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
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+# 2D SDF Rendering Skill
+
+## Use Cases
+
+- 2D shape rendering: circles, rectangles, triangles, ellipses, line segments, Bezier curves, etc.
+- UI elements and icons: drawn with math functions, naturally resolution-independent
+- Anti-aliased graphics, shape boolean operations, outlines and glow
+- Motion graphics and animation, 2D soft shadows and lighting
+
+## Core Principles
+
+For each pixel, compute the signed distance `d` to the shape boundary: `d < 0` inside, `d = 0` boundary, `d > 0` outside.
+
+Map to color via `smoothstep`/`clamp`:
+- **Fill**: color when `d < 0`
+- **Anti-aliasing**: `smoothstep(-aa, aa, d)`
+- **Stroke**: apply smoothstep to `abs(d) - strokeWidth`
+- **Boolean operations**: `min(d1, d2)` union, `max(d1, d2)` intersection, `max(-d1, d2)` subtraction
+
+Key formulas:
+```
+Circle:       d = length(p - center) - radius
+Rectangle:    d = length(max(abs(p) - halfSize, 0.0)) + min(max(abs(p).x - halfSize.x, abs(p).y - halfSize.y), 0.0)
+Line segment: d = length(p - a - clamp(dot(p-a, b-a)/dot(b-a, b-a), 0, 1) * (b-a)) - width/2
+Smooth union: d = mix(d2, d1, h) - k*h*(1-h),  h = clamp(0.5 + 0.5*(d2-d1)/k, 0, 1)
+```
+
+## Implementation Steps
+
+### Step 1: Coordinate Normalization
+
+```glsl
+// Origin at center, y range [-1, 1] (standard approach)
+vec2 p = (2.0 * fragCoord - iResolution.xy) / iResolution.y;
+
+// Pixel space (suitable for fixed pixel-size UI)
+vec2 p = fragCoord.xy;
+vec2 center = iResolution.xy * 0.5;
+
+// [0, 1] range (requires manual aspect ratio handling)
+vec2 uv = fragCoord.xy / iResolution.xy;
+```
+
+### Step 2: SDF Primitive Functions
+
+```glsl
+float sdCircle(vec2 p, float radius) {
+    return length(p) - radius;
+}
+
+// halfSize is half-width/half-height, radius is corner rounding
+float sdBox(vec2 p, vec2 halfSize, float radius) {
+    halfSize -= vec2(radius);
+    vec2 d = abs(p) - halfSize;
+    return min(max(d.x, d.y), 0.0) + length(max(d, 0.0)) - radius;
+}
+
+float sdLine(vec2 p, vec2 start, vec2 end, float width) {
+    vec2 dir = end - start;
+    float h = clamp(dot(p - start, dir) / dot(dir, dir), 0.0, 1.0);
+    return length(p - start - dir * h) - width * 0.5;
+}
+
+// Exact signed distance, requires only one sqrt
+float sdTriangle(vec2 p, vec2 p0, vec2 p1, vec2 p2) {
+    vec2 e0 = p1 - p0, v0 = p - p0;
+    vec2 e1 = p2 - p1, v1 = p - p1;
+    vec2 e2 = p0 - p2, v2 = p - p2;
+    float d0 = dot(v0 - e0 * clamp(dot(v0, e0) / dot(e0, e0), 0.0, 1.0),
+                   v0 - e0 * clamp(dot(v0, e0) / dot(e0, e0), 0.0, 1.0));
+    float d1 = dot(v1 - e1 * clamp(dot(v1, e1) / dot(e1, e1), 0.0, 1.0),
+                   v1 - e1 * clamp(dot(v1, e1) / dot(e1, e1), 0.0, 1.0));
+    float d2 = dot(v2 - e2 * clamp(dot(v2, e2) / dot(e2, e2), 0.0, 1.0),
+                   v2 - e2 * clamp(dot(v2, e2) / dot(e2, e2), 0.0, 1.0));
+    float o = e0.x * e2.y - e0.y * e2.x;
+    vec2 d = min(min(vec2(d0, o * (v0.x * e0.y - v0.y * e0.x)),
+                     vec2(d1, o * (v1.x * e1.y - v1.y * e1.x))),
+                     vec2(d2, o * (v2.x * e2.y - v2.y * e2.x)));
+    return -sqrt(d.x) * sign(d.y);
+}
+
+// Approximate ellipse SDF
+float sdEllipse(vec2 p, vec2 center, float a, float b) {
+    float a2 = a * a, b2 = b * b;
+    vec2 d = p - center;
+    return (b2 * d.x * d.x + a2 * d.y * d.y - a2 * b2) / (a2 * b2);
+}
+```
+
+### Step 3: CSG Boolean Operations
+
+```glsl
+float opUnion(float d1, float d2) { return min(d1, d2); }
+float opIntersect(float d1, float d2) { return max(d1, d2); }
+float opSubtract(float d1, float d2) { return max(-d1, d2); }
+float opXor(float d1, float d2) { return min(max(-d1, d2), max(-d2, d1)); }
+
+// k controls transition width
+float opSmoothUnion(float d1, float d2, float k) {
+    float h = clamp(0.5 + 0.5 * (d2 - d1) / k, 0.0, 1.0);
+    return mix(d2, d1, h) - k * h * (1.0 - h);
+}
+```
+
+### Step 4: Coordinate Transforms
+
+```glsl
+vec2 translate(vec2 p, vec2 t) { return p - t; }
+
+vec2 rotateCCW(vec2 p, float angle) {
+    mat2 m = mat2(cos(angle), sin(angle), -sin(angle), cos(angle));
+    return p * m;
+}
+
+// Usage: translate first, then rotate
+float d = sdBox(rotateCCW(translate(p, vec2(0.5, 0.3)), iTime), vec2(0.2), 0.05);
+```
+
+### Step 5: Rendering and Anti-Aliasing
+
+```glsl
+// smoothstep anti-aliasing (recommended)
+float px = 2.0 / iResolution.y;
+float mask = smoothstep(px, -px, d);  // 1.0 inside, 0.0 outside
+vec3 col = mix(backgroundColor, shapeColor, mask);
+
+// fwidth adaptive anti-aliasing (suitable for scaled scenes)
+float anti = fwidth(d) * 1.0;
+float mask = 1.0 - smoothstep(-anti, anti, d);
+
+// Classic distance field debug visualization
+vec3 col = (d > 0.0) ? vec3(0.9, 0.6, 0.3) : vec3(0.65, 0.85, 1.0);
+col *= 1.0 - exp(-12.0 * abs(d));
+col *= 0.8 + 0.2 * cos(120.0 * d);
+col = mix(col, vec3(1.0), smoothstep(1.5*px, 0.0, abs(d) - 0.002));
+```
+
+### Step 6: Stroke and Border
+
+```glsl
+// Fill + stroke rendering (fwidth adaptive)
+vec4 renderShape(float d, vec3 color, float stroke) {
+    float anti = fwidth(d) * 1.0;
+    vec4 strokeLayer = vec4(vec3(0.05), 1.0 - smoothstep(-anti, anti, d - stroke));
+    vec4 colorLayer  = vec4(color,      1.0 - smoothstep(-anti, anti, d));
+    if (stroke < 0.0001) return colorLayer;
+    return vec4(mix(strokeLayer.rgb, colorLayer.rgb, colorLayer.a), strokeLayer.a);
+}
+
+float fillMask(float d) { return clamp(-d, 0.0, 1.0); }
+float innerBorderMask(float d, float width) {
+    return clamp(d + width, 0.0, 1.0) - clamp(d, 0.0, 1.0);
+}
+float outerBorderMask(float d, float width) {
+    return clamp(d, 0.0, 1.0) - clamp(d - width, 0.0, 1.0);
+}
+```
+
+### Step 7: Multi-Layer Compositing
+
+```glsl
+vec3 bgColor = vec3(1.0, 0.8, 0.7 - 0.07 * p.y) * (1.0 - 0.25 * length(p));
+
+float d1 = sdCircle(translate(p, pos1), 0.3);
+vec4 layer1 = renderShape(d1, vec3(0.9, 0.3, 0.2), 0.02);
+
+float d2 = sdBox(translate(p, pos2), vec2(0.2), 0.05);
+vec4 layer2 = renderShape(d2, vec3(0.2, 0.5, 0.8), 0.0);
+
+// Composite back to front
+vec3 col = bgColor;
+col = mix(col, layer1.rgb, layer1.a);
+col = mix(col, layer2.rgb, layer2.a);
+fragColor = vec4(col, 1.0);
+```
+
+## Full Code Template
+
+```glsl
+// ===== 2D SDF Full Template (runs directly in ShaderToy) =====
+
+#define AA_WIDTH 1.0           // Anti-aliasing width factor
+#define STROKE_WIDTH 0.015     // Stroke width
+#define SMOOTH_K 0.05          // Smooth union transition width
+#define CONTOUR_FREQ 80.0      // Contour line frequency (for debugging)
+#define ANIM_SPEED 1.0         // Animation speed multiplier
+
+// --- SDF Primitives ---
+float sdCircle(vec2 p, float r) { return length(p) - r; }
+
+float sdBox(vec2 p, vec2 b, float r) {
+    b -= vec2(r);
+    vec2 d = abs(p) - b;
+    return min(max(d.x, d.y), 0.0) + length(max(d, 0.0)) - r;
+}
+
+float sdLine(vec2 p, vec2 a, vec2 b, float w) {
+    vec2 d = b - a;
+    float h = clamp(dot(p - a, d) / dot(d, d), 0.0, 1.0);
+    return length(p - a - d * h) - w * 0.5;
+}
+
+float sdTriangle(vec2 p, vec2 p0, vec2 p1, vec2 p2) {
+    vec2 e0 = p1 - p0, v0 = p - p0;
+    vec2 e1 = p2 - p1, v1 = p - p1;
+    vec2 e2 = p0 - p2, v2 = p - p2;
+    float d0 = dot(v0 - e0 * clamp(dot(v0,e0)/dot(e0,e0),0.0,1.0),
+                   v0 - e0 * clamp(dot(v0,e0)/dot(e0,e0),0.0,1.0));
+    float d1 = dot(v1 - e1 * clamp(dot(v1,e1)/dot(e1,e1),0.0,1.0),
+                   v1 - e1 * clamp(dot(v1,e1)/dot(e1,e1),0.0,1.0));
+    float d2 = dot(v2 - e2 * clamp(dot(v2,e2)/dot(e2,e2),0.0,1.0),
+                   v2 - e2 * clamp(dot(v2,e2)/dot(e2,e2),0.0,1.0));
+    float o = e0.x*e2.y - e0.y*e2.x;
+    vec2 dd = min(min(vec2(d0, o*(v0.x*e0.y-v0.y*e0.x)),
+                      vec2(d1, o*(v1.x*e1.y-v1.y*e1.x))),
+                      vec2(d2, o*(v2.x*e2.y-v2.y*e2.x)));
+    return -sqrt(dd.x) * sign(dd.y);
+}
+
+// --- CSG ---
+float opUnion(float a, float b) { return min(a, b); }
+float opSubtract(float a, float b) { return max(-a, b); }
+float opIntersect(float a, float b) { return max(a, b); }
+float opSmoothUnion(float a, float b, float k) {
+    float h = clamp(0.5 + 0.5*(b - a)/k, 0.0, 1.0);
+    return mix(b, a, h) - k*h*(1.0-h);
+}
+float opXor(float a, float b) { return min(max(-a, b), max(-b, a)); }
+
+// --- Coordinate Transforms ---
+vec2 translate(vec2 p, vec2 t) { return p - t; }
+vec2 rotateCCW(vec2 p, float a) {
+    return mat2(cos(a), sin(a), -sin(a), cos(a)) * p;
+}
+
+// --- Rendering Utilities ---
+vec4 render(float d, vec3 color, float stroke) {
+    float anti = fwidth(d) * AA_WIDTH;
+    vec4 strokeLayer = vec4(vec3(0.05), 1.0 - smoothstep(-anti, anti, d - stroke));
+    vec4 colorLayer  = vec4(color,      1.0 - smoothstep(-anti, anti, d));
+    if (stroke < 0.0001) return colorLayer;
+    return vec4(mix(strokeLayer.rgb, colorLayer.rgb, colorLayer.a), strokeLayer.a);
+}
+
+float fillAA(float d, float px) { return smoothstep(px, -px, d); }
+
+// --- Scene ---
+float sceneDist(vec2 p) {
+    float t = iTime * ANIM_SPEED;
+    float c = sdCircle(translate(p, vec2(-0.6, 0.3)), 0.25);
+    float b = sdBox(translate(p, vec2(0.0, 0.3)), vec2(0.25, 0.18), 0.05);
+    vec2 tp = rotateCCW(translate(p, vec2(0.6, 0.3)), t * 0.5);
+    float tr = sdTriangle(tp, vec2(0.0, 0.25), vec2(-0.22, -0.12), vec2(0.22, -0.12));
+    float row1 = opUnion(c, opUnion(b, tr));
+
+    float c2 = sdCircle(translate(p, vec2(-0.5, -0.35)), 0.2);
+    float b2 = sdBox(translate(p, vec2(-0.3, -0.35)), vec2(0.15, 0.15), 0.0);
+    float smooth_demo = opSmoothUnion(c2, b2, SMOOTH_K);
+
+    float c3 = sdCircle(translate(p, vec2(0.15, -0.35)), 0.22);
+    float b3 = sdBox(translate(p, vec2(0.15, -0.35 + sin(t) * 0.15)), vec2(0.3, 0.08), 0.0);
+    float sub_demo = opSubtract(b3, c3);
+
+    float c4 = sdCircle(translate(p, vec2(0.65, -0.35)), 0.2);
+    float b4 = sdBox(translate(p, vec2(0.65, -0.35 + sin(t + 1.0) * 0.15)), vec2(0.3, 0.08), 0.0);
+    float xor_demo = opXor(b4, c4);
+
+    float row2 = opUnion(smooth_demo, opUnion(sub_demo, xor_demo));
+    return opUnion(row1, row2);
+}
+
+// --- Main Function ---
+void mainImage(out vec4 fragColor, in vec2 fragCoord) {
+    vec2 p = (2.0 * fragCoord - iResolution.xy) / iResolution.y;
+    float px = 2.0 / iResolution.y;
+    float d = sceneDist(p);
+
+    vec3 bgCol = vec3(0.15, 0.15, 0.18) + 0.05 * p.y;
+    bgCol *= 1.0 - 0.3 * length(p);
+
+    vec3 col = (d > 0.0) ? vec3(0.9, 0.6, 0.3) : vec3(0.4, 0.7, 1.0);
+    col *= 1.0 - exp(-10.0 * abs(d));
+    col *= 0.8 + 0.2 * cos(CONTOUR_FREQ * d);
+    col = mix(col, vec3(1.0), smoothstep(1.5 * px, 0.0, abs(d) - 0.002));
+    col = mix(bgCol, col, 0.85);
+
+    // Uncomment to switch to solid rendering mode:
+    // vec3 shapeCol = vec3(0.2, 0.8, 0.6);
+    // float mask = fillAA(d, px);
+    // col = mix(bgCol, shapeCol, mask);
+
+    col = pow(col, vec3(1.0 / 2.2));
+    fragColor = vec4(col, 1.0);
+}
+```
+
+## Common Variants
+
+### Variant 1: Solid Fill + Stroke Mode
+
+```glsl
+vec3 shapeColor = vec3(0.32, 0.56, 0.53);
+float strokeW = 0.015;
+vec4 shape = render(d, shapeColor, strokeW);
+vec3 col = bgCol;
+col = mix(col, shape.rgb, shape.a);
+```
+
+### Variant 2: Multi-Layer CSG Illustration
+
+```glsl
+float a = sdEllipse(p, vec2(0.0, 0.16), 0.25, 0.25);
+float b = sdEllipse(p, vec2(0.0, -0.03), 0.8, 0.35);
+float body = opIntersect(a, b);
+vec4 layer1 = render(body, vec3(0.32, 0.56, 0.53), fwidth(body) * 2.0);
+
+float handle = sdLine(p, vec2(0.0, 0.05), vec2(0.0, -0.42), 0.01);
+float arc = sdCircle(translate(p, vec2(-0.04, -0.42)), 0.04);
+float arcInner = sdCircle(translate(p, vec2(-0.04, -0.42)), 0.03);
+handle = opUnion(handle, opSubtract(arcInner, arc));
+vec4 layer0 = render(handle, vec3(0.4, 0.3, 0.28), STROKE_WIDTH);
+
+vec3 col = bgCol;
+col = mix(col, layer0.rgb, layer0.a);
+col = mix(col, layer1.rgb, layer1.a);
+```
+
+### Variant 3: Hexagonal Grid Tiling
+
+```glsl
+vec4 hexagon(vec2 p) {
+    vec2 q = vec2(p.x * 2.0 * 0.5773503, p.y + p.x * 0.5773503);
+    vec2 pi = floor(q);
+    vec2 pf = fract(q);
+    float v = mod(pi.x + pi.y, 3.0);
+    float ca = step(1.0, v);
+    float cb = step(2.0, v);
+    vec2 ma = step(pf.xy, pf.yx);
+    float e = dot(ma, 1.0 - pf.yx + ca*(pf.x+pf.y-1.0) + cb*(pf.yx-2.0*pf.xy));
+    p = vec2(q.x + floor(0.5 + p.y / 1.5), 4.0 * p.y / 3.0) * 0.5 + 0.5;
+    float f = length((fract(p) - 0.5) * vec2(1.0, 0.85));
+    return vec4(pi + ca - cb * ma, e, f);
+}
+
+#define HEX_SCALE 8.0
+vec4 h = hexagon(HEX_SCALE * p + 0.5 * iTime);
+vec3 col = 0.15 + 0.15 * hash1(h.xy + 1.2);
+col *= smoothstep(0.10, 0.11, h.z);
+col *= smoothstep(0.10, 0.11, h.w);
+```
+
+### Variant 4: Organic Shapes (Polar SDF)
+
+```glsl
+// Heart SDF
+p.y -= 0.25;
+float a = atan(p.x, p.y) / 3.141593;
+float r = length(p);
+float h = abs(a);
+float d = (13.0*h - 22.0*h*h + 10.0*h*h*h) / (6.0 - 5.0*h);
+
+// Pulse animation
+float tt = mod(iTime, 1.5) / 1.5;
+float ss = pow(tt, 0.2) * 0.5 + 0.5;
+ss = 1.0 + ss * 0.5 * sin(tt * 6.2831 * 3.0) * exp(-tt * 4.0);
+vec3 col = mix(bgCol, heartCol, smoothstep(-0.01, 0.01, d - r));
+```
+
+### Variant 5: Bezier Curve SDF
+
+```glsl
+vec3 solveCubic(float a, float b, float c) {
+    float p = b - a*a/3.0, p3 = p*p*p;
+    float q = a*(2.0*a*a - 9.0*b)/27.0 + c;
+    float d = q*q + 4.0*p3/27.0;
+    float offset = -a/3.0;
+    if (d >= 0.0) {
+        float z = sqrt(d);
+        vec2 x = (vec2(z,-z) - q) / 2.0;
+        vec2 uv = sign(x) * pow(abs(x), vec2(1.0/3.0));
+        return vec3(offset + uv.x + uv.y);
+    }
+    float v = acos(-sqrt(-27.0/p3)*q/2.0) / 3.0;
+    float m = cos(v), n = sin(v) * 1.732050808;
+    return vec3(m+m, -n-m, n-m) * sqrt(-p/3.0) + offset;
+}
+
+float sdBezier(vec2 A, vec2 B, vec2 C, vec2 p) {
+    B = mix(B + vec2(1e-4), B, step(1e-6, abs(B*2.0-A-C)));
+    vec2 a = B-A, b = A-B*2.0+C, c = a*2.0, d = A-p;
+    vec3 k = vec3(3.*dot(a,b), 2.*dot(a,a)+dot(d,b), dot(d,a)) / dot(b,b);
+    vec3 t = clamp(solveCubic(k.x, k.y, k.z), 0.0, 1.0);
+    vec2 pos = A+(c+b*t.x)*t.x; float dis = length(pos-p);
+    pos = A+(c+b*t.y)*t.y; dis = min(dis, length(pos-p));
+    pos = A+(c+b*t.z)*t.z; dis = min(dis, length(pos-p));
+    return dis * signBezier(A, B, C, p);
+}
+```
+
+## Extended 2D SDF Library
+
+```glsl
+// === Extended 2D SDF Library ===
+
+// Rounded Box with independent corner radii (vec4 r = top-right, bottom-right, top-left, bottom-left)
+float sdRoundedBox(vec2 p, vec2 b, vec4 r) {
+    r.xy = (p.x > 0.0) ? r.xy : r.zw;
+    r.x  = (p.y > 0.0) ? r.x  : r.y;
+    vec2 q = abs(p) - b + r.x;
+    return min(max(q.x, q.y), 0.0) + length(max(q, 0.0)) - r.x;
+}
+
+// Oriented Box (from point a to point b with thickness th)
+float sdOrientedBox(vec2 p, vec2 a, vec2 b, float th) {
+    float l = length(b - a);
+    vec2 d = (b - a) / l;
+    vec2 q = (p - (a + b) * 0.5);
+    q = mat2(d.x, -d.y, d.y, d.x) * q;
+    q = abs(q) - vec2(l, th) * 0.5;
+    return length(max(q, 0.0)) + min(max(q.x, q.y), 0.0);
+}
+
+// Arc (sc = vec2(sin,cos) of aperture angle, ra = radius, rb = thickness)
+float sdArc(vec2 p, vec2 sc, float ra, float rb) {
+    p.x = abs(p.x);
+    return ((sc.y * p.x > sc.x * p.y) ? length(p - sc * ra) : abs(length(p) - ra)) - rb;
+}
+
+// Pie / Sector (c = vec2(sin,cos) of aperture angle)
+float sdPie(vec2 p, vec2 c, float r) {
+    p.x = abs(p.x);
+    float l = length(p) - r;
+    float m = length(p - c * clamp(dot(p, c), 0.0, r));
+    return max(l, m * sign(c.y * p.x - c.x * p.y));
+}
+
+// Ring (n = vec2(sin,cos) of aperture, r = radius, th = thickness)
+float sdRing(vec2 p, vec2 n, float r, float th) {
+    p.x = abs(p.x);
+    float d = length(p);
+    // If within aperture angle
+    if (n.y * p.x > n.x * p.y) {
+        return abs(d - r) - th;
+    }
+    // Cap endpoints
+    return min(length(p - n * r), length(p + n * r)) - th;
+}
+
+// Moon shape
+float sdMoon(vec2 p, float d, float ra, float rb) {
+    p.y = abs(p.y);
+    float a = (ra * ra - rb * rb + d * d) / (2.0 * d);
+    float b2 = ra * ra - a * a;
+    if (d * (p.x * rb * rb - p.y * a * rb * rb - a * b2) > 0.0)
+        return length(p - vec2(a, sqrt(max(b2, 0.0))));
+    return max(length(p) - ra, -(length(p - vec2(d, 0.0)) - rb));
+}
+
+// Heart (approximate)
+float sdHeart(vec2 p) {
+    p.x = abs(p.x);
+    if (p.y + p.x > 1.0)
+        return sqrt(dot(p - vec2(0.25, 0.75), p - vec2(0.25, 0.75))) - sqrt(2.0) / 4.0;
+    return sqrt(min(dot(p - vec2(0.0, 1.0), p - vec2(0.0, 1.0)),
+                    dot(p - 0.5 * max(p.x + p.y, 0.0), p - 0.5 * max(p.x + p.y, 0.0)))) *
+           sign(p.x - p.y);
+}
+
+// Vesica (lens shape)
+float sdVesica(vec2 p, float w, float h) {
+    p = abs(p);
+    float b = sqrt(h * h + w * w * 0.25) / w;
+    return ((p.y - h) * b * w > p.x * b * h)
+        ? length(p - vec2(0.0, h))
+        : length(p - vec2(-w * 0.5, 0.0)) - b;
+}
+
+// Egg shape
+float sdEgg(vec2 p, float he, float ra, float rb) {
+    p.x = abs(p.x);
+    float r = (p.y < 0.0) ? ra : rb;
+    return length(vec2(p.x, p.y - clamp(p.y, -he, he))) - r;
+}
+
+// Equilateral Triangle
+float sdEquilateralTriangle(vec2 p, float r) {
+    const float k = sqrt(3.0);
+    p.x = abs(p.x) - r;
+    p.y = p.y + r / k;
+    if (p.x + k * p.y > 0.0) p = vec2(p.x - k * p.y, -k * p.x - p.y) / 2.0;
+    p.x -= clamp(p.x, -2.0 * r, 0.0);
+    return -length(p) * sign(p.y);
+}
+
+// Pentagon
+float sdPentagon(vec2 p, float r) {
+    const vec3 k = vec3(0.809016994, 0.587785252, 0.726542528);
+    p.x = abs(p.x);
+    p -= 2.0 * min(dot(vec2(-k.x, k.y), p), 0.0) * vec2(-k.x, k.y);
+    p -= 2.0 * min(dot(vec2(k.x, k.y), p), 0.0) * vec2(k.x, k.y);
+    p -= vec2(clamp(p.x, -r * k.z, r * k.z), r);
+    return length(p) * sign(p.y);
+}
+
+// Hexagon
+float sdHexagon(vec2 p, float r) {
+    const vec3 k = vec3(-0.866025404, 0.5, 0.577350269);
+    p = abs(p);
+    p -= 2.0 * min(dot(k.xy, p), 0.0) * k.xy;
+    p -= vec2(clamp(p.x, -k.z * r, k.z * r), r);
+    return length(p) * sign(p.y);
+}
+
+// Octagon
+float sdOctagon(vec2 p, float r) {
+    const vec3 k = vec3(-0.9238795325, 0.3826834323, 0.4142135623);
+    p = abs(p);
+    p -= 2.0 * min(dot(vec2(k.x, k.y), p), 0.0) * vec2(k.x, k.y);
+    p -= 2.0 * min(dot(vec2(-k.x, k.y), p), 0.0) * vec2(-k.x, k.y);
+    p -= vec2(clamp(p.x, -k.z * r, k.z * r), r);
+    return length(p) * sign(p.y);
+}
+
+// Star (n-pointed, m = inner radius ratio)
+float sdStar(vec2 p, float r, int n, float m) {
+    float an = 3.141593 / float(n);
+    float en = 3.141593 / m;
+    vec2 acs = vec2(cos(an), sin(an));
+    vec2 ecs = vec2(cos(en), sin(en));
+    float bn = mod(atan(p.x, p.y), 2.0 * an) - an;
+    p = length(p) * vec2(cos(bn), abs(sin(bn)));
+    p -= r * acs;
+    p += ecs * clamp(-dot(p, ecs), 0.0, r * acs.y / ecs.y);
+    return length(p) * sign(p.x);
+}
+
+// Quadratic Bezier curve SDF
+float sdBezier(vec2 pos, vec2 A, vec2 B, vec2 C) {
+    vec2 a = B - A;
+    vec2 b = A - 2.0 * B + C;
+    vec2 c = a * 2.0;
+    vec2 d = A - pos;
+    float kk = 1.0 / dot(b, b);
+    float kx = kk * dot(a, b);
+    float ky = kk * (2.0 * dot(a, a) + dot(d, b)) / 3.0;
+    float kz = kk * dot(d, a);
+    float res = 0.0;
+    float p2 = ky - kx * kx;
+    float q = kx * (2.0 * kx * kx - 3.0 * ky) + kz;
+    float h = q * q + 4.0 * p2 * p2 * p2;
+    if (h >= 0.0) {
+        h = sqrt(h);
+        vec2 x = (vec2(h, -h) - q) / 2.0;
+        vec2 uv2 = sign(x) * pow(abs(x), vec2(1.0 / 3.0));
+        float t = clamp(uv2.x + uv2.y - kx, 0.0, 1.0);
+        res = dot(d + (c + b * t) * t, d + (c + b * t) * t);
+    } else {
+        float z = sqrt(-p2);
+        float v = acos(q / (p2 * z * 2.0)) / 3.0;
+        float m2 = cos(v);
+        float n2 = sin(v) * 1.732050808;
+        vec3 t = clamp(vec3(m2 + m2, -n2 - m2, n2 - m2) * z - kx, 0.0, 1.0);
+        res = min(dot(d + (c + b * t.x) * t.x, d + (c + b * t.x) * t.x),
+                  dot(d + (c + b * t.y) * t.y, d + (c + b * t.y) * t.y));
+    }
+    return sqrt(res);
+}
+
+// Parabola
+float sdParabola(vec2 pos, float k) {
+    pos.x = abs(pos.x);
+    float ik = 1.0 / k;
+    float p2 = ik * (pos.y - 0.5 * ik) / 3.0;
+    float q = 0.25 * ik * ik * pos.x;
+    float h = q * q - p2 * p2 * p2;
+    float r = sqrt(abs(h));
+    float x = (h > 0.0) ?
+        pow(q + r, 1.0 / 3.0) + pow(abs(q - r), 1.0 / 3.0) * sign(p2) :
+        2.0 * cos(atan(r, q) / 3.0) * sqrt(p2);
+    return length(pos - vec2(x, k * x * x)) * sign(pos.x - x);
+}
+
+// Cross shape
+float sdCross(vec2 p, vec2 b, float r) {
+    p = abs(p); p = (p.y > p.x) ? p.yx : p.xy;
+    vec2 q = p - b;
+    float k = max(q.y, q.x);
+    vec2 w = (k > 0.0) ? q : vec2(b.y - p.x, -k);
+    return sign(k) * length(max(w, 0.0)) + r;
+}
+```
+
+## 2D SDF Modifiers
+
+```glsl
+// === 2D SDF Modifiers ===
+
+// Round any 2D SDF
+float opRound2D(float d, float r) { return d - r; }
+
+// Create annular (ring) version of any 2D SDF
+float opAnnular2D(float d, float r) { return abs(d) - r; }
+
+// Repeat a 2D SDF in a grid
+vec2 opRepeat2D(vec2 p, float s) { return mod(p + s * 0.5, s) - s * 0.5; }
+
+// Mirror across arbitrary 2D direction
+vec2 opMirror2D(vec2 p, vec2 dir) {
+    return p - 2.0 * dir * max(dot(p, dir), 0.0);
+}
+```
+
+## Performance & Composition Tips
+
+**Performance:**
+- In polygon SDFs, compare squared distances first; use a single `sqrt` at the end
+- For simple scenes, use fixed `px = 2.0/iResolution.y` instead of `fwidth(d)`; use `fwidth` when coordinate scaling is involved
+- For many primitives, spatially partition and skip distant ones early
+- Supersampling (2x2/3x3) only for offline rendering; for real-time, single-pixel AA with `smoothstep`/`fwidth` is sufficient
+- For 2D soft shadow marching, use adaptive step size `dt += max(1.0, abs(sd))`
+
+**Composition:**
+- **SDF + Noise**: `d += noise(p * 10.0 + iTime) * 0.05` to create organic edges
+- **SDF + 2D Lighting**: cone marching for soft shadows, query occlusion via `sceneDist()`
+- **SDF + Normal Mapping**: finite differences for normals + Blinn-Phong lighting to simulate bump effects
+- **SDF + Domain Repetition**: `fract`/`mod` for infinite repetition, `floor` for cell ID
+- **SDF + Animation**: parameters driven by `sin/cos` periodic motion, `exp` decay, `mod` looping
+
+## Further Reading
+
+Full step-by-step tutorials, mathematical derivations, and advanced usage in [reference](../reference/sdf-2d.md)