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<!doctype html>
<html>
<head>
<title>L-Systems.JS Playground</title>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
<script src="http://mrdoob.github.com/three.js/build/three.min.js"></script>
<script src="bootstrap.min.js"></script>
<script src="lsys.js"></script>
<link rel="stylesheet" href="bootstrap.css" type="text/css"/>
<link rel="stylesheet" href="style.css" type="text/css"/>
<link href="prettify.css" type="text/css" rel="stylesheet"/>
<script type="text/javascript" src="prettify.js"></script>
</head>
<body onload="prettyPrint()">
<div class="page">
<div class="container">
<div class="hero-unit">
<h1>L-Systems.JS</h1>
<p>Explore the power of L-Systems</p>
<p>
<a class="btn btn-large" href="https://raw.github.com/yuvadm/lsys.js/v0.1.1/lsys.js">Download L-Systems.JS (v0.1.1)</a>
<a class="btn btn-primary btn-large" href="http://github.com/yuvadm/lsys.js">L-Systems.JS on Github</a>
</p>
</div>
<h2>About</h2>
<div class="row">
<div class="span12">
<p><b>L-Systems (short for Lindenmayer systems) are instances of a formal grammar that are used to model growth processes of plant deveopment. L-Systems can be used to generate realistic, natural-looking organisms in simulated environments.</b></p>
<p>An L-System consists of an initial axiom string, for example: <code>F</code>, and a set of production rules, for example: <code>F -> F-F+FF</code>. The rules are used to iterativey expand the string to a larger one. In our example, two iterations on the string will yield the string <code>F-F+FF-F-F+FF+F-F+FFF-F+FF</code>. L-Systems also include a mechanism that converts the output string into a geometrical representation. The syntax includes:</p>
<ul>
<li><code>F</code> - a unit vector step forward that draws a line</li>
<li><code>+</code>,<code>-</code>,<code>&</code>,<code>^</code>,<code><</code>,<code>></code> - left and right turns on all three axises</li>
<li><code>|</code> - a vector direction flip</li>
<li><code>[</code>, <code>]</code> - state push and pop functions that enable branch creation.
</ul>
<p>Proper cartesian coordinates can then be generated from the result string, for processing in the front-end of your choice (WebGL, canvas or SVG).
</p>
<h3>References</h3>
<ul>
<li><a href="http://algorithmicbotany.org/papers/#abop">The Algorithmic Beauty of Plants (Prusinkiewicz, Lindenmayer)</a></li>
<li><a href="http://books.google.com/books/about/Turtle_Geometry.html?id=3geYp44hJVcC">Turtle Geometry:
The Computer As a Medium for Exploring Mathematics (Abelson, DiSessa)</a></li>
</ul>
<p>L-Systems.JS was created by <a href="http://y3xz.com">Yuval Adam</a>.</p>
</div>
</div>
<h2>Usage</h2>
<div class="row">
<div class="span12">
<p>The canonical usage would be to create the L-System itself by defining the axiom string and the production rules, running the iteration, and generating the respective cartesian coordinates.</p>
<pre class="prettyprint">
var lsys = new LSystem('F', { 'F': 'F-F+FF' }).iterate(2);
var tree = lsys.print();
console.log(tree); // F-F+FF-F-F+FF+F-F+FFF-F+FF
var coords = lsys.draw(Math.PI / 2);
console.log(coords); // [[[0,0,0], [0,1,0], [1,1,0], ... ]]</pre>
<p>These coordinates can now be plotted by any front-end. For example, using <a href="http://mrdoob.github.com/three.js/">THREE.js</a>:</p>
<pre class="prettyprint">
for (var i=0; i<coords.length; i++) {
var branch = [];
for (var j=0; j<coords[i].length; j++) {
branch.push(new THREE.Vector3(coords[i][j][0], coords[i][j][1], coords[i][j][2]));
}
var geometry = new THREE.Shape(branch).createPointsGeometry();
console.log(geometry);
draw_geometry(geometry);
}</pre>
</div>
</div>
<h2>Playground</h2>
<div class="row">
<div class="span3">
<ul class="nav nav-list">
<li class="nav-header">2D Basics</li>
<li><a href="#" class="lsys-link" data-lsys="koch_curve" data-dim="2D">Koch Curve</a></li>
<li><a href="#" class="lsys-link" data-lsys="sierpinski" data-dim="2D">Sierpinski Triangle</a></li>
<li><a href="#" class="lsys-link" data-lsys="dragon_curve" data-dim="2D">Dragon Curve</a></li>
<li><a href="#" class="lsys-link" data-lsys="hilbert_curve" data-dim="2D">Hilbert Curve</a></li>
<li><a href="#" class="lsys-link" data-lsys="fractal_plant" data-dim="2D">Fractal Plant</a></li>
<li class="nav-header">3D Basics</li>
<li><a href="#" class="lsys-link" data-lsys="tree1" data-dim="3D">Tree 1</a></li>
<li><a href="#" class="lsys-link" data-lsys="3d_hilbert_curve" data-dim="3D">3D Hilbert Curve</a></li>
<li><a href="#" class="lsys-link" data-lsys="3d_axises" data-dim="3D">3D Axises</a></li>
</ul>
</div>
<div class="span9">
<div id="render-container"></div>
<br/>
<form id="custom-form" class="well form-inline">
<input id="custom-axiom" type="text" class="span1" placeholder="Axiom">
<input id="custom-rules" type="text" class="span3" placeholder="Rules">
<input id="custom-draw-consts" type="text" class="span1" placeholder="Draw Constants">
<input id="custom-iterations" type="text" class="span1" placeholder="Iterations">
<input id="custom-angle" type="text" class="span1" placeholder="Angle">
<button id="custom-draw" type="submit" class="btn">Draw</button>
</form>
</div>
</div>
<h2>Contribute!</h2>
<div class="row">
<div class="span12">
<p>The L-Systems.JS project is in a very premature stage. Help us out by going over the <a href="https://github.com/yuvadm/lsys.js/issues">open project issues</a>.</p>
<p>Any other suggestions, feedback, or pull requests would be gladly accepted! :)</p>
</div>
</div>
</div>
</div>
<script>
var lsys_dir = {
'koch_curve': ['F', {'F': 'F+F-F-F+F'}, [], 3, Math.PI/2],
'sierpinski': ['A', {'A': 'B-A-B', 'B': 'A+B+A'}, ['A', 'B'], 4, Math.PI/3],
'dragon_curve': ['FX', {'X': 'X+YF', 'Y': 'FX-Y'}, [], 10, Math.PI/2],
'hilbert_curve': ['A', {'A': '-BF+AFA+FB-', 'B': '+AF-BFB-FA+'}, [], 1, Math.PI/2],
'fractal_plant': ['X', {'X': 'F-[[X]+X]+F[+FX]-X', 'F': 'FF'}, [], 6, Math.PI*25/180],
'tree1': ['F', {'F': 'F[-&<F][<+&F]|F[-&>F][+&F]'}, [], 3, Math.PI*23/180],
'3d_hilbert_curve': ['X', {'X': '^<XF^<XFX-F^>>XFX&F+>>XFX-F>X->'}, [], 1, Math.PI/2],
'3d_axises': ['F', {'F': '[FF]++[FF]++[FF]++[FF]>>[FF]<<<<[FF]'}, [], 1, Math.PI/4],
}
var WIDTH = 698; //window.innerWidth;
var HEIGHT = 300; //window.innerHeight;
var container;
var scene, camera, controls, renderer;
var lsys_tree, dim;
var mouseX = 0, mouseY = 0;
var windowHalfX = WIDTH / 2;
var windowHalfY = HEIGHT / 2;
init();
draw_axes();
animate();
function init() {
scene = new THREE.Scene();
camera = new THREE.PerspectiveCamera(20, WIDTH / HEIGHT, 1, 10000);
camera.position.z = 50;
scene.add(camera);
light = new THREE.DirectionalLight( 0xffffff );
light.position.set( 0, 0, 1 );
scene.add(light);
renderer = new THREE.WebGLRenderer( { antialias: true } );
renderer.setSize(WIDTH, HEIGHT);
container = document.getElementById('render-container');
container.appendChild(renderer.domElement);
controls = new THREE.TrackballControls(camera, renderer.domElement);
controls.rotateSpeed = 1.0;
controls.zoomSpeed = 1.2;
controls.panSpeed = 0.8;
controls.noZoom = false;
controls.noPan = false;
controls.staticMoving = true;
controls.dynamicDampingFactor = 0.3;
controls.keys = [65, 83, 68];
controls.addEventListener('change', render);
document.addEventListener('mousemove', onDocumentMouseMove, false);
}
function onDocumentMouseMove( event ) {
mouseX = (event.clientX - windowHalfX);
mouseY = (event.clientY - windowHalfY);
}
function draw_axes() {
var home = new THREE.Vector3(0,0,0);
var x_axis = [home, new THREE.Vector3(150,0,0)];
var y_axis = [home, new THREE.Vector3(0,150,0)];
var z_axis = [home, new THREE.Vector3(0,0,150)];
var axis_geometry = [
new THREE.Geometry(),
new THREE.Geometry(),
new THREE.Geometry()
];
axis_geometry[0].vertices = x_axis;
axis_geometry[1].vertices = y_axis;
axis_geometry[2].vertices = z_axis;
var axis_material = [
new THREE.LineBasicMaterial({ color : 0xff0000 }),
new THREE.LineBasicMaterial({ color : 0x00ff00 }),
new THREE.LineBasicMaterial({ color : 0x0000ff })
];
var axis_line = [
new THREE.Line(axis_geometry[0], axis_material[0]),
new THREE.Line(axis_geometry[1], axis_material[1]),
new THREE.Line(axis_geometry[2], axis_material[2])
];
scene.add(axis_line[0]);
scene.add(axis_line[1]);
scene.add(axis_line[2]);
}
function draw_lsys(coords) {
lsys_tree = new THREE.Object3D();
for (var i=0; i<coords.length; i++) {
var g = new THREE.Geometry();
for (var j=0; j<coords[i].length; j++) {
var v = new THREE.Vector3(coords[i][j][0], coords[i][j][1], coords[i][j][2]);
g.vertices.push(v);
}
var material = new THREE.LineBasicMaterial({
color : 0x111122,
linewidth : 2
});
var line = new THREE.Line(g, material);
lsys_tree.add(line);
}
scene.add(lsys_tree);
}
function animate() {
requestAnimationFrame(animate);
controls.update();
render();
}
function render() {
renderer.render(scene, camera);
}
$('a.lsys-link').click(function(e) {
dim = $(this).attr('data-dim');
var lsys = $(this).attr('data-lsys');
if (lsys_tree) {
scene.remove(lsys_tree);
}
var d = lsys_dir[lsys];
var new_lsys = new LSystem(d[0], d[1], d[2]).iterate(d[3]).draw(d[4]);
$('#custom-axiom').val(d[0]);
$('#custom-rules').val(JSON.stringify(d[1]).replace(/\"/g, "'"));
$('#custom-draw-consts').val(JSON.stringify(d[2]).replace(/\"/g, "'"));
$('#custom-iterations').val(d[3]);
$('#custom-angle').val(Math.round(d[4] * 180 / Math.PI));
draw_lsys(new_lsys);
return false;
});
$('#custom-draw').click(function(e) {
var axiom = $('#custom-axiom').val();
var rules = eval('(' + $('#custom-rules').val() + ')');
var draw_consts = eval('(' + $('#custom-draw-consts').val() + ')');
var iterations = $('#custom-iterations').val();
var angle = $('#custom-angle').val();
if (lsys_tree) {
scene.remove(lsys_tree);
}
var custom_lsys = new LSystem(axiom, rules, draw_consts).iterate(iterations).draw(angle * (Math.PI / 180));
draw_lsys(custom_lsys);
return false;
});
</script>
</body>
</html>
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