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monkeys_120-cell_right_screw.html
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<!DOCTYPE html>
<html lang="en">
<head>
<title>Quaternion Monkeys</title>
<!--
4D Monkeys
interactive webVR version (by Marc ten Bosch and Vi Hart) of a 4d monkey sculpture (by Henry Segerman and Will Segerman) inspired by work on 4 dimensional symmetry groups (by Henry Segerman and Vi Hart) inspired by work on 4d graphics (by Marc ten Bosch) and 3d modeling (by Will Segerman).
http://www.marctenbosch.com
http://vihart.com
http://www.segerman.org/
http://www.willsegerman.com/
It has oculus support for webVR browsers (thanks Mozilla!)
https://github.com/MozVR/vr-web-examples/tree/master/threejs-vr-boilerplate
And WASD + E/Q navigation support both in and out of VR (thanks, Andrea Hawksley!)
Enter to go into VR mode, S for sound,
Space to click links based on camera rotation
https://github.com/hawksley
-->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
<style>
body {
background-color: #000;
color: #fff;
margin: 0px;
padding: 0;
overflow: hidden;
}
</style>
</head>
<body>
<audio id='music' src="media/monkeygif.mp3"/>
</body>
<!--
three.js 3d library
-->
<script src="js/lib/three.min.js"></script>
<!--
library for fast quaternion rotation
-->
<script src="js/lib/gl-matrix.js"></script>
<!--
VRControls.js acquires positional information from connected VR devices and applies the transformations to a three.js camera object.
-->
<script src="js/vr/PhoneVR.js"></script>
<script src="js/vr/VRControlsMonkeys.js"></script>
<!--
VREffect.js handles stereo camera setup and rendering.
-->
<script src="js/vr/VREffect.js"></script>
<!-- Quaternions for the centers of the cells of the 120-cell -->
<script src="js/centers_120_cell.js"></script>
<script src="js/loaders/OBJLoader.js"></script>
<script type="x-shader/x-vertex" id="vertexShader">
// This shader moves vertices around
// Quaternion Multiplication
vec4 quatMult( in vec4 p, in vec4 q )
{
vec4 r;
r.w = + p.w*q.w - p.x*q.x - p.y*q.y - p.z*q.z;
r.x = + p.w*q.x + p.x*q.w + p.y*q.z - p.z*q.y;
r.y = + p.w*q.y - p.x*q.z + p.y*q.w + p.z*q.x;
r.z = + p.w*q.z + p.x*q.y - p.y*q.x + p.z*q.w;
return r;
}
// Project the vector p to the 3-space perpendicular to q
vec4 projVecPerp( in vec4 p, in vec4 q )
{
vec4 r;
float pDotq = dot(p,q);
float qDotq = dot(q,q);
float foo = pDotq / qDotq;
r = p - foo*q;
return r;
}
// point on geod in S3 from p in direction of q going distance dist
vec4 pointOnS3Geod( in vec4 p, in vec4 q, in float dist)
{
vec4 Q = normalize( q - dot(p,q) * p );
return cos(dist)*p + sin(dist)*Q;
}
// input
uniform float time; // global time in seconds
uniform vec4 quatPerMonkey; // quaternion that moves this monkey into 4-space, set once per monkey
uniform int fogType; // which type of fog to use
uniform vec2 mousePos;
uniform vec4 travelDir; //quaternion for which way we are rotating
uniform vec4 colourDir; //quaternion for which way we are colouring
// Hopf fibration coloring
// returns a color based on the 4D normal
vec3 HopfColor( in vec4 nBase ) /// head foot are all same colour
{
/////////first rotate the 4D normal to a space aligned with the 120-cell
//rotate colourDir to lie along (0,0,z,w), fixing (0,0,0,1)
//http://math.stackexchange.com/questions/293116/rotating-one-3-vector-to-another
vec3 A = vec3(colourDir.x, colourDir.y, colourDir.z) ;
vec3 B = vec3(0.,0.,1.0);
vec3 X = normalize( cross(A,B) );
float theta = acos(dot(A,B)/(length(A)*length(B))); ///dont care about sign
mat3 foo = mat3( vec3(0.,X.z,-X.y), //input is column vectors
vec3(-X.z,0.,X.x),
vec3(X.y,-X.x,0.)
);
mat3 Rot = mat3(1.0) + sin(theta)*foo + (1.-cos(theta))*foo*foo;
//input is column vectors
mat4 mat = mat4( vec4(Rot[0][0],Rot[0][1],Rot[0][2],0.),
vec4(Rot[1][0],Rot[1][1],Rot[1][2],0.),
vec4(Rot[2][0],Rot[2][1],Rot[2][2],0.),
vec4(0.,0.,0.,1.0)
);
// mat4 mat = mat4( vec4(-0.525731, 0., 0.850651,0.),
// vec4(0., 1., 0.,0.),
// vec4(-0.850651, 0., -0.525731,0.),
// vec4(0.,0.,0.,1.0)
// );
// float cosx = sqrt( 0.1*(5.+sqrt(5.)) );
// float sinx = sqrt( 0.1*(5.-sqrt(5.)) );
// // mat4 mat = mat4( vec4(1.,0.,0.,0.), vec4(0.,cosx,-sinx,0.), vec4(0.,sinx,cosx,0.), vec4(0.,0.,0.,1.) );
// mat4 mat = mat4( vec4(-sinx,0.,cosx,0.), vec4(0.,1.,0.,0.), vec4(cosx,0.,sinx,0.), vec4(0.,0.,0.,1.) );
vec4 n = mat * nBase;
// compute the color
float x = n.x;
float y = n.y;
float u = n.z;
float v = n.w;
float r = 2. * (u*x + v*y);
float g = 2. * (u*y - v*x);
float b = x*x + y*y - u*u - v*v;
/// first two coords are 2*z*conj(w), where z = x+iy, w = u+iv
/// rotate [0,0,-1] to [-1,-1,-1]/sqrt(3)
mat3 RotDownToDiag = mat3( vec3(0.707107, -0.707107, 0.), ///// input columns not rows?!?!?!
vec3(0.408248, 0.408248, -0.816497),
vec3(0.57735, 0.57735, 0.57735) );
vec3 newCol = vec3(r,g,b);
newCol = RotDownToDiag * newCol;
return vec3(newCol.x*0.5 + 0.5,newCol.y*0.5 + 0.5,newCol.z*0.5 + 0.5);
}
// output
varying vec3 vColor; // this shader computes the color of each vertex
// this gets called once per vertex of the monkey mesh (and numMonkeys times since there are numMonkeys monkeys)
void main()
{
// base position
// turn a 3D position of a monkey into a 4D position by adding a 1 as the w component then normalizing to get onto the unit 3-sphere
// vec4 p3sphere = normalize( vec4(position.zyx, 1.0) );
// wcoord = (1.0/4.0)*math.sqrt(50-22*math.sqrt(5)) * (7+3*math.sqrt(5))) /// = 3.07768
vec4 p3sphere = normalize( vec4(-position.zyx, 3.07768) );
// then rotate using this monkey's quaternion to place in 4D
vec4 pt0 = quatMult( p3sphere, quatPerMonkey ); //position at time = 0
// this is the normal to the point
// same concept as for the position, but we add a 0 as the w component
vec4 n3sphere = vec4( normal.zyx, 0.0);
// above is normal on a cubical cell of the hypercube, below we get the corresponding
// normal on the 3-sphere
n3sphere = projVecPerp( n3sphere, p3sphere );
// rotate the normal using this monkey's quaternion
vec4 nt0 = quatMult( n3sphere, quatPerMonkey );
// // also rotate everything over time
vec4 quatOverTime = pointOnS3Geod( vec4(0,0,0,1), travelDir, 0.5*time );
// vec4 quatOverTime = vec4(0,0,0,1);
vec4 p = quatMult( pt0, quatOverTime );
vec4 n = quatMult( nt0, quatOverTime );
// stereographic projection from 4D to 3D
vec3 pos3 = vec3( p.x / (-1.0-p.w), p.y / (-1.0-p.w), p.z / (-1.0-p.w) );
// compute the color from the normal
vColor = HopfColor(n);
vColor = HopfColor(p);
vec3 nColor = HopfColor(nt0);
vec3 pColor = HopfColor(pt0);
vColor = -0.3*(nColor-vec3(0.5,0.5,0.5)) + 1.0*(pColor-vec3(0.5,0.5,0.5)) + vec3(0.5,0.5,0.5);
// vColor = pColor;
// take the final 3D position and project it onto the screen
// gl_Position = projectionMatrix * modelViewMatrix * vec4( pos3 + vec3(0.0,-0.6,-1.5), 1.0 );
// gl_Position = projectionMatrix * modelViewMatrix * vec4( pos3 + vec3(0.0,-0.7,-2.3), 1.0 );
gl_Position = projectionMatrix * modelViewMatrix * vec4( pos3 , 1.0 );
// do fog
if ( fogType == 1 )
{
// ramp fog
// compute distance to camera from 0 to 1
float zz = gl_Position.z / gl_Position.w;
// go from 1 to 0 instead (0 is furthest and 1 is where the camera is )
// ( note that the computed distance is not linear )
float fogScale = 1. - zz;
// anything closer than 0.1 gets regular color
if ( fogScale > 0.1 )
fogScale = 1.0;
// everything else ramps from 0 to 1
else
fogScale = fogScale / 0.1;
// mutliply color by this value to make it go to black
vColor *= fogScale;
}
else if ( fogType == 2 )
{
// near fog
float zz = gl_Position.z / gl_Position.w;
// go from 1 to 0, and make the curve less straight
float fogScale = pow( 1. - zz, 0.7 );
// everything closer than 0.2 gets regular color
// but everything else stays the same, creating a discontinuity
if ( fogScale > 0.2 ) fogScale = 1.0;
// mutliply color by this value to make it go to black
vColor *= fogScale;
} else if (fogType == 3 ){
vColor.r *= mousePos.x/1000.;
vColor.g *= mousePos.y/1000.;
vColor.b *= abs(1. - (mousePos.x + mousePos.y)/1000.);
}
}
</script>
<script type="x-shader/x-vertex" id="fragmentShader">
// this gets called once per pixel
varying vec3 vColor;
void main()
{
// just use the color we computed and assign it to this pixel
gl_FragColor = vec4( vColor, 1. );
}
</script>
<script type="text/javascript" id="mainCode">
var camera;
var scene;
var renderer;
var mesh;
var effect;
var controls;
var clicky = 1;
var mouseX = 1;
var mouseY = 1;
// one quaternion per monkey
var quatPerMonkeyArray = centers_120_cell;
var numMonkeys = quatPerMonkeyArray.length;
var matArray = new Array(numMonkeys);
var travelDir = centers_120_cell[3]; //3 is down head/foot
var colourDir = centers_120_cell[3];
init();
animate();
function onkey(event) {
event.preventDefault();
if (event.keyCode == 90) { // z
controls.zeroSensor();
}
};
window.addEventListener("keydown", onkey, true);
document.body.addEventListener('dblclick', function () {
effect.setFullScreen(true);
});
function init()
{
start = Date.now();
scene = new THREE.Scene();
camera = new THREE.PerspectiveCamera(70, window.innerWidth / window.innerHeight, 0.1, 100);
camera.position.x = 0;
camera.position.z = 0;
// -----
// vr stuff
renderer = new THREE.WebGLRenderer({ antialias: true });
document.body.appendChild(renderer.domElement);
controls = new THREE.VRControls(camera);
effect = new THREE.VREffect(renderer);
effect.setSize(window.innerWidth, window.innerHeight);
// -----
// material for the monkeys is a shader
materialBase = new THREE.ShaderMaterial({
// these are the parameters for the shader
uniforms: {
// global time
time: {
type: "f",
value: 0.0
},
// quaternion that moves this monkey into 4-space, set once per monkey
quatPerMonkey: {
type: "v4",
value: new THREE.Vector4( 0, 0, 0, 0 )
},
fogType: {
type: "i",
value: 0
},
mousePos: {
type: "v2",
value: new THREE.Vector2(0,0)
},
travelDir: {
type: "v4",
value: new THREE.Vector4( 0, 0, 0, 0 )
},
colourDir: {
type: "v4",
value: new THREE.Vector4( 0, 0, 0, 0 )
}
},
vertexShader: document.getElementById('vertexShader').textContent,
fragmentShader: document.getElementById('fragmentShader').textContent
});
materialBase.side = THREE.FrontSide;
// one material per monkey, since they have a different quaternion
for (var i = 0; i < numMonkeys; i++)
{
matArray[i] = materialBase.clone();
}
// load the monkey mesh
var manager = new THREE.LoadingManager();
var loader = new THREE.OBJLoader(manager);
loader.load('media/120-cell_monkey_lowpoly_003_flip_normals.obj', function (object) {
// loader.load('media/dodecDualRot90.obj', function (object) {
// make numMonkeys copies of the mesh and assign them a unique material out of the numMonkeys we created previously
for (var i = 0; i < numMonkeys; i++)
{
var newObject = object.clone();
newObject.traverse(function (child) {
if (child instanceof THREE.Mesh) {
child.material = matArray[i];
child.frustumCulled = false;
}
});
scene.add(newObject);
}
});
window.addEventListener('resize', onWindowResize, false);
effect.render(scene, camera);
}
function animate() {
// send the time every frame so that we can rotate the monkeys over time
for (var i = 0; i < numMonkeys; i++)
{
matArray[i].uniforms['quatPerMonkey'].value = quatPerMonkeyArray[i];
matArray[i].uniforms['time'].value = .00025 * (Date.now() - start);
matArray[i].uniforms['fogType'].value = clicky;
matArray[i].uniforms['mousePos'].value = new THREE.Vector2(mouseX, mouseY);
matArray[i].uniforms['travelDir'].value = travelDir;
matArray[i].uniforms['colourDir'].value = colourDir;
}
controls.update();
effect.render(scene, camera);
requestAnimationFrame(animate);
}
//links
function link(){
window.location="http://vihart.github.io/webVR-playing-with/index.html";
}
//listen for mouse movement to get mouseX and mouseY
document.body.addEventListener( 'mousemove', function (event) {
mouseY = event.clientY;
mouseX = event.clientX;
});
//listen for click
document.body.addEventListener( 'click', function(){
clicky = (clicky + 1) % 4;
})
/*
Listen for double click event to enter full-screen VR mode
*/
document.body.addEventListener( 'dblclick', function() {
effect.setFullScreen( true );
});
/*
Listen for keyboard events
*/
function onkey(event) {
event.preventDefault();
if (event.keyCode == 90) { // z
controls.zeroSensor(); //zero rotation
} else if (event.keyCode == 70 || event.keyCode == 13) { //f or enter
effect.setFullScreen(true) //fullscreen
} else if (event.keyCode == 32) {//space
link();
}else if (event.keyCode === 73){ //i
infoSign.material.visible = !infoSign.material.visible;
}else if (event.keyCode == 80) {//p
var music = document.querySelector('#music');
if (music.paused){
music.play();
} else{
music.pause();
}
}
};
window.addEventListener("keydown", onkey, true);
//hold down keys to do rotations and stuff
// function key(event, sign) {
// var control = controls.manualControls[String.fromCharCode(event.keyCode).toLowerCase()];
// if (!control)
// return;
// if (sign === 1 && control.active || sign === -1 && !control.active)
// return;
// control.active = (sign === 1);
// controls.manualRotateRate[control.index] += sign * control.sign;
// }
document.addEventListener('keydown', function(event) { key(event, 1); }, false);
document.addEventListener('keyup', function(event) { key(event, -1); }, false);
/*
Handle window resizes
*/
function onWindowResize() {
camera.aspect = window.innerWidth / window.innerHeight;
camera.updateProjectionMatrix();
effect.setSize( window.innerWidth, window.innerHeight );
}
window.addEventListener( 'resize', onWindowResize, false );
</script>
</html>