This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Tutorial: Patchworking real tropical hypersurfaces ====== Viro's combinatorial patchworking method takes as its input a regular subdivision $\tau$ of a dilated standard simplex $d\cdot\Delta_n$ (where $\Delta_n = \mathrm{conv}{e_1,\ldots,e_n}$), and a sign distribution on its vertices $s:\tau_0\rightarrow\mathbb Z/2\mathbb Z$, and builds a polyhedral hypersurface (a pure codimension 1 polyhedral complex), that is of the same topological type as some real algebraic hypersurface of degree $d$ (i.e., a real algebraic variety $\mathbb RV(F)$ for some real polynomial $F$ with $\mathrm{deg}F=d$). We present an implementation of this method using real tropical hypersurfaces, with the induced regular subdivision of its Newton polytope taking the place of the above mentioned triangulation, as well as an efficient algorithm to compute the $\mathbb Z/2\mathbb Z$ homology of the resulting hypersurface, which also works for non-regular subdivisions (see below). For the math, see for example [[https://arxiv.org/abs/math/0611382|Viro]] or, for the case of tropical hypersurfaces, [[https://arxiv.org/abs/math/0403015|Mikhalkin]]. This polymake implementation is discussed in * Joswig & Vater: Real tropical hyperfaces by patchworking in polymake, in: Mathematical software – ICMS 2020 (Bigatti et al, eds.), Springer, LNCS 12097, [[htpps://doi.org/10.1007/978-3-030-52200-1_20|doi:10.1007/978-3-030-52200-1_20]]. ===== Nomenclature ===== In the case of a real tropical hypersurface $T_s(f)$ (i.e., a tropical hypersurface $T(f)$ together with a sign distribution $s$ on its support), patchworking works by symmetrically gluing together $2^n$ copies of $H$ (one for each orthant of the ambient space $\mathbb R^n$), and then forgetting certain facets of these copies (this depends on $s$). The quantity encoding which facets are remembered in which orthant is called its //real phase structure//. We call the resulting polyhedral hypersurface the corresponding //patchworked hypersurfaces//, or simply a //realization// of $T_s(f)$. ===== Basic Functionality ===== Naturally, we'll want to load Polymake's ''%%tropical%%'' application first: <code perl> > application "tropical"; </code> The simplest non-trivial example builds a polyhedral line from a tropical line. So let's first create a tropical line: <code perl> > $h1 = new Hypersurface<Min>(POLYNOMIAL=>toTropicalPolynomial("min(x,y,z)")); > print $h1->MONOMIALS; (3) (2 1) (3) (1 1) (3) (0 1) </code> The line consists of 3 rays eminating from the point (0,0,0). This gives us one vertex. The points where the rays intersect the plane at infinity are also considered vertices. <code perl> > print $h1->PROJECTIVE_VERTICES; 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 > print $h1->MAXIMAL_POLYTOPES; # the facets of the (original) tropical hypersurface {0 3} {1 3} {2 3} </code> The property ''%%MAXIMAL_POLYTOPES%%'' is an ''%%IncidenceMatrix%%''. An entry $k$ in the $i$-th row of ''%%MAXIMAL_POLYTOPES%%'' indicates the vertex (represented by the $k$-th row in ''%%PROJECTIVE_VERTICES%%'') contained in the $i$-th facet of the tropical line. We can now add a sign distribution on its monomials in the following way: <code perl> > $h1_pw1 = $h1->PATCHWORK(SIGNS=>[0,0,1]); # a real structure on $h1 > $h1_pw2 = $h1->PATCHWORK(SIGNS=>[1,0,1]); # another one, why not? </code> The property ''%%PATCHWORK%%'' represents a multiple subobject to a ''%%Hypersurface%%'' object (whether we deal with a ''%%Min%%'' or ''%%Max%%'' tropical hypersurface is irrelevant for the patchworking), parametrized by the property ''%%SIGNS%%'' with type ''%%Array<Bool>%%'', which represents the sign distribution on its support. This subobject carries the information about the real tropical hypersurface. Note that this allows us to create multiple "real structures" on the same tropical hypersurface object (as we did in the above example). <code perl> > print dense($h1_pw1->REAL_PHASE); 0 1 1 0 1 1 0 0 1 0 1 0 </code> The property ''%%REAL_PHASE%%'' is an ''%%IncidenceMatrix%%'', representing the real phase structure of the real tropical hypersurface, with the following semantics: Each orthant $o\subset\mathbb R^n$ corresponds to a subset $o\cap{-e_1,\ldots,-e_n}\subset{-e_1,\ldots,-e_n}$, whose characteristic vector is the binary representation of a unique natural number $0\leq N_o< 2^n$. E.g. in the plane, the positive orthant has binary representation $(00)_2 = 0$, and the negative $(11)_2 = 3$. The $j$-th entry in the $i$-th row of ''%%REAL_PHASE%%'' is now $1$ iff the $i$-th facet of the tropical hypersurface (represented by the $i$-th row of ''%%MAXIMAL_POLYTOPES%%''; see above) is remembered in the orthant with binary representation $j$. ==== Realization as a PolyhedralComplex ==== We can produce a realization of the patchworked hypersurface as a ''%%PolyhedralComplex%%'' with the user method ''%%...->realize()%%'': <code perl> > $h1_pw_r = $h1_pw1->realize(); > print $h1_pw_r->COMBINATORIAL_DIM; > svg($h1_pw_r->VISUAL); 1 Undefined subroutine &Polymake::User::svg called </code> Note that the realization is only unique up to combinatorial equivalence. ==== Some classic curves ==== There are convenience functions to produce some classic algebraic curves: <code perl> > $harnack = harnack_curve(6); # harnack curve of degree 6 > $ragsdale = ragsdale_counterexample(); # a counterexample to the ragsdale conjecture > $gudkov = gudkov_curve(); # gudkov curve (degree 6) </code> These return a ''%%Hypersurface%%'' object with a unique ''%%PATCHWORK%%'' property attached, to access it simply use ''%%...->PATCHWORK%%''. <code perl> > print $ragsdale->PATCHWORK->SIGNS; > svg($ragsdale->PATCHWORK->realize("uniform")->VISUAL); 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 Undefined subroutine &Polymake::User::svg called </code> ===== The $\mathbb Z/2\mathbb Z$ cellular homology of a patchworked hypersurface ===== Naive computation of the homology of a patchworked hypersurface is computationally expensive, since its size depends exponentially on the dimension (we glue together $2^n$ copies of the tropical hypersurface). Shaw & Renaudineau describe a way to exploit the symmetry of a patchworked hypersurface to compute its $\mathbb Z/2\mathbb Z$ homology directly from the triangulation + sign distribution, without needing to construct a polyhedral complex realization; cf. [[https://arxiv.org/abs/1805.02030|arXiv:1805.02030]] or the published version [[https://smf.emath.fr/publications/bornes-sur-les-nombres-de-betti-des-hypersurfaces-algebriques-reelles-proches-de-la|here]]. This leads to a straight forward algorithm, which is implemented in Polymake, and accessible in the following way: <code perl> > print $h1_pw1->CHAIN_COMPLEX_Z2; <0 1 1 1 1 0 1 0 1 > > print $h1_pw1->BETTI_NUMBERS_Z2; 1 1 </code> ===== Non-regular patchworking ===== It is possible to use this implementation starting with a (possibly non-regular) subdivision $\tau$ (i.e., without the data of a tropical hypersurface). The usage is similar, you just have to define the hypersurface via the ''%%DUAL_SUBDIVISION%%'' property (even if mathematically no such hypersurface exists, i.e. in the non-regular case), instead the tropical ''%%POLYNOMIAL%%''. Here is such a non-regular subdivision of $4\Delta_2$, the "mother of all examples": <code perl> > $moae = new fan::SubdivisionOfPoints(POINTS=>[[1,4,0,0],[1,0,4,0],[1,0,0,4],[1,2,1,1],[1,1,2,1],[1,1,1,2]], > MAXIMAL_CELLS=>[[0,1,3],[0,2,5],[0,3,5],[1,2,4],[1,3,4],[2,4,5],[3,4,5]]); > $moae->VISUAL; </code> <HTML> <!-- polymake for lenaweis Sat Feb 3 13:23:37 2024 pcom:moae --> <html> <head> <meta charset=utf-8> <title>pcom:moae</title> <style> /* // COMMON_CODE_BLOCK_BEGIN */ html {overflow: scroll;} strong{font-size: 18px;} canvas { z-index: 8; } input[type='radio'] {margin-left:0;} input[type='checkbox'] {margin-right:7px; margin-left: 0px; padding-left:0px;} .group{padding-bottom: 15px;} .settings * {z-index: 11; } .settings{z-index: 10; font-family: Arial, Helvetica, sans-serif; margin-left: 30px; visibility: hidden; width: 14em; height: 96%; border: solid 1px silver; padding: 2px; overflow-y: scroll; box-sizing: border-box; background-color: white; position: absolute;} .indented{margin-left: 20px; margin-top: 10px; padding-bottom: 0px;} .shownObjectsList{overflow: auto; max-width: 150px; max-height: 150px;} .showSettingsButton{visibility: visible; z-index: 12; position: absolute } .hideSettingsButton{visibility: hidden; z-index: 12; position: absolute; opacity: 0.5} button{margin-left: 0; margin-top: 10px} img{cursor: pointer;} .suboption{padding-top: 15px;} #model7172872226 { width: 100%; height: 100%; } .threejs_container { width: 100%; height: 75vh;} .settings{max-height: 74vh} input[type=range] { -webkit-appearance: none; padding:0; width:90%; margin-left: auto; margin-right: auto; margin-top: 15px; margin-bottom: 15px; display: block; } input[type=range]:focus { outline: none; } input[type=range]::-webkit-slider-runnable-track { height: 4px; cursor: pointer; animate: 0.2s; box-shadow: 0px 0px 0px #000000; background: #E3E3E3; border-radius: 0px; border: 0px solid #000000; } input[type=range]::-webkit-slider-thumb { box-shadow: 1px 1px 2px #B8B8B8; border: 1px solid #ABABAB; height: 13px; width: 25px; border-radius: 20px; background: #E0E0E0; cursor: pointer; -webkit-appearance: none; margin-top: -5px; } input[type=range]:focus::-webkit-slider-runnable-track { background: #E3E3E3; } input[type=range]::-moz-range-track { height: 4px; cursor: pointer; animate: 0.2s; box-shadow: 0px 0px 0px #000000; background: #E3E3E3; border-radius: 0px; border: 0px solid #000000; } input[type=range]::-moz-range-thumb { box-shadow: 1px 1px 2px #B8B8B8; border: 1px solid #ABABAB; height: 13px; width: 25px; border-radius: 20px; background: #E0E0E0; cursor: pointer; } input[type=range]::-ms-track { height: 4px; cursor: pointer; animate: 0.2s; background: transparent; border-color: transparent; color: transparent; } input[type=range]::-ms-fill-lower { background: #E3E3E3; border: 0px solid #000000; border-radius: 0px; box-shadow: 0px 0px 0px #000000; } input[type=range]::-ms-fill-upper { background: #E3E3E3; border: 0px solid #000000; border-radius: 0px; box-shadow: 0px 0px 0px #000000; } input[type=range]::-ms-thumb { box-shadow: 1px 1px 2px #B8B8B8; border: 1px solid #ABABAB; height: 13px; width: 25px; border-radius: 20px; background: #E0E0E0; cursor: pointer; } input[type=range]:focus::-ms-fill-lower { background: #E3E3E3; } input[type=range]:focus::-ms-fill-upper { background: #E3E3E3; } /* // COMMON_CODE_BLOCK_END */ </style> </head> <body> <div class='threejs_container'> <div id='settings_0' class='settings'> <div class=group id='explode_0'> <strong>Explode</strong> <input id='explodeRange_0' type='range' min='0.00001' max=6 step=0.01 value=0.00001> <div class=indented><input id='explodeCheckbox_0' type='checkbox'>Automatic explosion</div> <div class=suboption>Exploding speed</div> <input id='explodingSpeedRange_0' type='range' min=0 max=0.5 step=0.001 value=0.05> </div> <div class=group id='transparency_0' class='transparency'> <strong>Transparency</strong> <input id='transparencyRange_0' type='range' min=0 max=1 step=0.01 value=0> <div class=indented><input id='depthWriteCheckbox_0' type='checkbox'>depthWrite</div> </div> <div class=group id='rotation_0'> <strong>Rotation</strong> <div class=indented> <div><input type='checkbox' id='changeRotationX_0'> x-axis</div> <div><input type='checkbox' id='changeRotationY_0'> y-axis</div> <div><input type='checkbox' id='changeRotationZ_0'> z-axis</div> <button id='resetButton_0'>Reset</button> </div> <div class=suboption>Rotation speed</div> <input id='rotationSpeedRange_0' type='range' min=0 max=5 step=0.01 value=2> </div> <div class=group id='display_0'> <strong>Display</strong> <div class=indented> <div id='shownObjectTypesList_0' class='shownObjectsList'></div> </div> <div class=suboption>Objects</div> <div class=indented> <div id='shownObjectsList_0' class='shownObjectsList'></div> </div> </div> <div class=group id='camera_0'> <strong>Camera</strong> <div class=indented> <form> <select id="cameraType_0"> <option value='perspective' selected> Perspective<br></option> <option value='orthographic' > Orthographic<br></option> </select> </form> </div> </div> <div class=group id='svg_0'> <strong>SVG</strong> <div class=indented> <form> <input type="radio" name='screenshotMode' value='download' id='download_0' checked> Download<br> <input type="radio" name='screenshotMode' value='tab' id='tab_0' > New tab<br> </form> <button id='takeScreenshot_0'>Screenshot</button> </div> </div> </div> <!-- end of settings --> <img id='hideSettingsButton_0' class='hideSettingsButton' src='/kernelspecs/r118/polymake/close.svg' width=20px"> <img id='showSettingsButton_0' class='showSettingsButton' src='/kernelspecs/r118/polymake/menu.svg' width=20px"> <div id="model7172872226"></div> </div> <script> requirejs.config({ paths: { three: '/kernelspecs/r118/polymake/three', TrackballControls: '/kernelspecs/r118/polymake/TrackballControls', OrbitControls: '/kernelspecs/r118/polymake/OrbitControls', Projector: '/kernelspecs/r118/polymake/Projector', SVGRenderer: '/kernelspecs/r118/polymake/SVGRenderer', WEBGL: '/kernelspecs/r118/polymake/WebGL', }, shim: { 'three': { exports: 'THREE'}, 'SVGRenderer': { deps: [ 'three' ], exports: 'THREE.SVGRenderer' }, 'WEBGL': { deps: [ 'three' ], exports: 'THREE.WEBGL' }, 'Projector': { deps: [ 'three' ], exports: 'THREE.Projector' }, 'TrackballControls': { deps: [ 'three' ], exports: 'THREE.TrackballControls' }, 'OrbitControls': { deps: [ 'three' ], exports: 'THREE.OrbitControls' }, } }); require(['three'],function(THREE){ window.THREE = THREE; require(['TrackballControls', 'OrbitControls', 'Projector', 'SVGRenderer', 'WEBGL'], function(TrackballControls, OrbitControls, Projector, SVGRenderer, WEBGL) { 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: false, lines: false, edgelabels: false, faces: false, arrowheads: false }; const foldables = []; var three = document.getElementById("model7172872226"); 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, 1); svgRenderer.setClearColor(0xFFFFFF, 1); three.appendChild(renderer.domElement); var frustumSize = 4; var cameras = [new THREE.PerspectiveCamera(75, 1, 0.1, 1000), new THREE.OrthographicCamera()]; cameras.forEach(function(cam) { cam.position.set(0, 0, 5); cam.lookAt(0, 0, 0); cam.up.set(0, 1, 0); }); var controls = [new THREE.TrackballControls(cameras[0], three), new THREE.OrbitControls(cameras[1], three)]; 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) { this.vector = new THREE.Vector3(x,y,z); this.sprite = null; this.sphere = null; } PMPoint.prototype.addLabel = function(labelsprite) { this.sprite = labelsprite; this.sprite.position.copy(this.vector); } PMPoint.prototype.addSphere = function(spheremesh) { this.sphere = spheremesh; this.sphere.position.copy(this.vector); } PMPoint.prototype.set = function(x,y,z) { this.vector.set(x,y,z); 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('#model7172872226'); // create an observer instance var observer = new MutationObserver(function(mutations) { mutations.forEach(function(mutation) { if (mutation.removedNodes && mutation.removedNodes.length > 0) { cancelAnimationFrame(renderId); observer.disconnect(); console.log("cancelled frame "+renderId); } }); }); // configuration of the observer: var config = { childList: true, characterData: true } // pass in the target node, as well as the observer options while (target) { if (target.className=="output") { observer.observe(target, config); break; } target = target.parentNode; } // COMMON_CODE_BLOCK_END var obj0 = new THREE.Object3D(); obj0.name = "unnamed__1"; obj0.userData.explodable = 1; obj0.userData.points = []; obj0.userData.points.push(new PMPoint(4, 0, 0)); obj0.userData.points.push(new PMPoint(0, 4, 0)); obj0.userData.points.push(new PMPoint(2, 1, 1)); obj0.userData.pointradii = 0.02; <!-- Vertex style --> obj0.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } )]; obj0.userData.pointlabels = ["0", "1", "3"]; obj0.userData.edgeindices = [0, 1, 0, 2, 1, 2]; <!-- Edge style --> obj0.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: false } ); obj0.userData.facets = [[1, 0, 2]]; <!-- Facet style --> obj0.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, depthWrite: false, opacity: 0.5, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 0.5, side: THREE.DoubleSide, transparent: true } ); init_object(obj0); scene.add(obj0); var obj1 = new THREE.Object3D(); obj1.name = "unnamed__2"; obj1.userData.explodable = 1; obj1.userData.points = []; obj1.userData.points.push(new PMPoint(4, 0, 0)); obj1.userData.points.push(new PMPoint(0, 0, 4)); obj1.userData.points.push(new PMPoint(1, 1, 2)); obj1.userData.pointradii = 0.02; <!-- Vertex style --> obj1.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } )]; obj1.userData.pointlabels = ["0", "2", "5"]; obj1.userData.edgeindices = [0, 1, 0, 2, 1, 2]; <!-- Edge style --> obj1.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: false } ); obj1.userData.facets = [[1, 0, 2]]; <!-- Facet style --> obj1.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, depthWrite: false, opacity: 0.5, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 0.5, side: THREE.DoubleSide, transparent: true } ); init_object(obj1); scene.add(obj1); var obj2 = new THREE.Object3D(); obj2.name = "unnamed__3"; obj2.userData.explodable = 1; obj2.userData.points = []; obj2.userData.points.push(new PMPoint(4, 0, 0)); obj2.userData.points.push(new PMPoint(2, 1, 1)); obj2.userData.points.push(new PMPoint(1, 1, 2)); obj2.userData.pointradii = 0.02; <!-- Vertex style --> obj2.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } )]; obj2.userData.pointlabels = ["0", "3", "5"]; obj2.userData.edgeindices = [0, 1, 0, 2, 1, 2]; <!-- Edge style --> obj2.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: false } ); obj2.userData.facets = [[1, 0, 2]]; <!-- Facet style --> obj2.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, depthWrite: false, opacity: 0.5, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 0.5, side: THREE.DoubleSide, transparent: true } ); init_object(obj2); scene.add(obj2); var obj3 = new THREE.Object3D(); obj3.name = "unnamed__4"; obj3.userData.explodable = 1; obj3.userData.points = []; obj3.userData.points.push(new PMPoint(0, 4, 0)); obj3.userData.points.push(new PMPoint(0, 0, 4)); obj3.userData.points.push(new PMPoint(1, 2, 1)); obj3.userData.pointradii = 0.02; <!-- Vertex style --> obj3.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } )]; obj3.userData.pointlabels = ["1", "2", "4"]; obj3.userData.edgeindices = [0, 1, 0, 2, 1, 2]; <!-- Edge style --> obj3.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: false } ); obj3.userData.facets = [[0, 2, 1]]; <!-- Facet style --> obj3.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, depthWrite: false, opacity: 0.5, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 0.5, side: THREE.DoubleSide, transparent: true } ); init_object(obj3); scene.add(obj3); var obj4 = new THREE.Object3D(); obj4.name = "unnamed__5"; obj4.userData.explodable = 1; obj4.userData.points = []; obj4.userData.points.push(new PMPoint(0, 4, 0)); obj4.userData.points.push(new PMPoint(2, 1, 1)); obj4.userData.points.push(new PMPoint(1, 2, 1)); obj4.userData.pointradii = 0.02; <!-- Vertex style --> obj4.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } )]; obj4.userData.pointlabels = ["1", "3", "4"]; obj4.userData.edgeindices = [0, 1, 0, 2, 1, 2]; <!-- Edge style --> obj4.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: false } ); obj4.userData.facets = [[0, 1, 2]]; <!-- Facet style --> obj4.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, depthWrite: false, opacity: 0.5, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 0.5, side: THREE.DoubleSide, transparent: true } ); init_object(obj4); scene.add(obj4); var obj5 = new THREE.Object3D(); obj5.name = "unnamed__6"; obj5.userData.explodable = 1; obj5.userData.points = []; obj5.userData.points.push(new PMPoint(0, 0, 4)); obj5.userData.points.push(new PMPoint(1, 2, 1)); obj5.userData.points.push(new PMPoint(1, 1, 2)); obj5.userData.pointradii = 0.02; <!-- Vertex style --> obj5.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } )]; obj5.userData.pointlabels = ["2", "4", "5"]; obj5.userData.edgeindices = [0, 1, 0, 2, 1, 2]; <!-- Edge style --> obj5.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: false } ); obj5.userData.facets = [[0, 1, 2]]; <!-- Facet style --> obj5.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, depthWrite: false, opacity: 0.5, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 0.5, side: THREE.DoubleSide, transparent: true } ); init_object(obj5); scene.add(obj5); var obj6 = new THREE.Object3D(); obj6.name = "unnamed__7"; obj6.userData.explodable = 1; obj6.userData.points = []; obj6.userData.points.push(new PMPoint(2, 1, 1)); obj6.userData.points.push(new PMPoint(1, 2, 1)); obj6.userData.points.push(new PMPoint(1, 1, 2)); obj6.userData.pointradii = 0.02; <!-- Vertex style --> obj6.userData.pointmaterial = [new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } ), new THREE.MeshBasicMaterial( { color: 0xFF0000, side: THREE.DoubleSide, transparent: false } )]; obj6.userData.pointlabels = ["3", "4", "5"]; obj6.userData.edgeindices = [0, 1, 0, 2, 1, 2]; <!-- Edge style --> obj6.userData.edgematerial = new THREE.LineBasicMaterial( { color: 0x000000, linewidth: 1.5, transparent: false } ); obj6.userData.facets = [[1, 0, 2]]; <!-- Facet style --> obj6.userData.facetmaterial = new THREE.MeshBasicMaterial( { color: 0x77EC9E, depthFunc: THREE.LessDepth, depthWrite: false, opacity: 0.5, polygonOffset: true, polygonOffsetFactor: 1, polygonOffsetUnits: 0.5, side: THREE.DoubleSide, transparent: true } ); init_object(obj6); scene.add(obj6); // COMMON_CODE_BLOCK_BEGIN function textSpriteMaterial(message, parameters) { if ( parameters === undefined ) parameters = {}; var fontface = "Helvetica"; var fontsize = parameters.hasOwnProperty("fontsize") ? parameters["fontsize"] : 15; fontsize = fontsize*10; var lines = message.split('\\n'); var size = 512; for(var i = 0; i<lines.length; i++){ var tmp = lines[i].length; while(tmp*fontsize > size){ fontsize--; } } var canvas = document.createElement('canvas'); canvas.width = size; canvas.height = size; var context = canvas.getContext('2d'); context.fillStyle = "rgba(255, 255, 255, 0)"; context.fill(); context.font = fontsize + "px " + fontface; // text color context.fillStyle = "rgba(0, 0, 0, 1.0)"; for(var i = 0; i<lines.length; i++){ context.fillText(lines[i], size/2, size/2+i*fontsize); } // canvas contents will be used for a texture var texture = new THREE.Texture(canvas); texture.needsUpdate = true; var spriteMaterial = new THREE.SpriteMaterial({map: texture, depthTest: true, depthWrite: false, polygonOffset: true, polygonOffsetFactor: -1, polygonOffsetUnits: 1 }); return spriteMaterial; } // ---------------------- INITIALIZING OBJECTS-------------------------------------- // --------------------------------------------------------------------------------- function init_object(obj) { if (obj.userData.hasOwnProperty("pointmaterial")) { init_points(obj); modelContains.points = true; } if (obj.userData.hasOwnProperty("pointlabels")) { init_pointlabels(obj); modelContains.pointlabels = true; } if (obj.userData.hasOwnProperty("edgematerial")) { init_lines(obj); modelContains.lines = true; } if (obj.userData.hasOwnProperty("edgelabels")) { init_edgelabels(obj); modelContains.edgelabels = true; } if (obj.userData.hasOwnProperty("arrowstyle")) { init_arrowheads(obj); modelContains.arrowheads = true; } if (obj.userData.hasOwnProperty("facetmaterial")) { init_faces(obj); modelContains.faces = true; } } function init_points(obj) { var pointgroup = new THREE.Group(); pointgroup.name = "points"; var points = obj.userData.points; var radii = obj.userData.pointradii; var materials = obj.userData.pointmaterial; var geometry,material; if (!Array.isArray(radii)) { geometry = new THREE.SphereBufferGeometry(radii); } if (!Array.isArray(materials)) { material = materials; } for (var i=0; i<points.length; 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, material); 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 = "pointlabels"; if (Array.isArray(labels)) { for (var i=0; i<points.length; 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<points.length; 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('position', bufattr); if (Array.isArray(materials)) { for (var i=0; i<materials.length; i++) { geometry.addGroup(2*i,2,i); } } var lines = new THREE.LineSegments(geometry, materials); lines.name = "lines"; 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 = "edgelabels"; if (Array.isArray(labels)) { for (var i=0; i<edgeindices.length/2; i++) { var spriteMaterial = textSpriteMaterial( labels[i] ); var sprite = new THREE.Sprite(spriteMaterial); sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector,points[edgeindices[2*i+1]].vector).multiplyScalar(0.5)); edgelabels.add(sprite); } } else { var spriteMaterial = textSpriteMaterial( labels ); for (var i=0; i<edgeindices.length/2; i++) { var sprite = new THREE.Sprite(spriteMaterial); sprite.position.copy(new THREE.Vector3().addVectors(points[edgeindices[2*i]].vector,points[edgeindices[2*i+1]].vector).multiplyScalar(0.5)); edgelabels.add(sprite); } } obj.add(edgelabels); } function init_arrowheads(obj) { var arrowheads = new THREE.Group(); arrowheads.name = "arrowheads"; 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<edgeindices.length; i=i+2) { 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,start.vector); dir.normalize(); var axis = new THREE.Vector3().set(dir.z,0,-dir.x); axis.normalize(); var radians = Math.acos( dir.y ); var radius = dist/25; var height = dist/5; var geometry = new THREE.ConeBufferGeometry(radius,height); var position = new THREE.Vector3().addVectors(start.vector,dir.clone().multiplyScalar(start.radius()+dist-height/2)); if (Array.isArray(edgematerials)) { material = new THREE.MeshBasicMaterial( {color: edgematerials[i].color} ); } var cone = new THREE.Mesh( geometry, material ); cone.quaternion.setFromAxisAngle(axis,radians);; 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<facets.length; i++) { facet = facets[i]; for (var t=0; t<facet.length-2; t++) { obj.userData.triangleindices.push(facet[0],facet[t+1],facet[t+2]); } } var bufarr = new Float32Array( obj.userData.triangleindices.length * 3 ); var bufattr = new THREE.Float32BufferAttribute(bufarr,3); var materials = obj.userData.facetmaterial; var geometry = new THREE.BufferGeometry(); var frontmaterials = []; var backmaterials = []; geometry.setAttribute('position',bufattr); if (Array.isArray(materials)) { var tricount = 0; var facet; for (var i=0; i<facets.length; i++) { facet = facets[i]; geometry.addGroup(tricount,(facet.length-2)*3,i); tricount += (facet.length-2)*3; } for (var j=0; j<materials.length; 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, backmaterials]; } // duplicating the object with front and back should avoid transparency issues var backmesh = new THREE.Mesh(geometry, backmaterials); // meshname is used to show/hide objects backmesh.name = "backfaces"; obj.add(backmesh); var frontmesh = new THREE.Mesh(geometry, frontmaterials); frontmesh.name = "frontfaces"; obj.add(frontmesh); updateFacesPosition(obj); } // //INITIALIZING function updateFacesPosition(obj) { var points = obj.userData.points; var indices = obj.userData.triangleindices; var faces = obj.getObjectByName("frontfaces"); var ba = faces.geometry.getAttribute("position"); for (var i=0; i<indices.length; i++) { ba.setXYZ(i, points[indices[i]].vector.x, points[indices[i]].vector.y ,points[indices[i]].vector.z); } faces.geometry.attributes.position.needsUpdate = true; } function updateEdgesPosition(obj) { var points = obj.userData.points; var indices = obj.userData.edgeindices; var lines = obj.getObjectByName("lines"); var ba = lines.geometry.getAttribute("position"); for (var i=0; i<indices.length; i++) { ba.setXYZ(i, points[indices[i]].vector.x, points[indices[i]].vector.y ,points[indices[i]].vector.z); } lines.geometry.attributes.position.needsUpdate = true; } function onWindowResize() { renderer.setSize( three.clientWidth, three.clientHeight ); svgRenderer.setSize( three.clientWidth, three.clientHeight ); updateCamera(); } function updateCamera() { var width = three.clientWidth; var height = three.clientHeight; var aspect = width / height; if (camera.type == "OrthographicCamera") { camera.left = frustumSize * aspect / - 2; camera.right = frustumSize * aspect / 2; camera.top = frustumSize / 2; camera.bottom = - frustumSize / 2; } else if (camera.type == "PerspectiveCamera") { 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<controls.length; i++) { if (i!=selindex) { controls[i].enabled = false; } } updateCamera(); } var camtypenode = document.getElementById('cameraType_0'); camtypenode.onchange = changeCamera; camtypenode.dispatchEvent(new Event('change')); onWindowResize(); window.addEventListener('resize', onWindowResize); 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 // explode(updateFactor()); 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, camera); }; 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<scene.children.length; i++) { child = scene.children[i]; if ( child.userData.hasOwnProperty("facetmaterial") ) { if (Array.isArray(child.userData.facetmaterial)) { for (var j=0; j<child.userData.facetmaterial.length; 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<scene.children.length; i++) { child = scene.children[i]; if ( child.userData.hasOwnProperty("facetmaterial") ) { if (Array.isArray(child.userData.facetmaterial)) { for (var j=0; j<child.userData.facetmaterial.length; 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(0,0,0); camera.position.set(0,0,5); camera.up.set(0,1,0); } function showSettings(event){ document.getElementById('settings_0').style.visibility = 'visible'; document.getElementById('showSettingsButton_0').style.visibility = 'hidden'; document.getElementById('hideSettingsButton_0').style.visibility = 'visible'; settingsShown = true; } function hideSettings(event){ document.getElementById('settings_0').style.visibility = 'hidden'; document.getElementById('showSettingsButton_0').style.visibility = 'visible'; document.getElementById('hideSettingsButton_0').style.visibility = 'hidden'; 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))/L; 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))/L; 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))/L; 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<obj.userData.axes.length; j++) { rotateVertices(obj, j, scale); } update(obj); obj.userData.oldscale += scale; lookAtBarycenter(obj); } function lookAtBarycenter(obj){ control.target = barycenter(obj); } function barycenter(obj) { var center = new THREE.Vector3(0,0,0); var points = obj.userData.points; for (var i=0; i<points.length; i++){ center.add(points[i].vector); } center.divideScalar(points.length); return center; } function rotateVertices(obj, edge, scale) { 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<subtrees[edge].length; j++){ var rotP = rotate(points[subtrees[edge][j]].vector, points[axes[edge][0]].vector,points[axes[edge][1]].vector, scale * (Math.PI - angles[edge])); points[subtrees[edge][j]].set(rotP[0],rotP[1],rotP[2]); } } } function update(obj) { updateFacesPosition(obj); updateEdgesPosition(obj); } if (foldables.length) { var settings = document.getElementById('settings_0'); var foldDiv = document.createElement('div'); foldDiv.id = 'fold_0'; var title = document.createElement('strong'); title.innerHTML = 'Fold'; foldDiv.appendChild(title); foldDiv.className = 'group'; for (var i=0; i<foldables.length; i++) { var range = document.createElement('input'); range.type = 'range'; 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,settings.childNodes[0]); } // ---------------------- EXPLOSION ------------------------------------------------ // --------------------------------------------------------------------------------- if (explodableModel) { for (var i=0; i<scene.children.length; i++) { obj = scene.children[i]; if ( obj.userData.explodable ) { computeCentroid(obj); } } document.getElementById('explodeRange_0').oninput = triggerExplode; document.getElementById('explodeCheckbox_0').onchange = triggerAutomaticExplode; document.getElementById('explodingSpeedRange_0').oninput = setExplodingSpeed; 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<scene.children.length; i++) { var obj = scene.children[i]; if (obj.userData.hasOwnProperty("centroid")) { var c = obj.userData.centroid; obj.position.set(c.x*factor, c.y*factor, c.z*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, 25)); } function explodingInterval(){ explodeScale += explodingSpeed; if (explodeScale <= 6){ explode(explodeScale); } else{ explode(6); explodeScale = 6; clearIntervals(); timeouts.push(setTimeout(startUnexploding, 3000)); } document.getElementById('explodeRange_0').value = explodeScale; } function startUnexploding(){ intervals.push(setInterval(unexplodingInterval, 25)); } function unexplodingInterval(){ explodeScale -= explodingSpeed; if (explodeScale >= 0){ explode(explodeScale); } else { explode(0); explodeScale = 0; clearIntervals(); timeouts.push(setTimeout(startExploding, 3000)); } document.getElementById('explodeRange_0').value = explodeScale; } function clearIntervals(){ intervals.forEach(function(interval){ clearInterval(interval); }); intervals = []; timeouts.forEach(function(timeout){ clearTimeout(timeout); }); timeouts = []; } // ---------------------- DISPLAY -------------------------------------------------- // --------------------------------------------------------------------------------- const objectTypeInnerHTMLs = { points: "Points", pointlabels: "Point labels", lines: "Edges", edgelabels: "Edge labels", faces: "Faces", arrowheads: "Arrow heads" }; const objectTypeVisible = {}; Object.assign(objectTypeVisible,modelContains); const sortedObjectTypeKeys = Object.keys(objectTypeInnerHTMLs).sort(); const shownObjectTypesList = document.getElementById('shownObjectTypesList_0'); function setVisibility(bool,objname) { for (var i=0; i<scene.children.length; 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 == "faces") { setVisibility(checked,"frontfaces"); setVisibility(checked,"backfaces"); } else { setVisibility(checked,name); } } for (var i=0; i<sortedObjectTypeKeys.length; i++){ var key = sortedObjectTypeKeys[i]; if (modelContains[key]) { var objTypeNode = document.createElement('span'); objTypeNode.innerHTML = objectTypeInnerHTMLs[key] + '<br>'; var checkbox = document.createElement('input'); checkbox.type = 'checkbox'; 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('shownObjectsList_0'); for (var i=0; i<scene.children.length; i++){ obj = scene.children[i]; var objNode = document.createElement('span'); objNode.innerHTML = obj.name + '<br>'; var checkbox = document.createElement('input'); checkbox.type = 'checkbox'; checkbox.checked = true; checkbox.name = String(i); checkbox.onchange = toggleObjectVisibility; shownObjectsList.appendChild(checkbox); shownObjectsList.appendChild(objNode); } // ---------------------- SVG ------------------------------------------------------ // --------------------------------------------------------------------------------- function takeSvgScreenshot() { if (objectTypeVisible["pointlabels"]) { setVisibility(false,"pointlabels"); } if (objectTypeVisible["edgelabels"]) { setVisibility(false,"edgelabels"); } svgRenderer.render(scene,camera); svgElement = XMLS.serializeToString(svgRenderer.domElement); if (objectTypeVisible["pointlabels"]) { setVisibility(true,"pointlabels"); } if (objectTypeVisible["edgelabels"]) { setVisibility(true,"edgelabels"); } if (document.getElementById('tab_0').checked){ //show in new tab var myWindow = window.open("",""); myWindow.document.body.innerHTML = svgElement; } else{ // download svg file download("screenshot.svg", svgElement); } } function download(filename, text) { var element = document.createElement('a'); element.setAttribute('href', 'data:text/plain;charset=utf-8,' + encodeURIComponent(text)); element.setAttribute('download', filename); element.style.display = 'none'; document.body.appendChild(element); element.click(); document.body.removeChild(element); } document.getElementById('transparencyRange_0').oninput = changeTransparency; document.getElementById('depthWriteCheckbox_0').onchange = toggleDepthWrite; document.getElementById('changeRotationX_0').onchange = changeRotationX; document.getElementById('changeRotationY_0').onchange = changeRotationY; document.getElementById('changeRotationZ_0').onchange = changeRotationZ; document.getElementById('resetButton_0').onclick = resetScene; document.getElementById('rotationSpeedRange_0').oninput = changeRotationSpeedFactor; document.getElementById('takeScreenshot_0').onclick = takeSvgScreenshot; document.getElementById('showSettingsButton_0').onclick = showSettings; document.getElementById('hideSettingsButton_0').onclick = hideSettings; // ------------------ SHORTCUTS -------------------------------------------- // ------------------------------------------------------------------------- /** * http://www.openjs.com/scripts/events/keyboard_shortcuts/ * Version : 2.01.B * By Binny V A * License : BSD */ shortcut = { 'all_shortcuts':{},//All the shortcuts are stored in this array 'add': function(shortcut_combination,callback,opt) { //Provide a set of default options var default_options = { 'type':'keydown', 'propagate':false, 'disable_in_input':false, 'target':document, 'keycode':false } if(!opt) opt = default_options; else { for(var dfo in default_options) { if(typeof opt[dfo] == 'undefined') opt[dfo] = default_options[dfo]; } } var ele = opt.target; if(typeof opt.target == 'string') ele = document.getElementById(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['disable_in_input']) { //Don't enable shortcut keys in Input, Textarea fields 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 == 'INPUT' || element.tagName == 'TEXTAREA') return; } //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 the user presses , when the type is onkeydown if(code == 190) character="."; //If the user presses , when the type is onkeydown 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 = { "`":"~", "1":"!", "2":"@", "3":"#", "4":"$", "5":"%", "6":"^", "7":"&", "8":"*", "9":"(", "0":")", "-":"_", "=":"+", ";":":", "'":"\"", ",":"<", ".":">", "/":"?", "\\":"|" } //Special Keys - and their codes var special_keys = { 'esc':27, 'escape':27, 'tab':9, 'space':32, 'return':13, 'enter':13, 'backspace':8, 'scrolllock':145, 'scroll_lock':145, 'scroll':145, 'capslock':20, 'caps_lock':20, 'caps':20, 'numlock':144, 'num_lock':144, 'num':144, 'pause':19, 'break':19, 'insert':45, 'home':36, 'delete':46, 'end':35, 'pageup':33, 'page_up':33, 'pu':33, 'pagedown':34, 'page_down':34, 'pd':34, 'left':37, 'up':38, 'right':39, 'down':40, 'f1':112, 'f2':113, 'f3':114, 'f4':115, 'f5':116, 'f6':117, 'f7':118, 'f8':119, 'f9':120, 'f10':121, 'f11':122, 'f12':123 } var modifiers = { shift: { wanted:false, pressed:false}, ctrl : { wanted:false, pressed:false}, alt : { wanted:false, pressed:false}, meta : { wanted:false, pressed:false} //Meta is Mac specific }; if(e.ctrlKey) modifiers.ctrl.pressed = true; if(e.shiftKey) modifiers.shift.pressed = true; if(e.altKey) modifiers.alt.pressed = true; if(e.metaKey) modifiers.meta.pressed = true; for(var i=0; k=keys[i],i<keys.length; i++) { //Modifiers if(k == 'ctrl' || k == 'control') { kp++; modifiers.ctrl.wanted = true; } else if(k == 'shift') { kp++; modifiers.shift.wanted = true; } else if(k == 'alt') { kp++; modifiers.alt.wanted = true; } else if(k == 'meta') { 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['keycode']) { if(opt['keycode'] == code) kp++; } 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['propagate']) { //Stop the event //e.cancelBubble is supported by IE - this will kill the bubbling process. e.cancelBubble = true; e.returnValue = false; //e.stopPropagation works in Firefox. if (e.stopPropagation) { e.stopPropagation(); e.preventDefault(); } return false; } } } this.all_shortcuts[shortcut_combination] = { 'callback':func, 'target':ele, 'event': opt['type'] }; //Attach the function with the event if(ele.addEventListener) ele.addEventListener(opt['type'], func, false); else if(ele.attachEvent) ele.attachEvent('on'+opt['type'], func); else ele['on'+opt['type']] = func; }, //Remove the shortcut - just specify the shortcut and I will remove the binding 'remove':function(shortcut_combination) { shortcut_combination = shortcut_combination.toLowerCase(); var binding = this.all_shortcuts[shortcut_combination]; delete(this.all_shortcuts[shortcut_combination]) if(!binding) return; var type = binding['event']; var ele = binding['target']; var callback = binding['callback']; if(ele.detachEvent) ele.detachEvent('on'+type, callback); else if(ele.removeEventListener) ele.removeEventListener(type, callback, false); else ele['on'+type] = false; } } shortcut.add("Alt+Left",function() { var event = new Event('click'); if (settingsShown){ document.getElementById('hideSettingsButton_0').dispatchEvent(event); } else { document.getElementById('showSettingsButton_0').dispatchEvent(event); } }); // COMMON_CODE_BLOCK_END });}); </script> </body> </html> </HTML> <code perl> > $h2 = new Hypersurface<Min>(DUAL_SUBDIVISION=>$moae); > $h2_pw = $h2->PATCHWORK(SIGNS=>[0,0,0,1,1,0]); > print $h2_pw->BETTI_NUMBERS_Z2; 3 3 </code> user_guide/tutorials/master/patchwork.txt Last modified: 2024/02/07 05:58by 127.0.0.1