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initial commit (me too soon)

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elijah 2024-06-05 16:39:24 +02:00
parent bad1c209ac
commit 9fa8b19640
5 changed files with 1106 additions and 0 deletions
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@font-face {
font-family: 'workbench';
src: url('../assets/font.woff2') format('woff2');
}
body {
background-color: #333;
background-image:
linear-gradient(to bottom,
#000000,
#22770156,
#221100
);
background-size: 100% 3px;
background-repeat: repeat-y;
}
.navbar {
background:
radial-gradient(
farthest-corner at 50% 50%,
rgba(0, 0, 0, 0.6),
rgba(20, 20, 20, 0.6) 50%,
rgba(40, 40, 40, 0.6) 100%
);
background-size: 100% 300px;
background-position: 0% 100%;
padding: 1rem;
display: flex;
justify-content: space-between;
align-items: center;
}
.logo {
font-family: 'workbench', sans-serif;
font-size: 1.5rem;
color: #33ccffca;
text-shadow: 0 0 10px #33ccffbe;
}
.nav-links {
list-style: none;
margin: 0;
padding: 0;
display: flex;
align-items: center;
}
.nav-links li {
margin-right: 20px;
}
.nav-links a {
font-family: 'workbench', sans-serif;
font-size: 1.2rem;
color: #33ccffab; /* a pale blue color reminiscent of old CRTs */
text-decoration: none;
transition: color 0.2s ease;
text-shadow: 0 0 3px #33ccffaf;
}
.nav-links a:hover {
color: #33ccffda;
}

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const init = () => {
const renderer = new THREE.WebGLRenderer({ antialias:true });
document.body.appendChild(renderer.domElement);
const scene = new THREE.Scene();
const orthographiCamera = new THREE.OrthographicCamera(window.innerWidth / -2.0, window.innerWidth / +2.0, window.innerHeight / +2.0, window.innerHeight / -2.0, 0.0, 1.0);
const perspectiveCamera = new THREE.PerspectiveCamera(45.0, window.innerWidth / window.innerHeight, 0.1, 1000.0);
const controls = new THREE.OrbitControls(perspectiveCamera, renderer.domElement);
const clock = new THREE.Clock();
perspectiveCamera.position.set(0.0, 0.0, 5.0);
perspectiveCamera.lookAt(new THREE.Vector3(0.0, 0.0, 0.0));
const geometry = new THREE.PlaneBufferGeometry(window.innerWidth, window.innerHeight);
const uniforms = {
uApp: {
value: {
time: clock.getElapsedTime(),
resolution: new THREE.Vector2(window.innerWidth, window.innerHeight)
}
},
uCamera: {
value: {
position: perspectiveCamera.position,
viewMatrix: perspectiveCamera.matrixWorldInverse,
projectionMatrix: perspectiveCamera.projectionMatrix
}
},
uParams: {
value: {
numIterations: 30,
convergenceCriteria: 0.0001,
finiteDifferenceEpsilon: 0.0001
}
},
uScene: {
value: {
backgroundColor: new THREE.Vector3(0.0, 0.0, 0.0),
lights: [
{
direction: new THREE.Vector3(1.0, 1.0, 1.0),
ambientColor: new THREE.Vector3(1.0, 1.0, 1.0),
diffuseColor: new THREE.Vector3(1.0, 1.0, 0.0),
specularColor: new THREE.Vector3(1.0, 1.0, 0.0)
},
{
direction: new THREE.Vector3(-1.0, -1.0, -1.0),
ambientColor: new THREE.Vector3(1.0, 1.0, 1.0),
diffuseColor: new THREE.Vector3(1.0, 0.0, 1.0),
specularColor: new THREE.Vector3(1.0, 0.0, 1.0)
}
],
material: {
ambientColor: new THREE.Vector3(0.05, 0.05, 0.05),
diffuseColor: new THREE.Vector3(0.5, 0.5, 0.5),
specularColor: new THREE.Vector3(1.0, 1.0, 1.0),
emissionColor: new THREE.Vector3(0.0, 0.0, 0.0),
shininess: 64.0
},
bound: {
position: new THREE.Vector3(0.0, 0.0, 0.0),
radius: 2.0
},
fractal: {
power: 10,
numIterations: 4,
escapeCriteria: 2.0
}
}
}
}
const material = new THREE.ShaderMaterial({
vertexShader: document.getElementById('vertexShader').textContent,
fragmentShader: document.getElementById('fragmentShader').textContent,
uniforms: uniforms
});
scene.add(new THREE.Mesh(geometry, material));
const onWindowResize = (event) => {
uniforms.uApp.value.resolution.x = window.innerWidth * window.devicePixelRatio;
uniforms.uApp.value.resolution.y = window.innerHeight * window.devicePixelRatio;
// NOTE: https://ics.media/tutorial-three/renderer_resize/
renderer.setPixelRatio(window.devicePixelRatio);
renderer.setSize(window.innerWidth, window.innerHeight);
perspectiveCamera.aspect = window.innerWidth / window.innerHeight;
perspectiveCamera.updateProjectionMatrix();
}
onWindowResize();
window.addEventListener('resize', onWindowResize, false);
const animate = () => {
requestAnimationFrame(animate);
const update = () => {
controls.update();
perspectiveCamera.lookAt(new THREE.Vector3(0.0, 0.0, 0.0));
uniforms.uApp.value.time = clock.getElapsedTime();
uniforms.uCamera.value.position = perspectiveCamera.position;
uniforms.uCamera.value.viewMatrix = perspectiveCamera.matrixWorldInverse;
uniforms.uCamera.value.projectionMatrix = perspectiveCamera.projectionMatrix;
}
update();
renderer.render(scene, orthographiCamera);
};
animate();
}
window.addEventListener("load", init);

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<script id="vertexShader" type="x-shader/x-vertex">
void main(){
gl_Position = projectionMatrix * viewMatrix * modelMatrix * vec4(position, 1.0);
}
</script>
<script id="fragmentShader" type="x-shader/x-fragment">
#define SDF_DERIVATIVE_TYPE 0
#define NORMAL_DERIVATIVE_TYPE 0
// ================ variables ================ //
// ---------------- application ---------------- //
struct App
{
float time;
vec2 resolution;
};
struct Camera
{
vec3 position;
mat4 viewMatrix;
mat4 projectionMatrix;
};
struct Params
{
int numIterations;
float convergenceCriteria;
float finiteDifferenceEpsilon;
};
// ---------------- lighting ---------------- //
struct PointLight
{
vec3 position;
vec3 ambientColor;
vec3 diffuseColor;
vec3 specularColor;
};
struct DirectionalLight
{
vec3 direction;
vec3 ambientColor;
vec3 diffuseColor;
vec3 specularColor;
};
struct Material
{
vec3 ambientColor;
vec3 diffuseColor;
vec3 specularColor;
vec3 emissionColor;
float shininess;
};
// ---------------- primitives ---------------- //
struct Line
{
vec3 position;
vec3 direction;
};
struct Sphere
{
vec3 position;
float radius;
};
struct Intersection
{
vec3 position;
bool intersected;
};
// ---------------- scene ---------------- //
const int numLights = 2;
struct Fractal
{
int power;
int numIterations;
float escapeCriteria;
};
struct Scene
{
vec3 backgroundColor;
DirectionalLight lights[numLights];
Material material;
Sphere bound;
Fractal fractal;
};
// ---------------- uniform ---------------- //
uniform App uApp;
uniform Camera uCamera;
uniform Params uParams;
uniform Scene uScene;
// ================ functions ================ //
// ---------------- utilities ---------------- //
vec2 linmap(vec2 in_val, vec2 in_min, vec2 in_max, vec2 out_min, vec2 out_max)
{
return (in_val - in_min) / (in_max - in_min) * (out_max - out_min) + out_min;
}
// ---------------- primitives ---------------- //
float sdfSphere(Sphere sphere, vec3 position)
{
return length(position - sphere.position) - sphere.radius;
}
vec3 normalSphere(Sphere sphere, vec3 position)
{
return normalize(position - sphere.position);
}
Intersection intersectionSphereLine(Sphere sphere, Line line)
{
vec3 difference = line.position - sphere.position;
float a = dot(line.direction, line.direction);
float b = 2.0 * dot(difference, line.direction);
float c = dot(difference, difference) - pow(sphere.radius, 2.0);
float d = pow(b, 2.0) - 4.0 * a * c;
float t = (-b - sqrt(d)) / (2.0 * a);
return Intersection(line.position + t * line.direction, d >= 0.0);
}
// ---------------- constructive solid geometry ---------------- //
float csgUnion(float sd1, float sd2) { return min(sd1, sd2); }
float csgSubtraction(float sd1, float sd2) { return max(-sd1, sd2); }
float csgIntersection(float sd1, float sd2) { return max(sd1, sd2); }
// ---------------- complex ---------------- //
vec2 cAdd(vec2 c1, vec2 c2)
{
// return vec2(c1.x + c2.x, c1.y + c2.y);
return c1 + c2;
}
vec2 cSub(vec2 c1, vec2 c2)
{
// return vec2(c1.x - c2.x, c1.y - c2.y);
return c1 - c2;
}
vec2 cMul(vec2 c1, vec2 c2)
{
return vec2(c1.x * c2.x - c1.y * c2.y, c1.y * c2.x + c1.x * c2.y);
}
vec2 cConj(vec2 c)
{
return vec2(c.x, -c.y);
}
float cNorm(vec2 c)
{
// return sqrt(cMul(c, cConj(c)).x);
return length(c);
}
vec2 cInv(vec2 c)
{
return cConj(c) / pow(cNorm(c), 2.0);
}
vec2 cDiv(vec2 c1, vec2 c2)
{
return cMul(c1, cInv(c2));
}
vec2 cPow(vec2 c, int n)
{
vec2 p = vec2(1.0, 0.0);
for (int i = 0; i < n; ++i)
{
p = cMul(p, c);
}
return p;
}
// ---------------- quaternion ---------------- //
vec4 qAdd(vec4 q1, vec4 q2)
{
// return vec4(q1.x + q2.x, q1.yzw + q2.yzw);
return q1 + q2;
}
vec4 qSub(vec4 q1, vec4 q2)
{
// return vec4(q1.x - q2.x, q1.yzw - q2.yzw);
return q1 - q2;
}
vec4 qMul(vec4 q1, vec4 q2)
{
return vec4(q1.x * q2.x - dot(q1.yzw, q2.yzw), q2.x * q1.yzw + q1.x * q2.yzw + cross(q1.yzw, q2.yzw));
}
vec4 qConj(vec4 q)
{
return vec4(q.x, -q.yzw);
}
float qNorm(vec4 q)
{
// return sqrt(qMul(q, qConj(q)).x);
return length(q);
}
vec4 qInv(vec4 q)
{
return qConj(q) / pow(qNorm(q), 2.0);
}
vec4 qDiv(vec4 q1, vec4 q2)
{
return qMul(q1, qInv(q2));
}
vec4 qPow(vec4 q, int n)
{
vec4 p = vec4(1.0, vec3(0.0));
for (int i = 0; i < n; ++i)
{
p = qMul(p, q);
}
return p;
}
// ---------------- trinion ---------------- //
vec3 tAdd(vec3 t1, vec3 t2)
{
return t1 + t2;
}
vec3 tSub(vec3 t1, vec3 t2)
{
return t1 - t2;
}
vec3 tMul(vec3 t1, vec3 t2)
{
float r1 = length(t1);
float r2 = length(t2);
if (r1 > 0.0 && r2 > 0.0)
{
float a1 = asin(t1.z / r1);
float a2 = asin(t2.z / r2);
float b1 = atan(t1.y, t1.x);
float b2 = atan(t2.y, t2.x);
float r = r1 * r2;
float a = a1 + a2;
float b = b1 + b2;
float x = r * cos(a) * cos(b);
float y = r * cos(a) * sin(b);
float z = r * sin(a);
return vec3(x, y, z);
}
else
{
return vec3(0.0);
}
}
vec3 tPow(vec3 t, int n)
{
/* NOTE: This does not work
vec3 p = vec3(1.0, vec2(0.0));
for (int i = 0; i < n; ++i)
{
p = tMul(p, t);
}
return p;
*/
float r = length(t);
if (r > 0.0)
{
float a = asin(t.z / r);
float b = atan(t.y, t.x);
float pr = pow(r, float(n));
float pa = a * float(n);
float pb = b * float(n);
float x = pr * cos(pa) * cos(pb);
float y = pr * cos(pa) * sin(pb);
float z = pr * sin(pa);
return vec3(x, y, z);
}
else
{
return vec3(0.0);
}
}
// ---------------- dual ---------------- //
struct DualQ
{
vec4 q;
vec4 d;
};
DualQ dqAdd(DualQ dq1, DualQ dq2)
{
return DualQ(qAdd(dq1.q, dq2.q), qAdd(dq1.d, dq2.d));
}
DualQ dqSub(DualQ dq1, DualQ dq2)
{
return DualQ(qSub(dq1.q, dq2.q), qSub(dq1.d, dq2.d));
}
DualQ dqMul(DualQ dq1, DualQ dq2)
{
return DualQ(qMul(dq1.q, dq2.q), qAdd(qMul(dq1.d, dq2.q), qMul(dq1.q, dq2.d)));
}
DualQ dqDiv(DualQ dq1, DualQ dq2)
{
return DualQ(qDiv(dq1.q, dq2.q), qDiv(qSub(qMul(dq1.d, dq2.q), qMul(dq1.q, dq2.d)), qMul(dq2.q, dq2.q)));
}
DualQ dqPow(DualQ dq, int n)
{
DualQ dp = DualQ(vec4(1.0, vec3(0.0)), vec4(0.0, vec3(0.0)));
for (int i = 0; i < n; ++i)
{
dp = dqMul(dp, dq);
}
return dp;
}
struct DualS
{
float s;
float d;
};
DualS dAdd(DualS d1, DualS d2)
{
return DualS(d1.s + d2.s, d1.d + d2.d);
}
DualS dSub(DualS d1, DualS d2)
{
return DualS(d1.s - d2.s, d1.d - d2.d);
}
DualS dMul(DualS d1, DualS d2)
{
return DualS(d1.s * d2.s, d1.d * d2.s + d1.s * d2.d);
}
DualS dDiv(DualS d1, DualS d2)
{
return DualS(d1.s / d2.s, (d1.d * d2.s - d1.s * d2.d) / (d2.s * d2.s));
}
DualS dPow(DualS d, float n)
{
return DualS(pow(d.s, n), d.d * n * pow(d.s, n - 1.0));
}
DualS dSqrt(DualS d)
{
return DualS(sqrt(d.s), d.d * 0.5 / sqrt(d.s));
}
DualS dSin(DualS d)
{
return DualS(sin(d.s), d.d * cos(d.s));
}
DualS dCos(DualS d)
{
return DualS(cos(d.s), d.d * -sin(d.s));
}
DualS dTan(DualS d)
{
return DualS(tan(d.s), d.d / pow(cos(d.s), 2.0));
}
DualS dArcSin(DualS d)
{
return DualS(asin(d.s), d.d / sqrt(1.0 - pow(d.s, 2.0)));
}
DualS dArcCos(DualS d)
{
return DualS(acos(d.s), d.d / -sqrt(1.0 - pow(d.s, 2.0)));
}
DualS dArcTan(DualS d)
{
return DualS(atan(d.s), d.d / (1.0 + pow(d.s, 2.0)));
}
struct DualT
{
vec3 t;
vec3 d;
};
DualT dtAdd(DualT dt1, DualT dt2)
{
return DualT(dt1.t + dt2.t, dt1.d + dt2.d);
}
DualT dtSub(DualT dt1, DualT dt2)
{
return DualT(dt1.t - dt2.t, dt1.d - dt2.d);
}
DualT dtMul(DualT dt1, DualT dt2)
{
// return DualT(tMul(dt1.t, dt2.t), tAdd(tMul(dt1.d, dt2.t), tMul(dt1.t, dt2.d)));
DualS dx1 = DualS(dt1.t.x, dt1.d.x);
DualS dy1 = DualS(dt1.t.y, dt1.d.y);
DualS dz1 = DualS(dt1.t.z, dt1.d.z);
DualS dx2 = DualS(dt2.t.x, dt2.d.x);
DualS dy2 = DualS(dt2.t.y, dt2.d.y);
DualS dz2 = DualS(dt2.t.z, dt2.d.z);
DualS dr1 = dSqrt(dAdd(dPow(dx1, 2.0), dAdd(dPow(dy1, 2.0), dPow(dz1, 2.0))));
DualS dr2 = dSqrt(dAdd(dPow(dx2, 2.0), dAdd(dPow(dy2, 2.0), dPow(dz2, 2.0))));
if (dr1.s > 0.0 && dr2.s > 0.0)
{
DualS da1 = dArcSin(dDiv(dz1, dr1));
DualS da2 = dArcSin(dDiv(dz2, dr2));
DualS db1 = dArcTan(dDiv(dy1, dx1));
DualS db2 = dArcTan(dDiv(dy2, dx2));
DualS dr = dMul(dr1, dr2);
DualS da = dAdd(da1, da2);
DualS db = dAdd(db1, db2);
DualS dx = dMul(dr, dMul(dCos(da), dCos(db)));
DualS dy = dMul(dr, dMul(dCos(da), dSin(db)));
DualS dz = dMul(dr, dSin(da));
return DualT(vec3(dx.s, dy.s, dz.s), vec3(dx.d, dy.d, dz.d));
}
else
{
return DualT(vec3(0.0), vec3(0.0));
}
}
DualT dtPow(DualT dt, int n)
{
/* NOTE: This does not work
DualT dp = DualT(vec3(1.0, vec2(0.0)), vec3(0.0, vec2(0.0)));
for (int i = 0; i < n; ++i)
{
dp = dtMul(dp, dt);
}
return dp;
*/
DualS dx = DualS(dt.t.x, dt.d.x);
DualS dy = DualS(dt.t.y, dt.d.y);
DualS dz = DualS(dt.t.z, dt.d.z);
DualS dr = dSqrt(dAdd(dPow(dx, 2.0), dAdd(dPow(dy, 2.0), dPow(dz, 2.0))));
if (dr.s > 0.0)
{
DualS da = dArcSin(dDiv(dz, dr));
DualS db = dArcTan(dDiv(dy, dx));
DualS dpr = dPow(dr, float(n));
DualS dpa = dMul(da, DualS(float(n), 0.0));
DualS dpb = dMul(db, DualS(float(n), 0.0));
DualS dx = dMul(dpr, dMul(dCos(dpa), dCos(dpb)));
DualS dy = dMul(dpr, dMul(dCos(dpa), dSin(dpb)));
DualS dz = dMul(dpr, dSin(dpa));
return DualT(vec3(dx.s, dy.s, dz.s), vec3(dx.d, dy.d, dz.d));
}
else
{
return DualT(vec3(0.0), vec3(0.0));
}
}
// ---------------- fractals ---------------- //
#if SDF_DERIVATIVE_TYPE == 0
float sdfJulia(Fractal fractal, vec4 z, vec4 c)
{
DualQ dzx = DualQ(z, vec4(1.0, 0.0, 0.0, 0.0));
DualQ dzy = DualQ(z, vec4(0.0, 1.0, 0.0, 0.0));
DualQ dzz = DualQ(z, vec4(0.0, 0.0, 1.0, 0.0));
DualQ dzw = DualQ(z, vec4(0.0, 0.0, 0.0, 1.0));
DualQ dcx = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcy = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcz = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcw = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
for (int i = 0; i < fractal.numIterations; ++i)
{
// forward-mode automatic differentiation
dzx = dqAdd(dqPow(dzx, fractal.power), dcx);
dzy = dqAdd(dqPow(dzy, fractal.power), dcy);
dzz = dqAdd(dqPow(dzz, fractal.power), dcz);
dzw = dqAdd(dqPow(dzw, fractal.power), dcw);
if (qNorm(dzx.q) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx.d, dzy.d, dzz.d, dzw.d);
return (qNorm(dzx.q) * log(qNorm(dzx.q))) / (2.0 * qNorm(normalize(dzx.q) * J));
}
float sdfMandelbrot(Fractal fractal, vec4 c, vec4 z)
{
DualQ dzx = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dzy = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dzz = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dzw = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcx = DualQ(c, vec4(1.0, 0.0, 0.0, 0.0));
DualQ dcy = DualQ(c, vec4(0.0, 1.0, 0.0, 0.0));
DualQ dcz = DualQ(c, vec4(0.0, 0.0, 1.0, 0.0));
DualQ dcw = DualQ(c, vec4(0.0, 0.0, 0.0, 1.0));
for (int i = 0; i < fractal.numIterations; ++i)
{
// forward-mode automatic differentiation
dzx = dqAdd(dqPow(dzx, fractal.power), dcx);
dzy = dqAdd(dqPow(dzy, fractal.power), dcy);
dzz = dqAdd(dqPow(dzz, fractal.power), dcz);
dzw = dqAdd(dqPow(dzw, fractal.power), dcw);
if (qNorm(dzx.q) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx.d, dzy.d, dzz.d, dzw.d);
return (qNorm(dzx.q) * log(qNorm(dzx.q))) / (2.0 * qNorm(normalize(dzx.q) * J));
}
float sdfMandelbulb(Fractal fractal, vec3 c, vec3 z)
{
DualT dzx = DualT(z, vec3(0.0, 0.0, 0.0));
DualT dzy = DualT(z, vec3(0.0, 0.0, 0.0));
DualT dzz = DualT(z, vec3(0.0, 0.0, 0.0));
DualT dcx = DualT(c, vec3(1.0, 0.0, 0.0));
DualT dcy = DualT(c, vec3(0.0, 1.0, 0.0));
DualT dcz = DualT(c, vec3(0.0, 0.0, 1.0));
for (int i = 0; i < fractal.numIterations; ++i)
{
// forward-mode automatic differentiation
dzx = dtAdd(dtPow(dzx, fractal.power), dcx);
dzy = dtAdd(dtPow(dzy, fractal.power), dcy);
dzz = dtAdd(dtPow(dzz, fractal.power), dcz);
if (length(dzx.t) > fractal.escapeCriteria) break;
}
mat3 J = mat3(dzx.d, dzy.d, dzz.d);
return (length(dzx.t) * log(length(dzx.t))) / (2.0 * length(normalize(dzx.t) * J));
}
#elif SDF_DERIVATIVE_TYPE == 1
float sdfJulia(Fractal fractal, vec4 z, vec4 c)
{
vec4 dzx = vec4(1.0, 0.0, 0.0, 0.0);
vec4 dzy = vec4(0.0, 1.0, 0.0, 0.0);
vec4 dzz = vec4(0.0, 0.0, 1.0, 0.0);
vec4 dzw = vec4(0.0, 0.0, 0.0, 1.0);
vec4 dcx = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcy = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcz = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcw = vec4(0.0, 0.0, 0.0, 0.0);
for (int i = 0; i < fractal.numIterations; ++i)
{
vec4 zp = qPow(z, fractal.power - 1);
// forward-mode manual differentiation
dzx = qAdd(float(fractal.power) * qMul(zp, dzx), dcx);
dzy = qAdd(float(fractal.power) * qMul(zp, dzy), dcy);
dzz = qAdd(float(fractal.power) * qMul(zp, dzz), dcz);
dzw = qAdd(float(fractal.power) * qMul(zp, dzw), dcw);
z = qAdd(qMul(zp, z), c);
if (qNorm(z) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx, dzy, dzz, dzw);
return (qNorm(z) * log(qNorm(z))) / (2.0 * qNorm(normalize(z) * J));
}
float sdfMandelbrot(Fractal fractal, vec4 c, vec4 z)
{
vec4 dzx = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dzy = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dzz = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dzw = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcx = vec4(1.0, 0.0, 0.0, 0.0);
vec4 dcy = vec4(0.0, 1.0, 0.0, 0.0);
vec4 dcz = vec4(0.0, 0.0, 1.0, 0.0);
vec4 dcw = vec4(0.0, 0.0, 0.0, 1.0);
for (int i = 0; i < fractal.numIterations; ++i)
{
vec4 zp = qPow(z, fractal.power - 1);
// forward-mode manual differentiation
dzx = qAdd(float(fractal.power) * qMul(zp, dzx), dcx);
dzy = qAdd(float(fractal.power) * qMul(zp, dzy), dcy);
dzz = qAdd(float(fractal.power) * qMul(zp, dzz), dcz);
dzw = qAdd(float(fractal.power) * qMul(zp, dzw), dcw);
z = qAdd(qMul(zp, z), c);
if (qNorm(z) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx, dzy, dzz, dzw);
return (qNorm(z) * log(qNorm(z))) / (2.0 * qNorm(normalize(z) * J));
}
#else
#endif
#if NORMAL_DERIVATIVE_TYPE == 0
vec4 normalJulia(Fractal fractal, vec4 z, vec4 c)
{
DualQ dzx = DualQ(z, vec4(1.0, 0.0, 0.0, 0.0));
DualQ dzy = DualQ(z, vec4(0.0, 1.0, 0.0, 0.0));
DualQ dzz = DualQ(z, vec4(0.0, 0.0, 1.0, 0.0));
DualQ dzw = DualQ(z, vec4(0.0, 0.0, 0.0, 1.0));
DualQ dcx = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcy = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcz = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcw = DualQ(c, vec4(0.0, 0.0, 0.0, 0.0));
for (int i = 0; i < fractal.numIterations; ++i)
{
// forward-mode automatic differentiation
dzx = dqAdd(dqPow(dzx, fractal.power), dcx);
dzy = dqAdd(dqPow(dzy, fractal.power), dcy);
dzz = dqAdd(dqPow(dzz, fractal.power), dcz);
dzw = dqAdd(dqPow(dzw, fractal.power), dcw);
if (qNorm(dzx.q) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx.d, dzy.d, dzz.d, dzw.d);
return dzx.q * J;
}
vec4 normalMandelbrot(Fractal fractal, vec4 c, vec4 z)
{
DualQ dzx = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dzy = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dzz = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dzw = DualQ(z, vec4(0.0, 0.0, 0.0, 0.0));
DualQ dcx = DualQ(c, vec4(1.0, 0.0, 0.0, 0.0));
DualQ dcy = DualQ(c, vec4(0.0, 1.0, 0.0, 0.0));
DualQ dcz = DualQ(c, vec4(0.0, 0.0, 1.0, 0.0));
DualQ dcw = DualQ(c, vec4(0.0, 0.0, 0.0, 1.0));
for (int i = 0; i < fractal.numIterations; ++i)
{
// forward-mode automatic differentiation
dzx = dqAdd(dqPow(dzx, fractal.power), dcx);
dzy = dqAdd(dqPow(dzy, fractal.power), dcy);
dzz = dqAdd(dqPow(dzz, fractal.power), dcz);
dzw = dqAdd(dqPow(dzw, fractal.power), dcw);
if (qNorm(dzx.q) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx.d, dzy.d, dzz.d, dzw.d);
return dzx.q * J;
}
vec3 normalMandelbulb(Fractal fractal, vec3 c, vec3 z)
{
DualT dzx = DualT(z, vec3(0.0, 0.0, 0.0));
DualT dzy = DualT(z, vec3(0.0, 0.0, 0.0));
DualT dzz = DualT(z, vec3(0.0, 0.0, 0.0));
DualT dcx = DualT(c, vec3(1.0, 0.0, 0.0));
DualT dcy = DualT(c, vec3(0.0, 1.0, 0.0));
DualT dcz = DualT(c, vec3(0.0, 0.0, 1.0));
for (int i = 0; i < fractal.numIterations; ++i)
{
// forward-mode automatic differentiation
dzx = dtAdd(dtPow(dzx, fractal.power), dcx);
dzy = dtAdd(dtPow(dzy, fractal.power), dcy);
dzz = dtAdd(dtPow(dzz, fractal.power), dcz);
if (length(dzx.t) > fractal.escapeCriteria) break;
}
mat3 J = mat3(dzx.d, dzy.d, dzz.d);
return dzx.t * J;
}
#elif NORMAL_DERIVATIVE_TYPE == 1
vec4 normalJulia(Fractal fractal, vec4 z, vec4 c)
{
vec4 dzx = vec4(1.0, 0.0, 0.0, 0.0);
vec4 dzy = vec4(0.0, 1.0, 0.0, 0.0);
vec4 dzz = vec4(0.0, 0.0, 1.0, 0.0);
vec4 dzw = vec4(0.0, 0.0, 0.0, 1.0);
vec4 dcx = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcy = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcz = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcw = vec4(0.0, 0.0, 0.0, 0.0);
for (int i = 0; i < fractal.numIterations; ++i)
{
vec4 zp = qPow(z, fractal.power - 1);
// forward-mode manual differentiation
dzx = qAdd(float(fractal.power) * qMul(zp, dzx), dcx);
dzy = qAdd(float(fractal.power) * qMul(zp, dzy), dcy);
dzz = qAdd(float(fractal.power) * qMul(zp, dzz), dcz);
dzw = qAdd(float(fractal.power) * qMul(zp, dzw), dcw);
z = qAdd(qMul(zp, z), c);
if (qNorm(z) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx, dzy, dzz, dzw);
return z * J;
}
vec4 normalMandelbrot(Fractal fractal, vec4 c, vec4 z)
{
vec4 dzx = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dzy = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dzz = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dzw = vec4(0.0, 0.0, 0.0, 0.0);
vec4 dcx = vec4(1.0, 0.0, 0.0, 0.0);
vec4 dcy = vec4(0.0, 1.0, 0.0, 0.0);
vec4 dcz = vec4(0.0, 0.0, 1.0, 0.0);
vec4 dcw = vec4(0.0, 0.0, 0.0, 1.0);
for (int i = 0; i < fractal.numIterations; ++i)
{
vec4 zp = qPow(z, fractal.power - 1);
// forward-mode manual differentiation
dzx = qAdd(float(fractal.power) * qMul(zp, dzx), dcx);
dzy = qAdd(float(fractal.power) * qMul(zp, dzy), dcy);
dzz = qAdd(float(fractal.power) * qMul(zp, dzz), dcz);
dzw = qAdd(float(fractal.power) * qMul(zp, dzw), dcw);
z = qAdd(qMul(zp, z), c);
if (qNorm(z) > fractal.escapeCriteria) break;
}
mat4 J = mat4(dzx, dzy, dzz, dzw);
return z * J;
}
#else
#endif
// ---------------- reflection ---------------- //
vec3 phongReflection(vec3 surfaceNormal, vec3 viewDirection, DirectionalLight lights[numLights], Material material)
{
surfaceNormal = normalize(surfaceNormal);
viewDirection = normalize(viewDirection);
vec3 ambientColor = vec3(0.0);
vec3 diffuseColor = vec3(0.0);
vec3 specularColor = vec3(0.0);
for (int i = 0; i < lights.length(); ++i)
{
vec3 lightDirection = normalize(lights[i].direction);
vec3 reflectedDirection = reflect(lightDirection, surfaceNormal);
float diffuseCoefficient = max(dot(-lightDirection, surfaceNormal), 0.0);
float specularCoefficient = pow(max(dot(reflectedDirection, -viewDirection), 0.0), material.shininess);
ambientColor += lights[i].ambientColor * material.ambientColor;
diffuseColor += lights[i].diffuseColor * material.diffuseColor * diffuseCoefficient;
specularColor += lights[i].specularColor * material.specularColor * specularCoefficient;
}
vec3 color = clamp(ambientColor + diffuseColor + specularColor + material.emissionColor, 0.0, 1.0);
return color;
}
// ---------------- sphere tracing ---------------- //
vec3 sphereTracing(App app, Scene scene, Params params, Line ray)
{
Intersection intersection = intersectionSphereLine(scene.bound, ray);
if (intersection.intersected)
{
ray.position = intersection.position;
// The hyperparameter from Inigo Quilez (https://www.shadertoy.com/view/MsfGRr)
vec4 juliaType = 0.45 * cos(vec4(0.5, 3.9, 1.4, 1.1) + app.time * 0.15 * vec4(1.2, 1.7, 1.3, 2.5)) - vec4(0.3, 0.0, 0.0, 0.0);
vec4 criticalPoint = vec4(0.0);
for (int i = 0; i < params.numIterations; ++i)
{
float sd = sdfMandelbulb(scene.fractal, ray.position, criticalPoint.xyz);
// ray marching
ray.position += sd * ray.direction;
// collision detection
if (abs(sd) < params.convergenceCriteria)
{
vec3 surfaceNormal = normalize(normalMandelbulb(scene.fractal, ray.position, criticalPoint.xyz));
vec3 fragColor = phongReflection(surfaceNormal, ray.direction, scene.lights, scene.material);
return fragColor;
}
if (sdfSphere(scene.bound, ray.position) > 0.0) break;
}
}
return scene.backgroundColor;
}
// ---------------- main ---------------- //
void main()
{
vec2 fragCoord = linmap(gl_FragCoord.xy, vec2(0, 0), uApp.resolution, vec2(-1.0, -1.0), vec2(1.0, 1.0));
vec3 rayDirection = normalize(inverse(mat3(uCamera.projectionMatrix) * mat3(uCamera.viewMatrix)) * vec3(fragCoord, 1.0));
Line ray = Line(uCamera.position, rayDirection);
vec3 fragColor = sphereTracing(uApp, uScene, uParams, ray);
gl_FragColor = vec4(fragColor, 1.0);
}
</script>
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<script src="https://unpkg.com/three@0.139.2/examples/js/controls/OrbitControls.js"></script>

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