Small webgl example

glUtils.js

// augment Sylvester some
Matrix.Translation = function (v)
{
  if (v.elements.length == 2) {
    var r = Matrix.I(3);
    r.elements[2][0] = v.elements[0];
    r.elements[2][1] = v.elements[1];
    return r;
  }

  if (v.elements.length == 3) {
    var r = Matrix.I(4);
    r.elements[0][3] = v.elements[0];
    r.elements[1][3] = v.elements[1];
    r.elements[2][3] = v.elements[2];
    return r;
  }

  throw "Invalid length for Translation";
}

Matrix.prototype.flatten = function ()
{
    var result = [];
    if (this.elements.length == 0)
        return [];


    for (var j = 0; j < this.elements[0].length; j++)
        for (var i = 0; i < this.elements.length; i++)
            result.push(this.elements[i][j]);
    return result;
}

Matrix.prototype.ensure4x4 = function()
{
    if (this.elements.length == 4 &&
        this.elements[0].length == 4)
        return this;

    if (this.elements.length > 4 ||
        this.elements[0].length > 4)
        return null;

    for (var i = 0; i < this.elements.length; i++) {
        for (var j = this.elements[i].length; j < 4; j++) {
            if (i == j)
                this.elements[i].push(1);
            else
                this.elements[i].push(0);
        }
    }

    for (var i = this.elements.length; i < 4; i++) {
        if (i == 0)
            this.elements.push([1, 0, 0, 0]);
        else if (i == 1)
            this.elements.push([0, 1, 0, 0]);
        else if (i == 2)
            this.elements.push([0, 0, 1, 0]);
        else if (i == 3)
            this.elements.push([0, 0, 0, 1]);
    }

    return this;
};

Matrix.prototype.make3x3 = function()
{
    if (this.elements.length != 4 ||
        this.elements[0].length != 4)
        return null;

    return Matrix.create([[this.elements[0][0], this.elements[0][1], this.elements[0][2]],
                          [this.elements[1][0], this.elements[1][1], this.elements[1][2]],
                          [this.elements[2][0], this.elements[2][1], this.elements[2][2]]]);
};

Vector.prototype.flatten = function ()
{
    return this.elements;
};

function mht(m) {
    var s = "";
    if (m.length == 16) {
        for (var i = 0; i < 4; i++) {
            s += "<span style='font-family: monospace'>[" + m[i*4+0].toFixed(4) + "," + m[i*4+1].toFixed(4) + "," + m[i*4+2].toFixed(4) + "," + m[i*4+3].toFixed(4) + "]</span><br>";
        }
    } else if (m.length == 9) {
        for (var i = 0; i < 3; i++) {
            s += "<span style='font-family: monospace'>[" + m[i*3+0].toFixed(4) + "," + m[i*3+1].toFixed(4) + "," + m[i*3+2].toFixed(4) + "]</font><br>";
        }
    } else {
        return m.toString();
    }
    return s;
}

//
// gluLookAt
//
function makeLookAt(ex, ey, ez,
                    cx, cy, cz,
                    ux, uy, uz)
{
    var eye = $V([ex, ey, ez]);
    var center = $V([cx, cy, cz]);
    var up = $V([ux, uy, uz]);

    var mag;

    var z = eye.subtract(center).toUnitVector();
    var x = up.cross(z).toUnitVector();
    var y = z.cross(x).toUnitVector();

    var m = $M([[x.e(1), x.e(2), x.e(3), 0],
                [y.e(1), y.e(2), y.e(3), 0],
                [z.e(1), z.e(2), z.e(3), 0],
                [0, 0, 0, 1]]);

    var t = $M([[1, 0, 0, -ex],
                [0, 1, 0, -ey],
                [0, 0, 1, -ez],
                [0, 0, 0, 1]]);
    return m.x(t);
}

//
// glOrtho
//
function makeOrtho(left, right,
                   bottom, top,
                   znear, zfar)
{
    var tx = -(right+left)/(right-left);
    var ty = -(top+bottom)/(top-bottom);
    var tz = -(zfar+znear)/(zfar-znear);

    return $M([[2/(right-left), 0, 0, tx],
               [0, 2/(top-bottom), 0, ty],
               [0, 0, -2/(zfar-znear), tz],
               [0, 0, 0, 1]]);
}

//
// gluPerspective
//
function makePerspective(fovy, aspect, znear, zfar)
{
    var ymax = znear * Math.tan(fovy * Math.PI / 360.0);
    var ymin = -ymax;
    var xmin = ymin * aspect;
    var xmax = ymax * aspect;

    return makeFrustum(xmin, xmax, ymin, ymax, znear, zfar);
}

//
// glFrustum
//
function makeFrustum(left, right,
                     bottom, top,
                     znear, zfar)
{
    var X = 2*znear/(right-left);
    var Y = 2*znear/(top-bottom);
    var A = (right+left)/(right-left);
    var B = (top+bottom)/(top-bottom);
    var C = -(zfar+znear)/(zfar-znear);
    var D = -2*zfar*znear/(zfar-znear);

    return $M([[X, 0, A, 0],
               [0, Y, B, 0],
               [0, 0, C, D],
               [0, 0, -1, 0]]);
}

//
// glOrtho
//
function makeOrtho(left, right, bottom, top, znear, zfar)
{
    var tx = - (right + left) / (right - left);
    var ty = - (top + bottom) / (top - bottom);
    var tz = - (zfar + znear) / (zfar - znear);

    return $M([[2 / (right - left), 0, 0, tx],
           [0, 2 / (top - bottom), 0, ty],
           [0, 0, -2 / (zfar - znear), tz],
           [0, 0, 0, 1]]);
}

sceneNode.js

var mvMatrix;
var mvMatrixStack = [];

var perspectiveMatrix;

function SceneNode(){
    this.position = [0, 0, 0];
    this.rotation = [0, 0, 0];
    this.velocity = [0, 0, 0];
    this.elasticity = 0.3; 

    this.children = [];
    this.mvMatrix = Matrix.I(4);
}

SceneNode.prototype.pass = function(){
    mvPushMatrix();

    if(this.velocity[0] || this.velocity[1] || this.velocity[1]){
        this.animate();
    }

    mvTranslate(this.position);
    mvRotate(this.rotation[0], [1, 0, 0]);
    mvRotate(this.rotation[1], [0, 1, 0]);
    mvRotate(this.rotation[2], [0, 0, 1]);
    
    // save model view matrix 
    this.mvMatrix = mvMatrix;

    this.draw();

    this.children.forEach(function(child){
        child.pass();
    });

    mvPopMatrix();
}

SceneNode.prototype.draw = function(){
}

SceneNode.prototype.animate = function(){
    var currentTime = (new Date()).getTime();
    if(this.lastUpdateTime){
        var delta = currentTime - this.lastUpdateTime;

        // 1 - apply velocity to position (vx -> x)
        this.position[0] += this.velocity[0] * delta / 1000;
        this.position[1] += this.velocity[1] * delta / 1000;
        this.position[2] += this.velocity[2] * delta / 1000;

        // 2 - apply drag/friction to velocity
        this.velocity[0] -= .5 * this.velocity[0] * delta / 1000;
        this.velocity[1] -= .01 * this.velocity[1] * delta / 1000;
        this.velocity[2] -= .5 * this.velocity[2] * delta / 1000;
      
         // 3 - apply gravity to velocity
        this.velocity[1] -= .4 * delta / 1000;

        // 4 - collision with the ground
        if(this.colideGround()){
            this.position[1] = 0.5;
            this.velocity[1] = -this.velocity[1];
            this.velocity[1] *= this.elasticity; 
            if(this.velocity[1] < 0.05){
                this.velocity[1] = 0;
            }
        }
    }
    this.lastUpdateTime = currentTime;
}

SceneNode.prototype.colideGround = function(){
    if(this.position[1] - 0.5 < 0){
        return true;
    } 
    return false;
}

SceneNode.prototype.colide = function(node){
    if(Math.abs(this.position[0] - node.position[0]) < 1 &&
            Math.abs(this.position[1] - node.position[1]) < 1){
        return true;
    }
    return false;
}

function addArray3(a, b){
    a[0] += b[0];
    a[1] += b[1];
    a[2] += b[2];
}

function mult1Array3(v, a){
    a[0] *= v;
    a[1] *= v;
    a[2] *= v;
}

function loadIdentity() {
  mvMatrix = Matrix.I(4);
}

function multMatrix(m) {
  mvMatrix = mvMatrix.x(m);
}

function setMatrixUniforms() {
  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()));
}

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 mvTranslate(v){
    multMatrix(Matrix.Translation($V([v[0], v[1], v[2]])).ensure4x4());
}

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);
}

sylvester.js

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webgl.html

<html> 
<head> 
    <title>WebGL Demo</title> 
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
    
    <script src="sylvester.js" type="text/javascript"></script> 
    <script src="glUtils.js" type="text/javascript"></script>
    <script src="sceneNode.js" type="text/javascript"></script> 
    <script src="webgl.js" type="text/javascript"></script> 
    
    <!-- Fragment shader program --> 
 
    <script id="shader-fs" type="x-shader/x-fragment">
        varying lowp vec4 vColor;
    	
        void main(void){
            gl_FragColor = vColor;
        }
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    <!-- Vertex shader program --> 
    
    <script id="shader-vs" type="x-shader/x-vertex">
        attribute vec3 aVertexPosition;
        attribute vec4 aVertexColor;
    
        uniform mat4 uMVMatrix;
        uniform mat4 uPMatrix;
      
        varying lowp vec4 vColor;
    
        void main(void){
            gl_Position = uPMatrix * uMVMatrix * vec4(aVertexPosition, 1.0);
            vColor = aVertexColor;
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</head> 
	
<style type="text/css"> 
    canvas {
        border: 2px solid black;
        -moz-box-shadow: black 2px 2px 2px;
        width: 800px;
        height: 600px;
        background-color: black;
    }
</style> 
	
<body onload="start()"> 
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	Your browser doesn't appear to support the HTML5 <code>&lt;canvas&gt;</code> element.
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    <div id="message"></div>
    <div id="fps"></div>
</body> 
</html>