En fotball (buckyball)

Hva

Polygoner på en Buckyball

"Buckyball" [1] er et kjent fenomen både i matematikken, naturen og på fotballbanen. Formen på en buckyball er beskrevet ved hjelp av det gyldne snitt (1.61803399...). Dette forholdstallet kan beregnes som kvotienten mellom to nabotall i Fibonacci-rekka [2] og det inngår i mange resonnementer i matematikken og det finnes i naturlige former. Det tillegges også en estetisk betydning som et "naturlig" eller balansert forhold, f.eks. som forholdet mellom høyde og bredde i et rektangel. Det ser ut til at det gyldne snitt i en del sammenhenger beskriver fenomener som er forbundet med maksimal pakking av former.

Buckyball er et kjent begrep for kjemikere og beskriver en ordning av 60 carbonatomer i hjørnene til figuren. Figuren er oppkalt etter R. Buckminster Fuller [4] . En buckball har 60 hjørner, 20 6-kanter og 12 5-kanter. Figuren er fra GoldenNumber.net [5] . Dataene som er brukt til å tegne buckyball i denne modulen ser du her i Javascript form, slik de genereres i programmet: polygoner

En roterende ball ser slik ut (i en iframe):

Du kan også inspisere resultatet og kildekoden på en enklere side:
simple.html https://borres.hiof.no/wep/webgl/basis/ball/simple.html

Javascript

Det er to javascript involvert, foruten Sylvester og GLUtils: render.js som drar dynamikken og ball.js som lager selve ballen og forbereder punkter, normaler og materialer.

//globals
var canvas;
var gl;
var mvMatrix;
var perspectiveMatrix;
var shaderProgram;
var SIZE=20;
//shapes
var aBall;
//dynamic
var xRot=0.0;  
var yRot=0.0;
var deltayRot=0.5;
var deltaxRot=0.4;
// user controlled
var showBlack=true;
var showWhite=true;
var showLines=true;
//eofglobals
//start
function start() {
    canvas = document.getElementById("theball");
    initWebGL(canvas); 
    if (gl) {
        gl.clearColor(1.0, 1.0, 1.0, 1.0); 
        gl.clearDepth(1.0); 
        gl.enable(gl.DEPTH_TEST); 
        gl.depthFunc(gl.LEQUAL); 
        initBuffers();    
        initShaders(); 
        tick();
        
        // fill window, and draw
        onWindowResize();
        // pick up resizing
        window.addEventListener( 'resize', onWindowResize, false );
        }
}
//eofstart
 
 
function tick() {
    // using webgl-utils.js
    requestAnimFrame(tick,canvas);
    yRot+=deltayRot;
    xRot+=deltaxRot;
    drawScene();
}
//initWebGL
function initWebGL() {
    gl = null;
    // browser and versions reckognize webgl differently ?
    var names = ["webgl", "experimental-webgl", "webkit-3d", "moz-webgl"];
    for(var i = 0; i < names.length; i++){
        try {gl = canvas.getContext("experimental-webgl");}
        catch(e) {}
        if(gl){break;}
    }
    if (!gl) {
        // show captures instead
        showCaptureInstead();
   }
}
//eofinitWebGL
//initBuffers
function initBuffers() {
    // set up the ball
    aBall=new Ball();
}
//eofinitBuffers
//drawScene
function drawScene() {
    gl.viewport(0, 0, canvas.width, canvas.height);
    gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);    
    perspectiveMatrix = makeOrtho(-SIZE, SIZE ,
                                  -SIZE, SIZE, 
                                  0.0, 300.0);        
    loadIdentity();
    setLight(10,10,10);    
    //mvPushMatrix();
    mvScale([10.0,10.0,10.0]);
    mvTranslate([0.0, 0.0, -10.0]);
    mvRotate(yRot, [0, 1, 0]);
    mvRotate(xRot, [1, 0, 0]);
    setMatrixUniforms();
    aBall.draw();
}
//eofdrawScene
//initShaders
function initShaders() {
    var fragmentShader = getShader(gl, "shader-fs");
    var vertexShader = getShader(gl, "shader-vs");
    // Create the shader program  
    shaderProgram = gl.createProgram();
    gl.attachShader(shaderProgram, vertexShader);
    gl.attachShader(shaderProgram, fragmentShader);
    gl.linkProgram(shaderProgram);
    // ok? 
    if (!gl.getProgramParameter(shaderProgram, gl.LINK_STATUS)) {
    alert("Unable to initialize the shader program.");
    }
    gl.useProgram(shaderProgram);
    // let the shaderprogram remember the addresses
    // so we can use  when we fill the attribute buffers
    shaderProgram.vertexPositionAttribute = 
        gl.getAttribLocation(shaderProgram, "aVertexPosition");
    gl.enableVertexAttribArray(shaderProgram.vertexPositionAttribute);
    
    shaderProgram.vertexNormalAttribute = 
        gl.getAttribLocation(shaderProgram, "aVertexNormal");
    gl.enableVertexAttribArray(shaderProgram.vertexNormalAttribute);
    
    shaderProgram.vertexMaterialIndexAttribute = 
        gl.getAttribLocation(shaderProgram, "aMaterialIndex");
    gl.enableVertexAttribArray(shaderProgram.vertexMaterialIndexAttribute);
    
    // mark light 
    shaderProgram.ambientLightingColorUniform = 
        gl.getUniformLocation(shaderProgram, "uAmbientLightingColor");
    shaderProgram.pointLightingLocationUniform = 
        gl.getUniformLocation(shaderProgram, "uPointLightingLocation");
    shaderProgram.pointLightingDiffuseColorUniform = 
        gl.getUniformLocation(shaderProgram, "uPointLightingDiffuseColor");
    shaderProgram.pointLightingSpecularColorUniform = 
        gl.getUniformLocation(shaderProgram, "uPointLightingSpecularColor");}
//eofinitShaders
//getShader
function getShader(gl, id) {
    var shaderScript = document.getElementById(id);
    // ok? 
    if (!shaderScript) {
        return null;
    }
    // Building the shader source string. 
    var theSource = "";
    var currentChild = shaderScript.firstChild;
    while(currentChild) {
        if (currentChild.nodeType == 3) {
            theSource += currentChild.textContent;
        }   
        currentChild = currentChild.nextSibling;
    }
    // What type of shader, based on its MIME type.  
    var shader;  
    if (shaderScript.type == "x-shader/x-fragment") {
        shader = gl.createShader(gl.FRAGMENT_SHADER);
    } else if (shaderScript.type == "x-shader/x-vertex") {
        shader = gl.createShader(gl.VERTEX_SHADER);
    } else {
        return null;  // Unknown shader type
    }
    // Send the source to the shader object
    gl.shaderSource(shader, theSource);
    // Compile the shader program  
    gl.compileShader(shader);
    // See if it compiled successfully  
    if (!gl.getShaderParameter(shader, gl.COMPILE_STATUS)) {
        alert("An error occurred compiling the shaders: " + gl.getShaderInfoLog(shader));
        return null;
    }
    return shader;
}
//eofgetShader
// Matrix utility functions
//
function loadIdentity() {
    mvMatrix = Matrix.I(4);
}
function multMatrix(m) {
    mvMatrix = mvMatrix.x(m);
}
function mvTranslate(v) {
  multMatrix(Matrix.Translation($V([v[0], v[1], v[2]])).ensure4x4());
}
//setlightandcolor
function setLight(x,y,z)
{
    gl.uniform3f(shaderProgram.pointLightingLocationUniform,x,y,z);
    gl.uniform3f(shaderProgram.ambientLightingColorUniform, 1.0, 1.0, 1.0);
    gl.uniform3f(shaderProgram.pointLightingDiffuseColorUniform, 1.0, 1.0, 1.0);
    gl.uniform3f(shaderProgram.pointLightingSpecularColorUniform, 1.0, 1.0, 1.0);
    gl.uniform1i(shaderProgram.showSpecularHighlightsUniform, true);  
}
//eofsetlightandcolor
//setMatrixUniforms
function setMatrixUniforms() {
    // set al the transformation matrices (ModelView, perspective and normal
    var pUniform = gl.getUniformLocation(shaderProgram, "uPMatrix");
    gl.uniformMatrix4fv(pUniform, false, new Float32Array(perspectiveMatrix.flatten()));
    var mvUniform = gl.getUniformLocation(shaderProgram, "uMVMatrix");
    gl.uniformMatrix4fv(mvUniform, false, new Float32Array(mvMatrix.flatten()));
  
    var normalMatrix = mvMatrix.inverse();
    normalMatrix = normalMatrix.transpose();
    var nUniform = gl.getUniformLocation(shaderProgram, "uNormalMatrix");
    gl.uniformMatrix4fv(nUniform, false, new Float32Array(normalMatrix.flatten()));
}
//eofsetMatrixUniforms
var mvMatrixStack = [];
function mvPushMatrix(m) {
  if (m) {
    mvMatrixStack.push(m.dup());
    mvMatrix = m.dup();
  } else {
    mvMatrixStack.push(mvMatrix.dup());
  }
}
function mvPopMatrix() {
  if (!mvMatrixStack.length) {
    throw("Can't pop from an empty matrix stack.");
  }
  
  mvMatrix = mvMatrixStack.pop();
  return mvMatrix;
}
function mvRotate(angle, v) {
  var inRadians = angle * Math.PI / 180.0;
  
  var m = Matrix.Rotation(inRadians, $V([v[0], v[1], v[2]])).ensure4x4();
  multMatrix(m);
}
//requestFrame
//requestAnimationFrame in a cross browser way, from Googles webgl-lib
window.requestAnimFrame = (function() {
  return window.requestAnimationFrame ||
         window.webkitRequestAnimationFrame ||
         window.mozRequestAnimationFrame ||
         window.oRequestAnimationFrame ||
         window.msRequestAnimationFrame ||
         function(/* function FrameRequestCallback */ callback, 
                  /* DOMElement Element */ element) {
           window.setTimeout(callback, 1000/60);
         };
})();
//eofrequestFrame
//resizing
function onWindowResize() {
    canvas.width=canvas.height=Math.min(window.innerWidth,window.innerHeight)
    viewAspect=1.0*window.innerWidth / window.innerHeight;
    gl.viewport(0, 0, canvas.width, canvas.height);
    document.getElementById("menu").style.width=canvas.width+"px";
    document.getElementById("head").style.width=canvas.width+"px";
    // if not animated: drawScene();
}
//eofresizing

// a bucky ball with radius phi
function Ball()
{
    // golden ratio, the quotient between two consecutive fib-numbers
    var phi=1.61803398;
    // polygon objects
    var pol=new Array();
    // databuffers    
    var vertices=[];
    var normals=[];
    var indices=[];
    var matix=[];
    // colorflags
    var BLACK=0.9;
    var WHITE=2.2;
    
        
    function reduce(v)
    {
        return Vector.create([Math.round(v.e(1)*1000)/1000,
                              Math.round(v.e(2)*1000)/1000,
                              Math.round(v.e(3)*1000)/1000]);
    }
    
    // 5 or 6-sided closed polygon
    function poly(v1,v2,v3,v4,v5,v6)
    {
        // make a center point, adjust it and close the polygon
        var v0;
        if(v6)
        {
            v0=Vector.create([
            (v1.e(1)+v2.e(1)+v3.e(1)+v4.e(1)+v5.e(1)+v6.e(1))/6.0,
            (v1.e(2)+v2.e(2)+v3.e(2)+v4.e(2)+v5.e(2)+v6.e(2))/6.0,
            (v1.e(3)+v2.e(3)+v3.e(3)+v4.e(3)+v5.e(3)+v6.e(3))/6.0])
                .toUnitVector().multiply(phi);
            this.P=new Array(reduce(v0),reduce(v1),reduce(v2),reduce(v3),reduce(v4),reduce(v5),reduce(v6),reduce(v1));
        }
        else
        {
            v0=Vector.create([
            (v1.e(1)+v2.e(1)+v3.e(1)+v4.e(1)+v5.e(1))/5.0,
            (v1.e(2)+v2.e(2)+v3.e(2)+v4.e(2)+v5.e(2))/5.0,
            (v1.e(3)+v2.e(3)+v3.e(3)+v4.e(3)+v5.e(3))/5.0])
                .toUnitVector().multiply(phi);
            this.P=new Array(reduce(v0),reduce(v1),reduce(v2),reduce(v3),reduce(v4),reduce(v5),reduce(v1));
        }
        this.size=this.P.length;
    }
    // set up all polygons
    //---- 6 ---- [0..19]
    pol[0]=new poly( //1
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  -phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   -2*phi/3.0]),
          Vector.create([1/3.0,       -2/3.0-phi/3.0,   -2*phi/3.0]), 
          Vector.create([2/3.0,       -1/3.0-2*phi/3.0,  -phi/3.0]), 
          Vector.create([1/3.0,       -phi,         0.0]), 
          Vector.create([-1/3.0,      -phi,         0.0])
     );
    pol[1]=new poly( //2
          Vector.create([-2/3.0-phi/3.0,  -2*phi/3.0,       -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0, -phi/3.0,       -2/3.0]),
          Vector.create([-2*phi/3.0,     -1/3.0,       -2/3.0-phi/3.0]),
          Vector.create([-phi/3.0,      -2/3.0,       -1/3.0-2*phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   -2*phi/3.0]),
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  -phi/3.0])
     );
    pol[2]=new poly( //3
          Vector.create([-1/3.0,      -phi,         0.0]),
          Vector.create([1/3.0,       -phi,         0.0]),
          Vector.create([2/3.0,       -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([1/3.0,       -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  phi/3.0])
     );
    pol[3]=new poly( //4
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([-phi/3.0,      -2/3.0,       1/3.0+2*phi/3.0]),
          Vector.create([-2*phi/3.0,     -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0, -phi/3.0,       2/3.0]),
          Vector.create([-2/3.0-phi/3.0,  -2*phi/3.0,      1/3.0])
     );
    pol[4]=new poly(//5
          Vector.create([-2/3.0-phi/3.0,    -2*phi/3.0,    1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,     2/3.0]),
          Vector.create([-phi,          0.0,        1/3.0]),
          Vector.create([-phi,          0.0,        -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,     -2/3.0]),
          Vector.create([-2/3.0-phi/3.0,   -2*phi/3.0,     -1/3.0])
    );
    pol[5]=new poly( //6
          Vector.create([-1/3.0,        phi,        0.0]),
          Vector.create([1/3.0,         phi,        0.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0, -phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,  -2*phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  -2*phi/3.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, -phi/3.0])
     );
    pol[6]=new poly(//7
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, -phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  -2*phi/3.0]),
          Vector.create([-phi/3.0,        2/3.0,      -1/3.0-2*phi/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,      -2/3.0-phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      -2/3.0]),
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     -1/3.0])
     );
    pol[7]=new poly(//8
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  2*phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,  2*phi/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0, phi/3.0]),
          Vector.create([1/3.0,         phi,        0.0]),
          Vector.create([-1/3.0,        phi,        0.0])
     );
    pol[8]=new poly(//9
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      2/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,      2/3.0+phi/3.0]),
          Vector.create([-phi/3.0,        2/3.0,      1/3.0+2*phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  2*phi/3.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, phi/3.0])
     );
    pol[9]=new poly( //10
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      -2/3.0]),
          Vector.create([-phi,          0.0,        -1/3.0]),
          Vector.create([-phi,          0.0,        1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      2/3.0]),
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     1/3.0])
     );
    pol[10]=new poly(   //11
          Vector.create([-phi/3.0,        -2/3.0,     -1/3.0-2*phi/3.0]),
          Vector.create([-2*phi/3.0,      -1/3.0,      -2/3.0-phi/3.0,]),
          Vector.create([-2*phi/3.0,       1/3.0,      -2/3.0-phi/3.0]),
          Vector.create([-phi/3.0,         2/3.0,      -1/3.0-2*phi/3.0]),
          Vector.create([0.0,           1/3.0,      -phi]),
          Vector.create([0.0,           -1/3.0,     -phi])
     );
    pol[11]=new poly(   //12
          Vector.create([0.0,           -1/3.0,     -phi]),
          Vector.create([0.0,           1/3.0,      -phi]),
          Vector.create([phi/3.0,         2/3.0,      -1/3.0-2*phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,      -2/3.0-phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,     -2/3.0-phi/3.0]),
          Vector.create([phi/3.0,         -2/3.0,     -1/3.0-2*phi/3.0])
     );
    pol[12]=new poly(   //13
          Vector.create([phi/3.0,         -2/3.0,     -1/3.0-2*phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,     -2/3.0-phi/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,      -2/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,     -1/3.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0, -phi/3.0]),
          Vector.create([1/3.0,         -2/3.0-phi/3.0, -2*phi/3.0])
     );
    pol[13]=new poly(   //14
          Vector.create([0.0,           -1/3.0,       phi]),
          Vector.create([0.0,           1/3.0,        phi]),
          Vector.create([-phi/3.0,        2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,        2/3.0+phi/3.0]),
          Vector.create([-2*phi/3.0,       -1/3.0,        2/3.0+phi/3.0]),
          Vector.create([-phi/3.0,        -2/3.0,       1/3.0+2*phi/3.0])
     );
    pol[14]=new poly(   //15
          Vector.create([phi/3.0,         -2/3.0,       1/3.0+2*phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        2/3.0+phi/3.0]),
          Vector.create([phi/3.0,         2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([0.0,           1/3.0,        phi]),
          Vector.create([0.0,           -1/3.0,       phi])
     );
    pol[15]=new poly(   //16
          Vector.create([1/3.0,         -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       2/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([phi/3.0,         -2/3.0,       1/3.0+2*phi/3.0])
     );
    pol[16]=new poly(  //17
          Vector.create([1/3.0,         2/3.0+phi/3.0,    -2*phi/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   -phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        -2/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        -2/3.0-phi/3.0]),
          Vector.create([phi/3.0,         2/3.0,        -1/3.0-2*phi/3.0])
     );
    pol[17]=new poly(   //18
          Vector.create([phi/3.0,         2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        2/3.0+phi/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        2/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       1/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,    2*phi/3.0])
     );
    pol[18]=new poly(  //19
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       -2/3.0]),
          Vector.create([phi,           0.0,          -1/3.0]),
          Vector.create([phi,           0.0,          1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       2/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      1/3.0])
     );
    pol[19]=new poly(  //20
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        2/3.0]),
          Vector.create([phi,           0.0,          1/3.0]),
          Vector.create([phi,           0.0,          -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        -2/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       -1/3.0])
    );
    //---- 5 ---- [20..31]
    pol[20]=new poly( //21
          Vector.create([-2/3.0,        -1/3.0-2*phi/3.0,  -phi/3.0]),
          Vector.create([-1/3.0,        -phi,         0.0]),
          Vector.create([-2/3.0,        -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([-2/3.0-phi/3.0,    -2*phi/3.0,      1/3.0]),
          Vector.create([-2/3.0-phi/3.0,    -2*phi/3.0,      -1/3.0])
     );
    pol[21]=new poly(//22
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,       -1/3.0]),
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,       1/3.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0,   phi/3.0]),
          Vector.create([-1/3.0,        phi,          0.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0,   -phi/3.0])
     );
    pol[22]=new poly(   //23
          Vector.create([-phi/3.0,        -2/3.0,       -1/3.0-2*phi/3.0]),
          Vector.create([0.0,           -1/3.0,       -phi]),
          Vector.create([phi/3.0,         -2/3.0,       -1/3.0-2*phi/3.0]),
          Vector.create([1/3.0,         -2/3.0-phi/3.0,   -2*phi/3.0]),
          Vector.create([-1/3.0,        -2/3.0-phi/3.0,   -2*phi/3.0])
     );
    pol[23]=new poly(   //24
          Vector.create([-1 / 3.0, -2 / 3.0 - phi / 3.0, 2 * phi / 3.0]),
          Vector.create([1 / 3.0, -2 / 3.0 - phi / 3.0, 2 * phi / 3.0]),
          Vector.create([phi / 3.0, -2 / 3.0, 1 / 3.0 + 2 * phi / 3.0]),
          Vector.create([0.0, -1 / 3.0, phi]),
          Vector.create([-phi / 3.0, -2 / 3.0, 1 / 3.0 + 2 * phi / 3.0])
     );
    pol[24]=new poly(   //25
          Vector.create([-1/3.0,        2/3.0+phi/3.0,    -2*phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,    -2*phi/3.0]),
          Vector.create([phi/3.0,         2/3.0,        -1/3.0-2*phi/3.0]),
          Vector.create([0.0,           1/3.0,        -phi]),
          Vector.create([-phi/3.0,        2/3.0,        -1/3.0-2*phi/3.0])
     );
    pol[25]=new poly(   //26
          Vector.create([-phi/3.0,        2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([0.0,           1/3.0,        phi]),
          Vector.create([phi/3.0,         2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,    2*phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,    2*phi/3.0])
     );
    pol[26]=new poly(   //27
          Vector.create([1/3.0,         -phi,         0.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0,  -phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      -1/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      1/3.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0,  phi/3.0])
     );
    pol[27]=new poly(   //28
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       1/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       -1/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   -phi/3.0]),
          Vector.create([1/3.0,         phi,          0.0])
     );
    pol[28]=new poly(  //29
          Vector.create([-phi,           0.0,          -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,        -2/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,        -2/3.0-phi/3.0]),
          Vector.create([-2*phi/3.0,       -1/3.0,       -2/3.0-phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,       -2/3.0])
     );
    pol[29]=new poly(   //30
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,       2/3.0]),
          Vector.create([-2*phi/3.0,       -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,        2/3.0+phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,        2/3.0]),
          Vector.create([-phi,          0.0,          1/3.0])
     );
    pol[30]=new poly(   //31
          Vector.create([2*phi/3.0,        -1/3.0,       -2/3.0-phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        -2/3.0-phi/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        -2/3.0]),
          Vector.create([phi,           0.0,          -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       -2/3.0])
     );
    pol[31]=new poly(   //32
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       2/3.0]),
          Vector.create([phi,           0.0,          1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        2/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        2/3.0+phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,       2/3.0+phi/3.0])
     );
    
    //-------------------------------
    // set up indices, normals and material index
    var index=0;
    // set up for polygons (TRIANGLE_FAN)
    for(var ix=0;ix < pol.length; ix++)
    {
        for(var pix=0;pix < pol[ix].P.length;pix++)
        {
            vertices=vertices.concat([pol[ix].P[pix].e(1),pol[ix].P[pix].e(2),pol[ix].P[pix].e(3)]);
            //normal is same, except centerpoint but that is just ok
            normals=normals.concat([pol[ix].P[pix].e(1),pol[ix].P[pix].e(2),pol[ix].P[pix].e(3)]);
            if(ix > 19)
                matix=matix.concat([BLACK]);
            else
                matix=matix.concat([WHITE]);
            indices=indices.concat(index);
            index=index+1;
        }
    }
    // set up for outline (LINE_STRIP)
    for(var ix=0;ix < pol.length; ix++)
    {
        for(var pix=1;pix < pol[ix].P.length;pix++) // start at 1 to drop center point
        {
            vertices=vertices.concat([pol[ix].P[pix].e(1),pol[ix].P[pix].e(2),pol[ix].P[pix].e(3)]);
            //normal is same
            normals=normals.concat([pol[ix].P[pix].e(1),pol[ix].P[pix].e(2),pol[ix].P[pix].e(3)]);
            matix=matix.concat([BLACK]);
            indices=indices.concat(index);
            index=index+1;
        }
    }

    // prepare buffers once and for all
    this.verticesBuffer= gl.createBuffer();
    gl.bindBuffer(gl.ARRAY_BUFFER, this.verticesBuffer);
    gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(vertices), gl.STATIC_DRAW);
    
    this.verticesNormalBuffer= gl.createBuffer();  
    gl.bindBuffer(gl.ARRAY_BUFFER, this.verticesNormalBuffer);
    gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(normals), gl.STATIC_DRAW);
    
    this.verticesMaterialBuffer=gl.createBuffer();
    gl.bindBuffer(gl.ARRAY_BUFFER, this.verticesMaterialBuffer);
    gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(matix), gl.STATIC_DRAW);
    
    this.verticesIndexBuffer= gl.createBuffer(); 
    gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.verticesIndexBuffer);
    gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(indices), gl.STATIC_DRAW);
    this.verticesIndexBuffer.COUNT=indices.length;
    
    // draw based on set buffers
    // for each vertex: position, normal, materialix
    // indices
    this.draw=function()
    {
        // vertices
        gl.bindBuffer(gl.ARRAY_BUFFER, this.verticesBuffer);
        gl.vertexAttribPointer(shaderProgram.vertexPositionAttribute,3,gl.FLOAT,false,0,0);
        // Set the normal attribute for the vertices. 
        gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesNormalBuffer);
        gl.vertexAttribPointer(shaderProgram.vertexNormalAttribute,3,gl.FLOAT,false,0,0);
        // set material index attribute
        gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesMaterialBuffer);
        gl.vertexAttribPointer(shaderProgram.vertexMaterialIndexAttribute,1,gl.FLOAT,false,0,0);
        
        // Draw the ball.
        gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.verticesIndexBuffer);
        
        var startix=0;
        // whites  ( 6 edges)
        for(var pix=0; pix < 20; pix++)
        {
            if(showWhite)
                gl.drawElements(gl.TRIANGLE_FAN,pol[pix].size,gl.UNSIGNED_SHORT,startix);
            startix=startix+2*pol[pix].size;
        }
        // blacks (5 edges)
        for(var pix=20; pix < 32; pix++)
        {
            if(showBlack)
                gl.drawElements(gl.TRIANGLE_FAN,pol[pix].size,gl.UNSIGNED_SHORT,startix);
            startix=startix+2*pol[pix].size;                
        }
        // lines on white (6 edges)
        // size-1 to loose non-existing center point
        for(var pix=0; pix < 20; pix++)
        {
            if(showLines)
                gl.drawElements(gl.LINE_STRIP,pol[pix].size-1,gl.UNSIGNED_SHORT,startix);
            startix=startix+2*(pol[pix].size-1);
        }
    }
}

Shadere

#ifdef GL_ES
precision mediump float;
#endif
varying vec3 vTransformedNormal;
varying vec4 vPosition;
varying float materialIndex;
uniform vec3 uAmbientLightingColor;
uniform vec3 uPointLightingDiffuseColor;
uniform vec3 uPointLightingSpecularColor;
uniform vec3 uPointLightingLocation;
void main(void) {
    // we deal with the ball
    // assume whitish
    vec3 materialAmbientColor = vec3(0.25, 0.20725, 0.20725);
    vec3 materialDiffuseColor = vec3(1.0, 0.829, 0.829);
    vec3 materialSpecularColor = vec3(0.296648, 0.296648, 0.296648);
    vec3 materialEmissiveColor = vec3(0.3, 0.3, 0.3);
    float materialShininess=11.264;
    
    if(materialIndex < 1.999)//black
    {
        materialAmbientColor = vec3(0.0, 0.0, 0.0);
        materialDiffuseColor = vec3(0.01, 0.01, 0.01);
        materialSpecularColor = vec3(0.50, 0.50, 0.50);
        materialEmissiveColor = vec3(0.0, 0.0, 0.0);
        materialShininess=32.0;
    }
    vec3 ambientLightWeighting = uAmbientLightingColor;
    vec3 lightDirection = normalize(uPointLightingLocation - vPosition.xyz);
    vec3 normal = normalize(vTransformedNormal);
    vec3 specularLightWeighting = vec3(0.0, 0.0, 0.0);
    vec3 eyeDirection = normalize(-vPosition.xyz);
    vec3 reflectionDirection = reflect(-lightDirection, normal);
    float specularLightBrightness = 
        pow(max(dot(reflectionDirection, eyeDirection), 0.0), materialShininess);
    specularLightWeighting = uPointLightingSpecularColor * specularLightBrightness;
    float diffuseLightBrightness = max(dot(normal, lightDirection), 0.0);
    vec3 diffuseLightWeighting = uPointLightingDiffuseColor * diffuseLightBrightness;
    float alpha = 1.0;
    
    gl_FragColor = vec4(
            materialAmbientColor * ambientLightWeighting
            + materialDiffuseColor * diffuseLightWeighting
            + materialSpecularColor * specularLightWeighting
            + materialEmissiveColor,
            alpha
        );
}

attribute mediump vec3 aVertexNormal; // or in
attribute mediump vec3 aVertexPosition;
attribute mediump float aMaterialIndex;
uniform mediump mat4 uNormalMatrix;
uniform mediump mat4 uMVMatrix;
uniform mediump mat4 uPMatrix;

varying vec3 vTransformedNormal;
varying vec4 vPosition;
varying lowp vec4 vColor;
varying mediump vec3 vLighting;
varying float materialIndex;
void main(void) {
    vPosition = uMVMatrix * vec4(aVertexPosition, 1.0);
    gl_Position = uPMatrix * vPosition;
    vTransformedNormal=(uNormalMatrix * vec4(aVertexNormal, 1.0)).xyz;
    materialIndex=aMaterialIndex;
 
}

JSON

På lignende måte som i modulen Pipe kan vi skille datagenereringen fra framvisningen ved å lage en vevside som ikke har noen annen oppgave enn å generere en beskrivelse av geometrien i form av en JSON-string. I dette tilfellet kan det gjøres på mange måter. Her er valgt en svært enkel variant der vi uten videre dumper de listene som er laget som beskrevet ovenfor. Dette innebærer at ett og samme punkt beskrives mange ganger. Vi kunne lett redusert JSON-stringen betraktelig med noen litt smartere algoritmer.

Koden som lager JSON blir en forenklet variant av ball.js som beskrevet over:

// Describes a buckyball
// 20 white polygons with 6 edges and 12 polygons with 5 edges
// each polygon has attached a center point, p0
// a white polygon: p0,p1,p2,p3,p4,p5,p6,p1
// a black polygon: p0,p1,p2,p3,p4,p5,p1
// 2.2 trigger white and 0.9 trigger black
// everything is described with origo in center and radius phi (1.61803398).
// Normal is thus same as vertex, with the exception of the centerpoint (deviation is ignored)

function Ball()
{
    // golden ratio, the quotient between two consecutive fib-numbers
    var phi=1.61803398;
    var BLACK=0.9;
    var WHITE=2.2;
    // polygon objects
    var pol=new Array();
    
    Vector.prototype.id=function()
    {
        return this.elements[0]+','+this.elements[1]+','+this.elements[2];
    }
    
    function reduce(v)
    {
        return Vector.create([Math.round(v.e(1)*1000)/1000,
                              Math.round(v.e(2)*1000)/1000,
                              Math.round(v.e(3)*1000)/1000]);
    }
    
    // 5 or 6-sided closed polygon
    function poly(v1,v2,v3,v4,v5,v6)
    {
        // make a center point, adjust it and close the polygon
        var v0;
        if(v6)
        {
            v0=Vector.create([
            (v1.e(1)+v2.e(1)+v3.e(1)+v4.e(1)+v5.e(1)+v6.e(1))/6.0,
            (v1.e(2)+v2.e(2)+v3.e(2)+v4.e(2)+v5.e(2)+v6.e(2))/6.0,
            (v1.e(3)+v2.e(3)+v3.e(3)+v4.e(3)+v5.e(3)+v6.e(3))/6.0])
                .toUnitVector().multiply(phi);
            this.P=new Array(reduce(v0),reduce(v1),reduce(v2),reduce(v3),reduce(v4),reduce(v5),reduce(v6),reduce(v1));
        }
        else
        {
            v0=Vector.create([
            (v1.e(1)+v2.e(1)+v3.e(1)+v4.e(1)+v5.e(1))/5.0,
            (v1.e(2)+v2.e(2)+v3.e(2)+v4.e(2)+v5.e(2))/5.0,
            (v1.e(3)+v2.e(3)+v3.e(3)+v4.e(3)+v5.e(3))/5.0])
                .toUnitVector().multiply(phi);
            this.P=new Array(reduce(v0),reduce(v1),reduce(v2),reduce(v3),reduce(v4),reduce(v5),reduce(v1));
        }
        this.size=this.P.length;
    }
    // set up all polygons
    //---- 6 ---- [0..19]
    pol[0]=new poly( //1
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  -phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   -2*phi/3.0]),
          Vector.create([1/3.0,       -2/3.0-phi/3.0,   -2*phi/3.0]), 
          Vector.create([2/3.0,       -1/3.0-2*phi/3.0,  -phi/3.0]), 
          Vector.create([1/3.0,       -phi,         0.0]), 
          Vector.create([-1/3.0,      -phi,         0.0])
     );
    pol[1]=new poly( //2
          Vector.create([-2/3.0-phi/3.0,  -2*phi/3.0,       -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0, -phi/3.0,       -2/3.0]),
          Vector.create([-2*phi/3.0,     -1/3.0,       -2/3.0-phi/3.0]),
          Vector.create([-phi/3.0,      -2/3.0,       -1/3.0-2*phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   -2*phi/3.0]),
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  -phi/3.0])
     );
    pol[2]=new poly( //3
          Vector.create([-1/3.0,      -phi,         0.0]),
          Vector.create([1/3.0,       -phi,         0.0]),
          Vector.create([2/3.0,       -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([1/3.0,       -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  phi/3.0])
     );
    pol[3]=new poly( //4
          Vector.create([-2/3.0,      -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([-1/3.0,      -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([-phi/3.0,      -2/3.0,       1/3.0+2*phi/3.0]),
          Vector.create([-2*phi/3.0,     -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0, -phi/3.0,       2/3.0]),
          Vector.create([-2/3.0-phi/3.0,  -2*phi/3.0,      1/3.0])
     );
    pol[4]=new poly(//5
          Vector.create([-2/3.0-phi/3.0,    -2*phi/3.0,    1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,     2/3.0]),
          Vector.create([-phi,          0.0,        1/3.0]),
          Vector.create([-phi,          0.0,        -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,     -2/3.0]),
          Vector.create([-2/3.0-phi/3.0,   -2*phi/3.0,     -1/3.0])
    );
    pol[5]=new poly( //6
          Vector.create([-1/3.0,        phi,        0.0]),
          Vector.create([1/3.0,         phi,        0.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0, -phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,  -2*phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  -2*phi/3.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, -phi/3.0])
     );
    pol[6]=new poly(//7
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, -phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  -2*phi/3.0]),
          Vector.create([-phi/3.0,        2/3.0,      -1/3.0-2*phi/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,      -2/3.0-phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      -2/3.0]),
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     -1/3.0])
     );
    pol[7]=new poly(//8
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  2*phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,  2*phi/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0, phi/3.0]),
          Vector.create([1/3.0,         phi,        0.0]),
          Vector.create([-1/3.0,        phi,        0.0])
     );
    pol[8]=new poly(//9
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      2/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,      2/3.0+phi/3.0]),
          Vector.create([-phi/3.0,        2/3.0,      1/3.0+2*phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,  2*phi/3.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0, phi/3.0])
     );
    pol[9]=new poly( //10
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      -2/3.0]),
          Vector.create([-phi,          0.0,        -1/3.0]),
          Vector.create([-phi,          0.0,        1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,      2/3.0]),
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,     1/3.0])
     );
    pol[10]=new poly(   //11
          Vector.create([-phi/3.0,        -2/3.0,     -1/3.0-2*phi/3.0]),
          Vector.create([-2*phi/3.0,      -1/3.0,      -2/3.0-phi/3.0,]),
          Vector.create([-2*phi/3.0,       1/3.0,      -2/3.0-phi/3.0]),
          Vector.create([-phi/3.0,         2/3.0,      -1/3.0-2*phi/3.0]),
          Vector.create([0.0,           1/3.0,      -phi]),
          Vector.create([0.0,           -1/3.0,     -phi])
     );
    pol[11]=new poly(   //12
          Vector.create([0.0,           -1/3.0,     -phi]),
          Vector.create([0.0,           1/3.0,      -phi]),
          Vector.create([phi/3.0,         2/3.0,      -1/3.0-2*phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,      -2/3.0-phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,     -2/3.0-phi/3.0]),
          Vector.create([phi/3.0,         -2/3.0,     -1/3.0-2*phi/3.0])
     );
    pol[12]=new poly(   //13
          Vector.create([phi/3.0,         -2/3.0,     -1/3.0-2*phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,     -2/3.0-phi/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,      -2/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,     -1/3.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0, -phi/3.0]),
          Vector.create([1/3.0,         -2/3.0-phi/3.0, -2*phi/3.0])
     );
    pol[13]=new poly(   //14
          Vector.create([0.0,           -1/3.0,       phi]),
          Vector.create([0.0,           1/3.0,        phi]),
          Vector.create([-phi/3.0,        2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,        2/3.0+phi/3.0]),
          Vector.create([-2*phi/3.0,       -1/3.0,        2/3.0+phi/3.0]),
          Vector.create([-phi/3.0,        -2/3.0,       1/3.0+2*phi/3.0])
     );
    pol[14]=new poly(   //15
          Vector.create([phi/3.0,         -2/3.0,       1/3.0+2*phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        2/3.0+phi/3.0]),
          Vector.create([phi/3.0,         2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([0.0,           1/3.0,        phi]),
          Vector.create([0.0,           -1/3.0,       phi])
     );
    pol[15]=new poly(   //16
          Vector.create([1/3.0,         -2/3.0-phi/3.0,   2*phi/3.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       2/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([phi/3.0,         -2/3.0,       1/3.0+2*phi/3.0])
     );
    pol[16]=new poly(  //17
          Vector.create([1/3.0,         2/3.0+phi/3.0,    -2*phi/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   -phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        -2/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        -2/3.0-phi/3.0]),
          Vector.create([phi/3.0,         2/3.0,        -1/3.0-2*phi/3.0])
     );
    pol[17]=new poly(   //18
          Vector.create([phi/3.0,         2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        2/3.0+phi/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        2/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       1/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,    2*phi/3.0])
     );
    pol[18]=new poly(  //19
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       -2/3.0]),
          Vector.create([phi,           0.0,          -1/3.0]),
          Vector.create([phi,           0.0,          1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       2/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      1/3.0])
     );
    pol[19]=new poly(  //20
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        2/3.0]),
          Vector.create([phi,           0.0,          1/3.0]),
          Vector.create([phi,           0.0,          -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        -2/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       -1/3.0])
    );
    //---- 5 ---- [20..31]
    pol[20]=new poly( //21
          Vector.create([-2/3.0,        -1/3.0-2*phi/3.0,  -phi/3.0]),
          Vector.create([-1/3.0,        -phi,         0.0]),
          Vector.create([-2/3.0,        -1/3.0-2*phi/3.0,  phi/3.0]),
          Vector.create([-2/3.0-phi/3.0,    -2*phi/3.0,      1/3.0]),
          Vector.create([-2/3.0-phi/3.0,    -2*phi/3.0,      -1/3.0])
     );
    pol[21]=new poly(//22
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,       -1/3.0]),
          Vector.create([-2/3.0-phi/3.0,    2*phi/3.0,       1/3.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0,   phi/3.0]),
          Vector.create([-1/3.0,        phi,          0.0]),
          Vector.create([-2/3.0,        1/3.0+2*phi/3.0,   -phi/3.0])
     );
    pol[22]=new poly(   //23
          Vector.create([-phi/3.0,        -2/3.0,       -1/3.0-2*phi/3.0]),
          Vector.create([0.0,           -1/3.0,       -phi]),
          Vector.create([phi/3.0,         -2/3.0,       -1/3.0-2*phi/3.0]),
          Vector.create([1/3.0,         -2/3.0-phi/3.0,   -2*phi/3.0]),
          Vector.create([-1/3.0,        -2/3.0-phi/3.0,   -2*phi/3.0])
     );
    pol[23]=new poly(   //24
          Vector.create([-1 / 3.0, -2 / 3.0 - phi / 3.0, 2 * phi / 3.0]),
          Vector.create([1 / 3.0, -2 / 3.0 - phi / 3.0, 2 * phi / 3.0]),
          Vector.create([phi / 3.0, -2 / 3.0, 1 / 3.0 + 2 * phi / 3.0]),
          Vector.create([0.0, -1 / 3.0, phi]),
          Vector.create([-phi / 3.0, -2 / 3.0, 1 / 3.0 + 2 * phi / 3.0])
     );
    pol[24]=new poly(   //25
          Vector.create([-1/3.0,        2/3.0+phi/3.0,    -2*phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,    -2*phi/3.0]),
          Vector.create([phi/3.0,         2/3.0,        -1/3.0-2*phi/3.0]),
          Vector.create([0.0,           1/3.0,        -phi]),
          Vector.create([-phi/3.0,        2/3.0,        -1/3.0-2*phi/3.0])
     );
    pol[25]=new poly(   //26
          Vector.create([-phi/3.0,        2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([0.0,           1/3.0,        phi]),
          Vector.create([phi/3.0,         2/3.0,        1/3.0+2*phi/3.0]),
          Vector.create([1/3.0,         2/3.0+phi/3.0,    2*phi/3.0]),
          Vector.create([-1/3.0,        2/3.0+phi/3.0,    2*phi/3.0])
     );
    pol[26]=new poly(   //27
          Vector.create([1/3.0,         -phi,         0.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0,  -phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      -1/3.0]),
          Vector.create([2/3.0+phi/3.0,     -2*phi/3.0,      1/3.0]),
          Vector.create([2/3.0,         -1/3.0-2*phi/3.0,  phi/3.0])
     );
    pol[27]=new poly(   //28
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   phi/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       1/3.0]),
          Vector.create([2/3.0+phi/3.0,     2*phi/3.0,       -1/3.0]),
          Vector.create([2/3.0,         1/3.0+2*phi/3.0,   -phi/3.0]),
          Vector.create([1/3.0,         phi,          0.0])
     );
    pol[28]=new poly(  //29
          Vector.create([-phi,           0.0,          -1/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,        -2/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,        -2/3.0-phi/3.0]),
          Vector.create([-2*phi/3.0,       -1/3.0,       -2/3.0-phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,       -2/3.0])
     );
    pol[29]=new poly(   //30
          Vector.create([-1/3.0-2*phi/3.0,   -phi/3.0,       2/3.0]),
          Vector.create([-2*phi/3.0,       -1/3.0,       2/3.0+phi/3.0]),
          Vector.create([-2*phi/3.0,       1/3.0,        2/3.0+phi/3.0]),
          Vector.create([-1/3.0-2*phi/3.0,   phi/3.0,        2/3.0]),
          Vector.create([-phi,          0.0,          1/3.0])
     );
    pol[30]=new poly(   //31
          Vector.create([2*phi/3.0,        -1/3.0,       -2/3.0-phi/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        -2/3.0-phi/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        -2/3.0]),
          Vector.create([phi,           0.0,          -1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       -2/3.0])
     );
    pol[31]=new poly(   //32
          Vector.create([1/3.0+2*phi/3.0,    -phi/3.0,       2/3.0]),
          Vector.create([phi,           0.0,          1/3.0]),
          Vector.create([1/3.0+2*phi/3.0,    phi/3.0,        2/3.0]),
          Vector.create([2*phi/3.0,        1/3.0,        2/3.0+phi/3.0]),
          Vector.create([2*phi/3.0,        -1/3.0,       2/3.0+phi/3.0])
     );
     
     //--------------------------
     // uniquevectorlists     
     var uniqueVW=new Array();   // whites
     var uniqueVB=new Array();   // blacks
     var uniqueVAll=new Array(); // all whites + blacks
     // materials
     var materialIx=new Array();
    // indices
    var indexList=new Array();
     
    function findInList(List,id)
    {
        for(vix=0;vix < List.length; vix++)
            if(pol[ix].P[pix].id()==List[vix].id())
                return vix;
        return -1;
    }
    // make a compact point list for each color
    var counter=0;
    for(var ix=0;ix < pol.length; ix++)
    {
        if(pol[ix].size==8)
        {
            for(var pix=0;pix < pol[ix].P.length;pix++)
            {
                if(findInList(uniqueVW,pol[ix].P[pix].id())==-1)
                    uniqueVW=uniqueVW.concat([pol[ix].P[pix]]);
                materialIx[findInList(uniqueVW,pol[ix].P[pix].id())]=WHITE;
            }
        }
        else
        {
            for(var pix=0;pix < pol[ix].P.length;pix++)
            {
                if(findInList(uniqueVB,pol[ix].P[pix].id())==-1)
                    uniqueVB=uniqueVB.concat([pol[ix].P[pix]]);    
                materialIx[uniqueVW.length+findInList(uniqueVB,pol[ix].P[pix].id())]=BLACK;
            }
        }        
    }
    // join them
    uniqueVAll=uniqueVW.concat(uniqueVB);
    
    //set up vertex string
    var vertexStr='';
    for(var ix=0;ix < uniqueVAll.length;ix++)
    {
            vertexStr+=uniqueVAll[ix].e(1)+','+
                       uniqueVAll[ix].e(2)+','+
                       uniqueVAll[ix].e(3)+',';
    }
    vertexStr=vertexStr.substring(0,vertexStr.length-1);
    
    // indices
    for(var ix=0;ix < pol.length; ix++)
    {
        if(pol[ix].P.length==8)
        {
            for(var pix=0;pix < pol[ix].P.length;pix++)
            {
                indexList=
                indexList.concat([findInList(uniqueVW,pol[ix].P[pix].id())]);
            }
        }
        else
        {
            for(var pix=0;pix < pol[ix].P.length;pix++)
            {
                indexList=
                indexList.concat([uniqueVW.length+findInList(uniqueVB,pol[ix].P[pix].id())]);
            }
        }
    }
    
    var mStr=materialIx.join(',');
    var indexStr=indexList.join(',');
    
    // report it
    var dump="var Bucky='{'+\n"+
             "'"+'"indices" : ['+indexStr+"],'+\n"+
             "'"+'"vertexPositions" : ['+vertexStr+"],'+\n"+
             "'"+'"vertexMatIx" : ['+mStr+"]}';\n";
    document.getElementById('dump').innerHTML=dump;    
    
    /* while testing
    var msg="uniqueVAll.length: "+uniqueVAll.length+'\n'+
            "uniqueVW.length: "+uniqueVW.length+'\n'+
            "uniqueVB.length: "+uniqueVB.length+'\n'+
            "materialIx.length: "+materialIx.length+'\n'+
            "indexList.length: "+indexList.length;
    document.getElementById('test').innerHTML=msg;    
    
    */
}

Du kan inspisere resultatet her.
makejson https://borres.hiof.no/wep/webgl/basis/ball/makejson/index.html

Bruken av JSON-formatet, blir igjen en forenklet ball.js.

// a bucky ball with radius phi (1.61803398)
function Ball()
{
    // evaluate JSON
    var buckyObj=eval('('+Bucky+')');
    // make buffers and fill them from buckObj
    this.verticesBuffer= gl.createBuffer();
    this.verticesNormalBuffer= gl.createBuffer();  
    this.verticesMaterialBuffer=gl.createBuffer();
    this.verticesBlackMaterialBuffer=gl.createBuffer();
    this.verticesIndexBuffer= gl.createBuffer(); 
            
    gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesBuffer);
    gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(buckyObj.vertexPositions),gl.STATIC_DRAW);
    
    gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesNormalBuffer);
    gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(buckyObj.vertexPositions),gl.STATIC_DRAW);
    
    gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesMaterialBuffer);
    gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(buckyObj.vertexMatIx),gl.STATIC_DRAW);
    
    gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER,this.verticesIndexBuffer);
    gl.bufferData(gl.ELEMENT_ARRAY_BUFFER,new Uint16Array(buckyObj.indices),gl.STATIC_DRAW)    
    
    // want blackmaterial all over when we sraw outline
    var blacks=new Array();
    for (var ix=0;ix<buckyObj.vertexMatIx.length;ix++)
        blacks=blacks.concat([0.9]);
    
    gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesBlackMaterialBuffer);
    gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(blacks),gl.STATIC_DRAW);
   
    
    // draw based on prepared buffers
    this.draw=function()
    {
        // vertices
        gl.bindBuffer(gl.ARRAY_BUFFER, this.verticesBuffer);
        gl.vertexAttribPointer(shaderProgram.vertexPositionAttribute,3,gl.FLOAT,false,0,0);
        // Set the normal attribute for the vertices. 
        gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesNormalBuffer);
        gl.vertexAttribPointer(shaderProgram.vertexNormalAttribute,3,gl.FLOAT,false,0,0);
        // set material index attribute
        gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesMaterialBuffer);
        gl.vertexAttribPointer(shaderProgram.vertexMaterialIndexAttribute,1,gl.FLOAT,false,0,0);
        
        // Draw the ball.
        gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.verticesIndexBuffer);       
        var startix=0;
        // whites  ( 6 edges, one is doubled and a center is supplied)
        for(var pix=0; pix < 20; pix++)
        {
            if(showWhite)
                gl.drawElements(gl.TRIANGLE_FAN,8,gl.UNSIGNED_SHORT,startix);
            startix=startix+16;
        }

        // blacks (5 edges, one is doubled and a center is supplied))
        for(var pix=20; pix < 32; pix++)
        {
            if(showBlack)
                gl.drawElements(gl.TRIANGLE_FAN,7,gl.UNSIGNED_SHORT,startix);
            startix=startix+14;                
        }
        if(showLines)
        {
            // switch to all black 
            gl.bindBuffer(gl.ARRAY_BUFFER,this.verticesBlackMaterialBuffer);
            gl.vertexAttribPointer(shaderProgram.vertexMaterialIndexAttribute,1,gl.FLOAT,false,0,0);
            // lines on white (is all lines)
            // offset +2 to ignore center point
            startix=2;
            for(var pix=0; pix < 20; pix++)
            {
                gl.drawElements(gl.LINE_STRIP,7,gl.UNSIGNED_SHORT,startix);
                startix=startix+16; 
            }
        }
    }
}

Du kan inspisere resultatet på en enklere side:
showjson https://borres.hiof.no/wep/webgl/basis/ball/showjson/index.html

Referanser

Buckyballs – a new sphere of science Australian Academy of Science www.science.org.au/nova/024/024key.htm 14-03-2014

Fibonacci Numbers and the Golden Section www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html 24-05-2009

Sylvester sylvester.jcoglan.com/ 14-05-2011

R. Buckminster Fuller www.newciv.org/whole/bucky.html 24-05-2009

Bucky Balls GOLDENNUMBER.NET www.goldennumber.net/buckyball.htm 14-10-2011