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knot2.html
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<!DOCTYPE html>
<html>
<head>
<!--
Ray Marching demo by Kevin Roast
- Lots of code/ideas for this demo come from reading:
http://www.iquilezles.org/www/material/nvscene2008/rwwtt.pdf
http://www.pouet.net/topic.php?which=7931&page=1
http://www.pouet.net/topic.php?which=7920&page=1
http://iquilezles.org/www/articles/distfunctions/distfunctions.htm
https://www.shadertoy.com/
If you want to understand this stuff read through the PDF and pouet.net links above!
-->
<script src="scripts/dat.gui.min.js"></script>
<script src="scripts/stats.min.js"></script>
<script id="vertex" type="x-shader">
attribute vec2 aVertexPosition;
void main()
{
gl_Position = vec4(aVertexPosition, 0.0, 1.0);
}
</script>
<script id="fragment" type="x-shader">
#ifdef GL_ES
precision highp float;
#endif
uniform float time;
uniform vec2 resolution;
uniform vec3 cameraPos;
uniform vec3 cameraLookat;
uniform vec3 lightDir;
uniform vec3 lightColour;
uniform float specular;
uniform float specularHardness;
uniform vec3 diffuse;
uniform float ambientFactor;
uniform bool ao;
uniform bool shadows;
uniform bool rotateWorld;
uniform bool antialias;
uniform bool dof;
uniform bool textureSurface;
//Radius of the tubes
uniform float tubeRadius;
//Radius of the goup of tubes
uniform float groupRadius;
//Rotation Numerator X (integer): actually not a rotation. This is frequency in x direction
uniform float rotNumeratorX;
//Rotation Numerator Y (integer): actually not a rotation. This is frequency in y direction. (lissajou figure)
uniform float rotNumeratorY;
//Rotation Denominator (integer): this is the rotation "speed" in xz plane
uniform float rotDenominator;
//Rotations number: how many instances to check. related to the period of the knot.
uniform int rotations;
//Radius of the whole object (because it looks like a torus)
const float objectRadius = 1.0;
#define AO_SAMPLES 5
#define RAY_DEPTH 128
#define MAX_DEPTH 100.0
#define SHADOW_RAY_DEPTH 32
#define DISTANCE_MIN 0.001
#define PI 3.14159265
const vec2 delta = vec2(0.001, 0.);
float Hash(in float n)
{
return fract(sin(n)*43758.5453123*PI);
}
float Noise(in vec2 x)
{
vec2 p = floor(x);
vec2 f = fract(x);
f = f*f*(3.0-2.0*f);
float n = p.x + p.y*57.0;
float res = mix(mix( Hash(n+ 0.0), Hash(n+ 1.0),f.x),
mix( Hash(n+ 57.0), Hash(n+ 58.0),f.x),f.y);
return res;
}
float Noise(in vec3 x)
{
vec3 p = floor(x);
vec3 f = fract(x);
f = f*f*(3.0-2.0*f);
float n = p.x + p.y*157.0 + 113.0*p.z;
return mix(mix(mix( Hash(n+ 0.0), Hash(n+ 1.0),f.x),
mix( Hash(n+157.0), Hash(n+158.0),f.x),f.y),
mix(mix( Hash(n+113.0), Hash(n+114.0),f.x),
mix( Hash(n+270.0), Hash(n+271.0),f.x),f.y),f.z);
}
vec3 RotateY(vec3 p, float a)
{
float c,s;
vec3 q=p;
c = cos(a);
s = sin(a);
p.x = c * q.x + s * q.z;
p.z = -s * q.x + c * q.z;
return p;
}
float twist(vec3 p)
{
// seen from above it is a lissajou fugure
float ra = p.z*rotNumeratorX/rotDenominator;
float raz = p.z*rotNumeratorY/rotDenominator;
return length(p.xy-vec2(groupRadius*cos(ra)+objectRadius,groupRadius*sin(raz)+objectRadius))-tubeRadius;
}
// Distance estimator for "trefoil knot" - see http://blog.hvidtfeldts.net/index.php/2012/01/knots-and-polyhedra/
// and original formula from http://www.fractalforums.com/new-theories-and-research/not-fractal-but-funny-trefoil-knot-routine/
const float NoiseSize = 64.0;
const float NoiseRoughness = 0.15;
float Dist(vec3 p)
{
if (rotateWorld) p = RotateY(p, sin(time*0.05)*PI);
float r=length(p.xz), ang=atan(p.z,p.x), y=p.y;
float d=1.0;
for (int i=0; i<10; i++)
{
vec3 p = vec3(r,y,ang+2.0*PI*float(i));
p.x -= objectRadius;
d = min(d, twist(p));
if (i == rotations) break;
}
float flr = p.y+0.25;
if (d < flr)
{
if (textureSurface)
{
return d + Noise(p*NoiseSize)*NoiseRoughness/NoiseSize;
}
return d;
}
return flr;
}
// Based on original by IQ - optimized to remove a divide
float CalcAO(vec3 p, vec3 n)
{
float r = 0.0;
float w = 1.0;
for (int i=1; i<=AO_SAMPLES; i++)
{
float d0 = float(i) * 0.3;
r += w * (d0 - Dist(p + n * d0));
w *= 0.5;
}
return 1.0 - clamp(r,0.0,1.0);
}
// Based on original code by IQ
float SoftShadow(vec3 ro, vec3 rd, float k)
{
float res = 1.0;
float t = 0.1; // min-t see http://www.iquilezles.org/www/articles/rmshadows/rmshadows.htm
for (int i=0; i<SHADOW_RAY_DEPTH; i++)
{
float h = Dist(ro + rd * t);
res = min(res, k*h/t);
t += h;
if (t > 10.0) break; // max-t
}
return clamp(res, 0.0, 1.0);
}
vec3 GetNormal(vec3 pos)
{
vec3 n;
n.x = Dist( pos + delta.xyy ) - Dist( pos - delta.xyy );
n.y = Dist( pos + delta.yxy ) - Dist( pos - delta.yxy );
n.z = Dist( pos + delta.yyx ) - Dist( pos - delta.yyx );
return normalize(n);
}
vec3 checkerboard(vec3 p)
{
if (fract(p.x*.5)>.5)
if (fract(p.z*.5)>.5)
return vec3(0.,0.4,0.);
else
return vec3(0.,0.,0.4);
else
if (fract(p.z*.5)>.5)
return vec3(0.,0.,0.4);
else
return vec3(0.,0.4,0.);
}
// Based on a shading method by Ben Weston. Added AO and SoftShadows to original.
vec4 Shading(vec3 pos, vec3 rd, vec3 norm)
{
vec3 light;
// simple pos test on pos.y for floor - different colour and no spec for floor
if (pos.y > 0.0)
{
light = lightColour * max(0.0, dot(norm, lightDir));
vec3 heading = normalize(-rd + lightDir);
float spec = pow(max(0.0, dot(heading, norm)), specularHardness);
light = (diffuse * light) + (spec * specular * lightColour);
if (shadows) light *= SoftShadow(pos, lightDir, 16.0);
if (ao) light += CalcAO(pos, norm) * ambientFactor;
}
else
{
light = checkerboard(pos) * max(0.0, dot(norm, lightDir));
if (shadows) light *= SoftShadow(pos, lightDir, 16.0);
if (ao) light += CalcAO(pos, norm) * max(ambientFactor-0.25, 0.0);
}
return vec4(light, 1.0);
}
// Original method by David Hoskins
vec3 Sky(in vec3 rd)
{
float sunAmount = max(dot(rd, lightDir), 0.0);
float v = pow(1.0 - max(rd.y,0.0),6.);
vec3 sky = mix(vec3(.1, .2, .3), vec3(.32, .32, .32), v);
sky += lightColour * sunAmount * sunAmount * .25 + lightColour * min(pow(sunAmount, 800.0)*1.5, .3);
return clamp(sky, 0.0, 1.0);
}
vec4 March(vec3 ro, vec3 rd)
{
float t = 0.0;
float d = 1.0;
for (int i=0; i<RAY_DEPTH; i++)
{
vec3 p = ro + rd * t;
d = Dist(p);
if (abs(d) < DISTANCE_MIN)
{
return vec4(p, 1.0); // alpha indicates hit else "outside"
}
t += d;
if (t >= MAX_DEPTH) break;
}
return vec4(0.0);
}
// Camera function by TekF
// Compute ray from camera parameters
vec3 GetRay(vec3 dir, vec2 pos)
{
pos = pos - 0.5;
pos.x *= resolution.x/resolution.y;
dir = normalize(dir);
vec3 right = normalize(cross(vec3(0.,1.,0.),dir));
vec3 up = normalize(cross(dir,right));
return dir + right*pos.x + up*pos.y;
}
void main()
{
const int ANTIALIAS_SAMPLES = 4;
const int DOF_SAMPLES = 8;
vec4 res = vec4(0.0);
if (antialias)
{
float d_ang = 2.*PI / float(ANTIALIAS_SAMPLES);
float ang = d_ang * 0.33333;
float r = 0.3;
for (int i = 0; i < ANTIALIAS_SAMPLES; i++)
{
vec2 p = vec2((gl_FragCoord.x + cos(ang)*r) / resolution.x, (gl_FragCoord.y + sin(ang)*r) / resolution.y);
vec3 ro = cameraPos;
vec3 rd = normalize(GetRay(cameraLookat-cameraPos, p));
vec4 _res = March(ro, rd);
if (_res.a == 1.0) res.xyz += clamp(Shading(_res.xyz, rd, GetNormal(_res.xyz)).xyz, 0.0, 1.0);
else res.xyz += Sky(rd);
ang += d_ang;
}
res.xyz /= float(ANTIALIAS_SAMPLES);
}
else if (dof)
{
vec2 p = gl_FragCoord.xy / resolution.xy;
vec3 ro = cameraPos;
vec3 rd = normalize(GetRay(cameraLookat-cameraPos, p));
vec4 _res = March(ro, rd);
float d_ang = 2.*PI / float(DOF_SAMPLES);
float ang = d_ang * 0.33333;
// cheap DOF!
float r = abs(cameraLookat.z - _res.z) * 3.0;
for (int i = 0; i < DOF_SAMPLES; i++)
{
p = vec2((gl_FragCoord.x + cos(ang)*r) / resolution.x, (gl_FragCoord.y + sin(ang)*r) / resolution.y);
ro = cameraPos;
rd = normalize(GetRay(cameraLookat-cameraPos, p));
_res = March(ro, rd);
if (_res.a == 1.0) res.xyz += clamp(Shading(_res.xyz, rd, GetNormal(_res.xyz)).xyz, 0.0, 1.0);
else res.xyz += Sky(rd);
ang += d_ang;
}
res.xyz /= float(DOF_SAMPLES);
}
else
{
vec2 p = gl_FragCoord.xy / resolution.xy;
vec3 ro = cameraPos;
vec3 rd = normalize(GetRay(cameraLookat-cameraPos, p));
res = March(ro, rd);
if (res.a == 1.0) res.xyz = clamp(Shading(res.xyz, rd, GetNormal(res.xyz)).xyz, 0.0, 1.0);
else res.xyz = Sky(rd);
}
gl_FragColor = vec4(res.xyz, 1.0);
}
</script>
<script type="text/javascript">
var requestAnimationFrame = window.requestAnimationFrame || window.webkitRequestAnimationFrame ||
window.mozRequestAnimationFrame || window.msRequestAnimationFrame ||
function(c) {window.setTimeout(c, 15)};
var config = {
camera: {
x: 1.0, y: 6.0, z: -5.0
},
lookat: {
x: 0.0, y: 0.0, z: 0.0
},
lightDir: {
x: -5.0, y: 4.5, z: -2.0
},
lightColour: {
r: 1.7, g: 2.2, b: 2.5
},
surface: {
specular: 64.0,
specularHardness: 512.0,
diffuse: 0.25,
ambientFactor: 0.4,
textureSurface: true
},
global: {
ao: true,
shadows: true,
rotateWorld: true,
antialias: "None"// None|Classic|DOF
},
knot: {
tubeRadius: 0.15,
groupRadius: 0.9,
rotNumeratorX: 5,
rotNumeratorY: -5,
rotDenominator: 8,
rotations: 8
}
};
function init()
{
var pause = false;
document.addEventListener('keydown', function(e) {
switch (e.keyCode)
{
case 27: // ESC
pause = !pause;
break;
}
}, false);
// add GUI controls
var mobile = (navigator.userAgent.indexOf("Android") !== -1);
var gui = new dat.GUI();
var panel = gui.addFolder('Camera Position');
panel.add(config.camera, "x").min(-16.0).max(16.0).step(0.1);
panel.add(config.camera, "y").min(-16.0).max(16.0).step(0.1);
panel.add(config.camera, "z").min(-64.0).max(64.0).step(0.1);
panel = gui.addFolder('Camera LookAt');
panel.add(config.lookat, "x").min(-16.0).max(16.0).step(0.1);
panel.add(config.lookat, "y").min(-16.0).max(16.0).step(0.1);
panel.add(config.lookat, "z").min(-16.0).max(16.0).step(0.1);
panel = gui.addFolder('Light Direction');
panel.add(config.lightDir, "x").min(-16.0).max(16.0).step(0.1);
panel.add(config.lightDir, "y").min(-16.0).max(16.0).step(0.1);
panel.add(config.lightDir, "z").min(-16.0).max(16.0).step(0.1);
panel = gui.addFolder('Light Colour');
panel.add(config.lightColour, "r").min(0.0).max(3.0).step(0.1);
panel.add(config.lightColour, "g").min(0.0).max(3.0).step(0.1);
panel.add(config.lightColour, "b").min(0.0).max(3.0).step(0.1);
panel = gui.addFolder('Surface');
panel.add(config.surface, "specular").min(0).max(64);
panel.add(config.surface, "specularHardness").min(16).max(1024).step(16);
panel.add(config.surface, "diffuse").min(0).max(1).step(0.05);
panel.add(config.surface, "ambientFactor").min(0).max(1).step(0.05);
panel.add(config.surface, "textureSurface").name("Textured Surface");
if (!mobile) panel.open();
panel = gui.addFolder('Global');
panel.add(config.global, "antialias", ["None", "Classic", "DOF"]).name("Anti Alias");
panel.add(config.global, "shadows").name("Shadows");
panel.add(config.global, "ao").name("Ambient Occlusion");
panel.add(config.global, "rotateWorld").name("Rotate World");
if (!mobile) panel.open();
panel = gui.addFolder('Knot');
panel.add(config.knot, "tubeRadius").min(0.01).max(1.0).step(0.01);
panel.add(config.knot, "groupRadius").min(0.01).max(2.0).step(0.01);
panel.add(config.knot, "rotNumeratorX").min(-10).max(10).step(1);
panel.add(config.knot, "rotNumeratorY").min(-10).max(10).step(1);
panel.add(config.knot, "rotDenominator").min(1).max(20).step(1);
panel.add(config.knot, "rotations").min(1).max(10).step(1);
if (!mobile) panel.open();
var stats = new Stats();
document.body.appendChild(stats.domElement);
// create webgl context on the canvas element
var canvas = document.getElementById("canvas"),
aspect = canvas.width / canvas.height;
try
{
var gl = canvas.getContext("experimental-webgl");
}
catch (e)
{
document.write("Whoops! No useful WEB-GL impl available. Shame on you and your browser vendor.<br>" + e.message);
return;
}
gl.viewport(0, 0, canvas.width, canvas.height);
gl.clearColor(0, 0, 0, 1);
gl.clear(gl.COLOR_BUFFER_BIT);
// get the vertex and fragment shader source
var v = document.getElementById("vertex").firstChild.nodeValue;
var f = document.getElementById("fragment").firstChild.nodeValue;
// compile and link the shaders
var vs = gl.createShader(gl.VERTEX_SHADER);
gl.shaderSource(vs, v);
gl.compileShader(vs);
var fs = gl.createShader(gl.FRAGMENT_SHADER);
gl.shaderSource(fs, f);
gl.compileShader(fs);
var program = gl.createProgram();
gl.attachShader(program, vs);
gl.attachShader(program, fs);
gl.linkProgram(program);
// debug shader compile status
var error = false;
if (!gl.getShaderParameter(vs, gl.COMPILE_STATUS))
{
error = true;
console.log(gl.getShaderInfoLog(vs));
}
if (!gl.getShaderParameter(fs, gl.COMPILE_STATUS))
{
error = true;
console.log(gl.getShaderInfoLog(fs));
}
if (!gl.getProgramParameter(program, gl.LINK_STATUS))
{
error = true;
console.log(gl.getProgramInfoLog(program));
}
if (error) return;
var firstTime = Date.now();
(f = function() {
if (!pause)
{
stats.begin();
// create vertices to fill the canvas with a single quad
var vertices = new Float32Array(
[
-1, 1*aspect, 1, 1*aspect, 1, -1*aspect,
-1, 1*aspect, 1, -1*aspect, -1, -1*aspect
]);
var vbuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, vbuffer);
gl.bufferData(gl.ARRAY_BUFFER, vertices, gl.STATIC_DRAW);
var triCount = 2,
numItems = vertices.length / triCount;
gl.useProgram(program);
var time = (Date.now() - firstTime) / 1000.0;
program.time = gl.getUniformLocation(program, "time");
gl.uniform1f(program.time, time);
program.resolution = gl.getUniformLocation(program, "resolution");
gl.uniform2f(program.resolution, canvas.width, canvas.height);
program.cameraPos = gl.getUniformLocation(program, "cameraPos");
gl.uniform3f(program.cameraPos, config.camera.x, config.camera.y, config.camera.z);
program.cameraLookat = gl.getUniformLocation(program, "cameraLookat");
gl.uniform3f(program.cameraLookat, config.lookat.x, config.lookat.y, config.lookat.z);
program.lightDir = gl.getUniformLocation(program, "lightDir");
// pre normalise light dir
var x = config.lightDir.x, y = config.lightDir.y, z = config.lightDir.z;
var len = x*x + y*y + z*z;
len = 1.0 / Math.sqrt(len);
gl.uniform3f(program.lightDir, config.lightDir.x*len, config.lightDir.y*len, config.lightDir.z*len);
program.lightColour = gl.getUniformLocation(program, "lightColour");
gl.uniform3f(program.lightColour, config.lightColour.r, config.lightColour.g, config.lightColour.b);
program.specular = gl.getUniformLocation(program, "specular");
gl.uniform1f(program.specular, config.surface.specular);
program.specularHardness = gl.getUniformLocation(program, "specularHardness");
gl.uniform1f(program.specularHardness, config.surface.specularHardness);
program.diffuse = gl.getUniformLocation(program, "diffuse");
gl.uniform3f(program.diffuse, config.surface.diffuse,config.surface.diffuse,config.surface.diffuse);
program.ambientFactor = gl.getUniformLocation(program, "ambientFactor");
gl.uniform1f(program.ambientFactor, config.surface.ambientFactor);
program.textureSurface = gl.getUniformLocation(program, "textureSurface");
gl.uniform1f(program.textureSurface, config.surface.textureSurface);
program.rotateWorld = gl.getUniformLocation(program, "rotateWorld");
gl.uniform1f(program.rotateWorld, config.global.rotateWorld);
program.ao = gl.getUniformLocation(program, "ao");
gl.uniform1f(program.ao, config.global.ao);
program.shadows = gl.getUniformLocation(program, "shadows");
gl.uniform1f(program.shadows, config.global.shadows);
program.antialias = gl.getUniformLocation(program, "antialias");
gl.uniform1f(program.antialias, (config.global.antialias === "Classic"));
program.dof = gl.getUniformLocation(program, "dof");
gl.uniform1f(program.dof, (config.global.antialias === "DOF"));
program.tubeRadius = gl.getUniformLocation(program, "tubeRadius");
gl.uniform1f(program.tubeRadius, config.knot.tubeRadius);
program.groupRadius = gl.getUniformLocation(program, "groupRadius");
gl.uniform1f(program.groupRadius, config.knot.groupRadius);
program.rotNumeratorX = gl.getUniformLocation(program, "rotNumeratorX");
gl.uniform1f(program.rotNumeratorX, config.knot.rotNumeratorX);
program.rotNumeratorY = gl.getUniformLocation(program, "rotNumeratorY");
gl.uniform1f(program.rotNumeratorY, config.knot.rotNumeratorY);
program.rotDenominator = gl.getUniformLocation(program, "rotDenominator");
gl.uniform1f(program.rotDenominator, config.knot.rotDenominator);
program.rotations = gl.getUniformLocation(program, "rotations");
gl.uniform1i(program.rotations, config.knot.rotations);
program.aVertexPosition = gl.getAttribLocation(program, "aVertexPosition");
gl.enableVertexAttribArray(program.aVertexPosition);
gl.vertexAttribPointer(program.aVertexPosition, triCount, gl.FLOAT, false, 0, 0);
gl.drawArrays(gl.TRIANGLES, 0, numItems);
stats.end();
//pause = true;
}
requestAnimationFrame(f);
})();
}
</script>
</head>
<body onload="init()">
<canvas id="canvas" width="768" height="512">
</body>
</html>