 33 35 34 29
5 20 25 37 36 22
5 21 26 39 38 23
5 28 33 37 36 30
5 29 34 39 38 31
5 22 36 30 32 24
5 23 38 31 32 24
5 25 37 33 35 27
5 26 39 34 35 27
5 40 43 42 44 41
5 45 48 47 49 46
5 40 51 50 52 41
5 45 54 53 55 46
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/*
* Hypersolid, Four-dimensional solid viewer
*
* Copyright (c) 2014 Milosz Kosmider <milosz@milosz.ca>
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*
*/
(function(Hypersolid) {
/* Begin constants. */
DEFAULT_VIEWPORT_WIDTH = 480; // Width of canvas in pixels
DEFAULT_VIEWPORT_HEIGHT = 480; // Height of canvas in pixels
DEFAULT_VIEWPORT_SCALE = 2; // Maximum distance from origin (in math units) that will be displayed on the canvas
DEFAULT_VIEWPORT_FONT = 'italic 10px sans-serif';
DEFAULT_VIEWPORT_FONT_COLOR = '#000';
DEFAULT_VIEWPORT_LINE_WIDTH = 4;
DEFAULT_VIEWPORT_LINE_JOIN = 'round';
DEFAULT_CHECKBOX_VALUES = {
perspective: { checked: true },
indices: { checked: false },
edges: { checked: true }
};
/* End constants. */
/* Begin classes. */
Hypersolid.Shape = function() {
return new Shape(Array.prototype.slice.call(arguments, 0));
};
function Shape(argv) {
var self = this,
vertices = argv[0],
edges = argv[1];
// Rotations will always be relative to the original shape to avoid rounding errors.
// This is a structure for caching the rotated vertices.
var rotatedVertices = new Array(vertices.length);
copyVertices();
// This is where we store the current rotations about each axis.
var rotations = { xy: 0, xz: 0, xw: 0, yz: 0, yw: 0, zw: 0 };
var rotationOrder = {
yz: 1,
xw: 1,
yw: 1,
zw: 1,
xy: 1,
xz: 1,
};
// Multiplication by vector rotation matrices of dimension 4
var rotateVertex = {
xy: function(v, s, c) {
tmp = c * v.x + s * v.y;
v.y = -s * v.x + c * v.y;
v.x = tmp;
},
xz: function(v, s, c) {
tmp = c * v.x + s * v.z;
v.z = -s * v.x + c * v.z;
v.x = tmp;
},
xw: function(v, s, c) {
tmp = c * v.x + s * v.w;
v.w = -s * v.x + c * v.w;
v.x = tmp;
},
yz: function(v, s, c) {
tmp = c * v.y + s * v.z;
v.z = -s * v.y + c * v.z;
v.y = tmp;
},
yw: function(v, s, c) {
tmp = c * v.y - s * v.w;
v.w = s * v.y + c * v.w;
v.y = tmp;
},
zw: function(v, s, c) {
tmp = c * v.z - s * v.w;
v.w = s * v.z + c * v.w;
v.z = tmp;
}
};
var eventCallbacks = {};
self.getOriginalVertices = function() {
return vertices;
};
self.getVertices = function() {
return rotatedVertices;
};
self.getEdges = function() {
return edges;
};
self.getRotations = function() {
return rotations;
};
// This will copy the original shape and put a rotated version into rotatedVertices
self.rotate = function(axis, theta) {
addToRotation(axis, theta);
applyRotations();
triggerEventCallbacks('rotate');
};
self.on = function(eventName, callback) {
if (eventCallbacks[eventName] === undefined) {
eventCallbacks[eventName] = [];
}
eventCallbacks[eventName].push(callback);
};
function triggerEventCallbacks(eventName) {
if (eventCallbacks[eventName] !== undefined) {
for (index in eventCallbacks[eventName]) {
eventCallbacks[eventName][index].call(self);
}
}
}
function addToRotation(axis, theta) {
rotations[axis] = (rotations[axis] + theta) % (2 * Math.PI);
}
function applyRotations() {
copyVertices();
for (var axis in rotationOrder) {
// sin and cos precomputed for efficiency
var s = Math.sin(rotations[axis]);
var c = Math.cos(rotations[axis]);
for (var i in vertices)
{
rotateVertex[axis](rotatedVertices[i], s, c);
}
}
}
function copyVertices() {
for (var i in vertices) {
var vertex = vertices[i];
rotatedVertices[i] = {
x: vertex.x,
y: vertex.y,
z: vertex.z,
w: vertex.w
};
}
}
}
Hypersolid.Viewport = function() {
return new Viewport(Array.prototype.slice.call(arguments, 0));
};
function Viewport(argv) {
var self = this,
shape = argv[0],
canvas = argv[1],
options = argv[2];
options = options || {};
var scale = options.scale || DEFAULT_VIEWPORT_SCALE;
canvas.width = options.width || DEFAULT_VIEWPORT_WIDTH;
canvas.height = options.height || DEFAULT_VIEWPORT_HEIGHT;
var bound = Math.min(canvas.width, canvas.height) / 2;
var context = canvas.getContext('2d');
context.font = options.font || DEFAULT_VIEWPORT_FONT;
context.textBaseline = 'top';
context.fillStyle = options.fontColor || DEFAULT_VIEWPORT_FONT_COLOR;
context.lineWidth = options.lineWidth || DEFAULT_VIEWPORT_LINE_WIDTH;
context.lineJoin = options.lineJoin || DEFAULT_VIEWPORT_LINE_JOIN;
var checkboxes = options.checkboxes || DEFAULT_CHECKBOX_VALUES;
var clicked = false;
var startCoords;
self.draw = function() {
var vertices = shape.getVertices();
var edges = shape.getEdges();
context.clearRect(0, 0, canvas.width, canvas.height);
var adjusted = [];
for (var i in vertices) {
if (checkboxes.perspective.checked) {
var zratio = vertices[i].z / scale;
adjusted[i] = {
x: Math.floor(canvas.width / 2 + (0.90 + zratio * 0.30) * bound * (vertices[i].x / scale)) + 0.5,
y: Math.floor(canvas.height / 2 - (0.90 + zratio * 0.30) * bound * (vertices[i].y / scale)) + 0.5,
z: 0.50 + 0.40 * zratio,
w: 121 + Math.floor(134 * vertices[i].w / scale)
};
}
else {
adjusted[i] = {
x: Math.floor(canvas.width / 2 + bound * (vertices[i].x / scale)) + 0.5,
y: Math.floor(canvas.height / 2 - bound * (vertices[i].y / scale)) + 0.5,
z: 0.50 + 0.40 * vertices[i].z / scale,
w: 121 + Math.floor(134 * vertices[i].w / scale)
};
}
}
if (checkboxes.edges.checked) {
for (var i in edges) {
var x = [adjusted[edges[i][0]].x, adjusted[edges[i][1]].x];
var y = [adjusted[edges[i][0]].y, adjusted[edges[i][1]].y];
var z = [adjusted[edges[i][0]].z, adjusted[edges[i][1]].z];
var w = [adjusted[edges[i][0]].w, adjusted[edges[i][1]].w];
context.beginPath();
context.moveTo(x[0], y[0]);
context.lineTo(x[1], y[1]);
context.closePath();
var gradient = context.createLinearGradient(x[0], y[0], x[1], y[1]); // Distance fade effect
gradient.addColorStop(0, 'rgba(' + w[0] + ',94,' + (125-Math.round(w[0]/2)) +', ' + z[0] + ')');
gradient.addColorStop(1, 'rgba(' + w[1] + ',94,' + (125-Math.round(w[0]/2)) +', ' + z[1] + ')');
context.strokeStyle = gradient;
context.stroke();
}
}
if (checkboxes.indices.checked) {
for (var i in adjusted) {
context.fillText(i.toString(), adjusted[i].x, adjusted[i].y);
}
}
};
canvas.onmousedown = function(e) {
startCoords = mouseCoords(e, canvas);
startCoords.x -= Math.floor(canvas.width / 2);
startCoords.y = Math.floor(canvas.height / 2) - startCoords.y;
clicked = true;
};
document.onmousemove = function(e) {
if (!clicked) {
return true;
}
var currCoords = mouseCoords(e, canvas);
currCoords.x -= Math.floor(canvas.width / 2);
currCoords.y = Math.floor(canvas.height / 2) - currCoords.y;
var motion = { 'x': currCoords.x - startCoords.x, 'y': currCoords.y - startCoords.y };
if (e.shiftKey && (e.altKey || e.ctrlKey)) {
shape.rotate('xy', Math.PI * motion.x / bound); // Full canvas drag ~ 2*PI
shape.rotate('zw', Math.PI * motion.y / bound);
}
else if (e.shiftKey) {
// Interpretation of this rotation varies between left- and right- brained users
shape.rotate('xw', Math.PI * motion.x / bound);
shape.rotate('yw', Math.PI * motion.y / bound);
}
else {
shape.rotate('xz', Math.PI * motion.x / bound);
shape.rotate('yz', Math.PI * motion.y / bound);
}
startCoords = currCoords;
self.draw();
};
document.onmouseup = function() {
clicked = false;
};
checkboxes.onchange = function() {
self.draw();
};
}
/* End classes. */
/* Begin methods. */
// parse ascii files from http://paulbourke.net/geometry/hyperspace/
Hypersolid.parseVEF = function(text) {
var lines = text.split("\n");
var nV = parseInt(lines[0]); // number of vertices
var nE = parseInt(lines[1+nV]); // number of edges
var nF = parseInt(lines[2+nV+nE]); // number of faces
var vertices = lines.slice(1,1+nV).map(function(line) {
var d = line.split("\t").map(parseFloat);
return {
x: d[0],
y: d[1],
z: d[2],
w: d[3],
}
});
var edges = lines.slice(2+nV,2+nV+nE).map(function(line) {
var d = line.replace("\s","").split("\t").map(function(vertex) { return parseInt(vertex); });
return [d[0], d[1]];;
});
var faces = lines.slice(3+nV+nE,3+nV+nE+nF).map(function(line) {
var d = line.replace("\s","").split("\t").map(function(edge) { return parseInt(edge); });
return d;
});
return [vertices,edges,faces]
};
/* End methods. */
/* Begin helper routines. */
function mouseCoords(e, element) { // http://answers.oreilly.com/topic/1929-how-to-use-the-canvas-and-draw-elements-in-html5/
var x;
var y;
if (e.pageX || e.pageY) {
x = e.pageX;
y = e.pageY;
}
else {
x = e.clientX + document.body.scrollLeft + document.documentElement.scrollLeft;
y = e.clientY + document.body.scrollTop + document.documentElement.scrollTop;
}
x -= element.offsetLeft;
y -= element.offsetTop;
return { 'x': x, 'y': y };
}
/* End helper routines. */
})(window.Hypersolid = window.Hypersolid || {});
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8" />
<title>Dodecaplex</title>
<style>
html, body {
background: #fff;
color: #555;
width: 960px;
margin: 0 auto;
font-family: sans-serif;
}
canvas {
border: none;
margin: 0 280px;
}
#hypercube-options {
margin: 10px 0 0 85px;
}
label {
margin: 0 20px;
font-size: 15px;
cursor: pointer;
}
</style>
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min.js"></script>
<script type="text/javascript" src="hypersolid.js"></script>
</head>
<body>
<canvas id="octaplex-canvas">Unfortunately, your browser does not support coolness.</canvas>
<form id="hypercube-options">
<label><input type="checkbox" name="rotate_xy" />Rotate xy</label>
<label><input type="checkbox" name="rotate_yz" />Rotate yz</label>
<label><input type="checkbox" name="rotate_xz" />Rotate xz</label>
<label><input type="checkbox" name="rotate_xw" />Rotate xw</label>
<label><input type="checkbox" name="rotate_yw" />Rotate yw</label>
<label><input type="checkbox" name="rotate_zw" />Rotate zw</label>
</form>
<script type="text/javascript">
d3.text("120cell.ascii", function(err, text) {
var data = Hypersolid.parseVEF(text);
function NewShape() {};
Hypersolid.NewShape = function() {
return new NewShape();
};
NewShape.prototype = Hypersolid.Shape(data[0],data[1],data[2]);
var octaplex = Hypersolid.NewShape();
var octaplexView = Hypersolid.Viewport(octaplex, document.getElementById('octaplex-canvas'), {
width: 440,
height: 440,
scale: 2,
lineWidth: 2.5,
lineJoin: 'round'
});
octaplexView.draw();
// animation
options = document.getElementById('hypercube-options');
function render() {
if (options) {
checkboxes = options.getElementsByTagName('input');
}
if (options.rotate_xz.checked) {
rotate("xz", 0.008);
}
if (options.rotate_yz.checked) {
rotate("yz", 0.008);
}
if (options.rotate_xw.checked) {
rotate("xw", 0.008);
}
if (options.rotate_yw.checked) {
rotate("yw", 0.008);
}
if (options.rotate_xy.checked) {
rotate("xy", 0.008);
}
if (options.rotate_zw.checked) {
rotate("zw", 0.008);
}
};
function rotate(plane, x) {
octaplex.rotate(plane, x);
octaplexView.draw();
};
window.requestAnimFrame = window.requestAnimationFrame ||
window.webkitRequestAnimationFrame ||
window.mozRequestAnimationFrame ||
window.oRequestAnimationFrame ||
window.msRequestAnimationFrame ||
function( callback ){
window.setTimeout(callback, 1000 / 60);
};
(function animloop(){
requestAnimFrame(animloop);
render();
})();
});
</script>
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