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monkeys.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;
cursor: pointer;
}
</style>
</head>
<body>
</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>
<!-- spherical math functions -->
<script src="js/sphMath.js"></script>
<!-- Quaternions for the centers of the cells of the different polychora -->
<script src="js/centers_8_cell.js"></script>
<script src="js/centers_24_cell.js"></script>
<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
// glsl 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;
}
vec4 quatInv( in vec4 p )
{
vec4 r;
r.x = -p.x;
r.y = -p.y;
r.z = -p.z;
r.w = p.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
uniform mat4 HopfColorMatrix; //rotates colourDir to lie along (0,0,z,w)
uniform float modelScale; //p3sphere = normalize( vec4(-position.zyx, modelScale ) );
// 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
vec4 n = HopfColorMatrix * 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, modelScale ) );
// then rotate using this monkey's quaternion to place in 4D
vec4 pt0 = quatMult( quatPerMonkey, p3sphere ); //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(quatPerMonkey, n3sphere );
// // 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( quatOverTime, pt0 );
vec4 n = quatMult( quatOverTime, nt0 );
// 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
//// using HopfColor again...
vec3 nColor = HopfColor(nt0);
//// or the transported back to 1 normal
// vec4 nTransported = quatMult(quatInv(pt0), nt0);
// vec3 nColor = vec3(0.5,0.5,0.5) + 0.5*normalize( vec3( nTransported.x, nTransported.y, nTransported.z) );
vec3 pColor = HopfColor(pt0);
vColor = -0.5*(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;
// vColor = nColor;
// 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" src="js/monkeys.js"> </script>
</html>