Initial commit: add all skills files

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-10 16:52:49 +08:00
commit 6487becf60
396 changed files with 108871 additions and 0 deletions
--- a/shader-dev/techniques/domain-warping.md
+++ b/shader-dev/techniques/domain-warping.md
@@ -0,0 +1,414 @@
+# Domain Warping
+
+## Use Cases
+
+- **Marble/jade textures**: multi-layer warping produces streaked stone textures
+- **Fabric/silk appearance**: warping field creases simulate textile surfaces
+- **Geological formations**: rock strata, lava flows, surface erosion
+- **Gas giant atmospheres**: Jupiter-style banded circulation
+- **Smoke/fire/explosions**: fluid effects combined with volumetric rendering
+- **Abstract art backgrounds**: procedural organic patterns, suitable for UI backgrounds, music visualization
+- **Electric current/plasma effects**: ridged FBM variant produces sharp arc patterns
+
+Core advantage: relies only on math functions (no texture assets needed), outputs seamless tiling, animatable, GPU-friendly.
+
+## Core Principles
+
+Warp input coordinates with noise, then query the main function:
+
+```
+f(p) -> f(p + fbm(p))
+```
+
+Classic multi-layer recursive nesting:
+
+```
+result = fbm(p + fbm(p + fbm(p)))
+```
+
+Each FBM layer's output serves as a coordinate offset for the next layer; deeper nesting produces more organic deformation.
+
+**Key mathematical structure**:
+
+1. **Noise** `noise(p)`: pseudo-random values at integer lattice points + Hermite interpolation `f*f*(3.0-2.0*f)`
+2. **FBM**: `fbm(p) = sum of (0.5^i) * noise(p * 2^i * R^i)`, where `R` is a rotation matrix for decorrelation
+3. **Domain warping chain**: `fbm(p + fbm(p + fbm(p)))`
+
+The rotation matrix `mat2(0.80, 0.60, -0.60, 0.80)` (approx 36.87 deg) is the most widely used decorrelation transform.
+
+## Implementation Steps
+
+### Step 1: Hash Function
+
+```glsl
+// Map 2D integer coordinates to a pseudo-random float
+float hash(vec2 p) {
+    p = fract(p * 0.6180339887); // golden ratio pre-perturbation
+    p *= 25.0;
+    return fract(p.x * p.y * (p.x + p.y));
+}
+```
+
+> The classic `fract(sin(dot(p, vec2(127.1, 311.7))) * 43758.5453)` also works; the sin-free version above has more stable precision on some GPUs.
+
+### Step 2: Value Noise
+
+```glsl
+// Hash values at integer lattice points, Hermite smooth interpolation
+float noise(vec2 p) {
+    vec2 i = floor(p);
+    vec2 f = fract(p);
+    f = f * f * (3.0 - 2.0 * f);
+
+    return mix(
+        mix(hash(i + vec2(0.0, 0.0)), hash(i + vec2(1.0, 0.0)), f.x),
+        mix(hash(i + vec2(0.0, 1.0)), hash(i + vec2(1.0, 1.0)), f.x),
+        f.y
+    );
+}
+```
+
+### Step 3: FBM
+
+```glsl
+const mat2 mtx = mat2(0.80, 0.60, -0.60, 0.80); // rotation approx 36.87 deg
+
+float fbm(vec2 p) {
+    float f = 0.0;
+    f += 0.500000 * noise(p); p = mtx * p * 2.02;
+    f += 0.250000 * noise(p); p = mtx * p * 2.03;
+    f += 0.125000 * noise(p); p = mtx * p * 2.01;
+    f += 0.062500 * noise(p); p = mtx * p * 2.04;
+    f += 0.031250 * noise(p); p = mtx * p * 2.01;
+    f += 0.015625 * noise(p);
+    return f / 0.96875;
+}
+```
+
+> Lacunarity uses 2.01~2.04 rather than exactly 2.0 to avoid visual artifacts caused by lattice regularity.
+
+### Step 4: Domain Warping (Core)
+
+```glsl
+// Classic three-layer domain warping
+float pattern(vec2 p) {
+    return fbm(p + fbm(p + fbm(p)));
+}
+```
+
+### Step 5: Time Animation
+
+```glsl
+// Inject time into the first and last octaves: low frequency drives overall flow, high frequency adds detail variation
+float fbm(vec2 p) {
+    float f = 0.0;
+    f += 0.500000 * noise(p + iTime);       // lowest frequency: slow overall flow
+    p = mtx * p * 2.02;
+    f += 0.250000 * noise(p); p = mtx * p * 2.03;
+    f += 0.125000 * noise(p); p = mtx * p * 2.01;
+    f += 0.062500 * noise(p); p = mtx * p * 2.04;
+    f += 0.031250 * noise(p); p = mtx * p * 2.01;
+    f += 0.015625 * noise(p + sin(iTime));  // highest frequency: subtle detail motion
+    return f / 0.96875;
+}
+```
+
+### Step 6: Coloring
+
+```glsl
+// Map scalar field (0~1) to color using a mix chain
+// IMPORTANT: Note: GLSL is strictly typed. Variable declarations must be complete, e.g. vec3 col = vec3(0.2, 0.1, 0.4)
+// IMPORTANT: Decimals must be written as 0.x, not .x (division by zero errors)
+vec3 palette(float t) {
+    vec3 col = vec3(0.2, 0.1, 0.4);                               // deep purple base
+    col = mix(col, vec3(0.3, 0.05, 0.05), t);                     // dark red
+    col = mix(col, vec3(0.9, 0.9, 0.9), t * t);                   // high values toward white
+    col = mix(col, vec3(0.0, 0.2, 0.4), smoothstep(0.6, 0.8, t)); // blue highlight
+    return col * t * 2.0;
+}
+```
+
+## Full Code Template
+
+```glsl
+// Domain Warping — Full Runnable Template (ShaderToy)
+
+#define WARP_DEPTH 3        // Warp nesting depth (1=subtle, 2=moderate, 3=classic)
+#define NUM_OCTAVES 6       // FBM octave count (4=coarse fast, 6=fine)
+#define TIME_SCALE 1.0      // Animation speed (0.05=very slow, 1.0=fluid, 2.0=fast)
+#define WARP_STRENGTH 1.0   // Warp intensity (0.5=subtle, 1.0=standard, 2.0=strong)
+#define BASE_SCALE 3.0      // Overall noise scale (larger = denser texture)
+
+const mat2 mtx = mat2(0.80, 0.60, -0.60, 0.80);
+
+float hash(vec2 p) {
+    p = fract(p * 0.6180339887);
+    p *= 25.0;
+    return fract(p.x * p.y * (p.x + p.y));
+}
+
+float noise(vec2 p) {
+    vec2 i = floor(p);
+    vec2 f = fract(p);
+    f = f * f * (3.0 - 2.0 * f);
+
+    return mix(
+        mix(hash(i + vec2(0.0, 0.0)), hash(i + vec2(1.0, 0.0)), f.x),
+        mix(hash(i + vec2(0.0, 1.0)), hash(i + vec2(1.0, 1.0)), f.x),
+        f.y
+    );
+}
+
+float fbm(vec2 p) {
+    float f = 0.0;
+    float amp = 0.5;
+    float freq = 1.0;
+    float norm = 0.0;
+
+    for (int i = 0; i < NUM_OCTAVES; i++) {
+        float t = 0.0;
+        if (i == 0) t = iTime * TIME_SCALE;
+        if (i == NUM_OCTAVES - 1) t = sin(iTime * TIME_SCALE);
+
+        f += amp * noise(p + t);
+        norm += amp;
+        p = mtx * p * 2.02;
+        amp *= 0.5;
+    }
+    return f / norm;
+}
+
+float pattern(vec2 p) {
+    float val = fbm(p);
+
+    #if WARP_DEPTH >= 2
+    val = fbm(p + WARP_STRENGTH * val);
+    #endif
+
+    #if WARP_DEPTH >= 3
+    val = fbm(p + WARP_STRENGTH * val);
+    #endif
+
+    return val;
+}
+
+vec3 palette(float t) {
+    vec3 col = vec3(0.2, 0.1, 0.4);
+    col = mix(col, vec3(0.3, 0.05, 0.05), t);
+    col = mix(col, vec3(0.9, 0.9, 0.9), t * t);
+    col = mix(col, vec3(0.0, 0.2, 0.4), smoothstep(0.6, 0.8, t));
+    return col * t * 2.0;
+}
+
+void mainImage(out vec4 fragColor, in vec2 fragCoord) {
+    vec2 uv = (2.0 * fragCoord - iResolution.xy) / iResolution.y;
+    uv *= BASE_SCALE;
+
+    float shade = pattern(uv);
+    vec3 col = palette(shade);
+
+    // Vignette effect
+    vec2 q = fragCoord / iResolution.xy;
+    col *= 0.5 + 0.5 * sqrt(16.0 * q.x * q.y * (1.0 - q.x) * (1.0 - q.y));
+
+    fragColor = vec4(col, 1.0);
+}
+```
+
+## Common Variants
+
+### Variant 1: Multi-Resolution Layered Warping
+
+Different warp layers use FBM with different octave counts, outputting `vec2` for dual-axis displacement, with intermediate variables used for coloring.
+
+```glsl
+float fbm4(vec2 p) {
+    float f = 0.0;
+    f += 0.5000 * (-1.0 + 2.0 * noise(p)); p = mtx * p * 2.02;
+    f += 0.2500 * (-1.0 + 2.0 * noise(p)); p = mtx * p * 2.03;
+    f += 0.1250 * (-1.0 + 2.0 * noise(p)); p = mtx * p * 2.01;
+    f += 0.0625 * (-1.0 + 2.0 * noise(p));
+    return f / 0.9375;
+}
+
+float fbm6(vec2 p) {
+    float f = 0.0;
+    f += 0.500000 * noise(p); p = mtx * p * 2.02;
+    f += 0.250000 * noise(p); p = mtx * p * 2.03;
+    f += 0.125000 * noise(p); p = mtx * p * 2.01;
+    f += 0.062500 * noise(p); p = mtx * p * 2.04;
+    f += 0.031250 * noise(p); p = mtx * p * 2.01;
+    f += 0.015625 * noise(p);
+    return f / 0.96875;
+}
+
+vec2 fbm4_2(vec2 p) {
+    return vec2(fbm4(p + vec2(1.0)), fbm4(p + vec2(6.2)));
+}
+vec2 fbm6_2(vec2 p) {
+    return vec2(fbm6(p + vec2(9.2)), fbm6(p + vec2(5.7)));
+}
+
+float func(vec2 q, out vec2 o, out vec2 n) {
+    q += 0.05 * sin(vec2(0.11, 0.13) * iTime + length(q) * 4.0);
+    o = 0.5 + 0.5 * fbm4_2(q);
+    o += 0.02 * sin(vec2(0.13, 0.11) * iTime * length(o));
+    n = fbm6_2(4.0 * o);
+    vec2 p = q + 2.0 * n + 1.0;
+    float f = 0.5 + 0.5 * fbm4(2.0 * p);
+    f = mix(f, f * f * f * 3.5, f * abs(n.x));
+    return f;
+}
+
+// Coloring uses intermediate variables o, n
+vec3 col = vec3(0.2, 0.1, 0.4);
+col = mix(col, vec3(0.3, 0.05, 0.05), f);
+col = mix(col, vec3(0.9, 0.9, 0.9), dot(n, n));
+col = mix(col, vec3(0.5, 0.2, 0.2), 0.5 * o.y * o.y);
+col = mix(col, vec3(0.0, 0.2, 0.4), 0.5 * smoothstep(1.2, 1.3, abs(n.y) + abs(n.x)));
+col *= f * 2.0;
+```
+
+### Variant 2: Turbulence/Ridged Warping (Electric Arc/Plasma Effect)
+
+In FBM, apply `abs(noise - 0.5)` to produce ridged textures, with dual-axis independent displacement + time-reversed drift.
+
+```glsl
+float fbm_ridged(vec2 p) {
+    float z = 2.0;
+    float rz = 0.0;
+    for (float i = 1.0; i < 6.0; i++) {
+        rz += abs((noise(p) - 0.5) * 2.0) / z;
+        z *= 2.0;
+        p *= 2.0;
+    }
+    return rz;
+}
+
+float dualfbm(vec2 p) {
+    vec2 p2 = p * 0.7;
+    vec2 basis = vec2(
+        fbm_ridged(p2 - iTime * 0.24),
+        fbm_ridged(p2 + iTime * 0.26)
+    );
+    basis = (basis - 0.5) * 0.2;
+    p += basis;
+    return fbm_ridged(p * makem2(iTime * 0.03));
+}
+
+// Electric arc coloring
+vec3 col = vec3(0.2, 0.1, 0.4) / rz;
+```
+
+### Variant 3: Pseudo-3D Lit Domain Warping
+
+Estimate screen-space normals via finite differences, apply directional lighting for an embossed effect.
+
+```glsl
+float e = 2.0 / iResolution.y;
+vec3 nor = normalize(vec3(
+    pattern(p + vec2(e, 0.0)) - shade,
+    2.0 * e,
+    pattern(p + vec2(0.0, e)) - shade
+));
+
+vec3 lig = normalize(vec3(0.9, 0.2, -0.4));
+float dif = clamp(0.3 + 0.7 * dot(nor, lig), 0.0, 1.0);
+vec3 lin = vec3(0.70, 0.90, 0.95) * (nor.y * 0.5 + 0.5);
+lin += vec3(0.15, 0.10, 0.05) * dif;
+
+col *= 1.2 * lin;
+col = 1.0 - col;
+col = 1.1 * col * col;
+```
+
+### Variant 4: Flow Field Iterative Warping (Gas Giant Effect)
+
+Compute the FBM gradient field, Euler-integrate to iteratively advect coordinates, simulating fluid convection vortices.
+
+```glsl
+#define ADVECT_ITERATIONS 5
+
+vec2 field(vec2 p) {
+    float t = 0.2 * iTime;
+    p.x += t;
+    float n = fbm(p, t);
+    float e = 0.25;
+    float nx = fbm(p + vec2(e, 0.0), t);
+    float ny = fbm(p + vec2(0.0, e), t);
+    return vec2(n - ny, nx - n) / e;
+}
+
+vec3 distort(vec2 p) {
+    for (float i = 0.0; i < float(ADVECT_ITERATIONS); i++) {
+        p += field(p) / float(ADVECT_ITERATIONS);
+    }
+    return vec3(fbm(p, 0.0));
+}
+```
+
+### Variant 5: 3D Volumetric Domain Warping (Explosion/Fireball Effect)
+
+Displace a sphere SDF with 3D FBM, rendered via volumetric ray marching.
+
+```glsl
+#define NOISE_FREQ 4.0
+#define NOISE_AMP -0.5
+
+mat3 m3 = mat3(0.00, 0.80, 0.60,
+              -0.80, 0.36,-0.48,
+              -0.60,-0.48, 0.64);
+
+float noise3D(vec3 p) {
+    vec3 fl = floor(p);
+    vec3 fr = fract(p);
+    fr = fr * fr * (3.0 - 2.0 * fr);
+    float n = fl.x + fl.y * 157.0 + 113.0 * fl.z;
+    return mix(mix(mix(hash(n+0.0),   hash(n+1.0),   fr.x),
+                   mix(hash(n+157.0), hash(n+158.0), fr.x), fr.y),
+               mix(mix(hash(n+113.0), hash(n+114.0), fr.x),
+                   mix(hash(n+270.0), hash(n+271.0), fr.x), fr.y), fr.z);
+}
+
+float fbm3D(vec3 p) {
+    float f = 0.0;
+    f += 0.5000 * noise3D(p); p = m3 * p * 2.02;
+    f += 0.2500 * noise3D(p); p = m3 * p * 2.03;
+    f += 0.1250 * noise3D(p); p = m3 * p * 2.01;
+    f += 0.0625 * noise3D(p); p = m3 * p * 2.02;
+    f += 0.03125 * abs(noise3D(p));
+    return f / 0.9375;
+}
+
+float distanceFunc(vec3 p, out float displace) {
+    float d = length(p) - 0.5;
+    displace = fbm3D(p * NOISE_FREQ + vec3(0, -1, 0) * iTime);
+    d += displace * NOISE_AMP;
+    return d;
+}
+```
+
+## Performance & Composition
+
+### Performance Tips
+
+- Three warp layers x 6 octaves = 18 noise samples per pixel; adding lit finite differences can reach 54
+- **Reduce octaves**: 4 instead of 6, ~33% performance gain with minimal visual difference
+- **Reduce warp depth**: two layers `fbm(p + fbm(p))` is already organic enough, saving ~33%
+- **sin-product noise**: `sin(p.x)*sin(p.y)` is branchless and memory-free, suitable for mobile
+- **GPU built-in derivatives**: `dFdx/dFdy` instead of finite differences, 3x faster
+- **Texture noise**: pre-bake noise textures, trading computation for memory reads
+- **LOD adaptive**: reduce octave count for distant pixels
+- **Supersampling**: only use 2x2 when anti-aliasing is needed, 4x performance cost
+
+### Composition Suggestions
+
+- **Ray marching**: warped scalar field as SDF displacement function -> fire, explosions, organic forms
+- **Polar coordinate transform**: domain warping in polar space -> vortices, nebulae, spirals
+- **Cosine palette**: `a + b*cos(2*pi*(c*t+d))` is more flexible than mix chains
+- **Post-processing**: bloom glow, tone mapping `col/(1+col)`, chromatic aberration (RGB channel offset sampling)
+- **Particles/geometry**: scalar field driving particle velocity fields, vertex displacement, UV animation
+
+## Further Reading
+
+Full step-by-step tutorials, mathematical derivations, and advanced usage in [reference](../reference/domain-warping.md)