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Circle-Packings/.ipynb_checkpoints/Homework-checkpoint.ipynb
William Ball 95c3b0d050 cleaned up
2021-03-12 18:07:17 -08:00

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3.4 MiB
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{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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"<script>\n",
" if ( !window.THREE ) document.write(' \\\n",
"<script src=&quot;https://cdn.jsdelivr.net/gh/sagemath/threejs-sage@r124/build/three.min.js&quot;><\\/script> \\\n",
" ');\n",
"</script>\n",
" \n",
"<script>\n",
"\n",
" var scene = new THREE.Scene();\n",
"\n",
" var renderer = new THREE.WebGLRenderer( { antialias: true, preserveDrawingBuffer: true } );\n",
" renderer.setPixelRatio( window.devicePixelRatio );\n",
" renderer.setSize( window.innerWidth, window.innerHeight );\n",
" renderer.setClearColor( 0xffffff, 1 );\n",
" document.body.appendChild( renderer.domElement );\n",
"\n",
" var options = {&quot;animate&quot;: false, &quot;animationControls&quot;: true, &quot;aspectRatio&quot;: [1.0, 1.0, 1.0], &quot;autoPlay&quot;: true, &quot;axes&quot;: false, &quot;axesLabels&quot;: [&quot;x&quot;, &quot;y&quot;, &quot;z&quot;], &quot;decimals&quot;: 2, &quot;delay&quot;: 20, &quot;frame&quot;: true, &quot;loop&quot;: true, &quot;projection&quot;: &quot;perspective&quot;, &quot;viewpoint&quot;: false};\n",
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"\n",
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" b[0].y -= 1;\n",
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" + Math.pow( b[1].y - b[0].y, 2 ) );\n",
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" var zRange = b[1].z - b[0].z;\n",
"\n",
" var ar = options.aspectRatio;\n",
" var a = [ ar[0], ar[1], ar[2] ]; // aspect multipliers\n",
" var autoAspect = 2.5;\n",
" if ( zRange > autoAspect * rRange && a[2] === 1 ) a[2] = autoAspect * rRange / zRange;\n",
"\n",
" // Distance from (xMid,yMid,zMid) to any corner of the bounding box, after applying aspectRatio\n",
" var midToCorner = Math.sqrt( a[0]*a[0]*xRange*xRange + a[1]*a[1]*yRange*yRange + a[2]*a[2]*zRange*zRange ) / 2;\n",
"\n",
" var xMid = ( b[0].x + b[1].x ) / 2;\n",
" var yMid = ( b[0].y + b[1].y ) / 2;\n",
" var zMid = ( b[0].z + b[1].z ) / 2;\n",
"\n",
" var box = new THREE.Geometry();\n",
" box.vertices.push( new THREE.Vector3( a[0]*b[0].x, a[1]*b[0].y, a[2]*b[0].z ) );\n",
" box.vertices.push( new THREE.Vector3( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) );\n",
" var boxMesh = new THREE.Line( box );\n",
" if ( options.frame ) scene.add( new THREE.BoxHelper( boxMesh, 'black' ) );\n",
"\n",
" if ( options.axesLabels ) {\n",
"\n",
" var d = options.decimals; // decimals\n",
" var offsetRatio = 0.1;\n",
" var al = options.axesLabels;\n",
"\n",
" var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
" var xm = xMid.toFixed(d);\n",
" if ( /^-0.?0*$/.test(xm) ) xm = xm.substr(1);\n",
" addLabel( al[0] + '=' + xm, a[0]*xMid, a[1]*b[1].y+offset, a[2]*b[0].z );\n",
" addLabel( ( b[0].x ).toFixed(d), a[0]*b[0].x, a[1]*b[1].y+offset, a[2]*b[0].z );\n",
" addLabel( ( b[1].x ).toFixed(d), a[0]*b[1].x, a[1]*b[1].y+offset, a[2]*b[0].z );\n",
"\n",
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" var ym = yMid.toFixed(d);\n",
" if ( /^-0.?0*$/.test(ym) ) ym = ym.substr(1);\n",
" addLabel( al[1] + '=' + ym, a[0]*b[1].x+offset, a[1]*yMid, a[2]*b[0].z );\n",
" addLabel( ( b[0].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[0].y, a[2]*b[0].z );\n",
" addLabel( ( b[1].y ).toFixed(d), a[0]*b[1].x+offset, a[1]*b[1].y, a[2]*b[0].z );\n",
"\n",
" var offset = offsetRatio * a[1]*( b[1].y - b[0].y );\n",
" var zm = zMid.toFixed(d);\n",
" if ( /^-0.?0*$/.test(zm) ) zm = zm.substr(1);\n",
" addLabel( al[2] + '=' + zm, a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*zMid );\n",
" addLabel( ( b[0].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[0].z );\n",
" addLabel( ( b[1].z ).toFixed(d), a[0]*b[1].x, a[1]*b[0].y-offset, a[2]*b[1].z );\n",
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" fontStyle='normal', fontWeight='normal', opacity=1 ) {\n",
"\n",
" var canvas = document.createElement( 'canvas' );\n",
" var context = canvas.getContext( '2d' );\n",
" var pixelRatio = Math.round( window.devicePixelRatio );\n",
"\n",
" var font = [fontStyle, fontWeight, fontSize + 'px', fontFamily].join(' ');\n",
"\n",
" context.font = font;\n",
" var width = context.measureText( text ).width;\n",
" var height = fontSize;\n",
"\n",
" // The dimensions of the canvas's underlying image data need to be powers\n",
" // of two in order for the resulting texture to support mipmapping.\n",
" canvas.width = THREE.MathUtils.ceilPowerOfTwo( width * pixelRatio );\n",
" canvas.height = THREE.MathUtils.ceilPowerOfTwo( height * pixelRatio );\n",
"\n",
" // Re-compute the unscaled dimensions after the power of two conversion.\n",
" width = canvas.width / pixelRatio;\n",
" height = canvas.height / pixelRatio;\n",
"\n",
" canvas.style.width = width + 'px';\n",
" canvas.style.height = height + 'px';\n",
"\n",
" context.scale( pixelRatio, pixelRatio );\n",
" context.fillStyle = color;\n",
" context.font = font; // Must be set again after measureText.\n",
" context.textAlign = 'center';\n",
" context.textBaseline = 'middle';\n",
" context.fillText( text, width/2, height/2 );\n",
"\n",
" var texture = new THREE.Texture( canvas );\n",
" texture.needsUpdate = true;\n",
"\n",
" var materialOptions = { map: texture, sizeAttenuation: false };\n",
" if ( opacity < 1 ) {\n",
" // Setting opacity=1 would cause the texture's alpha component to be\n",
" // discarded, giving the text a black background instead of the\n",
" // background being transparent.\n",
" materialOptions.opacity = opacity;\n",
" }\n",
" var sprite = new THREE.Sprite( new THREE.SpriteMaterial( materialOptions ) );\n",
" sprite.position.set( x, y, z );\n",
"\n",
" // Scaling factor, chosen somewhat arbitrarily so that the size of the text\n",
" // is consistent with previously generated plots.\n",
" var scale = 1/625;\n",
" if ( options.projection === 'orthographic' ) {\n",
" scale = midToCorner/256; // Needs to scale along with the plot itself.\n",
" }\n",
" sprite.scale.set( scale * width, scale * height, 1 );\n",
"\n",
" scene.add( sprite );\n",
"\n",
" return sprite;\n",
"\n",
" }\n",
"\n",
" if ( options.axes ) scene.add( new THREE.AxesHelper( Math.min( a[0]*b[1].x, a[1]*b[1].y, a[2]*b[1].z ) ) );\n",
"\n",
" var camera = createCamera();\n",
" camera.up.set( 0, 0, 1 );\n",
" camera.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
"\n",
" var offset = new THREE.Vector3( a[0]*xRange, a[1]*yRange, a[2]*zRange );\n",
"\n",
" if ( options.viewpoint ) {\n",
"\n",
" var aa = options.viewpoint;\n",
" var axis = new THREE.Vector3( aa[0][0], aa[0][1], aa[0][2] ).normalize();\n",
" var angle = aa[1] * Math.PI / 180;\n",
" var q = new THREE.Quaternion().setFromAxisAngle( axis, angle ).inverse();\n",
"\n",
" offset.set( 0, 0, offset.length() );\n",
" offset.applyQuaternion( q );\n",
"\n",
" }\n",
"\n",
" camera.position.add( offset );\n",
"\n",
" function createCamera() {\n",
"\n",
" var aspect = window.innerWidth / window.innerHeight;\n",
"\n",
" if ( options.projection === 'orthographic' ) {\n",
" var camera = new THREE.OrthographicCamera( -1, 1, 1, -1, -1000, 1000 );\n",
" updateCameraAspect( camera, aspect );\n",
" return camera;\n",
" }\n",
"\n",
" return new THREE.PerspectiveCamera( 45, aspect, 0.1, 1000 );\n",
"\n",
" }\n",
"\n",
" function updateCameraAspect( camera, aspect ) {\n",
"\n",
" if ( camera.isPerspectiveCamera ) {\n",
" camera.aspect = aspect;\n",
" } else if ( camera.isOrthographicCamera ) {\n",
" // Fit the camera frustum to the bounding box's diagonal so that the entire plot fits\n",
" // within at the default zoom level and camera position.\n",
" if ( aspect > 1 ) { // Wide window\n",
" camera.top = midToCorner;\n",
" camera.right = midToCorner * aspect;\n",
" } else { // Tall or square window\n",
" camera.top = midToCorner / aspect;\n",
" camera.right = midToCorner;\n",
" }\n",
" camera.bottom = -camera.top;\n",
" camera.left = -camera.right;\n",
" }\n",
"\n",
" camera.updateProjectionMatrix();\n",
"\n",
" }\n",
"\n",
" var lights = [{&quot;x&quot;:-5, &quot;y&quot;:3, &quot;z&quot;:0, &quot;color&quot;:&quot;#7f7f7f&quot;, &quot;parent&quot;:&quot;camera&quot;}];\n",
" for ( var i=0 ; i < lights.length ; i++ ) {\n",
" var light = new THREE.DirectionalLight( lights[i].color, 1 );\n",
" light.position.set( a[0]*lights[i].x, a[1]*lights[i].y, a[2]*lights[i].z );\n",
" if ( lights[i].parent === 'camera' ) {\n",
" light.target.position.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
" scene.add( light.target );\n",
" camera.add( light );\n",
" } else scene.add( light );\n",
" }\n",
" scene.add( camera );\n",
"\n",
" var ambient = {&quot;color&quot;:&quot;#7f7f7f&quot;};\n",
" scene.add( new THREE.AmbientLight( ambient.color, 1 ) );\n",
"\n",
" var controls = new THREE.OrbitControls( camera, renderer.domElement );\n",
" controls.target.set( a[0]*xMid, a[1]*yMid, a[2]*zMid );\n",
" controls.addEventListener( 'change', function() { if ( !animate ) render(); } );\n",
"\n",
" window.addEventListener( 'resize', function() {\n",
"\n",
" renderer.setSize( window.innerWidth, window.innerHeight );\n",
" updateCameraAspect( camera, window.innerWidth / window.innerHeight );\n",
" if ( !animate ) render();\n",
"\n",
" } );\n",
"\n",
" var texts = [];\n",
" for ( var i=0 ; i < texts.length ; i++ ) addText( texts[i] );\n",
"\n",
" function addText( json ) {\n",
" json.fontFamily = json.fontFamily.map( function( f ) {\n",
" // Need to put quotes around fonts that have whitespace in their names.\n",
" return /\\s/.test( f ) ? '&quot;' + f + '&quot;' : f;\n",
" }).join(', ');\n",
" var sprite = addLabel( json.text, a[0]*json.x, a[1]*json.y, a[2]*json.z, json.color,\n",
" json.fontSize, json.fontFamily, json.fontStyle, json.fontWeight,\n",
" json.opacity );\n",
" sprite.userData = json;\n",
" }\n",
"\n",
" var points = [];\n",
" for ( var i=0 ; i < points.length ; i++ ) addPoint( points[i] );\n",
"\n",
" function addPoint( json ) {\n",
"\n",
" var geometry = new THREE.Geometry();\n",
" var v = json.point;\n",
" geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
"\n",
" var canvas = document.createElement( 'canvas' );\n",
" canvas.width = 128;\n",
" canvas.height = 128;\n",
"\n",
" var context = canvas.getContext( '2d' );\n",
" context.arc( 64, 64, 64, 0, 2 * Math.PI );\n",
" context.fillStyle = json.color;\n",
" context.fill();\n",
"\n",
" var texture = new THREE.Texture( canvas );\n",
" texture.needsUpdate = true;\n",
"\n",
" var transparent = json.opacity < 1 ? true : false;\n",
" var size = camera.isOrthographicCamera ? json.size : json.size/100;\n",
" var material = new THREE.PointsMaterial( { size: size, map: texture,\n",
" transparent: transparent, opacity: json.opacity,\n",
" alphaTest: .1 } );\n",
"\n",
" var c = new THREE.Vector3();\n",
" geometry.computeBoundingBox();\n",
" geometry.boundingBox.getCenter( c );\n",
" geometry.translate( -c.x, -c.y, -c.z );\n",
"\n",
" var mesh = new THREE.Points( geometry, material );\n",
" mesh.position.set( c.x, c.y, c.z );\n",
" mesh.userData = json;\n",
" scene.add( mesh );\n",
"\n",
" }\n",
"\n",
" var lines = [];\n",
" for ( var i=0 ; i < lines.length ; i++ ) addLine( lines[i] );\n",
"\n",
" function addLine( json ) {\n",
"\n",
" var geometry = new THREE.Geometry();\n",
" for ( var i=0 ; i < json.points.length ; i++ ) {\n",
" var v = json.points[i];\n",
" geometry.vertices.push( new THREE.Vector3( a[0]*v[0], a[1]*v[1], a[2]*v[2] ) );\n",
" }\n",
"\n",
" var transparent = json.opacity < 1 ? true : false;\n",
" var material = new THREE.LineBasicMaterial( { color: json.color, linewidth: json.linewidth,\n",
" transparent: transparent, opacity: json.opacity } );\n",
"\n",
" var c = new THREE.Vector3();\n",
" geometry.computeBoundingBox();\n",
" geometry.boundingBox.getCenter( c );\n",
" geometry.translate( -c.x, -c.y, -c.z );\n",
"\n",
" var mesh = new THREE.Line( geometry, material );\n",
" mesh.position.set( c.x, c.y, c.z );\n",
" mesh.userData = json;\n",
" scene.add( mesh );\n",
"\n",
" }\n",
"\n",
" var surfaces = [{&quot;vertices&quot;: [{&quot;x&quot;: 2.8775303643724692, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: -3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: -2.968623481781377}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.9455128205128189, &quot;z&quot;: -3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: 2.9686234817813775}, {&quot;x&quot;: 2.8775303643724692, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: 3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.9455128205128189, &quot;z&quot;: 3.0}, {&quot;x&quot;: 2.918016194331985, &quot;y&quot;: -0.6923076923076921, &quot;z&quot;: -3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: -2.968623481781377}, {&quot;x&quot;: 2.8775303643724692, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: -3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.6923076923076921, &quot;z&quot;: -2.9281376518218627}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: -2.968623481781377}, {&quot;x&quot;: 2.918016194331985, &quot;y&quot;: -0.6923076923076921, &quot;z&quot;: -3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.6923076923076921, &quot;z&quot;: 2.9281376518218627}, {&quot;x&quot;: 2.8775303643724692, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: 3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: 2.9686234817813775}, {&quot;x&quot;: 2.918016194331985, &quot;y&quot;: -0.6923076923076921, &quot;z&quot;: 3.0}, {&quot;x&quot;: 2.8775303643724692, &quot;y&quot;: -0.8461538461538458, &quot;z&quot;: 3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: -0.6923076923076921, &quot;z&quot;: 2.9281376518218627}, {&quot;x&quot;: 2.9504048582995956, &quot;y&quot;: -0.5384615384615383, &quot;z&quot;: -3.0}, {&quot;x&quot;: 2.8461538461538467, &quot;y&quot;: 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30434], [30435, 30436, 30437], [30438, 30439, 30440], [30441, 30442, 30443], [30444, 30445, 30446], [30447, 30448, 30449], [30450, 30451, 30452], [30453, 30454, 30455], [30456, 30457, 30458], [30459, 30460, 30461], [30462, 30463, 30464], [30465, 30466, 30467], [30468, 30469, 30470], [30471, 30472, 30473], [30474, 30475, 30476], [30477, 30478, 30479], [30480, 30481, 30482], [30483, 30484, 30485], [30486, 30487, 30488], [30489, 30490, 30491], [30492, 30493, 30494], [30495, 30496, 30497], [30498, 30499, 30500], [30501, 30502, 30503], [30504, 30505, 30506], [30507, 30508, 30509], [30510, 30511, 30512], [30513, 30514, 30515], [30516, 30517, 30518], [30519, 30520, 30521], [30522, 30523, 30524], [30525, 30526, 30527], [30528, 30529, 30530], [30531, 30532, 30533], [30534, 30535, 30536], [30537, 30538, 30539], [30540, 30541, 30542], [30543, 30544, 30545], [30546, 30547, 30548], [30549, 30550, 30551], [30552, 30553, 30554], [30555, 30556, 30557], [30558, 30559, 30560], [30561, 30562, 30563], 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30694, 30695], [30696, 30697, 30698], [30699, 30700, 30701], [30702, 30703, 30704], [30705, 30706, 30707], [30708, 30709, 30710], [30711, 30712, 30713], [30714, 30715, 30716], [30717, 30718, 30719], [30720, 30721, 30722], [30723, 30724, 30725], [30726, 30727, 30728], [30729, 30730, 30731], [30732, 30733, 30734], [30735, 30736, 30737], [30738, 30739, 30740], [30741, 30742, 30743], [30744, 30745, 30746], [30747, 30748, 30749], [30750, 30751, 30752], [30753, 30754, 30755], [30756, 30757, 30758], [30759, 30760, 30761], [30762, 30763, 30764], [30765, 30766, 30767], [30768, 30769, 30770], [30771, 30772, 30773], [30774, 30775, 30776], [30777, 30778, 30779], [30780, 30781, 30782], [30783, 30784, 30785], [30786, 30787, 30788], [30789, 30790, 30791], [30792, 30793, 30794], [30795, 30796, 30797], [30798, 30799, 30800], [30801, 30802, 30803], [30804, 30805, 30806], [30807, 30808, 30809], [30810, 30811, 30812], [30813, 30814, 30815], [30816, 30817, 30818], [30819, 30820, 30821], [30822, 30823, 30824], [30825, 30826, 30827], [30828, 30829, 30830], [30831, 30832, 30833], [30834, 30835, 30836], [30837, 30838, 30839], [30840, 30841, 30842], [30843, 30844, 30845], [30846, 30847, 30848], [30849, 30850, 30851], [30852, 30853, 30854], [30855, 30856, 30857], [30858, 30859, 30860], [30861, 30862, 30863], [30864, 30865, 30866], [30867, 30868, 30869], [30870, 30871, 30872], [30873, 30874, 30875], [30876, 30877, 30878], [30879, 30880, 30881], [30882, 30883, 30884], [30885, 30886, 30887], [30888, 30889, 30890], [30891, 30892, 30893], [30894, 30895, 30896], [30897, 30898, 30899], [30900, 30901, 30902], [30903, 30904, 30905], [30906, 30907, 30908], [30909, 30910, 30911], [30912, 30913, 30914], [30915, 30916, 30917], [30918, 30919, 30920], [30921, 30922, 30923], [30924, 30925, 30926], [30927, 30928, 30929], [30930, 30931, 30932], [30933, 30934, 30935], [30936, 30937, 30938], [30939, 30940, 30941], [30942, 30943, 30944], [30945, 30946, 30947], [30948, 30949, 30950], [30951, 30952, 30953], [30954, 30955, 30956], [30957, 30958, 30959], [30960, 30961, 30962], [30963, 30964, 30965], [30966, 30967, 30968], [30969, 30970, 30971], [30972, 30973, 30974], [30975, 30976, 30977], [30978, 30979, 30980], [30981, 30982, 30983], [30984, 30985, 30986], [30987, 30988, 30989], [30990, 30991, 30992], [30993, 30994, 30995], [30996, 30997, 30998], [30999, 31000, 31001], [31002, 31003, 31004], [31005, 31006, 31007], [31008, 31009, 31010], [31011, 31012, 31013], [31014, 31015, 31016], [31017, 31018, 31019], [31020, 31021, 31022], [31023, 31024, 31025], [31026, 31027, 31028], [31029, 31030, 31031], [31032, 31033, 31034], [31035, 31036, 31037], [31038, 31039, 31040], [31041, 31042, 31043], [31044, 31045, 31046], [31047, 31048, 31049], [31050, 31051, 31052], [31053, 31054, 31055], [31056, 31057, 31058], [31059, 31060, 31061], [31062, 31063, 31064], [31065, 31066, 31067], [31068, 31069, 31070], [31071, 31072, 31073], [31074, 31075, 31076], [31077, 31078, 31079], [31080, 31081, 31082], [31083, 31084, 31085], [31086, 31087, 31088], [31089, 31090, 31091], [31092, 31093, 31094], [31095, 31096, 31097], [31098, 31099, 31100], [31101, 31102, 31103], [31104, 31105, 31106], [31107, 31108, 31109], [31110, 31111, 31112], [31113, 31114, 31115], [31116, 31117, 31118], [31119, 31120, 31121], [31122, 31123, 31124], [31125, 31126, 31127], [31128, 31129, 31130], [31131, 31132, 31133], [31134, 31135, 31136], [31137, 31138, 31139], [31140, 31141, 31142], [31143, 31144, 31145], [31146, 31147, 31148], [31149, 31150, 31151], [31152, 31153, 31154], [31155, 31156, 31157], [31158, 31159, 31160], [31161, 31162, 31163], [31164, 31165, 31166], [31167, 31168, 31169], [31170, 31171, 31172], [31173, 31174, 31175], [31176, 31177, 31178], [31179, 31180, 31181], [31182, 31183, 31184], [31185, 31186, 31187], [31188, 31189, 31190], [31191, 31192, 31193], [31194, 31195, 31196], [31197, 31198, 31199], [31200, 31201, 31202], [31203, 31204, 31205], [31206, 31207, 31208], [31209, 31210, 31211], [31212, 31213, 31214], [31215, 31216, 31217], [31218, 31219, 31220], [31221, 31222, 31223], [31224, 31225, 31226], [31227, 31228, 31229], [31230, 31231, 31232], [31233, 31234, 31235], [31236, 31237, 31238], [31239, 31240, 31241], [31242, 31243, 31244], [31245, 31246, 31247], [31248, 31249, 31250], [31251, 31252, 31253], [31254, 31255, 31256], [31257, 31258, 31259], [31260, 31261, 31262], [31263, 31264, 31265], [31266, 31267, 31268], [31269, 31270, 31271], [31272, 31273, 31274], [31275, 31276, 31277], [31278, 31279, 31280], [31281, 31282, 31283], [31284, 31285, 31286], [31287, 31288, 31289], [31290, 31291, 31292], [31293, 31294, 31295], [31296, 31297, 31298], [31299, 31300, 31301], [31302, 31303, 31304], [31305, 31306, 31307], [31308, 31309, 31310], [31311, 31312, 31313], [31314, 31315, 31316], [31317, 31318, 31319], [31320, 31321, 31322], [31323, 31324, 31325], [31326, 31327, 31328], [31329, 31330, 31331], [31332, 31333, 31334], [31335, 31336, 31337], [31338, 31339, 31340], [31341, 31342, 31343], [31344, 31345, 31346], [31347, 31348, 31349], [31350, 31351, 31352], [31353, 31354, 31355], [31356, 31357, 31358], [31359, 31360, 31361], [31362, 31363, 31364], [31365, 31366, 31367], [31368, 31369, 31370], [31371, 31372, 31373], [31374, 31375, 31376], [31377, 31378, 31379], [31380, 31381, 31382], [31383, 31384, 31385], [31386, 31387, 31388], [31389, 31390, 31391], [31392, 31393, 31394], [31395, 31396, 31397], [31398, 31399, 31400], [31401, 31402, 31403], [31404, 31405, 31406], [31407, 31408, 31409], [31410, 31411, 31412], [31413, 31414, 31415], [31416, 31417, 31418], [31419, 31420, 31421], [31422, 31423, 31424], [31425, 31426, 31427], [31428, 31429, 31430], [31431, 31432, 31433], [31434, 31435, 31436], [31437, 31438, 31439], [31440, 31441, 31442], [31443, 31444, 31445], [31446, 31447, 31448], [31449, 31450, 31451], [31452, 31453, 31454], [31455, 31456, 31457], [31458, 31459, 31460], [31461, 31462, 31463], [31464, 31465, 31466], [31467, 31468, 31469], [31470, 31471, 31472], [31473, 31474, 31475], [31476, 31477, 31478], [31479, 31480, 31481], [31482, 31483, 31484], [31485, 31486, 31487], [31488, 31489, 31490], [31491, 31492, 31493], [31494, 31495, 31496], [31497, 31498, 31499], [31500, 31501, 31502], [31503, 31504, 31505], [31506, 31507, 31508], [31509, 31510, 31511], [31512, 31513, 31514], [31515, 31516, 31517], [31518, 31519, 31520], [31521, 31522, 31523]], &quot;color&quot;: &quot;#6666ff&quot;, &quot;opacity&quot;: 1.0}];\n",
" for ( var i=0 ; i < surfaces.length ; i++ ) addSurface( surfaces[i] );\n",
"\n",
" function addSurface( json ) {\n",
"\n",
" var useFaceColors = 'faceColors' in json ? true : false;\n",
"\n",
" var geometry = new THREE.Geometry();\n",
" for ( var i=0 ; i < json.vertices.length ; i++ ) {\n",
" var v = json.vertices[i];\n",
" geometry.vertices.push( new THREE.Vector3( a[0]*v.x, a[1]*v.y, a[2]*v.z ) );\n",
" }\n",
" for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
" var f = json.faces[i];\n",
" for ( var j=0 ; j < f.length - 2 ; j++ ) {\n",
" var face = new THREE.Face3( f[0], f[j+1], f[j+2] );\n",
" if ( useFaceColors ) face.color.set( json.faceColors[i] );\n",
" geometry.faces.push( face );\n",
" }\n",
" }\n",
" geometry.computeVertexNormals();\n",
"\n",
" var side = json.singleSide ? THREE.FrontSide : THREE.DoubleSide;\n",
" var transparent = json.opacity < 1 ? true : false;\n",
" var flatShading = json.useFlatShading ? json.useFlatShading : false;\n",
"\n",
" var material = new THREE.MeshPhongMaterial( { side: side,\n",
" color: useFaceColors ? 'white' : json.color,\n",
" vertexColors: useFaceColors ? THREE.FaceColors : THREE.NoColors,\n",
" transparent: transparent, opacity: json.opacity,\n",
" shininess: 20, flatShading: flatShading } );\n",
"\n",
" var c = new THREE.Vector3();\n",
" geometry.computeBoundingBox();\n",
" geometry.boundingBox.getCenter( c );\n",
" geometry.translate( -c.x, -c.y, -c.z );\n",
"\n",
" var mesh = new THREE.Mesh( geometry, material );\n",
" mesh.position.set( c.x, c.y, c.z );\n",
" if ( transparent && json.renderOrder ) mesh.renderOrder = json.renderOrder;\n",
" mesh.userData = json;\n",
" scene.add( mesh );\n",
"\n",
" if ( json.showMeshGrid ) {\n",
"\n",
" var geometry = new THREE.Geometry();\n",
"\n",
" for ( var i=0 ; i < json.faces.length ; i++ ) {\n",
" var f = json.faces[i];\n",
" for ( var j=0 ; j < f.length ; j++ ) {\n",
" var k = j === f.length-1 ? 0 : j+1;\n",
" var v1 = json.vertices[f[j]];\n",
" var v2 = json.vertices[f[k]];\n",
" // vertices in opposite directions on neighboring faces\n",
" var nudge = f[j] < f[k] ? .0005*zRange : -.0005*zRange;\n",
" geometry.vertices.push( new THREE.Vector3( a[0]*v1.x, a[1]*v1.y, a[2]*(v1.z+nudge) ) );\n",
" geometry.vertices.push( new THREE.Vector3( a[0]*v2.x, a[1]*v2.y, a[2]*(v2.z+nudge) ) );\n",
" }\n",
" }\n",
"\n",
" var material = new THREE.LineBasicMaterial( { color: 'black', linewidth: 1 } );\n",
"\n",
" var c = new THREE.Vector3();\n",
" geometry.computeBoundingBox();\n",
" geometry.boundingBox.getCenter( c );\n",
" geometry.translate( -c.x, -c.y, -c.z );\n",
"\n",
" var mesh = new THREE.LineSegments( geometry, material );\n",
" mesh.position.set( c.x, c.y, c.z );\n",
" mesh.userData = json;\n",
" scene.add( mesh );\n",
"\n",
" }\n",
"\n",
" }\n",
"\n",
" function render() {\n",
"\n",
" if ( window.updateAnimation ) animate = updateAnimation();\n",
" if ( animate ) requestAnimationFrame( render );\n",
"\n",
" renderer.render( scene, camera );\n",
"\n",
" }\n",
"\n",
" render();\n",
" controls.update();\n",
" if ( !animate ) render();\n",
"\n",
"\n",
" // menu functions\n",
"\n",
" function toggleMenu() {\n",
"\n",
" var m = document.getElementById( 'menu-content' );\n",
" if ( m.style.display === 'block' ) m.style.display = 'none'\n",
" else m.style.display = 'block';\n",
"\n",
" }\n",
"\n",
"\n",
" function saveAsPNG() {\n",
"\n",
" var a = document.body.appendChild( document.createElement( 'a' ) );\n",
" a.href = renderer.domElement.toDataURL( 'image/png' );\n",
" a.download = 'screenshot';\n",
" a.click();\n",
"\n",
" }\n",
"\n",
" function saveAsHTML() {\n",
"\n",
" toggleMenu(); // otherwise visible in output\n",
" event.stopPropagation();\n",
"\n",
" var blob = new Blob( [ '<!DOCTYPE html>\\n' + document.documentElement.outerHTML ] );\n",
" var a = document.body.appendChild( document.createElement( 'a' ) );\n",
" a.href = window.URL.createObjectURL( blob );\n",
" a.download = 'graphic.html';\n",
" a.click();\n",
"\n",
" }\n",
"\n",
" function getViewpoint() {\n",
"\n",
" function roundTo( x, n ) { return +x.toFixed(n); }\n",
"\n",
" var v = camera.quaternion.inverse();\n",
" var r = Math.sqrt( v.x*v.x + v.y*v.y + v.z*v.z );\n",
" var axis = [ roundTo( v.x / r, 4 ), roundTo( v.y / r, 4 ), roundTo( v.z / r, 4 ) ];\n",
" var angle = roundTo( 2 * Math.atan2( r, v.w ) * 180 / Math.PI, 2 );\n",
"\n",
" var textArea = document.createElement( 'textarea' );\n",
" textArea.textContent = JSON.stringify( axis ) + ',' + angle;\n",
" textArea.style.csstext = 'position: absolute; top: -100%';\n",
" document.body.append( textArea );\n",
" textArea.select();\n",
" document.execCommand( 'copy' );\n",
"\n",
" var m = document.getElementById( 'menu-message' );\n",
" m.innerHTML = 'Viewpoint copied to clipboard';\n",
" m.style.display = 'block';\n",
" setTimeout( function() { m.style.display = 'none'; }, 2000 );\n",
"\n",
" }\n",
"\n",
"</script>\n",
"\n",
"<div id=&quot;menu-container&quot; onclick=&quot;toggleMenu()&quot;>&#x24d8;\n",
"<div id=&quot;menu-message&quot;></div>\n",
"<div id=&quot;menu-content&quot;>\n",
"<div onclick=&quot;saveAsPNG()&quot;>Save as PNG</div>\n",
"<div onclick=&quot;saveAsHTML()&quot;>Save as HTML</div>\n",
"<div onclick=&quot;getViewpoint()&quot;>Get Viewpoint</div>\n",
"<div>Close Menu</div>\n",
"</div></div>\n",
"\n",
"\n",
"</body>\n",
"</html>\n",
"\"\n",
" width=\"100%\"\n",
" height=\"400\"\n",
" style=\"border: 0;\">\n",
"</iframe>\n"
],
"text/plain": [
"Graphics3d Object"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('x,y,z')\n",
"implicit_plot3d(x^2 + y^2 - z^2 == 0, (x,-3,3), (y,-3,3), (z,-3,3))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.2",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.2"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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