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<!DOCTYPE html>
<html><head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<title>Realization of s-Permutahedron 0333</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
<style>
body { margin: 0px; overflow: hidden; }
</style>
</head>
<body>
<script src="js/three.js"></script>
<script src="js/OrbitControls.js"></script>
<script>
var scene = new THREE.Scene();
var renderer = new THREE.WebGLRenderer( { antialias: true } );
renderer.setSize( window.innerWidth, window.innerHeight );
renderer.setClearColor( 0xffffff, 1 );
document.body.appendChild( renderer.domElement );
var options = {"aspect_ratio": [1.0, 1.0, 1.0], "decimals": 2, "frame": false, "axes": false, "axes_labels": false};
// When animations are supported by the viewer, the value 'false'
// will be replaced with an option set in Python by the user
var animate = false; //options.animate;
var lights = [{x:0, y:0, z:10}, {x:0, y:0, z:-10}];
for ( var i=0 ; i < lights.length ; i++ ) {
var light = new THREE.DirectionalLight( 0xdddddd, 1 );
light.position.set( lights[i].x, lights[i].y, lights[i].z );
scene.add( light );
}
scene.add( new THREE.AmbientLight( 0x404040, 1 ) );
var b = [{x:0.0, y:-9.0, z:-30.0}, {x:42.0, y:33.0, z:18.0}]; // bounds
if ( b[0].x === b[1].x ) {
b[0].x -= 1;
b[1].x += 1;
}
if ( b[0].y === b[1].y ) {
b[0].y -= 1;
b[1].y += 1;
}
if ( b[0].z === b[1].z ) {
b[0].z -= 1;
b[1].z += 1;
}
var rRange = Math.sqrt( Math.pow( b[1].x - b[0].x, 2 )
+ Math.pow( b[1].x - b[0].x, 2 ) );
var xRange = b[1].x - b[0].x;
var yRange = b[1].y - b[0].y;
var zRange = b[1].z - b[0].z;
var ar = options.aspect_ratio;
var a = [ ar[0], ar[1], ar[2] ]; // aspect multipliers
var autoAspect = 2.5;
if ( zRange > autoAspect * rRange && a[2] === 1 ) a[2] = autoAspect * rRange / zRange;
var xMid = ( b[0].x + b[1].x ) / 2;
var yMid = ( b[0].y + b[1].y ) / 2;
var zMid = ( b[0].z + b[1].z ) / 2;
scene.position.set( -a[0]*xMid, -a[1]*yMid, -a[2]*zMid );
var box = new THREE.Geometry();
box.vertices.push( new THREE.Vector3( a[0]*b[0].x, a[1]*b[0].y, a[2]*b[0].z ) );
box.vertices.push( new THREE.Vector3( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) );
var boxMesh = new THREE.LineSegments( box );
if ( options.frame ) scene.add( new THREE.BoxHelper( boxMesh, 'black' ) );
if ( options.axes_labels ) {
var d = options.decimals; // decimals
var offsetRatio = 0.1;
var al = options.axes_labels;
var offset = offsetRatio * ( b[1].y - b[0].y );
var xm = xMid.toFixed(d);
if ( /^-0.?0*$/.test(xm) ) xm = xm.substr(1);
addLabel( al[0] + '=' + xm, a[0]*xMid, a[1]*b[1].y+offset, a[2]*b[0].z );
addLabel( ( b[0].x ).toFixed(d), a[0]*b[0].x, a[1]*b[1].y+offset, a[2]*b[0].z );
addLabel( ( b[1].x ).toFixed(d), a[0]*b[1].x, a[1]*b[1].y+offset, a[2]*b[0].z );
var offset = offsetRatio * ( b[1].x - b[0].x );
var ym = yMid.toFixed(d);
if ( /^-0.?0*$/.test(ym) ) ym = ym.substr(1);
addLabel( al[1] + '=' + ym, a[0]*b[1].x+offset, a[1]*yMid, a[2]*b[0].z );
addLabel( ( b[0].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[0].y, a[2]*b[0].z );
addLabel( ( b[1].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[1].y, a[2]*b[0].z );
var offset = offsetRatio * ( b[1].y - b[0].y );
var zm = zMid.toFixed(d);
if ( /^-0.?0*$/.test(zm) ) zm = zm.substr(1);
addLabel( al[2] + '=' + zm, a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*zMid );
addLabel( ( b[0].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[0].z );
addLabel( ( b[1].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[1].z );
}
var texts = [];
for ( var i=0 ; i < texts.length ; i++ )
addLabel( texts[i].text, texts[i].x, texts[i].y, texts[i].z );
function addLabel( text, x, y, z ) {
var fontsize = 14;
var canvas = document.createElement( 'canvas' );
canvas.width = 128;
canvas.height = 32; // powers of two
var context = canvas.getContext( '2d' );
context.fillStyle = 'black';
context.font = fontsize + 'px monospace';
context.textAlign = 'center';
context.textBaseline = 'middle';
context.fillText( text, .5*canvas.width, .5*canvas.height );
var texture = new THREE.Texture( canvas );
texture.needsUpdate = true;
var sprite = new THREE.Sprite( new THREE.SpriteMaterial( { map: texture } ) );
sprite.position.set( x, y, z );
sprite.scale.set( 1, .25 ); // ratio of width to height
scene.add( sprite );
}
if ( options.axes ) scene.add( new THREE.AxisHelper( Math.min( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) ) );
var camera = new THREE.PerspectiveCamera( 45, window.innerWidth / window.innerHeight, 0.1, 1000 );
camera.up.set( 0, 0, 1 );
var cameraOut = Math.max( a[0]*xRange, a[1]*yRange, a[2]*zRange );
camera.position.set( cameraOut, cameraOut, cameraOut );
camera.lookAt( scene.position );
var controls = new THREE.OrbitControls( camera, renderer.domElement );
controls.addEventListener( 'change', function() { if ( !animate ) render(); } );
window.addEventListener( 'resize', function() {
renderer.setSize( window.innerWidth, window.innerHeight );
camera.aspect = window.innerWidth / window.innerHeight;
camera.updateProjectionMatrix();
if ( !animate ) render();
} );
var points = [];
for ( var i=0 ; i < points.length ; i++ ) addPoint( points[i] );
function addPoint( json ) {
var geometry = new THREE.Geometry();
var v = json.point;
geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );
var canvas = document.createElement( 'canvas' );
canvas.width = 128;
canvas.height = 128;
var context = canvas.getContext( '2d' );
context.arc( 64, 64, 64, 0, 2 * Math.PI );
context.fillStyle = json.color;
context.fill();
var texture = new THREE.Texture( canvas );
texture.needsUpdate = true;
var material = new THREE.PointsMaterial( { size: json.size/100, map: texture,
transparent: true, opacity: json.opacity,
alphaTest: .1 } );
scene.add( new THREE.Points( geometry, material ) );
}
var lines = [{"points": [[30.0, 9.0, -21.0], [34.0, 10.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[30.0, 9.0, -21.0], [31.0, 13.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[30.0, 9.0, -21.0], [31.0, 10.0, -17.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[34.0, 10.0, -20.0], [35.0, 14.0, -19.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[34.0, 10.0, -20.0], [35.0, 11.0, -16.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[1.0, 16.0, -11.0], [8.0, 16.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[1.0, 16.0, -11.0], [2.0, 20.0, -10.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[1.0, 16.0, -11.0], [2.0, 17.0, -7.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[8.0, 16.0, -18.0], [13.0, 16.0, -23.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[8.0, 16.0, -18.0], [10.0, 20.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[8.0, 16.0, -18.0], [12.0, 18.0, -12.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[13.0, 16.0, -23.0], [17.0, 17.0, -22.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[13.0, 16.0, -23.0], [14.0, 20.0, -22.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[17.0, 17.0, -22.0], [20.0, 14.0, -22.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[17.0, 17.0, -22.0], [18.0, 21.0, -21.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[17.0, 17.0, -22.0], [18.0, 18.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[20.0, 14.0, -22.0], [23.0, 11.0, -22.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[20.0, 14.0, -22.0], [25.0, 19.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[20.0, 14.0, -22.0], [21.0, 15.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[23.0, 11.0, -22.0], [26.0, 8.0, -22.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[23.0, 11.0, -22.0], [28.0, 16.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[23.0, 11.0, -22.0], [24.0, 12.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[26.0, 8.0, -22.0], [30.0, 9.0, -21.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[26.0, 8.0, -22.0], [27.0, 9.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[18.0, 21.0, -21.0], [22.0, 22.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[18.0, 21.0, -21.0], [19.0, 25.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[18.0, 21.0, -21.0], [19.0, 22.0, -17.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[35.0, 14.0, -19.0], [36.0, 18.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[35.0, 14.0, -19.0], [36.0, 15.0, -15.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[2.0, 20.0, -10.0], [10.0, 20.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[2.0, 20.0, -10.0], [3.0, 24.0, -9.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[2.0, 20.0, -10.0], [3.0, 21.0, -6.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[10.0, 20.0, -18.0], [14.0, 20.0, -22.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[10.0, 20.0, -18.0], [12.0, 24.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[10.0, 20.0, -18.0], [14.0, 22.0, -12.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[14.0, 20.0, -22.0], [18.0, 21.0, -21.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[14.0, 20.0, -22.0], [15.0, 24.0, -21.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[22.0, 22.0, -20.0], [25.0, 19.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[22.0, 22.0, -20.0], [23.0, 26.0, -19.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[22.0, 22.0, -20.0], [23.0, 23.0, -16.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[25.0, 19.0, -20.0], [28.0, 16.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[25.0, 19.0, -20.0], [30.0, 24.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[25.0, 19.0, -20.0], [26.0, 20.0, -16.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[28.0, 16.0, -20.0], [31.0, 13.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[28.0, 16.0, -20.0], [33.0, 21.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[28.0, 16.0, -20.0], [29.0, 17.0, -16.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[31.0, 13.0, -20.0], [35.0, 14.0, -19.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[31.0, 13.0, -20.0], [32.0, 14.0, -16.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[19.0, 25.0, -20.0], [23.0, 26.0, -19.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[19.0, 25.0, -20.0], [20.0, 26.0, -16.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[23.0, 26.0, -19.0], [27.0, 27.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[23.0, 26.0, -19.0], [24.0, 27.0, -15.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[3.0, 24.0, -9.0], [12.0, 24.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[3.0, 24.0, -9.0], [4.0, 25.0, -5.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[12.0, 24.0, -18.0], [15.0, 24.0, -21.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[12.0, 24.0, -18.0], [16.0, 26.0, -12.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[15.0, 24.0, -21.0], [19.0, 25.0, -20.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[27.0, 27.0, -18.0], [30.0, 24.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[27.0, 27.0, -18.0], [28.0, 28.0, -14.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[30.0, 24.0, -18.0], [33.0, 21.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[30.0, 24.0, -18.0], [31.0, 25.0, -14.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[33.0, 21.0, -18.0], [36.0, 18.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[33.0, 21.0, -18.0], [34.0, 22.0, -14.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[36.0, 18.0, -18.0], [37.0, 19.0, -14.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[25.0, -8.0, -11.0], [29.0, -7.0, -10.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[25.0, -8.0, -11.0], [25.0, -1.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[25.0, -8.0, -11.0], [26.0, -7.0, -7.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[29.0, -7.0, -10.0], [33.0, -6.0, -9.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[29.0, -7.0, -10.0], [29.0, 1.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[29.0, -7.0, -10.0], [30.0, -6.0, -6.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[33.0, -6.0, -9.0], [33.0, 3.0, -18.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[33.0, -6.0, -9.0], [34.0, -5.0, -5.0]], "color": "#6666ff", "opacity": 1.0, "linewidth": 1.0}, {"points": [[15.0, -9.0, -6.0], [21.0, -9.0, -12.0]], "color": "#6666ff", 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for ( var i=0 ; i < lines.length ; i++ ) addLine( lines[i] );
function addLine( json ) {
var geometry = new THREE.Geometry();
for ( var i=0 ; i < json.points.length - 1 ; i++ ) {
var v = json.points[i];
geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );
var v = json.points[i+1];
geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );
}
var material = new THREE.LineBasicMaterial( { color: json.color, linewidth: json.linewidth,
transparent: true, opacity: json.opacity } );
scene.add( new THREE.LineSegments( geometry, material ) );
}
var surfaces = [];
for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );
function addSurface( json ) {
var geometry = new THREE.Geometry();
for ( var i=0 ; i < json.vertices.length ; i++ ) {
var v = json.vertices[i];
geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );
}
for ( var i=0 ; i < json.faces.length ; i++ ) {
var f = json.faces[i];
for ( var j=0 ; j < f.length - 2 ; j++ ) {
geometry.faces.push( new THREE.Face3( f[0], f[j+1], f[j+2] ) );
}
}
geometry.computeVertexNormals();
var depthWrite = json.opacity < 1 ? false : true;
var material = new THREE.MeshPhongMaterial( {
color: json.color , side: THREE.DoubleSide,
transparent: true, opacity: json.opacity,
shininess: 20, depthWrite: depthWrite } );
scene.add( new THREE.Mesh( geometry, material ) );
}
var scratch = new THREE.Vector3();
function render() {
if ( animate ) requestAnimationFrame( render );
renderer.render( scene, camera );
for ( var i=0 ; i < scene.children.length ; i++ ) {
if ( scene.children[i].type === 'Sprite' ) {
var sprite = scene.children[i];
var adjust = scratch.addVectors( sprite.position, scene.position )
.sub( camera.position ).length() / 5;
sprite.scale.set( adjust, .25*adjust ); // ratio of canvas width to height
}
}
}
render();
if ( !animate ) render();
</script><canvas width="1855" height="980" style="width: 1855px; height: 980px;"></canvas>
</body></html>