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+ | ====== polymake and Optimization ====== | ||
+ | |||
+ | By Sebastian Pokutta and Marc E. Pfetsch. | ||
+ | |||
+ | ===== Introduction ===== | ||
+ | |||
+ | Polymake offers many interesting features that can help (discrete) optimizers to analyze optimization problems. For example | ||
+ | |||
+ | * linear optimization can be performed exactly and visualized in small dimensions | ||
+ | * the convex hull of feasible points of an integer program can be computed and analyzed | ||
+ | * Hilbert bases can be computed | ||
+ | |||
+ | There are several other tutorials that cover similar topics: | ||
+ | |||
+ | * [[ilp_and_hilbertbases|ILP and Hilbert Bases]] | ||
+ | * [[branchnbound|Gomory Cuts]] | ||
+ | * [[gomory|Branch and Bound]] | ||
+ | * [[lattice_polytopes_tutorial|Tutorial for Lattice Polytopes]] | ||
+ | |||
+ | This tutorial is targeted towards the optimization community, since, surprisingly, | ||
+ | |||
+ | You can find files of the example LPs in the folder demo/ | ||
+ | |||
+ | ===== Input: lp2poly ===== | ||
+ | |||
+ | The first important step is to get the desired input into '' | ||
+ | |||
+ | < | ||
+ | Minimize | ||
+ | | ||
+ | Subject to | ||
+ | C1: x1 + x2 + x3 <= 2 | ||
+ | Bounds | ||
+ | 0 <= x1 <= 1 | ||
+ | 0 <= x2 <= 1 | ||
+ | 0 <= x3 <= 1 | ||
+ | End | ||
+ | </ | ||
+ | Thus, the file describes a 0/1-cube in three dimensions. It should be easy to adapt this format to other cases (If for example '' | ||
+ | |||
+ | Now assume that this example is contained in file '' | ||
+ | |||
+ | <code perl> | ||
+ | > $f=lp2poly(' | ||
+ | </ | ||
+ | The polytope '' | ||
+ | |||
+ | <code perl> | ||
+ | > print $f-> | ||
+ | Polytope< | ||
+ | </ | ||
+ | We convert it to a rational polytope via: | ||
+ | |||
+ | <code perl> | ||
+ | > $p = new Polytope< | ||
+ | </ | ||
+ | Now, '' | ||
+ | |||
+ | ===== Linear Optimization ===== | ||
+ | |||
+ | Polymake can be used to perform several actions related to linear optimization (linear programming - LP). For instance, one can exactly solve a linear program (via lrs or cdd). Before we explain the corresponding usage, we first need to have a linear optimization problem at hand. | ||
+ | |||
+ | Assuming that we are given the above example in variable '' | ||
+ | |||
+ | <code perl> | ||
+ | > print $p-> | ||
+ | 0 1 1 1 | ||
+ | </ | ||
+ | Thus - as described in the file - the objective function coefficients are 1 for all three variables (and there is an offset of 0). | ||
+ | |||
+ | Now, we can solve the corresponding linear program via | ||
+ | |||
+ | <code perl> | ||
+ | > print $p-> | ||
+ | 2 | ||
+ | </ | ||
+ | Thus, the maximal value that we can obtain via the above linear objective function is 2. We can also get an optimal vertex via | ||
+ | |||
+ | <code perl> | ||
+ | > print $p-> | ||
+ | 1 0 1 1 | ||
+ | </ | ||
+ | This vertex corresponds to setting '' | ||
+ | |||
+ | <code perl> | ||
+ | > print $p-> | ||
+ | {4 5 6} | ||
+ | </ | ||
+ | This means that the optimal face is the convex hull of three vertices (with indices 4, 5, 6). | ||
+ | |||
+ | Of course, by replacing '' | ||
+ | |||
+ | The directed graph obtained by directing the graph of the polytope in the direction of increasing objective function can be obtained via | ||
+ | |||
+ | <code perl> | ||
+ | > $p-> | ||
+ | </ | ||
+ | < | ||
+ | <!-- | ||
+ | polymake for knusper | ||
+ | Thu Mar 3 00:38:23 2022 | ||
+ | c3t | ||
+ | --> | ||
+ | |||
+ | |||
+ | < | ||
+ | < | ||
+ | <meta charset=utf-8> | ||
+ | < | ||
+ | < | ||
+ | /* | ||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | */ | ||
+ | html {overflow: scroll;} | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
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+ | | ||
+ | # | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | } | ||
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+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | /* | ||
+ | // COMMON_CODE_BLOCK_END | ||
+ | */ | ||
+ | </ | ||
+ | </ | ||
+ | < | ||
+ | < | ||
+ | <div id=' | ||
+ | <div class=group id=' | ||
+ | < | ||
+ | < | ||
+ | <div class=indented>< | ||
+ | <div class=suboption> | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | < | ||
+ | <div class=indented>< | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | <div class=suboption> | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | </ | ||
+ | <div class=suboption> | ||
+ | <div class=indented> | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | <select id=" | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | </ | ||
+ | <img id=' | ||
+ | <img id=' | ||
+ | <div id=" | ||
+ | </ | ||
+ | < | ||
+ | requirejs.config({ | ||
+ | paths: { | ||
+ | three: '/ | ||
+ | TrackballControls: | ||
+ | OrbitControls: | ||
+ | Projector: '/ | ||
+ | SVGRenderer: | ||
+ | WEBGL: '/ | ||
+ | }, | ||
+ | shim: { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | }); | ||
+ | | ||
+ | require([' | ||
+ | window.THREE = THREE; | ||
+ | require([' | ||
+ | | ||
+ | THREE.TrackballControls = TrackballControls; | ||
+ | THREE.OrbitControls = OrbitControls; | ||
+ | THREE.Projector = Projector; | ||
+ | THREE.SVGRenderer = SVGRenderer; | ||
+ | THREE.WEBGL = WEBGL; | ||
+ | |||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | |||
+ | const intervalLength = 25; // for automatic animations | ||
+ | const explodableModel = true; | ||
+ | const modelContains = { points: false, pointlabels: | ||
+ | const foldables = []; | ||
+ | |||
+ | var three = document.getElementById(" | ||
+ | var scene = new THREE.Scene(); | ||
+ | var renderer = new THREE.WebGLRenderer( { antialias: true } ); | ||
+ | var svgRenderer = new THREE.SVGRenderer( { antialias: true } ); | ||
+ | renderer.setPixelRatio( window.devicePixelRatio ); | ||
+ | renderer.setClearColor(0xFFFFFF, | ||
+ | svgRenderer.setClearColor(0xFFFFFF, | ||
+ | three.appendChild(renderer.domElement); | ||
+ | |||
+ | var frustumSize = 4; | ||
+ | var cameras = [new THREE.PerspectiveCamera(75, | ||
+ | cameras.forEach(function(cam) { | ||
+ | cam.position.set(0, | ||
+ | cam.lookAt(0, | ||
+ | cam.up.set(0, | ||
+ | }); | ||
+ | var controls = [new THREE.TrackballControls(cameras[0], | ||
+ | var camera, control; | ||
+ | |||
+ | controls[0].zoomSpeed = 0.2; | ||
+ | controls[0].rotateSpeed = 4; | ||
+ | |||
+ | |||
+ | // class to allow move points together with labels and spheres | ||
+ | var PMPoint = function (x,y,z) { | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.addLabel = function(labelsprite) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.addSphere = function(spheremesh) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.set = function(x, | ||
+ | | ||
+ | if (this.sprite) { | ||
+ | this.sprite.position.copy(this.vector); | ||
+ | } | ||
+ | if (this.sphere) { | ||
+ | this.sphere.position.copy(this.vector); | ||
+ | } | ||
+ | } | ||
+ | PMPoint.prototype.radius = function() { | ||
+ | if (this.sphere) { | ||
+ | return this.sphere.geometry.parameters.radius; | ||
+ | } else { | ||
+ | return 0; | ||
+ | } | ||
+ | }; | ||
+ | // select the target node | ||
+ | var target = document.querySelector('# | ||
+ | |||
+ | // create an observer instance | ||
+ | var observer = new MutationObserver(function(mutations) { | ||
+ | | ||
+ | if (mutation.removedNodes && mutation.removedNodes.length > 0) { | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | }); | ||
+ | }); | ||
+ | |||
+ | // configuration of the observer: | ||
+ | var config = { childList: true, characterData: | ||
+ | |||
+ | // pass in the target node, as well as the observer options | ||
+ | while (target) { | ||
+ | if (target.className==" | ||
+ | observer.observe(target, | ||
+ | break; | ||
+ | } | ||
+ | | ||
+ | } | ||
+ | |||
+ | // COMMON_CODE_BLOCK_END | ||
+ | |||
+ | var obj0 = new THREE.Object3D(); | ||
+ | obj0.name = " | ||
+ | obj0.userData.explodable = 1; | ||
+ | obj0.userData.points = []; | ||
+ | obj0.userData.points.push(new PMPoint(0, 0, 1)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 0, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 0, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 1, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 1, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 0, 1)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 1, 1)); | ||
+ | |||
+ | obj0.userData.pointradii = 0.02; | ||
+ | < | ||
+ | obj0.userData.pointmaterial = new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | obj0.userData.pointlabels = [" | ||
+ | obj0.userData.edgeindices = [0, 2, 1, 2, 2, 3, 1, 4, 3, 4, 0, 5, 1, 5, 4, 5, 0, 6, 3, 6, 4, 6, 5, 6]; | ||
+ | obj0.userData.facets = [[5, 4, 6], [6, 3, 2, 0], [1, 4, 5], [5, 0, 2, 1], [6, 4, 3], [3, 4, 1, 2], [5, 6, 0]]; | ||
+ | < | ||
+ | obj0.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | init_object(obj0); | ||
+ | scene.add(obj0); | ||
+ | |||
+ | var obj1 = new THREE.Object3D(); | ||
+ | obj1.name = "GRAPH directed with LP unnamed# | ||
+ | obj1.userData.explodable = 1; | ||
+ | obj1.userData.points = []; | ||
+ | obj1.userData.points.push(new PMPoint(0, 0, 1)); | ||
+ | obj1.userData.points.push(new PMPoint(1, 0, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(0, 0, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(0, 1, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(1, 1, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(1, 0, 1)); | ||
+ | obj1.userData.points.push(new PMPoint(0, 1, 1)); | ||
+ | |||
+ | obj1.userData.edgeindices = [0, 5, 0, 6, 1, 4, 1, 5, 2, 0, 2, 1, 2, 3, 3, 4, 3, 6]; | ||
+ | < | ||
+ | obj1.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: | ||
+ | obj1.userData.arrowstyle = 1; | ||
+ | init_object(obj1); | ||
+ | scene.add(obj1); | ||
+ | |||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | function textSpriteMaterial(message, | ||
+ | if ( parameters === undefined ) parameters = {}; | ||
+ | var fontface = " | ||
+ | var fontsize = parameters.hasOwnProperty(" | ||
+ | fontsize = fontsize*10; | ||
+ | var lines = message.split(' | ||
+ | var size = 512; | ||
+ | for(var i = 0; i< | ||
+ | var tmp = lines[i].length; | ||
+ | while(tmp*fontsize > size){ | ||
+ | | ||
+ | } | ||
+ | } | ||
+ | | ||
+ | var canvas = document.createElement(' | ||
+ | canvas.width = size; | ||
+ | canvas.height = size; | ||
+ | var context = canvas.getContext(' | ||
+ | context.fillStyle = " | ||
+ | context.fill(); | ||
+ | context.font = fontsize + "px " + fontface; | ||
+ | | ||
+ | // text color | ||
+ | context.fillStyle = " | ||
+ | | ||
+ | context.fillText(lines[i], | ||
+ | } | ||
+ | | ||
+ | // canvas contents will be used for a texture | ||
+ | var texture = new THREE.Texture(canvas); | ||
+ | texture.needsUpdate = true; | ||
+ | | ||
+ | var spriteMaterial = new THREE.SpriteMaterial({map: | ||
+ | return spriteMaterial; | ||
+ | } | ||
+ | |||
+ | |||
+ | // ---------------------- INITIALIZING OBJECTS-------------------------------------- | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | function init_object(obj) { | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_points(obj); | ||
+ | modelContains.points = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_pointlabels(obj); | ||
+ | modelContains.pointlabels = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_lines(obj); | ||
+ | modelContains.lines = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_edgelabels(obj); | ||
+ | modelContains.edgelabels = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_arrowheads(obj); | ||
+ | modelContains.arrowheads = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_faces(obj); | ||
+ | modelContains.faces = true; | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function init_points(obj) { | ||
+ | var pointgroup = new THREE.Group(); | ||
+ | pointgroup.name = " | ||
+ | var points = obj.userData.points; | ||
+ | var radii = obj.userData.pointradii; | ||
+ | var materials = obj.userData.pointmaterial; | ||
+ | var geometry, | ||
+ | if (!Array.isArray(radii)) { | ||
+ | geometry = new THREE.SphereBufferGeometry(radii); | ||
+ | } | ||
+ | if (!Array.isArray(materials)) { | ||
+ | material = materials; | ||
+ | } | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | if (Array.isArray(radii)) { | ||
+ | if (radii[i] == 0) { | ||
+ | continue; | ||
+ | } | ||
+ | geometry = new THREE.SphereBufferGeometry(radii[i]); | ||
+ | } | ||
+ | if (Array.isArray(materials)) { | ||
+ | material = materials[i]; | ||
+ | } | ||
+ | var sphere = new THREE.Mesh(geometry, | ||
+ | point.addSphere(sphere); | ||
+ | pointgroup.add(sphere); | ||
+ | } | ||
+ | obj.add(pointgroup); | ||
+ | } | ||
+ | |||
+ | function init_pointlabels(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var labels = obj.userData.pointlabels; | ||
+ | var pointlabels = new THREE.Group(); | ||
+ | pointlabels.name = " | ||
+ | if (Array.isArray(labels)) { | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | var spriteMaterial = textSpriteMaterial( labels[i] ); | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | point.addLabel(sprite); | ||
+ | pointlabels.add(sprite); | ||
+ | } | ||
+ | } else { | ||
+ | var spriteMaterial = textSpriteMaterial( labels ); | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | point.addLabel(sprite); | ||
+ | pointlabels.add(sprite); | ||
+ | } | ||
+ | } | ||
+ | obj.add(pointlabels); | ||
+ | } | ||
+ | |||
+ | function init_lines(obj) { | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var points = obj.userData.points; | ||
+ | var materials = obj.userData.edgematerial; | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | var bufarr = new Float32Array( obj.userData.edgeindices.length * 3 ); | ||
+ | var bufattr = new THREE.Float32BufferAttribute( bufarr, 3 ); | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | geometry.setAttribute(' | ||
+ | if (Array.isArray(materials)) { | ||
+ | for (var i=0; i< | ||
+ | geometry.addGroup(2*i, | ||
+ | } | ||
+ | } | ||
+ | var lines = new THREE.LineSegments(geometry, | ||
+ | lines.name = " | ||
+ | obj.add(lines); | ||
+ | updateEdgesPosition(obj); | ||
+ | } | ||
+ | |||
+ | function init_edgelabels(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var labels = obj.userData.edgelabels; | ||
+ | var edgelabels = new THREE.Group(); | ||
+ | edgelabels.name = " | ||
+ | if (Array.isArray(labels)) { | ||
+ | for (var i=0; i< | ||
+ | var spriteMaterial = textSpriteMaterial( labels[i] ); | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector, | ||
+ | edgelabels.add(sprite); | ||
+ | } | ||
+ | } else { | ||
+ | var spriteMaterial = textSpriteMaterial( labels ); | ||
+ | for (var i=0; i< | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector, | ||
+ | edgelabels.add(sprite); | ||
+ | } | ||
+ | } | ||
+ | obj.add(edgelabels); | ||
+ | } | ||
+ | |||
+ | function init_arrowheads(obj) { | ||
+ | var arrowheads = new THREE.Group(); | ||
+ | arrowheads.name = " | ||
+ | var arrowstyle = obj.userData.arrowstyle; | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var edgematerials = obj.userData.edgematerial; | ||
+ | var points = obj.userData.points; | ||
+ | var material; | ||
+ | if (!Array.isArray(edgematerials)) { | ||
+ | material = new THREE.MeshBasicMaterial( {color: edgematerials.color} ); | ||
+ | } | ||
+ | |||
+ | for (var i=0; i< | ||
+ | var start = points[edgeindices[i]]; | ||
+ | var end = points[edgeindices[i+1]]; | ||
+ | var dist = start.vector.distanceTo( end.vector ) - start.radius() - end.radius(); | ||
+ | if (dist <= 0) { | ||
+ | continue; | ||
+ | } | ||
+ | var dir = new THREE.Vector3().subVectors(end.vector, | ||
+ | dir.normalize(); | ||
+ | var axis = new THREE.Vector3().set(dir.z, | ||
+ | axis.normalize(); | ||
+ | var radians = Math.acos( dir.y ); | ||
+ | var radius = dist/25; | ||
+ | var height = dist/5; | ||
+ | var geometry = new THREE.ConeBufferGeometry(radius, | ||
+ | var position = new THREE.Vector3().addVectors(start.vector, | ||
+ | if (Array.isArray(edgematerials)) { | ||
+ | material = new THREE.MeshBasicMaterial( {color: edgematerials[i].color} ); | ||
+ | } | ||
+ | var cone = new THREE.Mesh( geometry, material ); | ||
+ | cone.quaternion.setFromAxisAngle(axis, | ||
+ | cone.position.copy(position);; | ||
+ | arrowheads.add(cone); | ||
+ | } | ||
+ | obj.add(arrowheads); | ||
+ | } | ||
+ | |||
+ | function init_faces(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var facets = obj.userData.facets; | ||
+ | obj.userData.triangleindices = []; | ||
+ | for (var i=0; i< | ||
+ | facet = facets[i]; | ||
+ | for (var t=0; t< | ||
+ | obj.userData.triangleindices.push(facet[0], | ||
+ | } | ||
+ | } | ||
+ | var bufarr = new Float32Array( obj.userData.triangleindices.length * 3 ); | ||
+ | var bufattr = new THREE.Float32BufferAttribute(bufarr, | ||
+ | | ||
+ | var materials = obj.userData.facetmaterial; | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | var frontmaterials = []; | ||
+ | var backmaterials = []; | ||
+ | geometry.setAttribute(' | ||
+ | if (Array.isArray(materials)) { | ||
+ | var tricount = 0; | ||
+ | var facet; | ||
+ | for (var i=0; i< | ||
+ | facet = facets[i]; | ||
+ | geometry.addGroup(tricount, | ||
+ | tricount += (facet.length-2)*3; | ||
+ | } | ||
+ | for (var j=0; j< | ||
+ | var fmat = materials[j].clone() | ||
+ | fmat.side = THREE.FrontSide; | ||
+ | frontmaterials.push(fmat); | ||
+ | var bmat = materials[j].clone() | ||
+ | bmat.side = THREE.BackSide; | ||
+ | backmaterials.push(bmat); | ||
+ | obj.userData.facetmaterial = frontmaterials.concat(backmaterials); | ||
+ | } | ||
+ | } else if (materials instanceof THREE.Material) { | ||
+ | frontmaterials = materials.clone() | ||
+ | frontmaterials.side = THREE.FrontSide; | ||
+ | backmaterials = materials.clone() | ||
+ | backmaterials.side = THREE.BackSide; | ||
+ | obj.userData.facetmaterial = [frontmaterials, | ||
+ | } | ||
+ | // duplicating the object with front and back should avoid transparency issues | ||
+ | var backmesh = new THREE.Mesh(geometry, | ||
+ | // meshname is used to show/hide objects | ||
+ | backmesh.name = " | ||
+ | obj.add(backmesh); | ||
+ | var frontmesh = new THREE.Mesh(geometry, | ||
+ | frontmesh.name = " | ||
+ | obj.add(frontmesh); | ||
+ | updateFacesPosition(obj); | ||
+ | } | ||
+ | // // | ||
+ | |||
+ | |||
+ | function updateFacesPosition(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var indices = obj.userData.triangleindices; | ||
+ | var faces = obj.getObjectByName(" | ||
+ | var ba = faces.geometry.getAttribute(" | ||
+ | for (var i=0; i< | ||
+ | ba.setXYZ(i, | ||
+ | } | ||
+ | faces.geometry.attributes.position.needsUpdate = true; | ||
+ | | ||
+ | } | ||
+ | |||
+ | function updateEdgesPosition(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var indices = obj.userData.edgeindices; | ||
+ | var lines = obj.getObjectByName(" | ||
+ | var ba = lines.geometry.getAttribute(" | ||
+ | for (var i=0; i< | ||
+ | ba.setXYZ(i, | ||
+ | } | ||
+ | lines.geometry.attributes.position.needsUpdate = true; | ||
+ | } | ||
+ | |||
+ | function onWindowResize() { | ||
+ | renderer.setSize( three.clientWidth, | ||
+ | svgRenderer.setSize( three.clientWidth, | ||
+ | updateCamera(); | ||
+ | } | ||
+ | |||
+ | function updateCamera() { | ||
+ | var width = three.clientWidth; | ||
+ | var height = three.clientHeight; | ||
+ | var aspect = width / height; | ||
+ | if (camera.type == " | ||
+ | camera.left = frustumSize * aspect / - 2; | ||
+ | camera.right = frustumSize * aspect / 2; | ||
+ | camera.top = frustumSize / 2; | ||
+ | camera.bottom = - frustumSize / 2; | ||
+ | } else if (camera.type == " | ||
+ | camera.aspect = aspect; | ||
+ | } | ||
+ | camera.updateProjectionMatrix(); | ||
+ | } | ||
+ | |||
+ | function changeCamera(event) { | ||
+ | var selindex = event.currentTarget.selectedIndex; | ||
+ | camera = cameras[selindex]; | ||
+ | control = controls[selindex]; | ||
+ | control.enabled = true; | ||
+ | for (var i=0; i< | ||
+ | if (i!=selindex) { | ||
+ | controls[i].enabled = false; | ||
+ | } | ||
+ | } | ||
+ | updateCamera(); | ||
+ | } | ||
+ | |||
+ | var camtypenode = document.getElementById(' | ||
+ | camtypenode.onchange = changeCamera; | ||
+ | camtypenode.dispatchEvent(new Event(' | ||
+ | |||
+ | onWindowResize(); | ||
+ | window.addEventListener(' | ||
+ | |||
+ | |||
+ | var xRotationEnabled = false; | ||
+ | var yRotationEnabled = false; | ||
+ | var zRotationEnabled = false; | ||
+ | var rotationSpeedFactor = 1; | ||
+ | var settingsShown = false; | ||
+ | var labelsShown = true; | ||
+ | var intervals = []; | ||
+ | var timeouts = []; | ||
+ | var explodingSpeed = 0.05; | ||
+ | var explodeScale = 0.000001; | ||
+ | var XMLS = new XMLSerializer(); | ||
+ | var svgElement; | ||
+ | var renderId; | ||
+ | |||
+ | var render = function () { | ||
+ | |||
+ | renderId = requestAnimationFrame(render); | ||
+ | |||
+ | // comment in for automatic explosion | ||
+ | // | ||
+ | |||
+ | var phi = 0.02 * rotationSpeedFactor; | ||
+ | |||
+ | if (xRotationEnabled) { | ||
+ | scene.rotation.x += phi; | ||
+ | } | ||
+ | if (yRotationEnabled) { | ||
+ | scene.rotation.y += phi; | ||
+ | } | ||
+ | if (zRotationEnabled) { | ||
+ | scene.rotation.z += phi; | ||
+ | } | ||
+ | |||
+ | control.update(); | ||
+ | renderer.render(scene, | ||
+ | }; | ||
+ | |||
+ | if ( THREE.WEBGL.isWebGLAvailable() ) { | ||
+ | render(); | ||
+ | } else { | ||
+ | var warning = WEBGL.getWebGLErrorMessage(); | ||
+ | three.appendChild( warning ); | ||
+ | } | ||
+ | | ||
+ | function changeTransparency() { | ||
+ | var opacity = 1-Number(event.currentTarget.value); | ||
+ | for (var i=0; i< | ||
+ | child = scene.children[i]; | ||
+ | if ( child.userData.hasOwnProperty(" | ||
+ | if (Array.isArray(child.userData.facetmaterial)) { | ||
+ | for (var j=0; j< | ||
+ | child.userData.facetmaterial[j].opacity = opacity; | ||
+ | } | ||
+ | } else { | ||
+ | child.userData.facetmaterial.opacity = opacity; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function toggleDepthWrite(event) { | ||
+ | depthwrite = event.currentTarget.checked; | ||
+ | for (var i=0; i< | ||
+ | child = scene.children[i]; | ||
+ | if ( child.userData.hasOwnProperty(" | ||
+ | if (Array.isArray(child.userData.facetmaterial)) { | ||
+ | for (var j=0; j< | ||
+ | child.userData.facetmaterial[j].depthWrite = depthwrite; | ||
+ | } | ||
+ | } else { | ||
+ | child.userData.facetmaterial.depthWrite = depthWrite; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function changeRotationX(event){ | ||
+ | xRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | function changeRotationY(event){ | ||
+ | yRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | function changeRotationZ(event){ | ||
+ | zRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | |||
+ | function changeRotationSpeedFactor(event){ | ||
+ | rotationSpeedFactor = Number(event.currentTarget.value); | ||
+ | } | ||
+ | |||
+ | function resetScene(){ | ||
+ | scene.rotation.set(0, | ||
+ | camera.position.set(0, | ||
+ | camera.up.set(0, | ||
+ | } | ||
+ | |||
+ | function showSettings(event){ | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | settingsShown = true; | ||
+ | } | ||
+ | |||
+ | function hideSettings(event){ | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | settingsShown = false; | ||
+ | } | ||
+ | |||
+ | |||
+ | |||
+ | var pos = 150* Math.PI; | ||
+ | |||
+ | function updateFactor() { | ||
+ | pos++; | ||
+ | return Math.sin(.01*pos)+1; | ||
+ | } | ||
+ | |||
+ | // ------------------------ FOLDING ------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | // rotate point p around axis defined by points p1 and p2 by given angle | ||
+ | function rotate(p, p1, p2, angle ){ | ||
+ | angle = -angle; | ||
+ | var x = p.x, y = p.y, z = p.z, | ||
+ | a = p1.x, b = p1.y, c = p1.z, | ||
+ | u = p2.x-p1.x, v = p2.y-p1.y, w = p2.z-p1.z; | ||
+ | var result = []; | ||
+ | var L = u*u + v*v + w*w; | ||
+ | var sqrt = Math.sqrt; | ||
+ | var cos = Math.cos; | ||
+ | var sin = Math.sin; | ||
+ | |||
+ | result[0] = ((a*(v*v+w*w)-u*(b*v+c*w-u*x-v*y-w*z))*(1-cos(angle))+L*x*cos(angle)+sqrt(L)*(-c*v+b*w-w*y+v*z)*sin(angle))/ | ||
+ | result[1] = ((b*(u*u+w*w)-v*(a*u+c*w-u*x-v*y-w*z))*(1-cos(angle))+L*y*cos(angle)+sqrt(L)*(c*u-a*w+w*x-u*z)*sin(angle))/ | ||
+ | result[2] = ((c*(u*u+v*v)-w*(a*u+b*v-u*x-v*y-w*z))*(1-cos(angle))+L*z*cos(angle)+sqrt(L)*(-b*u+a*v-v*x+u*y)*sin(angle))/ | ||
+ | |||
+ | return result; | ||
+ | } | ||
+ | |||
+ | var fold = function(event){ | ||
+ | var obj = foldables[Number(event.currentTarget.name)]; | ||
+ | var foldvalue = Number(event.currentTarget.value); | ||
+ | var scale = foldvalue - obj.userData.oldscale; | ||
+ | |||
+ | for (var j=0; j< | ||
+ | rotateVertices(obj, | ||
+ | } | ||
+ | update(obj); | ||
+ | obj.userData.oldscale += scale; | ||
+ | lookAtBarycenter(obj); | ||
+ | } | ||
+ | |||
+ | function lookAtBarycenter(obj){ | ||
+ | control.target = barycenter(obj); | ||
+ | } | ||
+ | |||
+ | function barycenter(obj) { | ||
+ | var center = new THREE.Vector3(0, | ||
+ | var points = obj.userData.points; | ||
+ | for (var i=0; i< | ||
+ | center.add(points[i].vector); | ||
+ | } | ||
+ | center.divideScalar(points.length); | ||
+ | return center; | ||
+ | } | ||
+ | |||
+ | function rotateVertices(obj, | ||
+ | var axes = obj.userData.axes; | ||
+ | var subtrees = obj.userData.subtrees; | ||
+ | var points = obj.userData.points; | ||
+ | var angles = obj.userData.angles; | ||
+ | if (edge < axes.length){ | ||
+ | for (var j=0; j< | ||
+ | var rotP = rotate(points[subtrees[edge][j]].vector, | ||
+ | points[subtrees[edge][j]].set(rotP[0], | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function update(obj) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | |||
+ | if (foldables.length) { | ||
+ | var settings = document.getElementById(' | ||
+ | var foldDiv = document.createElement(' | ||
+ | foldDiv.id = ' | ||
+ | var title = document.createElement(' | ||
+ | title.innerHTML = ' | ||
+ | foldDiv.appendChild(title); | ||
+ | foldDiv.className = ' | ||
+ | for (var i=0; i< | ||
+ | var range = document.createElement(' | ||
+ | range.type = ' | ||
+ | range.min = 0; | ||
+ | range.max = 1; | ||
+ | range.value = 0; | ||
+ | range.step = 0.001; | ||
+ | range.name = String(i); | ||
+ | range.oninput = fold; | ||
+ | foldDiv.appendChild(range); | ||
+ | } | ||
+ | lookAtBarycenter(foldables[0]); | ||
+ | settings.insertBefore(foldDiv, | ||
+ | } | ||
+ | |||
+ | | ||
+ | // ---------------------- EXPLOSION ------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | if (explodableModel) { | ||
+ | for (var i=0; i< | ||
+ | obj = scene.children[i]; | ||
+ | if ( obj.userData.explodable ) { | ||
+ | computeCentroid(obj); | ||
+ | } | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | explode(0.000001); | ||
+ | } | ||
+ | |||
+ | function computeCentroid(obj) { | ||
+ | centroid = new THREE.Vector3(); | ||
+ | obj.userData.points.forEach(function(pmpoint) { | ||
+ | centroid.add(pmpoint.vector); | ||
+ | }); | ||
+ | centroid.divideScalar(obj.userData.points.length); | ||
+ | obj.userData.centroid = centroid; | ||
+ | } | ||
+ | |||
+ | function explode(factor) { | ||
+ | for (var i=0; i< | ||
+ | var obj = scene.children[i]; | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | var c = obj.userData.centroid; | ||
+ | obj.position.set(c.x*factor, | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function triggerExplode(event){ | ||
+ | explodeScale = Number(event.currentTarget.value); | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | |||
+ | function setExplodingSpeed(event){ | ||
+ | explodingSpeed = Number(event.currentTarget.value); | ||
+ | } | ||
+ | |||
+ | function triggerAutomaticExplode(event){ | ||
+ | if (event.currentTarget.checked){ | ||
+ | startExploding(); | ||
+ | } else { | ||
+ | clearIntervals(); | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function startExploding(){ | ||
+ | intervals.push(setInterval(explodingInterval, | ||
+ | } | ||
+ | |||
+ | |||
+ | function explodingInterval(){ | ||
+ | explodeScale += explodingSpeed; | ||
+ | if (explodeScale <= 6){ | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | else{ | ||
+ | explode(6); | ||
+ | explodeScale = 6; | ||
+ | clearIntervals(); | ||
+ | timeouts.push(setTimeout(startUnexploding, | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | |||
+ | |||
+ | function startUnexploding(){ | ||
+ | intervals.push(setInterval(unexplodingInterval, | ||
+ | } | ||
+ | |||
+ | function unexplodingInterval(){ | ||
+ | explodeScale -= explodingSpeed; | ||
+ | if (explodeScale >= 0){ | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | else { | ||
+ | explode(0); | ||
+ | explodeScale = 0; | ||
+ | clearIntervals(); | ||
+ | timeouts.push(setTimeout(startExploding, | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | |||
+ | function clearIntervals(){ | ||
+ | intervals.forEach(function(interval){ | ||
+ | clearInterval(interval); | ||
+ | }); | ||
+ | intervals = []; | ||
+ | timeouts.forEach(function(timeout){ | ||
+ | clearTimeout(timeout); | ||
+ | }); | ||
+ | timeouts = []; | ||
+ | } | ||
+ | |||
+ | // ---------------------- DISPLAY -------------------------------------------------- | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | const objectTypeInnerHTMLs = { points: " | ||
+ | const objectTypeVisible = {}; | ||
+ | Object.assign(objectTypeVisible, | ||
+ | const sortedObjectTypeKeys = Object.keys(objectTypeInnerHTMLs).sort(); | ||
+ | const shownObjectTypesList = document.getElementById(' | ||
+ | |||
+ | function setVisibility(bool, | ||
+ | for (var i=0; i< | ||
+ | var obj = scene.children[i].getObjectByName(objname); | ||
+ | if (obj) { | ||
+ | obj.visible = bool; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function toggleObjectTypeVisibility(event){ | ||
+ | var name = event.currentTarget.name; | ||
+ | var checked = event.currentTarget.checked; | ||
+ | objectTypeVisible[name] = checked; | ||
+ | if (name == " | ||
+ | setVisibility(checked," | ||
+ | setVisibility(checked," | ||
+ | } else { | ||
+ | setVisibility(checked, | ||
+ | } | ||
+ | } | ||
+ | |||
+ | for (var i=0; i< | ||
+ | var key = sortedObjectTypeKeys[i]; | ||
+ | if (modelContains[key]) { | ||
+ | var objTypeNode = document.createElement(' | ||
+ | objTypeNode.innerHTML = objectTypeInnerHTMLs[key] + '< | ||
+ | var checkbox = document.createElement(' | ||
+ | checkbox.type = ' | ||
+ | checkbox.checked = true; | ||
+ | checkbox.name = key; | ||
+ | checkbox.onchange = toggleObjectTypeVisibility; | ||
+ | shownObjectTypesList.appendChild(checkbox); | ||
+ | shownObjectTypesList.appendChild(objTypeNode); | ||
+ | } | ||
+ | } | ||
+ | |||
+ | // ------------------------------------------------------ | ||
+ | |||
+ | function toggleObjectVisibility(event){ | ||
+ | var nr = Number(event.currentTarget.name); | ||
+ | scene.children[nr].visible = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | // append checkboxes for displaying or hiding objects | ||
+ | var shownObjectsList = document.getElementById(' | ||
+ | for (var i=0; i< | ||
+ | obj = scene.children[i]; | ||
+ | var objNode = document.createElement(' | ||
+ | objNode.innerHTML = obj.name + '< | ||
+ | var checkbox = document.createElement(' | ||
+ | checkbox.type = ' | ||
+ | checkbox.checked = true; | ||
+ | checkbox.name = String(i); | ||
+ | checkbox.onchange = toggleObjectVisibility; | ||
+ | shownObjectsList.appendChild(checkbox); | ||
+ | shownObjectsList.appendChild(objNode); | ||
+ | } | ||
+ | |||
+ | // ---------------------- SVG ------------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | function takeSvgScreenshot() { | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(false," | ||
+ | } | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(false," | ||
+ | } | ||
+ | svgRenderer.render(scene, | ||
+ | svgElement = XMLS.serializeToString(svgRenderer.domElement); | ||
+ | | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(true," | ||
+ | } | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(true," | ||
+ | } | ||
+ | |||
+ | if (document.getElementById(' | ||
+ | //show in new tab | ||
+ | var myWindow = window.open("","" | ||
+ | myWindow.document.body.innerHTML = svgElement; | ||
+ | } else{ | ||
+ | // download svg file | ||
+ | download(" | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function download(filename, | ||
+ | var element = document.createElement(' | ||
+ | element.setAttribute(' | ||
+ | element.setAttribute(' | ||
+ | |||
+ | element.style.display = ' | ||
+ | document.body.appendChild(element); | ||
+ | |||
+ | element.click(); | ||
+ | |||
+ | document.body.removeChild(element); | ||
+ | } | ||
+ | |||
+ | |||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | |||
+ | |||
+ | // ------------------ SHORTCUTS -------------------------------------------- | ||
+ | // ------------------------------------------------------------------------- | ||
+ | |||
+ | /** | ||
+ | * http:// | ||
+ | * Version : 2.01.B | ||
+ | * By Binny V A | ||
+ | * License : BSD | ||
+ | */ | ||
+ | shortcut = { | ||
+ | ' | ||
+ | ' | ||
+ | //Provide a set of default options | ||
+ | var default_options = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | if(!opt) opt = default_options; | ||
+ | else { | ||
+ | for(var dfo in default_options) { | ||
+ | if(typeof opt[dfo] == ' | ||
+ | } | ||
+ | } | ||
+ | |||
+ | var ele = opt.target; | ||
+ | if(typeof opt.target == ' | ||
+ | var ths = this; | ||
+ | shortcut_combination = shortcut_combination.toLowerCase(); | ||
+ | |||
+ | //The function to be called at keypress | ||
+ | var func = function(e) { | ||
+ | e = e || window.event; | ||
+ | |||
+ | if(opt[' | ||
+ | var element; | ||
+ | if(e.target) element=e.target; | ||
+ | else if(e.srcElement) element=e.srcElement; | ||
+ | if(element.nodeType==3) element=element.parentNode; | ||
+ | |||
+ | if(element.tagName == ' | ||
+ | } | ||
+ | |||
+ | //Find Which key is pressed | ||
+ | if (e.keyCode) code = e.keyCode; | ||
+ | else if (e.which) code = e.which; | ||
+ | var character = String.fromCharCode(code).toLowerCase(); | ||
+ | |||
+ | if(code == 188) character=","; | ||
+ | if(code == 190) character=" | ||
+ | |||
+ | var keys = shortcut_combination.split(" | ||
+ | //Key Pressed - counts the number of valid keypresses - if it is same as the number of keys, the shortcut function is invoked | ||
+ | var kp = 0; | ||
+ | |||
+ | //Work around for stupid Shift key bug created by using lowercase - as a result the shift+num combination was broken | ||
+ | var shift_nums = { | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | ";":":", | ||
+ | "'":" | ||
+ | ",":"<", | ||
+ | " | ||
+ | "/":"?", | ||
+ | " | ||
+ | } | ||
+ | // | ||
+ | var special_keys = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | |||
+ | var modifiers = { | ||
+ | shift: { wanted: | ||
+ | ctrl : { wanted: | ||
+ | alt | ||
+ | meta : { wanted: | ||
+ | }; | ||
+ | | ||
+ | if(e.ctrlKey) modifiers.ctrl.pressed = true; | ||
+ | if(e.shiftKey) modifiers.shift.pressed = true; | ||
+ | if(e.altKey) modifiers.alt.pressed = true; | ||
+ | if(e.metaKey) | ||
+ | | ||
+ | for(var i=0; k=keys[i], | ||
+ | // | ||
+ | if(k == ' | ||
+ | kp++; | ||
+ | modifiers.ctrl.wanted = true; | ||
+ | |||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.shift.wanted = true; | ||
+ | |||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.alt.wanted = true; | ||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.meta.wanted = true; | ||
+ | } else if(k.length > 1) { //If it is a special key | ||
+ | if(special_keys[k] == code) kp++; | ||
+ | |||
+ | } else if(opt[' | ||
+ | if(opt[' | ||
+ | |||
+ | } else { //The special keys did not match | ||
+ | if(character == k) kp++; | ||
+ | else { | ||
+ | if(shift_nums[character] && e.shiftKey) { //Stupid Shift key bug created by using lowercase | ||
+ | character = shift_nums[character]; | ||
+ | if(character == k) kp++; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | if(kp == keys.length && | ||
+ | modifiers.ctrl.pressed == modifiers.ctrl.wanted && | ||
+ | modifiers.shift.pressed == modifiers.shift.wanted && | ||
+ | modifiers.alt.pressed == modifiers.alt.wanted && | ||
+ | modifiers.meta.pressed == modifiers.meta.wanted) { | ||
+ | callback(e); | ||
+ | |||
+ | if(!opt[' | ||
+ | // | ||
+ | e.cancelBubble = true; | ||
+ | e.returnValue = false; | ||
+ | |||
+ | // | ||
+ | if (e.stopPropagation) { | ||
+ | e.stopPropagation(); | ||
+ | e.preventDefault(); | ||
+ | } | ||
+ | return false; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | this.all_shortcuts[shortcut_combination] = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | }; | ||
+ | //Attach the function with the event | ||
+ | if(ele.addEventListener) ele.addEventListener(opt[' | ||
+ | else if(ele.attachEvent) ele.attachEvent(' | ||
+ | else ele[' | ||
+ | }, | ||
+ | |||
+ | //Remove the shortcut - just specify the shortcut and I will remove the binding | ||
+ | ' | ||
+ | shortcut_combination = shortcut_combination.toLowerCase(); | ||
+ | var binding = this.all_shortcuts[shortcut_combination]; | ||
+ | delete(this.all_shortcuts[shortcut_combination]) | ||
+ | if(!binding) return; | ||
+ | var type = binding[' | ||
+ | var ele = binding[' | ||
+ | var callback = binding[' | ||
+ | |||
+ | if(ele.detachEvent) ele.detachEvent(' | ||
+ | else if(ele.removeEventListener) ele.removeEventListener(type, | ||
+ | else ele[' | ||
+ | } | ||
+ | } | ||
+ | |||
+ | shortcut.add(" | ||
+ | var event = new Event(' | ||
+ | if (settingsShown){ | ||
+ | document.getElementById(' | ||
+ | } else { | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | }); | ||
+ | |||
+ | |||
+ | // COMMON_CODE_BLOCK_END | ||
+ | |||
+ | });}); | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | The minimal and maximal faces can be visualized via | ||
+ | |||
+ | <code perl> | ||
+ | > $p-> | ||
+ | </ | ||
+ | < | ||
+ | <!-- | ||
+ | polymake for knusper | ||
+ | Thu Mar 3 00:38:23 2022 | ||
+ | c3t | ||
+ | --> | ||
+ | |||
+ | |||
+ | < | ||
+ | < | ||
+ | <meta charset=utf-8> | ||
+ | < | ||
+ | < | ||
+ | /* | ||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | */ | ||
+ | html {overflow: scroll;} | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | # | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | /* | ||
+ | // COMMON_CODE_BLOCK_END | ||
+ | */ | ||
+ | </ | ||
+ | </ | ||
+ | < | ||
+ | < | ||
+ | <div id=' | ||
+ | <div class=group id=' | ||
+ | < | ||
+ | < | ||
+ | <div class=indented>< | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | <div class=suboption> | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | </ | ||
+ | <div class=suboption> | ||
+ | <div class=indented> | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | <select id=" | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | </ | ||
+ | <img id=' | ||
+ | <img id=' | ||
+ | <div id=" | ||
+ | </ | ||
+ | < | ||
+ | requirejs.config({ | ||
+ | paths: { | ||
+ | three: '/ | ||
+ | TrackballControls: | ||
+ | OrbitControls: | ||
+ | Projector: '/ | ||
+ | SVGRenderer: | ||
+ | WEBGL: '/ | ||
+ | }, | ||
+ | shim: { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | }); | ||
+ | | ||
+ | require([' | ||
+ | window.THREE = THREE; | ||
+ | require([' | ||
+ | | ||
+ | THREE.TrackballControls = TrackballControls; | ||
+ | THREE.OrbitControls = OrbitControls; | ||
+ | THREE.Projector = Projector; | ||
+ | THREE.SVGRenderer = SVGRenderer; | ||
+ | THREE.WEBGL = WEBGL; | ||
+ | |||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | |||
+ | const intervalLength = 25; // for automatic animations | ||
+ | const explodableModel = false; | ||
+ | const modelContains = { points: false, pointlabels: | ||
+ | const foldables = []; | ||
+ | |||
+ | var three = document.getElementById(" | ||
+ | var scene = new THREE.Scene(); | ||
+ | var renderer = new THREE.WebGLRenderer( { antialias: true } ); | ||
+ | var svgRenderer = new THREE.SVGRenderer( { antialias: true } ); | ||
+ | renderer.setPixelRatio( window.devicePixelRatio ); | ||
+ | renderer.setClearColor(0xFFFFFF, | ||
+ | svgRenderer.setClearColor(0xFFFFFF, | ||
+ | three.appendChild(renderer.domElement); | ||
+ | |||
+ | var frustumSize = 4; | ||
+ | var cameras = [new THREE.PerspectiveCamera(75, | ||
+ | cameras.forEach(function(cam) { | ||
+ | cam.position.set(0, | ||
+ | cam.lookAt(0, | ||
+ | cam.up.set(0, | ||
+ | }); | ||
+ | var controls = [new THREE.TrackballControls(cameras[0], | ||
+ | var camera, control; | ||
+ | |||
+ | controls[0].zoomSpeed = 0.2; | ||
+ | controls[0].rotateSpeed = 4; | ||
+ | |||
+ | |||
+ | // class to allow move points together with labels and spheres | ||
+ | var PMPoint = function (x,y,z) { | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.addLabel = function(labelsprite) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.addSphere = function(spheremesh) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.set = function(x, | ||
+ | | ||
+ | if (this.sprite) { | ||
+ | this.sprite.position.copy(this.vector); | ||
+ | } | ||
+ | if (this.sphere) { | ||
+ | this.sphere.position.copy(this.vector); | ||
+ | } | ||
+ | } | ||
+ | PMPoint.prototype.radius = function() { | ||
+ | if (this.sphere) { | ||
+ | return this.sphere.geometry.parameters.radius; | ||
+ | } else { | ||
+ | return 0; | ||
+ | } | ||
+ | }; | ||
+ | // select the target node | ||
+ | var target = document.querySelector('# | ||
+ | |||
+ | // create an observer instance | ||
+ | var observer = new MutationObserver(function(mutations) { | ||
+ | | ||
+ | if (mutation.removedNodes && mutation.removedNodes.length > 0) { | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | }); | ||
+ | }); | ||
+ | |||
+ | // configuration of the observer: | ||
+ | var config = { childList: true, characterData: | ||
+ | |||
+ | // pass in the target node, as well as the observer options | ||
+ | while (target) { | ||
+ | if (target.className==" | ||
+ | observer.observe(target, | ||
+ | break; | ||
+ | } | ||
+ | | ||
+ | } | ||
+ | |||
+ | // COMMON_CODE_BLOCK_END | ||
+ | |||
+ | var obj0 = new THREE.Object3D(); | ||
+ | obj0.name = " | ||
+ | obj0.userData.explodable = 1; | ||
+ | obj0.userData.points = []; | ||
+ | obj0.userData.points.push(new PMPoint(0, 0, 1)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 0, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 0, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 1, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 1, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 0, 1)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 1, 1)); | ||
+ | |||
+ | obj0.userData.pointradii = 0.02; | ||
+ | < | ||
+ | obj0.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | new THREE.MeshBasicMaterial( { color: 0xFFFF00, side: THREE.DoubleSide, | ||
+ | new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | obj0.userData.pointlabels = [" | ||
+ | obj0.userData.edgeindices = [0, 2, 1, 2, 2, 3, 1, 4, 3, 4, 0, 5, 1, 5, 4, 5, 0, 6, 3, 6, 4, 6, 5, 6]; | ||
+ | < | ||
+ | obj0.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: | ||
+ | obj0.userData.facets = [[5, 4, 6], [6, 3, 2, 0], [1, 4, 5], [5, 0, 2, 1], [6, 4, 3], [3, 4, 1, 2], [5, 6, 0]]; | ||
+ | < | ||
+ | obj0.userData.facetmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, depthFunc: THREE.LessDepth, | ||
+ | new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | init_object(obj0); | ||
+ | scene.add(obj0); | ||
+ | |||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | function textSpriteMaterial(message, | ||
+ | if ( parameters === undefined ) parameters = {}; | ||
+ | var fontface = " | ||
+ | var fontsize = parameters.hasOwnProperty(" | ||
+ | fontsize = fontsize*10; | ||
+ | var lines = message.split(' | ||
+ | var size = 512; | ||
+ | for(var i = 0; i< | ||
+ | var tmp = lines[i].length; | ||
+ | while(tmp*fontsize > size){ | ||
+ | | ||
+ | } | ||
+ | } | ||
+ | | ||
+ | var canvas = document.createElement(' | ||
+ | canvas.width = size; | ||
+ | canvas.height = size; | ||
+ | var context = canvas.getContext(' | ||
+ | context.fillStyle = " | ||
+ | context.fill(); | ||
+ | context.font = fontsize + "px " + fontface; | ||
+ | | ||
+ | // text color | ||
+ | context.fillStyle = " | ||
+ | | ||
+ | context.fillText(lines[i], | ||
+ | } | ||
+ | | ||
+ | // canvas contents will be used for a texture | ||
+ | var texture = new THREE.Texture(canvas); | ||
+ | texture.needsUpdate = true; | ||
+ | | ||
+ | var spriteMaterial = new THREE.SpriteMaterial({map: | ||
+ | return spriteMaterial; | ||
+ | } | ||
+ | |||
+ | |||
+ | // ---------------------- INITIALIZING OBJECTS-------------------------------------- | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | function init_object(obj) { | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_points(obj); | ||
+ | modelContains.points = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_pointlabels(obj); | ||
+ | modelContains.pointlabels = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_lines(obj); | ||
+ | modelContains.lines = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_edgelabels(obj); | ||
+ | modelContains.edgelabels = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_arrowheads(obj); | ||
+ | modelContains.arrowheads = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_faces(obj); | ||
+ | modelContains.faces = true; | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function init_points(obj) { | ||
+ | var pointgroup = new THREE.Group(); | ||
+ | pointgroup.name = " | ||
+ | var points = obj.userData.points; | ||
+ | var radii = obj.userData.pointradii; | ||
+ | var materials = obj.userData.pointmaterial; | ||
+ | var geometry, | ||
+ | if (!Array.isArray(radii)) { | ||
+ | geometry = new THREE.SphereBufferGeometry(radii); | ||
+ | } | ||
+ | if (!Array.isArray(materials)) { | ||
+ | material = materials; | ||
+ | } | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | if (Array.isArray(radii)) { | ||
+ | if (radii[i] == 0) { | ||
+ | continue; | ||
+ | } | ||
+ | geometry = new THREE.SphereBufferGeometry(radii[i]); | ||
+ | } | ||
+ | if (Array.isArray(materials)) { | ||
+ | material = materials[i]; | ||
+ | } | ||
+ | var sphere = new THREE.Mesh(geometry, | ||
+ | point.addSphere(sphere); | ||
+ | pointgroup.add(sphere); | ||
+ | } | ||
+ | obj.add(pointgroup); | ||
+ | } | ||
+ | |||
+ | function init_pointlabels(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var labels = obj.userData.pointlabels; | ||
+ | var pointlabels = new THREE.Group(); | ||
+ | pointlabels.name = " | ||
+ | if (Array.isArray(labels)) { | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | var spriteMaterial = textSpriteMaterial( labels[i] ); | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | point.addLabel(sprite); | ||
+ | pointlabels.add(sprite); | ||
+ | } | ||
+ | } else { | ||
+ | var spriteMaterial = textSpriteMaterial( labels ); | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | point.addLabel(sprite); | ||
+ | pointlabels.add(sprite); | ||
+ | } | ||
+ | } | ||
+ | obj.add(pointlabels); | ||
+ | } | ||
+ | |||
+ | function init_lines(obj) { | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var points = obj.userData.points; | ||
+ | var materials = obj.userData.edgematerial; | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | var bufarr = new Float32Array( obj.userData.edgeindices.length * 3 ); | ||
+ | var bufattr = new THREE.Float32BufferAttribute( bufarr, 3 ); | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | geometry.setAttribute(' | ||
+ | if (Array.isArray(materials)) { | ||
+ | for (var i=0; i< | ||
+ | geometry.addGroup(2*i, | ||
+ | } | ||
+ | } | ||
+ | var lines = new THREE.LineSegments(geometry, | ||
+ | lines.name = " | ||
+ | obj.add(lines); | ||
+ | updateEdgesPosition(obj); | ||
+ | } | ||
+ | |||
+ | function init_edgelabels(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var labels = obj.userData.edgelabels; | ||
+ | var edgelabels = new THREE.Group(); | ||
+ | edgelabels.name = " | ||
+ | if (Array.isArray(labels)) { | ||
+ | for (var i=0; i< | ||
+ | var spriteMaterial = textSpriteMaterial( labels[i] ); | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector, | ||
+ | edgelabels.add(sprite); | ||
+ | } | ||
+ | } else { | ||
+ | var spriteMaterial = textSpriteMaterial( labels ); | ||
+ | for (var i=0; i< | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector, | ||
+ | edgelabels.add(sprite); | ||
+ | } | ||
+ | } | ||
+ | obj.add(edgelabels); | ||
+ | } | ||
+ | |||
+ | function init_arrowheads(obj) { | ||
+ | var arrowheads = new THREE.Group(); | ||
+ | arrowheads.name = " | ||
+ | var arrowstyle = obj.userData.arrowstyle; | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var edgematerials = obj.userData.edgematerial; | ||
+ | var points = obj.userData.points; | ||
+ | var material; | ||
+ | if (!Array.isArray(edgematerials)) { | ||
+ | material = new THREE.MeshBasicMaterial( {color: edgematerials.color} ); | ||
+ | } | ||
+ | |||
+ | for (var i=0; i< | ||
+ | var start = points[edgeindices[i]]; | ||
+ | var end = points[edgeindices[i+1]]; | ||
+ | var dist = start.vector.distanceTo( end.vector ) - start.radius() - end.radius(); | ||
+ | if (dist <= 0) { | ||
+ | continue; | ||
+ | } | ||
+ | var dir = new THREE.Vector3().subVectors(end.vector, | ||
+ | dir.normalize(); | ||
+ | var axis = new THREE.Vector3().set(dir.z, | ||
+ | axis.normalize(); | ||
+ | var radians = Math.acos( dir.y ); | ||
+ | var radius = dist/25; | ||
+ | var height = dist/5; | ||
+ | var geometry = new THREE.ConeBufferGeometry(radius, | ||
+ | var position = new THREE.Vector3().addVectors(start.vector, | ||
+ | if (Array.isArray(edgematerials)) { | ||
+ | material = new THREE.MeshBasicMaterial( {color: edgematerials[i].color} ); | ||
+ | } | ||
+ | var cone = new THREE.Mesh( geometry, material ); | ||
+ | cone.quaternion.setFromAxisAngle(axis, | ||
+ | cone.position.copy(position);; | ||
+ | arrowheads.add(cone); | ||
+ | } | ||
+ | obj.add(arrowheads); | ||
+ | } | ||
+ | |||
+ | function init_faces(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var facets = obj.userData.facets; | ||
+ | obj.userData.triangleindices = []; | ||
+ | for (var i=0; i< | ||
+ | facet = facets[i]; | ||
+ | for (var t=0; t< | ||
+ | obj.userData.triangleindices.push(facet[0], | ||
+ | } | ||
+ | } | ||
+ | var bufarr = new Float32Array( obj.userData.triangleindices.length * 3 ); | ||
+ | var bufattr = new THREE.Float32BufferAttribute(bufarr, | ||
+ | | ||
+ | var materials = obj.userData.facetmaterial; | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | var frontmaterials = []; | ||
+ | var backmaterials = []; | ||
+ | geometry.setAttribute(' | ||
+ | if (Array.isArray(materials)) { | ||
+ | var tricount = 0; | ||
+ | var facet; | ||
+ | for (var i=0; i< | ||
+ | facet = facets[i]; | ||
+ | geometry.addGroup(tricount, | ||
+ | tricount += (facet.length-2)*3; | ||
+ | } | ||
+ | for (var j=0; j< | ||
+ | var fmat = materials[j].clone() | ||
+ | fmat.side = THREE.FrontSide; | ||
+ | frontmaterials.push(fmat); | ||
+ | var bmat = materials[j].clone() | ||
+ | bmat.side = THREE.BackSide; | ||
+ | backmaterials.push(bmat); | ||
+ | obj.userData.facetmaterial = frontmaterials.concat(backmaterials); | ||
+ | } | ||
+ | } else if (materials instanceof THREE.Material) { | ||
+ | frontmaterials = materials.clone() | ||
+ | frontmaterials.side = THREE.FrontSide; | ||
+ | backmaterials = materials.clone() | ||
+ | backmaterials.side = THREE.BackSide; | ||
+ | obj.userData.facetmaterial = [frontmaterials, | ||
+ | } | ||
+ | // duplicating the object with front and back should avoid transparency issues | ||
+ | var backmesh = new THREE.Mesh(geometry, | ||
+ | // meshname is used to show/hide objects | ||
+ | backmesh.name = " | ||
+ | obj.add(backmesh); | ||
+ | var frontmesh = new THREE.Mesh(geometry, | ||
+ | frontmesh.name = " | ||
+ | obj.add(frontmesh); | ||
+ | updateFacesPosition(obj); | ||
+ | } | ||
+ | // // | ||
+ | |||
+ | |||
+ | function updateFacesPosition(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var indices = obj.userData.triangleindices; | ||
+ | var faces = obj.getObjectByName(" | ||
+ | var ba = faces.geometry.getAttribute(" | ||
+ | for (var i=0; i< | ||
+ | ba.setXYZ(i, | ||
+ | } | ||
+ | faces.geometry.attributes.position.needsUpdate = true; | ||
+ | | ||
+ | } | ||
+ | |||
+ | function updateEdgesPosition(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var indices = obj.userData.edgeindices; | ||
+ | var lines = obj.getObjectByName(" | ||
+ | var ba = lines.geometry.getAttribute(" | ||
+ | for (var i=0; i< | ||
+ | ba.setXYZ(i, | ||
+ | } | ||
+ | lines.geometry.attributes.position.needsUpdate = true; | ||
+ | } | ||
+ | |||
+ | function onWindowResize() { | ||
+ | renderer.setSize( three.clientWidth, | ||
+ | svgRenderer.setSize( three.clientWidth, | ||
+ | updateCamera(); | ||
+ | } | ||
+ | |||
+ | function updateCamera() { | ||
+ | var width = three.clientWidth; | ||
+ | var height = three.clientHeight; | ||
+ | var aspect = width / height; | ||
+ | if (camera.type == " | ||
+ | camera.left = frustumSize * aspect / - 2; | ||
+ | camera.right = frustumSize * aspect / 2; | ||
+ | camera.top = frustumSize / 2; | ||
+ | camera.bottom = - frustumSize / 2; | ||
+ | } else if (camera.type == " | ||
+ | camera.aspect = aspect; | ||
+ | } | ||
+ | camera.updateProjectionMatrix(); | ||
+ | } | ||
+ | |||
+ | function changeCamera(event) { | ||
+ | var selindex = event.currentTarget.selectedIndex; | ||
+ | camera = cameras[selindex]; | ||
+ | control = controls[selindex]; | ||
+ | control.enabled = true; | ||
+ | for (var i=0; i< | ||
+ | if (i!=selindex) { | ||
+ | controls[i].enabled = false; | ||
+ | } | ||
+ | } | ||
+ | updateCamera(); | ||
+ | } | ||
+ | |||
+ | var camtypenode = document.getElementById(' | ||
+ | camtypenode.onchange = changeCamera; | ||
+ | camtypenode.dispatchEvent(new Event(' | ||
+ | |||
+ | onWindowResize(); | ||
+ | window.addEventListener(' | ||
+ | |||
+ | |||
+ | var xRotationEnabled = false; | ||
+ | var yRotationEnabled = false; | ||
+ | var zRotationEnabled = false; | ||
+ | var rotationSpeedFactor = 1; | ||
+ | var settingsShown = false; | ||
+ | var labelsShown = true; | ||
+ | var intervals = []; | ||
+ | var timeouts = []; | ||
+ | var explodingSpeed = 0.05; | ||
+ | var explodeScale = 0.000001; | ||
+ | var XMLS = new XMLSerializer(); | ||
+ | var svgElement; | ||
+ | var renderId; | ||
+ | |||
+ | var render = function () { | ||
+ | |||
+ | renderId = requestAnimationFrame(render); | ||
+ | |||
+ | // comment in for automatic explosion | ||
+ | // | ||
+ | |||
+ | var phi = 0.02 * rotationSpeedFactor; | ||
+ | |||
+ | if (xRotationEnabled) { | ||
+ | scene.rotation.x += phi; | ||
+ | } | ||
+ | if (yRotationEnabled) { | ||
+ | scene.rotation.y += phi; | ||
+ | } | ||
+ | if (zRotationEnabled) { | ||
+ | scene.rotation.z += phi; | ||
+ | } | ||
+ | |||
+ | control.update(); | ||
+ | renderer.render(scene, | ||
+ | }; | ||
+ | |||
+ | if ( THREE.WEBGL.isWebGLAvailable() ) { | ||
+ | render(); | ||
+ | } else { | ||
+ | var warning = WEBGL.getWebGLErrorMessage(); | ||
+ | three.appendChild( warning ); | ||
+ | } | ||
+ | | ||
+ | function changeTransparency() { | ||
+ | var opacity = 1-Number(event.currentTarget.value); | ||
+ | for (var i=0; i< | ||
+ | child = scene.children[i]; | ||
+ | if ( child.userData.hasOwnProperty(" | ||
+ | if (Array.isArray(child.userData.facetmaterial)) { | ||
+ | for (var j=0; j< | ||
+ | child.userData.facetmaterial[j].opacity = opacity; | ||
+ | } | ||
+ | } else { | ||
+ | child.userData.facetmaterial.opacity = opacity; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function toggleDepthWrite(event) { | ||
+ | depthwrite = event.currentTarget.checked; | ||
+ | for (var i=0; i< | ||
+ | child = scene.children[i]; | ||
+ | if ( child.userData.hasOwnProperty(" | ||
+ | if (Array.isArray(child.userData.facetmaterial)) { | ||
+ | for (var j=0; j< | ||
+ | child.userData.facetmaterial[j].depthWrite = depthwrite; | ||
+ | } | ||
+ | } else { | ||
+ | child.userData.facetmaterial.depthWrite = depthWrite; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function changeRotationX(event){ | ||
+ | xRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | function changeRotationY(event){ | ||
+ | yRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | function changeRotationZ(event){ | ||
+ | zRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | |||
+ | function changeRotationSpeedFactor(event){ | ||
+ | rotationSpeedFactor = Number(event.currentTarget.value); | ||
+ | } | ||
+ | |||
+ | function resetScene(){ | ||
+ | scene.rotation.set(0, | ||
+ | camera.position.set(0, | ||
+ | camera.up.set(0, | ||
+ | } | ||
+ | |||
+ | function showSettings(event){ | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | settingsShown = true; | ||
+ | } | ||
+ | |||
+ | function hideSettings(event){ | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | settingsShown = false; | ||
+ | } | ||
+ | |||
+ | |||
+ | |||
+ | var pos = 150* Math.PI; | ||
+ | |||
+ | function updateFactor() { | ||
+ | pos++; | ||
+ | return Math.sin(.01*pos)+1; | ||
+ | } | ||
+ | |||
+ | // ------------------------ FOLDING ------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | // rotate point p around axis defined by points p1 and p2 by given angle | ||
+ | function rotate(p, p1, p2, angle ){ | ||
+ | angle = -angle; | ||
+ | var x = p.x, y = p.y, z = p.z, | ||
+ | a = p1.x, b = p1.y, c = p1.z, | ||
+ | u = p2.x-p1.x, v = p2.y-p1.y, w = p2.z-p1.z; | ||
+ | var result = []; | ||
+ | var L = u*u + v*v + w*w; | ||
+ | var sqrt = Math.sqrt; | ||
+ | var cos = Math.cos; | ||
+ | var sin = Math.sin; | ||
+ | |||
+ | result[0] = ((a*(v*v+w*w)-u*(b*v+c*w-u*x-v*y-w*z))*(1-cos(angle))+L*x*cos(angle)+sqrt(L)*(-c*v+b*w-w*y+v*z)*sin(angle))/ | ||
+ | result[1] = ((b*(u*u+w*w)-v*(a*u+c*w-u*x-v*y-w*z))*(1-cos(angle))+L*y*cos(angle)+sqrt(L)*(c*u-a*w+w*x-u*z)*sin(angle))/ | ||
+ | result[2] = ((c*(u*u+v*v)-w*(a*u+b*v-u*x-v*y-w*z))*(1-cos(angle))+L*z*cos(angle)+sqrt(L)*(-b*u+a*v-v*x+u*y)*sin(angle))/ | ||
+ | |||
+ | return result; | ||
+ | } | ||
+ | |||
+ | var fold = function(event){ | ||
+ | var obj = foldables[Number(event.currentTarget.name)]; | ||
+ | var foldvalue = Number(event.currentTarget.value); | ||
+ | var scale = foldvalue - obj.userData.oldscale; | ||
+ | |||
+ | for (var j=0; j< | ||
+ | rotateVertices(obj, | ||
+ | } | ||
+ | update(obj); | ||
+ | obj.userData.oldscale += scale; | ||
+ | lookAtBarycenter(obj); | ||
+ | } | ||
+ | |||
+ | function lookAtBarycenter(obj){ | ||
+ | control.target = barycenter(obj); | ||
+ | } | ||
+ | |||
+ | function barycenter(obj) { | ||
+ | var center = new THREE.Vector3(0, | ||
+ | var points = obj.userData.points; | ||
+ | for (var i=0; i< | ||
+ | center.add(points[i].vector); | ||
+ | } | ||
+ | center.divideScalar(points.length); | ||
+ | return center; | ||
+ | } | ||
+ | |||
+ | function rotateVertices(obj, | ||
+ | var axes = obj.userData.axes; | ||
+ | var subtrees = obj.userData.subtrees; | ||
+ | var points = obj.userData.points; | ||
+ | var angles = obj.userData.angles; | ||
+ | if (edge < axes.length){ | ||
+ | for (var j=0; j< | ||
+ | var rotP = rotate(points[subtrees[edge][j]].vector, | ||
+ | points[subtrees[edge][j]].set(rotP[0], | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function update(obj) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | |||
+ | if (foldables.length) { | ||
+ | var settings = document.getElementById(' | ||
+ | var foldDiv = document.createElement(' | ||
+ | foldDiv.id = ' | ||
+ | var title = document.createElement(' | ||
+ | title.innerHTML = ' | ||
+ | foldDiv.appendChild(title); | ||
+ | foldDiv.className = ' | ||
+ | for (var i=0; i< | ||
+ | var range = document.createElement(' | ||
+ | range.type = ' | ||
+ | range.min = 0; | ||
+ | range.max = 1; | ||
+ | range.value = 0; | ||
+ | range.step = 0.001; | ||
+ | range.name = String(i); | ||
+ | range.oninput = fold; | ||
+ | foldDiv.appendChild(range); | ||
+ | } | ||
+ | lookAtBarycenter(foldables[0]); | ||
+ | settings.insertBefore(foldDiv, | ||
+ | } | ||
+ | |||
+ | | ||
+ | // ---------------------- EXPLOSION ------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | if (explodableModel) { | ||
+ | for (var i=0; i< | ||
+ | obj = scene.children[i]; | ||
+ | if ( obj.userData.explodable ) { | ||
+ | computeCentroid(obj); | ||
+ | } | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | explode(0.000001); | ||
+ | } | ||
+ | |||
+ | function computeCentroid(obj) { | ||
+ | centroid = new THREE.Vector3(); | ||
+ | obj.userData.points.forEach(function(pmpoint) { | ||
+ | centroid.add(pmpoint.vector); | ||
+ | }); | ||
+ | centroid.divideScalar(obj.userData.points.length); | ||
+ | obj.userData.centroid = centroid; | ||
+ | } | ||
+ | |||
+ | function explode(factor) { | ||
+ | for (var i=0; i< | ||
+ | var obj = scene.children[i]; | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | var c = obj.userData.centroid; | ||
+ | obj.position.set(c.x*factor, | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function triggerExplode(event){ | ||
+ | explodeScale = Number(event.currentTarget.value); | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | |||
+ | function setExplodingSpeed(event){ | ||
+ | explodingSpeed = Number(event.currentTarget.value); | ||
+ | } | ||
+ | |||
+ | function triggerAutomaticExplode(event){ | ||
+ | if (event.currentTarget.checked){ | ||
+ | startExploding(); | ||
+ | } else { | ||
+ | clearIntervals(); | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function startExploding(){ | ||
+ | intervals.push(setInterval(explodingInterval, | ||
+ | } | ||
+ | |||
+ | |||
+ | function explodingInterval(){ | ||
+ | explodeScale += explodingSpeed; | ||
+ | if (explodeScale <= 6){ | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | else{ | ||
+ | explode(6); | ||
+ | explodeScale = 6; | ||
+ | clearIntervals(); | ||
+ | timeouts.push(setTimeout(startUnexploding, | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | |||
+ | |||
+ | function startUnexploding(){ | ||
+ | intervals.push(setInterval(unexplodingInterval, | ||
+ | } | ||
+ | |||
+ | function unexplodingInterval(){ | ||
+ | explodeScale -= explodingSpeed; | ||
+ | if (explodeScale >= 0){ | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | else { | ||
+ | explode(0); | ||
+ | explodeScale = 0; | ||
+ | clearIntervals(); | ||
+ | timeouts.push(setTimeout(startExploding, | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | |||
+ | function clearIntervals(){ | ||
+ | intervals.forEach(function(interval){ | ||
+ | clearInterval(interval); | ||
+ | }); | ||
+ | intervals = []; | ||
+ | timeouts.forEach(function(timeout){ | ||
+ | clearTimeout(timeout); | ||
+ | }); | ||
+ | timeouts = []; | ||
+ | } | ||
+ | |||
+ | // ---------------------- DISPLAY -------------------------------------------------- | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | const objectTypeInnerHTMLs = { points: " | ||
+ | const objectTypeVisible = {}; | ||
+ | Object.assign(objectTypeVisible, | ||
+ | const sortedObjectTypeKeys = Object.keys(objectTypeInnerHTMLs).sort(); | ||
+ | const shownObjectTypesList = document.getElementById(' | ||
+ | |||
+ | function setVisibility(bool, | ||
+ | for (var i=0; i< | ||
+ | var obj = scene.children[i].getObjectByName(objname); | ||
+ | if (obj) { | ||
+ | obj.visible = bool; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function toggleObjectTypeVisibility(event){ | ||
+ | var name = event.currentTarget.name; | ||
+ | var checked = event.currentTarget.checked; | ||
+ | objectTypeVisible[name] = checked; | ||
+ | if (name == " | ||
+ | setVisibility(checked," | ||
+ | setVisibility(checked," | ||
+ | } else { | ||
+ | setVisibility(checked, | ||
+ | } | ||
+ | } | ||
+ | |||
+ | for (var i=0; i< | ||
+ | var key = sortedObjectTypeKeys[i]; | ||
+ | if (modelContains[key]) { | ||
+ | var objTypeNode = document.createElement(' | ||
+ | objTypeNode.innerHTML = objectTypeInnerHTMLs[key] + '< | ||
+ | var checkbox = document.createElement(' | ||
+ | checkbox.type = ' | ||
+ | checkbox.checked = true; | ||
+ | checkbox.name = key; | ||
+ | checkbox.onchange = toggleObjectTypeVisibility; | ||
+ | shownObjectTypesList.appendChild(checkbox); | ||
+ | shownObjectTypesList.appendChild(objTypeNode); | ||
+ | } | ||
+ | } | ||
+ | |||
+ | // ------------------------------------------------------ | ||
+ | |||
+ | function toggleObjectVisibility(event){ | ||
+ | var nr = Number(event.currentTarget.name); | ||
+ | scene.children[nr].visible = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | // append checkboxes for displaying or hiding objects | ||
+ | var shownObjectsList = document.getElementById(' | ||
+ | for (var i=0; i< | ||
+ | obj = scene.children[i]; | ||
+ | var objNode = document.createElement(' | ||
+ | objNode.innerHTML = obj.name + '< | ||
+ | var checkbox = document.createElement(' | ||
+ | checkbox.type = ' | ||
+ | checkbox.checked = true; | ||
+ | checkbox.name = String(i); | ||
+ | checkbox.onchange = toggleObjectVisibility; | ||
+ | shownObjectsList.appendChild(checkbox); | ||
+ | shownObjectsList.appendChild(objNode); | ||
+ | } | ||
+ | |||
+ | // ---------------------- SVG ------------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | function takeSvgScreenshot() { | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(false," | ||
+ | } | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(false," | ||
+ | } | ||
+ | svgRenderer.render(scene, | ||
+ | svgElement = XMLS.serializeToString(svgRenderer.domElement); | ||
+ | | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(true," | ||
+ | } | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(true," | ||
+ | } | ||
+ | |||
+ | if (document.getElementById(' | ||
+ | //show in new tab | ||
+ | var myWindow = window.open("","" | ||
+ | myWindow.document.body.innerHTML = svgElement; | ||
+ | } else{ | ||
+ | // download svg file | ||
+ | download(" | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function download(filename, | ||
+ | var element = document.createElement(' | ||
+ | element.setAttribute(' | ||
+ | element.setAttribute(' | ||
+ | |||
+ | element.style.display = ' | ||
+ | document.body.appendChild(element); | ||
+ | |||
+ | element.click(); | ||
+ | |||
+ | document.body.removeChild(element); | ||
+ | } | ||
+ | |||
+ | |||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | |||
+ | |||
+ | // ------------------ SHORTCUTS -------------------------------------------- | ||
+ | // ------------------------------------------------------------------------- | ||
+ | |||
+ | /** | ||
+ | * http:// | ||
+ | * Version : 2.01.B | ||
+ | * By Binny V A | ||
+ | * License : BSD | ||
+ | */ | ||
+ | shortcut = { | ||
+ | ' | ||
+ | ' | ||
+ | //Provide a set of default options | ||
+ | var default_options = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | if(!opt) opt = default_options; | ||
+ | else { | ||
+ | for(var dfo in default_options) { | ||
+ | if(typeof opt[dfo] == ' | ||
+ | } | ||
+ | } | ||
+ | |||
+ | var ele = opt.target; | ||
+ | if(typeof opt.target == ' | ||
+ | var ths = this; | ||
+ | shortcut_combination = shortcut_combination.toLowerCase(); | ||
+ | |||
+ | //The function to be called at keypress | ||
+ | var func = function(e) { | ||
+ | e = e || window.event; | ||
+ | |||
+ | if(opt[' | ||
+ | var element; | ||
+ | if(e.target) element=e.target; | ||
+ | else if(e.srcElement) element=e.srcElement; | ||
+ | if(element.nodeType==3) element=element.parentNode; | ||
+ | |||
+ | if(element.tagName == ' | ||
+ | } | ||
+ | |||
+ | //Find Which key is pressed | ||
+ | if (e.keyCode) code = e.keyCode; | ||
+ | else if (e.which) code = e.which; | ||
+ | var character = String.fromCharCode(code).toLowerCase(); | ||
+ | |||
+ | if(code == 188) character=","; | ||
+ | if(code == 190) character=" | ||
+ | |||
+ | var keys = shortcut_combination.split(" | ||
+ | //Key Pressed - counts the number of valid keypresses - if it is same as the number of keys, the shortcut function is invoked | ||
+ | var kp = 0; | ||
+ | |||
+ | //Work around for stupid Shift key bug created by using lowercase - as a result the shift+num combination was broken | ||
+ | var shift_nums = { | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | ";":":", | ||
+ | "'":" | ||
+ | ",":"<", | ||
+ | " | ||
+ | "/":"?", | ||
+ | " | ||
+ | } | ||
+ | // | ||
+ | var special_keys = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | |||
+ | var modifiers = { | ||
+ | shift: { wanted: | ||
+ | ctrl : { wanted: | ||
+ | alt | ||
+ | meta : { wanted: | ||
+ | }; | ||
+ | | ||
+ | if(e.ctrlKey) modifiers.ctrl.pressed = true; | ||
+ | if(e.shiftKey) modifiers.shift.pressed = true; | ||
+ | if(e.altKey) modifiers.alt.pressed = true; | ||
+ | if(e.metaKey) | ||
+ | | ||
+ | for(var i=0; k=keys[i], | ||
+ | // | ||
+ | if(k == ' | ||
+ | kp++; | ||
+ | modifiers.ctrl.wanted = true; | ||
+ | |||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.shift.wanted = true; | ||
+ | |||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.alt.wanted = true; | ||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.meta.wanted = true; | ||
+ | } else if(k.length > 1) { //If it is a special key | ||
+ | if(special_keys[k] == code) kp++; | ||
+ | |||
+ | } else if(opt[' | ||
+ | if(opt[' | ||
+ | |||
+ | } else { //The special keys did not match | ||
+ | if(character == k) kp++; | ||
+ | else { | ||
+ | if(shift_nums[character] && e.shiftKey) { //Stupid Shift key bug created by using lowercase | ||
+ | character = shift_nums[character]; | ||
+ | if(character == k) kp++; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | if(kp == keys.length && | ||
+ | modifiers.ctrl.pressed == modifiers.ctrl.wanted && | ||
+ | modifiers.shift.pressed == modifiers.shift.wanted && | ||
+ | modifiers.alt.pressed == modifiers.alt.wanted && | ||
+ | modifiers.meta.pressed == modifiers.meta.wanted) { | ||
+ | callback(e); | ||
+ | |||
+ | if(!opt[' | ||
+ | // | ||
+ | e.cancelBubble = true; | ||
+ | e.returnValue = false; | ||
+ | |||
+ | // | ||
+ | if (e.stopPropagation) { | ||
+ | e.stopPropagation(); | ||
+ | e.preventDefault(); | ||
+ | } | ||
+ | return false; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | this.all_shortcuts[shortcut_combination] = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | }; | ||
+ | //Attach the function with the event | ||
+ | if(ele.addEventListener) ele.addEventListener(opt[' | ||
+ | else if(ele.attachEvent) ele.attachEvent(' | ||
+ | else ele[' | ||
+ | }, | ||
+ | |||
+ | //Remove the shortcut - just specify the shortcut and I will remove the binding | ||
+ | ' | ||
+ | shortcut_combination = shortcut_combination.toLowerCase(); | ||
+ | var binding = this.all_shortcuts[shortcut_combination]; | ||
+ | delete(this.all_shortcuts[shortcut_combination]) | ||
+ | if(!binding) return; | ||
+ | var type = binding[' | ||
+ | var ele = binding[' | ||
+ | var callback = binding[' | ||
+ | |||
+ | if(ele.detachEvent) ele.detachEvent(' | ||
+ | else if(ele.removeEventListener) ele.removeEventListener(type, | ||
+ | else ele[' | ||
+ | } | ||
+ | } | ||
+ | |||
+ | shortcut.add(" | ||
+ | var event = new Event(' | ||
+ | if (settingsShown){ | ||
+ | document.getElementById(' | ||
+ | } else { | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | }); | ||
+ | |||
+ | |||
+ | // COMMON_CODE_BLOCK_END | ||
+ | |||
+ | });}); | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | ===== Computing Facets ===== | ||
+ | |||
+ | An important action that is often needed to come up with new facet describing inequalities for combinatorial optimization problems is the computation of convex hulls for small examples. | ||
+ | |||
+ | ==== Pure Integer Case ==== | ||
+ | |||
+ | We begin with the case in which all variables are required to be integral, i.e., the //pure integer case//. Moreover, the approach depends on whether the polyhedron is bounded or not. | ||
+ | |||
+ | === Bounded Polyhedra === | ||
+ | |||
+ | Let us illustrate the approach via the example of the //stable set problem//: Here one is given an (undirected) Graph G = (V,E) with node set V and edges E. The goal is to find a largest subset of nodes V' such that any two nodes in V' are not connected by an edge. | ||
+ | |||
+ | For our example consider the 5-cycle, i.e., the graph C< | ||
+ | |||
+ | < | ||
+ | Maximize | ||
+ | obj: x#1 + x#2 + x#3 + x#4 + x#5 | ||
+ | Subject to | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | Bounds | ||
+ | 0 <= x#1 <= 1 | ||
+ | 0 <= x#2 <= 1 | ||
+ | 0 <= x#3 <= 1 | ||
+ | 0 <= x#4 <= 1 | ||
+ | 0 <= x#5 <= 1 | ||
+ | General | ||
+ | x#1 x#2 x#3 x#4 x#5 | ||
+ | End | ||
+ | </ | ||
+ | Here, '' | ||
+ | |||
+ | We assume that the above information is contained in the file '' | ||
+ | |||
+ | <code perl> | ||
+ | > $f=lp2poly(' | ||
+ | > $p = new Polytope< | ||
+ | </ | ||
+ | We are now interested in all feasible solutions to the above problem, i.e., all assignments of 0 or 1 to the variables such that the above inequalities are satisfied. These feasible points can be computed via: | ||
+ | |||
+ | <code perl> | ||
+ | > $p-> | ||
+ | </ | ||
+ | To understand these points and make computational use of this information, | ||
+ | |||
+ | <code perl> | ||
+ | > $s=new Polytope(POINTS=> | ||
+ | </ | ||
+ | Here, the coordinate labels, i.e., the variable names, are copied to the new polytope. | ||
+ | |||
+ | Now, the facets of the new polytope can be computed and listed via: | ||
+ | |||
+ | <code perl> | ||
+ | > print_constraints($s); | ||
+ | Facets: | ||
+ | 0: x#3 >= 0 | ||
+ | 1: -x#4 - x#5 >= -1 | ||
+ | 2: x#1 >= 0 | ||
+ | 3: -x#2 - x#3 >= -1 | ||
+ | 4: -x#1 - x#2 - x#3 - x#4 - x#5 >= -2 | ||
+ | 5: -x#1 - x#2 >= -1 | ||
+ | 6: x#4 >= 0 | ||
+ | 7: -x#1 - x#5 >= -1 | ||
+ | 8: -x#3 - x#4 >= -1 | ||
+ | 9: x#2 >= 0 | ||
+ | 10: x#5 >= 0 | ||
+ | |||
+ | </ | ||
+ | The facet defining inequalities can be interpreted as follows: | ||
+ | |||
+ | * There are five trivial inequalities '' | ||
+ | * The five original ' | ||
+ | * We have the so-called //odd-cycle inequality// | ||
+ | |||
+ | Of course, one can also use the usual polymake output, e.g., '' | ||
+ | |||
+ | This example showed one of the routine actions often performed by discrete optimizers. Of course, this action can also be performed by a script, which makes the computation a one-line command. | ||
+ | |||
+ | Note that the size of instances that can be handled will probably be small. Usually, things become difficult from dimension 15 on, but it depends on the particular structure of your instances, i.e., on the number of facets and lattice points. | ||
+ | |||
+ | === Unbounded Polyhedra === | ||
+ | |||
+ | If the underlying polyhedron is unbounded, the approach above does not work anymore, since there are infinitely many lattice points. Arguably, this case occurs less often than the bounded case, but it is a excellent show-case for polymake' | ||
+ | |||
+ | The following mathematical insights are important to treat the unbounded case. First, we have to assume that the data, i.e., the inequality description of the polyhedron '' | ||
+ | |||
+ | To illustrate the construction, | ||
+ | |||
+ | < | ||
+ | Minimize | ||
+ | | ||
+ | Subject to | ||
+ | C1: x1 + x2 >= 0.5 | ||
+ | C2: x1 - 2 x2 <= 1.5 | ||
+ | C3: x2 - 2 x1 <= 1.5 | ||
+ | General | ||
+ | x1 x2 | ||
+ | End | ||
+ | </ | ||
+ | < | ||
+ | |||
+ | We now assume that the example is contained in the file '' | ||
+ | |||
+ | <code perl> | ||
+ | > $f = lp2poly(' | ||
+ | > $pin = new Polytope< | ||
+ | </ | ||
+ | The visualization in the picture can be generated with '' | ||
+ | |||
+ | We now extract the rays of the recession cone | ||
+ | |||
+ | <code perl> | ||
+ | > $rays = $pin-> | ||
+ | </ | ||
+ | This command first computes all vertices of the polyhedron (this includes unbounded vertices); note that is involves a convex hull computation. The set '' | ||
+ | |||
+ | <code perl> | ||
+ | > print $rays; | ||
+ | 0 1 1/2 | ||
+ | 0 1 2 | ||
+ | </ | ||
+ | Thus, there are two rays that are generators of the recession cone. | ||
+ | |||
+ | We now have to construct the Minkowski hull of all intervals '' | ||
+ | |||
+ | <code perl> | ||
+ | > $zero = unit_vector< | ||
+ | > $B = new Polytope< | ||
+ | > foreach my $r (@$rays) | ||
+ | > { | ||
+ | > $M = new Matrix< | ||
+ | > | ||
+ | > $M = $M / $zero; | ||
+ | > | ||
+ | > $B = minkowski_sum($B, | ||
+ | > } | ||
+ | </ | ||
+ | The code first generates a polytope '' | ||
+ | |||
+ | The next step is to obtain the bounded part '' | ||
+ | |||
+ | <code perl> | ||
+ | > $Qpoints = $pin-> | ||
+ | > $Q = new Polytope< | ||
+ | </ | ||
+ | The two polytopes are now combined: | ||
+ | |||
+ | <code perl> | ||
+ | > $p = minkowski_sum($Q, | ||
+ | </ | ||
+ | We now generate the lattice points (as in the bounded part) and add the rays from above: | ||
+ | |||
+ | <code perl> | ||
+ | > $latticemat = new Matrix< | ||
+ | > $newpoints = new Matrix< | ||
+ | </ | ||
+ | Here, '' | ||
+ | |||
+ | Finally, the polytope we are interested in is: | ||
+ | |||
+ | <code perl> | ||
+ | > $q = new Polytope(POINTS=> | ||
+ | </ | ||
+ | The facets can be viewed as usual: | ||
+ | |||
+ | <code perl> | ||
+ | > print_constraints($q); | ||
+ | Facets: | ||
+ | 0: 2 x1 - x2 >= -1 | ||
+ | 1: 0 >= -1 | ||
+ | 2: -x1 + 2 x2 >= -1 | ||
+ | 3: x1 + x2 >= 1 | ||
+ | |||
+ | </ | ||
+ | < | ||
+ | |||
+ | Note that the upper right part (including the red vertices) arises from truncation of the polyhedron for visualization. | ||
+ | |||
+ | ==== Mixed-Integer Case ==== | ||
+ | |||
+ | Let us now briefly discuss how to proceed if there are variables that are allowed to be integral. In this case there are several different types of information that one might be interested in. Let us first consider the question of how to compute the convex hull of all feasible integral variables, i.e., we consider the projection to the integral variables and then consider the convex hull of all feasible solutions. We only consider the bounded case, i.e., the original polyhedron is bounded. | ||
+ | |||
+ | Consider the following example: | ||
+ | |||
+ | < | ||
+ | Minimize | ||
+ | | ||
+ | Subject to | ||
+ | C1: s1 - 10 x1 <= 0 | ||
+ | C2: s2 - 10 x2 <= 0 | ||
+ | C3: s1 + s2 <= 1.5 | ||
+ | C4: s1 + s2 >= 0.5 | ||
+ | Bounds | ||
+ | 0 <= s1 | ||
+ | 0 <= s2 | ||
+ | 0 <= x1 <= 1 | ||
+ | 0 <= x2 <= 1 | ||
+ | General | ||
+ | x1 x2 | ||
+ | End | ||
+ | </ | ||
+ | In this example there are two integral variables '' | ||
+ | |||
+ | <code perl> | ||
+ | > $m=lp2poly(' | ||
+ | > $p = new Polytope< | ||
+ | </ | ||
+ | We project the polyhedron in '' | ||
+ | |||
+ | <code perl> | ||
+ | > $q=projection($p, | ||
+ | </ | ||
+ | We now construct the convex hull of all feasible points as above: | ||
+ | |||
+ | <code perl> | ||
+ | > $s=new Polytope(POINTS=> | ||
+ | > print_constraints($s); | ||
+ | Facets: | ||
+ | 0: -x1 >= -1 | ||
+ | 1: -x2 >= -1 | ||
+ | 2: x1 + x2 >= 1 | ||
+ | |||
+ | </ | ||
+ | Thus, as expected, the convex hull equals the triangle with vertices '' | ||
+ | |||
+ | ===== Integral Polytopes and Total Unimodularity ===== | ||
+ | |||
+ | As explained in the previous example, the integral points in a polytope are of particular interest in discrete optimization. These points are called //lattice points// in polymake and the corresponding convex hull //lattice polytope//. The handling of such polytopes is explained in more detail in the [[lattice_polytopes_tutorial|Tutorial for Lattice Polytopes]]. | ||
+ | |||
+ | Of particular interest for discrete optimization are properties of the original inequality system to define a lattice polytope, i.e., a polytope such that all of its vertices are integral (this can be tested by checking the property '' | ||
+ | |||
+ | Using the polymake extension [[https:// | ||
+ | |||
+ | ==== Example: Explicit Matrix ==== | ||
+ | |||
+ | In a first example, we directly create an integral matrix | ||
+ | |||
+ | <code perl> | ||
+ | > $M=new Matrix< | ||
+ | </ | ||
+ | The total unimodularity of this matrix can be checked as follows: | ||
+ | |||
+ | <code perl> | ||
+ | > print totally_unimodular($M); | ||
+ | true | ||
+ | </ | ||
+ | Thus, the given matrix is totally unimodular. | ||
+ | |||
+ | ==== Example: Matrix from Input ==== | ||
+ | |||
+ | In the second example, we reuse the file '' | ||
+ | |||
+ | <code perl> | ||
+ | > $f=lp2poly(' | ||
+ | > $p = new Polytope< | ||
+ | </ | ||
+ | We now want to check whether the constraint matrix defined by the inequalities is totally unimodular (note that there are no equations in this example). Thus we first extract the inequality matrix without the first column (as an integer matrix) and then perform the test: | ||
+ | |||
+ | <code perl> | ||
+ | > $A = new Matrix< | ||
+ | > print totally_unimodular($A); | ||
+ | true | ||
+ | </ | ||
+ | Thus, this matrix is totally unimodular as well. | ||
+ | |||
+ | ===== Total dual integrality ===== | ||
+ | |||
+ | Computations with respect to total dual integrality (TDI) can also be performed in polymake. Currently (August 2013), you need the perpetual beta version of polymake to access this functionality. | ||
+ | |||
+ | The main functions are: | ||
+ | |||
+ | * The function '' | ||
+ | * The function '' | ||
+ | |||
+ | Note that the input has to be full-dimensional in order to use these functions. | ||
+ | |||
+ | To demonstrate the behavior of these functions, consider the 5-cycle example from above again: | ||
+ | |||
+ | < | ||
+ | Maximize | ||
+ | obj: x#1 + x#2 + x#3 + x#4 + x#5 | ||
+ | Subject to | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | Bounds | ||
+ | 0 <= x#1 <= 1 | ||
+ | 0 <= x#2 <= 1 | ||
+ | 0 <= x#3 <= 1 | ||
+ | 0 <= x#4 <= 1 | ||
+ | 0 <= x#5 <= 1 | ||
+ | General | ||
+ | x#1 x#2 x#3 x#4 x#5 | ||
+ | End | ||
+ | </ | ||
+ | Let us test whether the inequality system of this example is TDI. Thus, we first load the data as usual: | ||
+ | |||
+ | <code perl> | ||
+ | > $f = lp2poly(' | ||
+ | > $p = new Polytope< | ||
+ | </ | ||
+ | We now extract the corresponding inequality system and check it for TDIness: | ||
+ | |||
+ | <code perl> | ||
+ | > $M = new Matrix< | ||
+ | > print totally_dual_integral($M); | ||
+ | false | ||
+ | </ | ||
+ | The system is not TDI, which we expected from general theory, since we know that the polytope is not integral, but the system has integral coefficients. Consequently, | ||
+ | |||
+ | <code perl> | ||
+ | > $q = make_totally_dual_integral($p); | ||
+ | > print_constraints($q); | ||
+ | Inequalities: | ||
+ | 0: x5 >= 0 | ||
+ | 1: x4 >= 0 | ||
+ | 2: x3 >= 0 | ||
+ | 3: x2 >= 0 | ||
+ | 4: x1 >= 0 | ||
+ | 5: -x1 - x2 >= -1 | ||
+ | 6: -x1 - x5 >= -1 | ||
+ | 7: -x2 - x3 >= -1 | ||
+ | 8: -x3 - x4 >= -1 | ||
+ | 9: -x4 - x5 >= -1 | ||
+ | 10: -x1 - x2 - x3 - x4 - x5 >= -5/2 | ||
+ | 11: 0 >= -1 | ||
+ | |||
+ | </ | ||
+ | As expected, the right hand side is non integral (otherwise, we know from general theory that the polytope would be integral as well). The result is now TDI: | ||
+ | |||
+ | <code perl> | ||
+ | > $N = new Matrix< | ||
+ | > print totally_dual_integral($N); | ||
+ | true | ||
+ | </ | ||
+ | //Note// that we need to take the inequalities instead of facets here, since facets are irredundant and thus might not be TDI, although the complete set of inequalities is TDI. | ||
+ | |||
+ | ===== Chvátal-Gomory Closure ===== | ||
+ | |||
+ | In the following we want to briefly show how closures of polytopes with respect to certain cutting-plane operators can be computed. We consider the two well-known cutting-plane operators here. The first one is the Chvátal-Gomory generator and the second one is the Lift-and-project operator as defined by Balas. For simplicity we will assume that the considered polytope is full-dimensional. | ||
+ | |||
+ | ==== Chvátal-Gomory Closure - Example 1 ==== | ||
+ | |||
+ | We first consider the polytope from the stable set problem from above: | ||
+ | |||
+ | < | ||
+ | Maximize | ||
+ | obj: x#1 + x#2 + x#3 + x#4 + x#5 | ||
+ | Subject to | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | Bounds | ||
+ | 0 <= x#1 <= 1 | ||
+ | 0 <= x#2 <= 1 | ||
+ | 0 <= x#3 <= 1 | ||
+ | 0 <= x#4 <= 1 | ||
+ | 0 <= x#5 <= 1 | ||
+ | General | ||
+ | x#1 x#2 x#3 x#4 x#5 | ||
+ | End | ||
+ | </ | ||
+ | As before we read in the file using '' | ||
+ | |||
+ | <code perl> | ||
+ | > $f = lp2poly(' | ||
+ | > $p = new Polytope< | ||
+ | </ | ||
+ | The Chvátal-Gomory closure of a polytope can be computed with the function '' | ||
+ | |||
+ | <code perl> | ||
+ | > $g = gc_closure($p); | ||
+ | > print print_constraints($g); | ||
+ | Inequalities: | ||
+ | 0: x5 >= 0 | ||
+ | 1: x4 >= 0 | ||
+ | 2: x3 >= 0 | ||
+ | 3: x2 >= 0 | ||
+ | 4: x1 >= 0 | ||
+ | 5: -x1 - x2 >= -1 | ||
+ | 6: -x1 - x5 >= -1 | ||
+ | 7: -x2 - x3 >= -1 | ||
+ | 8: -x3 - x4 >= -1 | ||
+ | 9: -x4 - x5 >= -1 | ||
+ | 10: -x1 - x2 - x3 - x4 - x5 >= -2 | ||
+ | 11: 0 >= -1 | ||
+ | |||
+ | </ | ||
+ | Let us check whether the resulting polytope is integral: | ||
+ | |||
+ | <code perl> | ||
+ | > print $g-> | ||
+ | true | ||
+ | </ | ||
+ | Thus, in this case, we have obtained the integer hull by one step of the Chvatal-Gomory-closure. | ||
+ | |||
+ | ==== Chvátal-Gomory Closure - Example 2 ==== | ||
+ | |||
+ | Let us now consider the classical example of a polytope with the vertices of simplex in d dimensions and the point 1/2 times (1, ..., 1). It can be shown that such a polytope has rank at least log(d) - 1, see [[http:// | ||
+ | |||
+ | <code perl> | ||
+ | > $M = new Matrix< | ||
+ | > $t = new Polytope< | ||
+ | > $t1 = gc_closure($t); | ||
+ | > $t1-> | ||
+ | > print_constraints($t1); | ||
+ | Facets: | ||
+ | 0: x4 >= 0 | ||
+ | 1: x3 >= 0 | ||
+ | 2: x2 >= 0 | ||
+ | 3: x1 >= 0 | ||
+ | 4: -x1 - x2 - x3 >= -1 | ||
+ | 5: -x1 - x2 - x4 >= -1 | ||
+ | 6: -x1 - x3 - x4 >= -1 | ||
+ | 7: -x2 - x3 - x4 >= -1 | ||
+ | |||
+ | > print $t1-> | ||
+ | false | ||
+ | </ | ||
+ | Thus, one round was not enough to produce an integral polytope. Indeed, the vertices are | ||
+ | |||
+ | <code perl> | ||
+ | > $t1-> | ||
+ | > print $t1-> | ||
+ | 1 1 0 0 0 | ||
+ | 1 0 0 0 0 | ||
+ | 1 1/3 1/3 1/3 1/3 | ||
+ | 1 0 1 0 0 | ||
+ | 1 0 0 1 0 | ||
+ | 1 0 0 0 1 | ||
+ | </ | ||
+ | However, one more round is enough: | ||
+ | |||
+ | <code perl> | ||
+ | > $t2 = gc_closure($t1); | ||
+ | > $t2-> | ||
+ | > print_constraints($t2); | ||
+ | Facets: | ||
+ | 0: x4 >= 0 | ||
+ | 1: x3 >= 0 | ||
+ | 2: x2 >= 0 | ||
+ | 3: x1 >= 0 | ||
+ | 4: -x1 - x2 - x3 - x4 >= -1 | ||
+ | |||
+ | > print $t2-> | ||
+ | true | ||
+ | </ | ||
+ | ===== Lift-and-project closure ===== | ||
+ | |||
+ | The lift-and-project closure of a 0/ | ||
+ | |||
+ | <code perl> | ||
+ | use application " | ||
+ | |||
+ | sub lpclosure | ||
+ | { | ||
+ | my $p = shift; | ||
+ | my $d = $p-> | ||
+ | my $q = new Polytope< | ||
+ | for (my $k = 0; $k < $d; $k = $k+1) | ||
+ | { | ||
+ | if ( $q->DIM == -1 ) # can stop as soon as $q is empty | ||
+ | { | ||
+ | | ||
+ | } | ||
+ | | ||
+ | # create reversed opposite inequalities of 0/1-cube and corresponding polyhedra | ||
+ | my $v1 = new Vector< | ||
+ | my $v2 = new Vector< | ||
+ | | ||
+ | # create intersection of corresponding polyhedra with iterated polyhedron $q | ||
+ | my $b1 = new Polytope< | ||
+ | my $b2 = new Polytope< | ||
+ | | ||
+ | if ( ($b1-> | ||
+ | { | ||
+ | my $c = conv($b1, $b2); | ||
+ | $q = intersection($q, | ||
+ | } | ||
+ | elsif ( ($b1-> | ||
+ | { | ||
+ | $q = intersection($q, | ||
+ | } | ||
+ | elsif ( ($b1-> | ||
+ | { | ||
+ | $q = intersection($q, | ||
+ | } | ||
+ | } | ||
+ | return $q; | ||
+ | } | ||
+ | > script(" | ||
+ | </ | ||
+ | ==== Lift-and-Project Closure - Example 1 ==== | ||
+ | |||
+ | For our well known stable set example, we get the following: | ||
+ | |||
+ | <code perl> | ||
+ | > $q = lpclosure($p); | ||
+ | > $q-> | ||
+ | > print_constraints($q); | ||
+ | Facets: | ||
+ | 0: -x1 - x2 >= -1 | ||
+ | 1: x3 >= 0 | ||
+ | 2: x2 >= 0 | ||
+ | 3: x4 >= 0 | ||
+ | 4: -x3 - x4 >= -1 | ||
+ | 5: -x4 - x5 >= -1 | ||
+ | 6: x1 >= 0 | ||
+ | 7: -x2 - x3 >= -1 | ||
+ | 8: -x1 - x2 - x3 - x4 - x5 >= -2 | ||
+ | 9: -x1 - x5 >= -1 | ||
+ | 10: x5 >= 0 | ||
+ | |||
+ | </ | ||
+ | Thus, the lift-and-project closure in this case gives the integral hull (as we have seen above). | ||
+ | |||
+ | ==== Lift-and-Project Closure - Example 2 ==== | ||
+ | |||
+ | Let us now consider the same example as for CG-closures: | ||
+ | |||
+ | <code perl> | ||
+ | > $M = new Matrix< | ||
+ | > $p = new Polytope< | ||
+ | > $q = lpclosure($p); | ||
+ | > $q-> | ||
+ | > print_constraints($q); | ||
+ | Facets: | ||
+ | 0: x1 >= 0 | ||
+ | 1: x4 >= 0 | ||
+ | 2: -x1 - x2 - x3 - x4 >= -1 | ||
+ | 3: x2 >= 0 | ||
+ | 4: x3 >= 0 | ||
+ | |||
+ | </ | ||
+ | Thus, we have obtained the integral hull in a single step of the lift-and-project closure as opposed to two steps in the CG-closure. | ||
+ | |||
+ | ==== Alternative Input: mps2poly ==== | ||
+ | |||
+ | Another input format that '' | ||
+ | |||
+ | < | ||
+ | Name 0/1-cube | ||
+ | Rows | ||
+ | | ||
+ | | ||
+ | COLUMNS | ||
+ | x1 C0000000 | ||
+ | x2 C0000000 | ||
+ | x3 C0000000 | ||
+ | RHS | ||
+ | B | ||
+ | BOUNDS | ||
+ | LO BND | ||
+ | UP BND | ||
+ | LO BND | ||
+ | UP BND | ||
+ | LO BND | ||
+ | UP BND | ||
+ | ENDDATA | ||
+ | </ | ||
+ | This is again a description of the same 0/1-Cube like above.\\ | ||
+ | If the example is contained in the file '' | ||
+ | |||
+ | <code perl> | ||
+ | > $p = mps2poly(' | ||
+ | </ | ||
+ | It gives use the same polytope with the same linear program as above. | ||
+ | |||
+ | <code perl> | ||
+ | > print $p-> | ||
+ | </ | ||
+ | < | ||
+ | <!-- | ||
+ | polymake for knusper | ||
+ | Thu Mar 3 00:38:29 2022 | ||
+ | p | ||
+ | --> | ||
+ | |||
+ | |||
+ | < | ||
+ | < | ||
+ | <meta charset=utf-8> | ||
+ | < | ||
+ | < | ||
+ | /* | ||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | */ | ||
+ | html {overflow: scroll;} | ||
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+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | | ||
+ | | ||
+ | } | ||
+ | /* | ||
+ | // COMMON_CODE_BLOCK_END | ||
+ | */ | ||
+ | </ | ||
+ | </ | ||
+ | < | ||
+ | < | ||
+ | <div id=' | ||
+ | <div class=group id=' | ||
+ | < | ||
+ | < | ||
+ | <div class=indented>< | ||
+ | <div class=suboption> | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | < | ||
+ | <div class=indented>< | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | <div class=suboption> | ||
+ | < | ||
+ | </ | ||
+ | |||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | </ | ||
+ | <div class=suboption> | ||
+ | <div class=indented> | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | < | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | <select id=" | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | <div class=group id=' | ||
+ | < | ||
+ | <div class=indented> | ||
+ | < | ||
+ | < | ||
+ | < | ||
+ | </ | ||
+ | < | ||
+ | </ | ||
+ | </ | ||
+ | |||
+ | </ | ||
+ | <img id=' | ||
+ | <img id=' | ||
+ | <div id=" | ||
+ | </ | ||
+ | < | ||
+ | requirejs.config({ | ||
+ | paths: { | ||
+ | three: '/ | ||
+ | TrackballControls: | ||
+ | OrbitControls: | ||
+ | Projector: '/ | ||
+ | SVGRenderer: | ||
+ | WEBGL: '/ | ||
+ | }, | ||
+ | shim: { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | }); | ||
+ | | ||
+ | require([' | ||
+ | window.THREE = THREE; | ||
+ | require([' | ||
+ | | ||
+ | THREE.TrackballControls = TrackballControls; | ||
+ | THREE.OrbitControls = OrbitControls; | ||
+ | THREE.Projector = Projector; | ||
+ | THREE.SVGRenderer = SVGRenderer; | ||
+ | THREE.WEBGL = WEBGL; | ||
+ | |||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | |||
+ | const intervalLength = 25; // for automatic animations | ||
+ | const explodableModel = true; | ||
+ | const modelContains = { points: false, pointlabels: | ||
+ | const foldables = []; | ||
+ | |||
+ | var three = document.getElementById(" | ||
+ | var scene = new THREE.Scene(); | ||
+ | var renderer = new THREE.WebGLRenderer( { antialias: true } ); | ||
+ | var svgRenderer = new THREE.SVGRenderer( { antialias: true } ); | ||
+ | renderer.setPixelRatio( window.devicePixelRatio ); | ||
+ | renderer.setClearColor(0xFFFFFF, | ||
+ | svgRenderer.setClearColor(0xFFFFFF, | ||
+ | three.appendChild(renderer.domElement); | ||
+ | |||
+ | var frustumSize = 4; | ||
+ | var cameras = [new THREE.PerspectiveCamera(75, | ||
+ | cameras.forEach(function(cam) { | ||
+ | cam.position.set(0, | ||
+ | cam.lookAt(0, | ||
+ | cam.up.set(0, | ||
+ | }); | ||
+ | var controls = [new THREE.TrackballControls(cameras[0], | ||
+ | var camera, control; | ||
+ | |||
+ | controls[0].zoomSpeed = 0.2; | ||
+ | controls[0].rotateSpeed = 4; | ||
+ | |||
+ | |||
+ | // class to allow move points together with labels and spheres | ||
+ | var PMPoint = function (x,y,z) { | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.addLabel = function(labelsprite) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.addSphere = function(spheremesh) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | PMPoint.prototype.set = function(x, | ||
+ | | ||
+ | if (this.sprite) { | ||
+ | this.sprite.position.copy(this.vector); | ||
+ | } | ||
+ | if (this.sphere) { | ||
+ | this.sphere.position.copy(this.vector); | ||
+ | } | ||
+ | } | ||
+ | PMPoint.prototype.radius = function() { | ||
+ | if (this.sphere) { | ||
+ | return this.sphere.geometry.parameters.radius; | ||
+ | } else { | ||
+ | return 0; | ||
+ | } | ||
+ | }; | ||
+ | // select the target node | ||
+ | var target = document.querySelector('# | ||
+ | |||
+ | // create an observer instance | ||
+ | var observer = new MutationObserver(function(mutations) { | ||
+ | | ||
+ | if (mutation.removedNodes && mutation.removedNodes.length > 0) { | ||
+ | | ||
+ | | ||
+ | | ||
+ | } | ||
+ | }); | ||
+ | }); | ||
+ | |||
+ | // configuration of the observer: | ||
+ | var config = { childList: true, characterData: | ||
+ | |||
+ | // pass in the target node, as well as the observer options | ||
+ | while (target) { | ||
+ | if (target.className==" | ||
+ | observer.observe(target, | ||
+ | break; | ||
+ | } | ||
+ | | ||
+ | } | ||
+ | |||
+ | // COMMON_CODE_BLOCK_END | ||
+ | |||
+ | var obj0 = new THREE.Object3D(); | ||
+ | obj0.name = " | ||
+ | obj0.userData.explodable = 1; | ||
+ | obj0.userData.points = []; | ||
+ | obj0.userData.points.push(new PMPoint(0, 0, 1)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 0, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 0, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 1, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 1, 0)); | ||
+ | obj0.userData.points.push(new PMPoint(1, 0, 1)); | ||
+ | obj0.userData.points.push(new PMPoint(0, 1, 1)); | ||
+ | |||
+ | obj0.userData.pointradii = 0.02; | ||
+ | < | ||
+ | obj0.userData.pointmaterial = new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, | ||
+ | obj0.userData.pointlabels = [" | ||
+ | obj0.userData.edgeindices = [0, 2, 1, 2, 2, 3, 1, 4, 3, 4, 0, 5, 1, 5, 4, 5, 0, 6, 3, 6, 4, 6, 5, 6]; | ||
+ | obj0.userData.facets = [[5, 4, 6], [6, 3, 2, 0], [1, 4, 5], [5, 0, 2, 1], [6, 4, 3], [3, 4, 1, 2], [5, 6, 0]]; | ||
+ | < | ||
+ | obj0.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, | ||
+ | init_object(obj0); | ||
+ | scene.add(obj0); | ||
+ | |||
+ | var obj1 = new THREE.Object3D(); | ||
+ | obj1.name = "GRAPH directed with LP "; | ||
+ | obj1.userData.explodable = 1; | ||
+ | obj1.userData.points = []; | ||
+ | obj1.userData.points.push(new PMPoint(0, 0, 1)); | ||
+ | obj1.userData.points.push(new PMPoint(1, 0, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(0, 0, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(0, 1, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(1, 1, 0)); | ||
+ | obj1.userData.points.push(new PMPoint(1, 0, 1)); | ||
+ | obj1.userData.points.push(new PMPoint(0, 1, 1)); | ||
+ | |||
+ | obj1.userData.edgeindices = [0, 5, 0, 6, 1, 4, 1, 5, 2, 0, 2, 1, 2, 3, 3, 4, 3, 6]; | ||
+ | < | ||
+ | obj1.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: | ||
+ | obj1.userData.arrowstyle = 1; | ||
+ | init_object(obj1); | ||
+ | scene.add(obj1); | ||
+ | |||
+ | // COMMON_CODE_BLOCK_BEGIN | ||
+ | function textSpriteMaterial(message, | ||
+ | if ( parameters === undefined ) parameters = {}; | ||
+ | var fontface = " | ||
+ | var fontsize = parameters.hasOwnProperty(" | ||
+ | fontsize = fontsize*10; | ||
+ | var lines = message.split(' | ||
+ | var size = 512; | ||
+ | for(var i = 0; i< | ||
+ | var tmp = lines[i].length; | ||
+ | while(tmp*fontsize > size){ | ||
+ | | ||
+ | } | ||
+ | } | ||
+ | | ||
+ | var canvas = document.createElement(' | ||
+ | canvas.width = size; | ||
+ | canvas.height = size; | ||
+ | var context = canvas.getContext(' | ||
+ | context.fillStyle = " | ||
+ | context.fill(); | ||
+ | context.font = fontsize + "px " + fontface; | ||
+ | | ||
+ | // text color | ||
+ | context.fillStyle = " | ||
+ | | ||
+ | context.fillText(lines[i], | ||
+ | } | ||
+ | | ||
+ | // canvas contents will be used for a texture | ||
+ | var texture = new THREE.Texture(canvas); | ||
+ | texture.needsUpdate = true; | ||
+ | | ||
+ | var spriteMaterial = new THREE.SpriteMaterial({map: | ||
+ | return spriteMaterial; | ||
+ | } | ||
+ | |||
+ | |||
+ | // ---------------------- INITIALIZING OBJECTS-------------------------------------- | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | function init_object(obj) { | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_points(obj); | ||
+ | modelContains.points = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_pointlabels(obj); | ||
+ | modelContains.pointlabels = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_lines(obj); | ||
+ | modelContains.lines = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_edgelabels(obj); | ||
+ | modelContains.edgelabels = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_arrowheads(obj); | ||
+ | modelContains.arrowheads = true; | ||
+ | } | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | init_faces(obj); | ||
+ | modelContains.faces = true; | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function init_points(obj) { | ||
+ | var pointgroup = new THREE.Group(); | ||
+ | pointgroup.name = " | ||
+ | var points = obj.userData.points; | ||
+ | var radii = obj.userData.pointradii; | ||
+ | var materials = obj.userData.pointmaterial; | ||
+ | var geometry, | ||
+ | if (!Array.isArray(radii)) { | ||
+ | geometry = new THREE.SphereBufferGeometry(radii); | ||
+ | } | ||
+ | if (!Array.isArray(materials)) { | ||
+ | material = materials; | ||
+ | } | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | if (Array.isArray(radii)) { | ||
+ | if (radii[i] == 0) { | ||
+ | continue; | ||
+ | } | ||
+ | geometry = new THREE.SphereBufferGeometry(radii[i]); | ||
+ | } | ||
+ | if (Array.isArray(materials)) { | ||
+ | material = materials[i]; | ||
+ | } | ||
+ | var sphere = new THREE.Mesh(geometry, | ||
+ | point.addSphere(sphere); | ||
+ | pointgroup.add(sphere); | ||
+ | } | ||
+ | obj.add(pointgroup); | ||
+ | } | ||
+ | |||
+ | function init_pointlabels(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var labels = obj.userData.pointlabels; | ||
+ | var pointlabels = new THREE.Group(); | ||
+ | pointlabels.name = " | ||
+ | if (Array.isArray(labels)) { | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | var spriteMaterial = textSpriteMaterial( labels[i] ); | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | point.addLabel(sprite); | ||
+ | pointlabels.add(sprite); | ||
+ | } | ||
+ | } else { | ||
+ | var spriteMaterial = textSpriteMaterial( labels ); | ||
+ | for (var i=0; i< | ||
+ | var point = points[i]; | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | point.addLabel(sprite); | ||
+ | pointlabels.add(sprite); | ||
+ | } | ||
+ | } | ||
+ | obj.add(pointlabels); | ||
+ | } | ||
+ | |||
+ | function init_lines(obj) { | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var points = obj.userData.points; | ||
+ | var materials = obj.userData.edgematerial; | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | var bufarr = new Float32Array( obj.userData.edgeindices.length * 3 ); | ||
+ | var bufattr = new THREE.Float32BufferAttribute( bufarr, 3 ); | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | geometry.setAttribute(' | ||
+ | if (Array.isArray(materials)) { | ||
+ | for (var i=0; i< | ||
+ | geometry.addGroup(2*i, | ||
+ | } | ||
+ | } | ||
+ | var lines = new THREE.LineSegments(geometry, | ||
+ | lines.name = " | ||
+ | obj.add(lines); | ||
+ | updateEdgesPosition(obj); | ||
+ | } | ||
+ | |||
+ | function init_edgelabels(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var labels = obj.userData.edgelabels; | ||
+ | var edgelabels = new THREE.Group(); | ||
+ | edgelabels.name = " | ||
+ | if (Array.isArray(labels)) { | ||
+ | for (var i=0; i< | ||
+ | var spriteMaterial = textSpriteMaterial( labels[i] ); | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector, | ||
+ | edgelabels.add(sprite); | ||
+ | } | ||
+ | } else { | ||
+ | var spriteMaterial = textSpriteMaterial( labels ); | ||
+ | for (var i=0; i< | ||
+ | var sprite = new THREE.Sprite(spriteMaterial); | ||
+ | sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector, | ||
+ | edgelabels.add(sprite); | ||
+ | } | ||
+ | } | ||
+ | obj.add(edgelabels); | ||
+ | } | ||
+ | |||
+ | function init_arrowheads(obj) { | ||
+ | var arrowheads = new THREE.Group(); | ||
+ | arrowheads.name = " | ||
+ | var arrowstyle = obj.userData.arrowstyle; | ||
+ | var edgeindices = obj.userData.edgeindices; | ||
+ | var edgematerials = obj.userData.edgematerial; | ||
+ | var points = obj.userData.points; | ||
+ | var material; | ||
+ | if (!Array.isArray(edgematerials)) { | ||
+ | material = new THREE.MeshBasicMaterial( {color: edgematerials.color} ); | ||
+ | } | ||
+ | |||
+ | for (var i=0; i< | ||
+ | var start = points[edgeindices[i]]; | ||
+ | var end = points[edgeindices[i+1]]; | ||
+ | var dist = start.vector.distanceTo( end.vector ) - start.radius() - end.radius(); | ||
+ | if (dist <= 0) { | ||
+ | continue; | ||
+ | } | ||
+ | var dir = new THREE.Vector3().subVectors(end.vector, | ||
+ | dir.normalize(); | ||
+ | var axis = new THREE.Vector3().set(dir.z, | ||
+ | axis.normalize(); | ||
+ | var radians = Math.acos( dir.y ); | ||
+ | var radius = dist/25; | ||
+ | var height = dist/5; | ||
+ | var geometry = new THREE.ConeBufferGeometry(radius, | ||
+ | var position = new THREE.Vector3().addVectors(start.vector, | ||
+ | if (Array.isArray(edgematerials)) { | ||
+ | material = new THREE.MeshBasicMaterial( {color: edgematerials[i].color} ); | ||
+ | } | ||
+ | var cone = new THREE.Mesh( geometry, material ); | ||
+ | cone.quaternion.setFromAxisAngle(axis, | ||
+ | cone.position.copy(position);; | ||
+ | arrowheads.add(cone); | ||
+ | } | ||
+ | obj.add(arrowheads); | ||
+ | } | ||
+ | |||
+ | function init_faces(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var facets = obj.userData.facets; | ||
+ | obj.userData.triangleindices = []; | ||
+ | for (var i=0; i< | ||
+ | facet = facets[i]; | ||
+ | for (var t=0; t< | ||
+ | obj.userData.triangleindices.push(facet[0], | ||
+ | } | ||
+ | } | ||
+ | var bufarr = new Float32Array( obj.userData.triangleindices.length * 3 ); | ||
+ | var bufattr = new THREE.Float32BufferAttribute(bufarr, | ||
+ | | ||
+ | var materials = obj.userData.facetmaterial; | ||
+ | var geometry = new THREE.BufferGeometry(); | ||
+ | var frontmaterials = []; | ||
+ | var backmaterials = []; | ||
+ | geometry.setAttribute(' | ||
+ | if (Array.isArray(materials)) { | ||
+ | var tricount = 0; | ||
+ | var facet; | ||
+ | for (var i=0; i< | ||
+ | facet = facets[i]; | ||
+ | geometry.addGroup(tricount, | ||
+ | tricount += (facet.length-2)*3; | ||
+ | } | ||
+ | for (var j=0; j< | ||
+ | var fmat = materials[j].clone() | ||
+ | fmat.side = THREE.FrontSide; | ||
+ | frontmaterials.push(fmat); | ||
+ | var bmat = materials[j].clone() | ||
+ | bmat.side = THREE.BackSide; | ||
+ | backmaterials.push(bmat); | ||
+ | obj.userData.facetmaterial = frontmaterials.concat(backmaterials); | ||
+ | } | ||
+ | } else if (materials instanceof THREE.Material) { | ||
+ | frontmaterials = materials.clone() | ||
+ | frontmaterials.side = THREE.FrontSide; | ||
+ | backmaterials = materials.clone() | ||
+ | backmaterials.side = THREE.BackSide; | ||
+ | obj.userData.facetmaterial = [frontmaterials, | ||
+ | } | ||
+ | // duplicating the object with front and back should avoid transparency issues | ||
+ | var backmesh = new THREE.Mesh(geometry, | ||
+ | // meshname is used to show/hide objects | ||
+ | backmesh.name = " | ||
+ | obj.add(backmesh); | ||
+ | var frontmesh = new THREE.Mesh(geometry, | ||
+ | frontmesh.name = " | ||
+ | obj.add(frontmesh); | ||
+ | updateFacesPosition(obj); | ||
+ | } | ||
+ | // // | ||
+ | |||
+ | |||
+ | function updateFacesPosition(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var indices = obj.userData.triangleindices; | ||
+ | var faces = obj.getObjectByName(" | ||
+ | var ba = faces.geometry.getAttribute(" | ||
+ | for (var i=0; i< | ||
+ | ba.setXYZ(i, | ||
+ | } | ||
+ | faces.geometry.attributes.position.needsUpdate = true; | ||
+ | | ||
+ | } | ||
+ | |||
+ | function updateEdgesPosition(obj) { | ||
+ | var points = obj.userData.points; | ||
+ | var indices = obj.userData.edgeindices; | ||
+ | var lines = obj.getObjectByName(" | ||
+ | var ba = lines.geometry.getAttribute(" | ||
+ | for (var i=0; i< | ||
+ | ba.setXYZ(i, | ||
+ | } | ||
+ | lines.geometry.attributes.position.needsUpdate = true; | ||
+ | } | ||
+ | |||
+ | function onWindowResize() { | ||
+ | renderer.setSize( three.clientWidth, | ||
+ | svgRenderer.setSize( three.clientWidth, | ||
+ | updateCamera(); | ||
+ | } | ||
+ | |||
+ | function updateCamera() { | ||
+ | var width = three.clientWidth; | ||
+ | var height = three.clientHeight; | ||
+ | var aspect = width / height; | ||
+ | if (camera.type == " | ||
+ | camera.left = frustumSize * aspect / - 2; | ||
+ | camera.right = frustumSize * aspect / 2; | ||
+ | camera.top = frustumSize / 2; | ||
+ | camera.bottom = - frustumSize / 2; | ||
+ | } else if (camera.type == " | ||
+ | camera.aspect = aspect; | ||
+ | } | ||
+ | camera.updateProjectionMatrix(); | ||
+ | } | ||
+ | |||
+ | function changeCamera(event) { | ||
+ | var selindex = event.currentTarget.selectedIndex; | ||
+ | camera = cameras[selindex]; | ||
+ | control = controls[selindex]; | ||
+ | control.enabled = true; | ||
+ | for (var i=0; i< | ||
+ | if (i!=selindex) { | ||
+ | controls[i].enabled = false; | ||
+ | } | ||
+ | } | ||
+ | updateCamera(); | ||
+ | } | ||
+ | |||
+ | var camtypenode = document.getElementById(' | ||
+ | camtypenode.onchange = changeCamera; | ||
+ | camtypenode.dispatchEvent(new Event(' | ||
+ | |||
+ | onWindowResize(); | ||
+ | window.addEventListener(' | ||
+ | |||
+ | |||
+ | var xRotationEnabled = false; | ||
+ | var yRotationEnabled = false; | ||
+ | var zRotationEnabled = false; | ||
+ | var rotationSpeedFactor = 1; | ||
+ | var settingsShown = false; | ||
+ | var labelsShown = true; | ||
+ | var intervals = []; | ||
+ | var timeouts = []; | ||
+ | var explodingSpeed = 0.05; | ||
+ | var explodeScale = 0.000001; | ||
+ | var XMLS = new XMLSerializer(); | ||
+ | var svgElement; | ||
+ | var renderId; | ||
+ | |||
+ | var render = function () { | ||
+ | |||
+ | renderId = requestAnimationFrame(render); | ||
+ | |||
+ | // comment in for automatic explosion | ||
+ | // | ||
+ | |||
+ | var phi = 0.02 * rotationSpeedFactor; | ||
+ | |||
+ | if (xRotationEnabled) { | ||
+ | scene.rotation.x += phi; | ||
+ | } | ||
+ | if (yRotationEnabled) { | ||
+ | scene.rotation.y += phi; | ||
+ | } | ||
+ | if (zRotationEnabled) { | ||
+ | scene.rotation.z += phi; | ||
+ | } | ||
+ | |||
+ | control.update(); | ||
+ | renderer.render(scene, | ||
+ | }; | ||
+ | |||
+ | if ( THREE.WEBGL.isWebGLAvailable() ) { | ||
+ | render(); | ||
+ | } else { | ||
+ | var warning = WEBGL.getWebGLErrorMessage(); | ||
+ | three.appendChild( warning ); | ||
+ | } | ||
+ | | ||
+ | function changeTransparency() { | ||
+ | var opacity = 1-Number(event.currentTarget.value); | ||
+ | for (var i=0; i< | ||
+ | child = scene.children[i]; | ||
+ | if ( child.userData.hasOwnProperty(" | ||
+ | if (Array.isArray(child.userData.facetmaterial)) { | ||
+ | for (var j=0; j< | ||
+ | child.userData.facetmaterial[j].opacity = opacity; | ||
+ | } | ||
+ | } else { | ||
+ | child.userData.facetmaterial.opacity = opacity; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function toggleDepthWrite(event) { | ||
+ | depthwrite = event.currentTarget.checked; | ||
+ | for (var i=0; i< | ||
+ | child = scene.children[i]; | ||
+ | if ( child.userData.hasOwnProperty(" | ||
+ | if (Array.isArray(child.userData.facetmaterial)) { | ||
+ | for (var j=0; j< | ||
+ | child.userData.facetmaterial[j].depthWrite = depthwrite; | ||
+ | } | ||
+ | } else { | ||
+ | child.userData.facetmaterial.depthWrite = depthWrite; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function changeRotationX(event){ | ||
+ | xRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | function changeRotationY(event){ | ||
+ | yRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | function changeRotationZ(event){ | ||
+ | zRotationEnabled = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | |||
+ | function changeRotationSpeedFactor(event){ | ||
+ | rotationSpeedFactor = Number(event.currentTarget.value); | ||
+ | } | ||
+ | |||
+ | function resetScene(){ | ||
+ | scene.rotation.set(0, | ||
+ | camera.position.set(0, | ||
+ | camera.up.set(0, | ||
+ | } | ||
+ | |||
+ | function showSettings(event){ | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | settingsShown = true; | ||
+ | } | ||
+ | |||
+ | function hideSettings(event){ | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | settingsShown = false; | ||
+ | } | ||
+ | |||
+ | |||
+ | |||
+ | var pos = 150* Math.PI; | ||
+ | |||
+ | function updateFactor() { | ||
+ | pos++; | ||
+ | return Math.sin(.01*pos)+1; | ||
+ | } | ||
+ | |||
+ | // ------------------------ FOLDING ------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | // rotate point p around axis defined by points p1 and p2 by given angle | ||
+ | function rotate(p, p1, p2, angle ){ | ||
+ | angle = -angle; | ||
+ | var x = p.x, y = p.y, z = p.z, | ||
+ | a = p1.x, b = p1.y, c = p1.z, | ||
+ | u = p2.x-p1.x, v = p2.y-p1.y, w = p2.z-p1.z; | ||
+ | var result = []; | ||
+ | var L = u*u + v*v + w*w; | ||
+ | var sqrt = Math.sqrt; | ||
+ | var cos = Math.cos; | ||
+ | var sin = Math.sin; | ||
+ | |||
+ | result[0] = ((a*(v*v+w*w)-u*(b*v+c*w-u*x-v*y-w*z))*(1-cos(angle))+L*x*cos(angle)+sqrt(L)*(-c*v+b*w-w*y+v*z)*sin(angle))/ | ||
+ | result[1] = ((b*(u*u+w*w)-v*(a*u+c*w-u*x-v*y-w*z))*(1-cos(angle))+L*y*cos(angle)+sqrt(L)*(c*u-a*w+w*x-u*z)*sin(angle))/ | ||
+ | result[2] = ((c*(u*u+v*v)-w*(a*u+b*v-u*x-v*y-w*z))*(1-cos(angle))+L*z*cos(angle)+sqrt(L)*(-b*u+a*v-v*x+u*y)*sin(angle))/ | ||
+ | |||
+ | return result; | ||
+ | } | ||
+ | |||
+ | var fold = function(event){ | ||
+ | var obj = foldables[Number(event.currentTarget.name)]; | ||
+ | var foldvalue = Number(event.currentTarget.value); | ||
+ | var scale = foldvalue - obj.userData.oldscale; | ||
+ | |||
+ | for (var j=0; j< | ||
+ | rotateVertices(obj, | ||
+ | } | ||
+ | update(obj); | ||
+ | obj.userData.oldscale += scale; | ||
+ | lookAtBarycenter(obj); | ||
+ | } | ||
+ | |||
+ | function lookAtBarycenter(obj){ | ||
+ | control.target = barycenter(obj); | ||
+ | } | ||
+ | |||
+ | function barycenter(obj) { | ||
+ | var center = new THREE.Vector3(0, | ||
+ | var points = obj.userData.points; | ||
+ | for (var i=0; i< | ||
+ | center.add(points[i].vector); | ||
+ | } | ||
+ | center.divideScalar(points.length); | ||
+ | return center; | ||
+ | } | ||
+ | |||
+ | function rotateVertices(obj, | ||
+ | var axes = obj.userData.axes; | ||
+ | var subtrees = obj.userData.subtrees; | ||
+ | var points = obj.userData.points; | ||
+ | var angles = obj.userData.angles; | ||
+ | if (edge < axes.length){ | ||
+ | for (var j=0; j< | ||
+ | var rotP = rotate(points[subtrees[edge][j]].vector, | ||
+ | points[subtrees[edge][j]].set(rotP[0], | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function update(obj) { | ||
+ | | ||
+ | | ||
+ | } | ||
+ | |||
+ | if (foldables.length) { | ||
+ | var settings = document.getElementById(' | ||
+ | var foldDiv = document.createElement(' | ||
+ | foldDiv.id = ' | ||
+ | var title = document.createElement(' | ||
+ | title.innerHTML = ' | ||
+ | foldDiv.appendChild(title); | ||
+ | foldDiv.className = ' | ||
+ | for (var i=0; i< | ||
+ | var range = document.createElement(' | ||
+ | range.type = ' | ||
+ | range.min = 0; | ||
+ | range.max = 1; | ||
+ | range.value = 0; | ||
+ | range.step = 0.001; | ||
+ | range.name = String(i); | ||
+ | range.oninput = fold; | ||
+ | foldDiv.appendChild(range); | ||
+ | } | ||
+ | lookAtBarycenter(foldables[0]); | ||
+ | settings.insertBefore(foldDiv, | ||
+ | } | ||
+ | |||
+ | | ||
+ | // ---------------------- EXPLOSION ------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | if (explodableModel) { | ||
+ | for (var i=0; i< | ||
+ | obj = scene.children[i]; | ||
+ | if ( obj.userData.explodable ) { | ||
+ | computeCentroid(obj); | ||
+ | } | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | explode(0.000001); | ||
+ | } | ||
+ | |||
+ | function computeCentroid(obj) { | ||
+ | centroid = new THREE.Vector3(); | ||
+ | obj.userData.points.forEach(function(pmpoint) { | ||
+ | centroid.add(pmpoint.vector); | ||
+ | }); | ||
+ | centroid.divideScalar(obj.userData.points.length); | ||
+ | obj.userData.centroid = centroid; | ||
+ | } | ||
+ | |||
+ | function explode(factor) { | ||
+ | for (var i=0; i< | ||
+ | var obj = scene.children[i]; | ||
+ | if (obj.userData.hasOwnProperty(" | ||
+ | var c = obj.userData.centroid; | ||
+ | obj.position.set(c.x*factor, | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function triggerExplode(event){ | ||
+ | explodeScale = Number(event.currentTarget.value); | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | |||
+ | function setExplodingSpeed(event){ | ||
+ | explodingSpeed = Number(event.currentTarget.value); | ||
+ | } | ||
+ | |||
+ | function triggerAutomaticExplode(event){ | ||
+ | if (event.currentTarget.checked){ | ||
+ | startExploding(); | ||
+ | } else { | ||
+ | clearIntervals(); | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function startExploding(){ | ||
+ | intervals.push(setInterval(explodingInterval, | ||
+ | } | ||
+ | |||
+ | |||
+ | function explodingInterval(){ | ||
+ | explodeScale += explodingSpeed; | ||
+ | if (explodeScale <= 6){ | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | else{ | ||
+ | explode(6); | ||
+ | explodeScale = 6; | ||
+ | clearIntervals(); | ||
+ | timeouts.push(setTimeout(startUnexploding, | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | |||
+ | |||
+ | function startUnexploding(){ | ||
+ | intervals.push(setInterval(unexplodingInterval, | ||
+ | } | ||
+ | |||
+ | function unexplodingInterval(){ | ||
+ | explodeScale -= explodingSpeed; | ||
+ | if (explodeScale >= 0){ | ||
+ | explode(explodeScale); | ||
+ | } | ||
+ | else { | ||
+ | explode(0); | ||
+ | explodeScale = 0; | ||
+ | clearIntervals(); | ||
+ | timeouts.push(setTimeout(startExploding, | ||
+ | } | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | |||
+ | function clearIntervals(){ | ||
+ | intervals.forEach(function(interval){ | ||
+ | clearInterval(interval); | ||
+ | }); | ||
+ | intervals = []; | ||
+ | timeouts.forEach(function(timeout){ | ||
+ | clearTimeout(timeout); | ||
+ | }); | ||
+ | timeouts = []; | ||
+ | } | ||
+ | |||
+ | // ---------------------- DISPLAY -------------------------------------------------- | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | const objectTypeInnerHTMLs = { points: " | ||
+ | const objectTypeVisible = {}; | ||
+ | Object.assign(objectTypeVisible, | ||
+ | const sortedObjectTypeKeys = Object.keys(objectTypeInnerHTMLs).sort(); | ||
+ | const shownObjectTypesList = document.getElementById(' | ||
+ | |||
+ | function setVisibility(bool, | ||
+ | for (var i=0; i< | ||
+ | var obj = scene.children[i].getObjectByName(objname); | ||
+ | if (obj) { | ||
+ | obj.visible = bool; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function toggleObjectTypeVisibility(event){ | ||
+ | var name = event.currentTarget.name; | ||
+ | var checked = event.currentTarget.checked; | ||
+ | objectTypeVisible[name] = checked; | ||
+ | if (name == " | ||
+ | setVisibility(checked," | ||
+ | setVisibility(checked," | ||
+ | } else { | ||
+ | setVisibility(checked, | ||
+ | } | ||
+ | } | ||
+ | |||
+ | for (var i=0; i< | ||
+ | var key = sortedObjectTypeKeys[i]; | ||
+ | if (modelContains[key]) { | ||
+ | var objTypeNode = document.createElement(' | ||
+ | objTypeNode.innerHTML = objectTypeInnerHTMLs[key] + '< | ||
+ | var checkbox = document.createElement(' | ||
+ | checkbox.type = ' | ||
+ | checkbox.checked = true; | ||
+ | checkbox.name = key; | ||
+ | checkbox.onchange = toggleObjectTypeVisibility; | ||
+ | shownObjectTypesList.appendChild(checkbox); | ||
+ | shownObjectTypesList.appendChild(objTypeNode); | ||
+ | } | ||
+ | } | ||
+ | |||
+ | // ------------------------------------------------------ | ||
+ | |||
+ | function toggleObjectVisibility(event){ | ||
+ | var nr = Number(event.currentTarget.name); | ||
+ | scene.children[nr].visible = event.currentTarget.checked; | ||
+ | } | ||
+ | |||
+ | // append checkboxes for displaying or hiding objects | ||
+ | var shownObjectsList = document.getElementById(' | ||
+ | for (var i=0; i< | ||
+ | obj = scene.children[i]; | ||
+ | var objNode = document.createElement(' | ||
+ | objNode.innerHTML = obj.name + '< | ||
+ | var checkbox = document.createElement(' | ||
+ | checkbox.type = ' | ||
+ | checkbox.checked = true; | ||
+ | checkbox.name = String(i); | ||
+ | checkbox.onchange = toggleObjectVisibility; | ||
+ | shownObjectsList.appendChild(checkbox); | ||
+ | shownObjectsList.appendChild(objNode); | ||
+ | } | ||
+ | |||
+ | // ---------------------- SVG ------------------------------------------------------ | ||
+ | // --------------------------------------------------------------------------------- | ||
+ | |||
+ | function takeSvgScreenshot() { | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(false," | ||
+ | } | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(false," | ||
+ | } | ||
+ | svgRenderer.render(scene, | ||
+ | svgElement = XMLS.serializeToString(svgRenderer.domElement); | ||
+ | | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(true," | ||
+ | } | ||
+ | if (objectTypeVisible[" | ||
+ | setVisibility(true," | ||
+ | } | ||
+ | |||
+ | if (document.getElementById(' | ||
+ | //show in new tab | ||
+ | var myWindow = window.open("","" | ||
+ | myWindow.document.body.innerHTML = svgElement; | ||
+ | } else{ | ||
+ | // download svg file | ||
+ | download(" | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function download(filename, | ||
+ | var element = document.createElement(' | ||
+ | element.setAttribute(' | ||
+ | element.setAttribute(' | ||
+ | |||
+ | element.style.display = ' | ||
+ | document.body.appendChild(element); | ||
+ | |||
+ | element.click(); | ||
+ | |||
+ | document.body.removeChild(element); | ||
+ | } | ||
+ | |||
+ | |||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | document.getElementById(' | ||
+ | |||
+ | |||
+ | // ------------------ SHORTCUTS -------------------------------------------- | ||
+ | // ------------------------------------------------------------------------- | ||
+ | |||
+ | /** | ||
+ | * http:// | ||
+ | * Version : 2.01.B | ||
+ | * By Binny V A | ||
+ | * License : BSD | ||
+ | */ | ||
+ | shortcut = { | ||
+ | ' | ||
+ | ' | ||
+ | //Provide a set of default options | ||
+ | var default_options = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | if(!opt) opt = default_options; | ||
+ | else { | ||
+ | for(var dfo in default_options) { | ||
+ | if(typeof opt[dfo] == ' | ||
+ | } | ||
+ | } | ||
+ | |||
+ | var ele = opt.target; | ||
+ | if(typeof opt.target == ' | ||
+ | var ths = this; | ||
+ | shortcut_combination = shortcut_combination.toLowerCase(); | ||
+ | |||
+ | //The function to be called at keypress | ||
+ | var func = function(e) { | ||
+ | e = e || window.event; | ||
+ | |||
+ | if(opt[' | ||
+ | var element; | ||
+ | if(e.target) element=e.target; | ||
+ | else if(e.srcElement) element=e.srcElement; | ||
+ | if(element.nodeType==3) element=element.parentNode; | ||
+ | |||
+ | if(element.tagName == ' | ||
+ | } | ||
+ | |||
+ | //Find Which key is pressed | ||
+ | if (e.keyCode) code = e.keyCode; | ||
+ | else if (e.which) code = e.which; | ||
+ | var character = String.fromCharCode(code).toLowerCase(); | ||
+ | |||
+ | if(code == 188) character=","; | ||
+ | if(code == 190) character=" | ||
+ | |||
+ | var keys = shortcut_combination.split(" | ||
+ | //Key Pressed - counts the number of valid keypresses - if it is same as the number of keys, the shortcut function is invoked | ||
+ | var kp = 0; | ||
+ | |||
+ | //Work around for stupid Shift key bug created by using lowercase - as a result the shift+num combination was broken | ||
+ | var shift_nums = { | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | ";":":", | ||
+ | "'":" | ||
+ | ",":"<", | ||
+ | " | ||
+ | "/":"?", | ||
+ | " | ||
+ | } | ||
+ | // | ||
+ | var special_keys = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | |||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | } | ||
+ | |||
+ | var modifiers = { | ||
+ | shift: { wanted: | ||
+ | ctrl : { wanted: | ||
+ | alt | ||
+ | meta : { wanted: | ||
+ | }; | ||
+ | | ||
+ | if(e.ctrlKey) modifiers.ctrl.pressed = true; | ||
+ | if(e.shiftKey) modifiers.shift.pressed = true; | ||
+ | if(e.altKey) modifiers.alt.pressed = true; | ||
+ | if(e.metaKey) | ||
+ | | ||
+ | for(var i=0; k=keys[i], | ||
+ | // | ||
+ | if(k == ' | ||
+ | kp++; | ||
+ | modifiers.ctrl.wanted = true; | ||
+ | |||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.shift.wanted = true; | ||
+ | |||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.alt.wanted = true; | ||
+ | } else if(k == ' | ||
+ | kp++; | ||
+ | modifiers.meta.wanted = true; | ||
+ | } else if(k.length > 1) { //If it is a special key | ||
+ | if(special_keys[k] == code) kp++; | ||
+ | |||
+ | } else if(opt[' | ||
+ | if(opt[' | ||
+ | |||
+ | } else { //The special keys did not match | ||
+ | if(character == k) kp++; | ||
+ | else { | ||
+ | if(shift_nums[character] && e.shiftKey) { //Stupid Shift key bug created by using lowercase | ||
+ | character = shift_nums[character]; | ||
+ | if(character == k) kp++; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | |||
+ | if(kp == keys.length && | ||
+ | modifiers.ctrl.pressed == modifiers.ctrl.wanted && | ||
+ | modifiers.shift.pressed == modifiers.shift.wanted && | ||
+ | modifiers.alt.pressed == modifiers.alt.wanted && | ||
+ | modifiers.meta.pressed == modifiers.meta.wanted) { | ||
+ | callback(e); | ||
+ | |||
+ | if(!opt[' | ||
+ | // | ||
+ | e.cancelBubble = true; | ||
+ | e.returnValue = false; | ||
+ | |||
+ | // | ||
+ | if (e.stopPropagation) { | ||
+ | e.stopPropagation(); | ||
+ | e.preventDefault(); | ||
+ | } | ||
+ | return false; | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | this.all_shortcuts[shortcut_combination] = { | ||
+ | ' | ||
+ | ' | ||
+ | ' | ||
+ | }; | ||
+ | //Attach the function with the event | ||
+ | if(ele.addEventListener) ele.addEventListener(opt[' | ||
+ | else if(ele.attachEvent) ele.attachEvent(' | ||
+ | else ele[' | ||
+ | }, | ||
+ | |||
+ | //Remove the shortcut - just specify the shortcut and I will remove the binding | ||
+ | ' | ||
+ | shortcut_combination = shortcut_combination.toLowerCase(); | ||
+ | var binding = this.all_shortcuts[shortcut_combination]; | ||
+ | delete(this.all_shortcuts[shortcut_combination]) | ||
+ | if(!binding) return; | ||
+ | var type = binding[' | ||
+ | var ele = binding[' | ||
+ | var callback = binding[' | ||
+ | |||
+ | if(ele.detachEvent) ele.detachEvent(' | ||
+ | else if(ele.removeEventListener) ele.removeEventListener(type, | ||
+ | else ele[' | ||
+ | } | ||
+ | } | ||
+ | |||
+ | shortcut.add(" | ||
+ | var event = new Event(' | ||
+ | if (settingsShown){ | ||
+ | document.getElementById(' | ||
+ | } else { | ||
+ | document.getElementById(' | ||
+ | } | ||
+ | }); | ||
+ | |||
+ | |||
+ | // COMMON_CODE_BLOCK_END | ||
+ | |||
+ | });}); | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | </ | ||
+ | ==== Multiple LP's for one Polytope ==== | ||
+ | |||
+ | You can add more than one linear program to one polytope. | ||
+ | |||
+ | <code perl> | ||
+ | > $p-> | ||
+ | </ | ||
+ | The different linear programs are saved in an array. The first one can still be accessed like befor: | ||
+ | |||
+ | <code perl> | ||
+ | > print $p-> | ||
+ | 0 1 1 1 | ||
+ | </ | ||
+ | The other ones can be accessed like the entries of an array. | ||
+ | |||
+ | <code perl> | ||
+ | > print $p-> | ||
+ | 0 1 1 -1 | ||
+ | </ | ||
+ | You can find more about this [[user_guide: | ||
+ | |||