name: shader-sdf
description: Signed Distance Functions (SDFs) in GLSL—2D/3D shape primitives, boolean operations (union, intersection, subtraction), smooth blending, repetition, and raymarching fundamentals. Use when creating procedural shapes, text effects, smooth morphing, or raymarched 3D scenes.

Shader SDFs

Signed Distance Functions return the distance from a point to a shape's surface. Negative = inside, positive = outside, zero = on surface.

Quick Start

// 2D circle SDF
float sdCircle(vec2 p, float r) {
  return length(p) - r;
}

// Usage
float d = sdCircle(uv - 0.5, 0.3);

// Render
vec3 color = d < 0.0 ? vec3(1.0) : vec3(0.0);           // Hard edge
vec3 color = vec3(smoothstep(0.01, 0.0, d));            // Soft edge
vec3 color = vec3(smoothstep(0.02, 0.0, abs(d)));       // Outline

2D Primitives

Circle

float sdCircle(vec2 p, float r) {
  return length(p) - r;
}

Box

float sdBox(vec2 p, vec2 b) {
  vec2 d = abs(p) - b;
  return length(max(d, 0.0)) + min(max(d.x, d.y), 0.0);
}

Rounded Box

float sdRoundedBox(vec2 p, vec2 b, float r) {
  vec2 d = abs(p) - b + r;
  return length(max(d, 0.0)) + min(max(d.x, d.y), 0.0) - r;
}

Line Segment

float sdSegment(vec2 p, vec2 a, vec2 b) {
  vec2 pa = p - a;
  vec2 ba = b - a;
  float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);
  return length(pa - ba * h);
}

Triangle

float sdTriangle(vec2 p, vec2 p0, vec2 p1, vec2 p2) {
  vec2 e0 = p1 - p0, e1 = p2 - p1, e2 = p0 - p2;
  vec2 v0 = p - p0, v1 = p - p1, v2 = p - p2;
  vec2 pq0 = v0 - e0 * clamp(dot(v0, e0) / dot(e0, e0), 0.0, 1.0);
  vec2 pq1 = v1 - e1 * clamp(dot(v1, e1) / dot(e1, e1), 0.0, 1.0);
  vec2 pq2 = v2 - e2 * clamp(dot(v2, e2) / dot(e2, e2), 0.0, 1.0);
  float s = sign(e0.x * e2.y - e0.y * e2.x);
  vec2 d = min(min(
    vec2(dot(pq0, pq0), s * (v0.x * e0.y - v0.y * e0.x)),
    vec2(dot(pq1, pq1), s * (v1.x * e1.y - v1.y * e1.x))),
    vec2(dot(pq2, pq2), s * (v2.x * e2.y - v2.y * e2.x)));
  return -sqrt(d.x) * sign(d.y);
}

Ring

float sdRing(vec2 p, float r, float thickness) {
  return abs(length(p) - r) - thickness;
}

Polygon (N-sided)

float sdPolygon(vec2 p, float r, int n) {
  float a = atan(p.x, p.y) + 3.141592;
  float s = 6.283185 / float(n);
  return cos(floor(0.5 + a / s) * s - a) * length(p) - r;
}

Star

float sdStar(vec2 p, float r, int n, float m) {
  float an = 3.141592 / float(n);
  float en = 3.141592 / 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);
}

3D Primitives

Sphere

float sdSphere(vec3 p, float r) {
  return length(p) - r;
}

Box

float sdBox(vec3 p, vec3 b) {
  vec3 q = abs(p) - b;
  return length(max(q, 0.0)) + min(max(q.x, max(q.y, q.z)), 0.0);
}

Rounded Box

float sdRoundBox(vec3 p, vec3 b, float r) {
  vec3 q = abs(p) - b;
  return length(max(q, 0.0)) + min(max(q.x, max(q.y, q.z)), 0.0) - r;
}

Cylinder

float sdCylinder(vec3 p, float h, float r) {
  vec2 d = abs(vec2(length(p.xz), p.y)) - vec2(r, h);
  return min(max(d.x, d.y), 0.0) + length(max(d, 0.0));
}

Torus

float sdTorus(vec3 p, vec2 t) {
  vec2 q = vec2(length(p.xz) - t.x, p.y);
  return length(q) - t.y;
}

Cone

float sdCone(vec3 p, vec2 c, float h) {
  vec2 q = h * vec2(c.x / c.y, -1.0);
  vec2 w = vec2(length(p.xz), p.y);
  vec2 a = w - q * clamp(dot(w, q) / dot(q, q), 0.0, 1.0);
  vec2 b = w - q * vec2(clamp(w.x / q.x, 0.0, 1.0), 1.0);
  float k = sign(q.y);
  float d = min(dot(a, a), dot(b, b));
  float s = max(k * (w.x * q.y - w.y * q.x), k * (w.y - q.y));
  return sqrt(d) * sign(s);
}

Capsule

float sdCapsule(vec3 p, vec3 a, vec3 b, float r) {
  vec3 pa = p - a, ba = b - a;
  float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);
  return length(pa - ba * h) - r;
}

Plane

float sdPlane(vec3 p, vec3 n, float h) {
  return dot(p, n) + h;
}

Boolean Operations

Union (OR)

float opUnion(float d1, float d2) {
  return min(d1, d2);
}

Intersection (AND)

float opIntersection(float d1, float d2) {
  return max(d1, d2);
}

Subtraction (NOT)

float opSubtraction(float d1, float d2) {
  return max(-d1, d2);
}

Smooth Union

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);
}

Smooth Intersection

float opSmoothIntersection(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);
}

Smooth Subtraction

float opSmoothSubtraction(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);
}

Transformations

Translation

// Move shape by offset
float d = sdCircle(p - offset, r);

Rotation (2D)

mat2 rot2D(float a) {
  float s = sin(a), c = cos(a);
  return mat2(c, -s, s, c);
}

// Rotate point around origin
vec2 rotatedP = rot2D(angle) * p;
float d = sdBox(rotatedP, size);

Rotation (3D)

mat3 rotateX(float a) {
  float s = sin(a), c = cos(a);
  return mat3(1, 0, 0, 0, c, -s, 0, s, c);
}

mat3 rotateY(float a) {
  float s = sin(a), c = cos(a);
  return mat3(c, 0, s, 0, 1, 0, -s, 0, c);
}

mat3 rotateZ(float a) {
  float s = sin(a), c = cos(a);
  return mat3(c, -s, 0, s, c, 0, 0, 0, 1);
}

Scale

// Scale shape
float d = sdCircle(p / scale, r) * scale;

Symmetry

// Mirror across Y axis
p.x = abs(p.x);
float d = sdCircle(p - vec2(0.3, 0.0), 0.1);

Domain Operations

Repetition (Infinite)

float opRepeat(vec2 p, vec2 spacing) {
  vec2 q = mod(p + spacing * 0.5, spacing) - spacing * 0.5;
  return sdCircle(q, 0.1);
}

Repetition (Limited)

float opRepeatLimited(vec3 p, float spacing, vec3 count) {
  vec3 q = p - spacing * clamp(round(p / spacing), -count, count);
  return sdSphere(q, 0.1);
}

Twist

float opTwist(vec3 p, float k) {
  float c = cos(k * p.y);
  float s = sin(k * p.y);
  mat2 m = mat2(c, -s, s, c);
  vec3 q = vec3(m * p.xz, p.y);
  return sdBox(q, vec3(0.5));
}

Bend

float opBend(vec3 p, float k) {
  float c = cos(k * p.x);
  float s = sin(k * p.x);
  mat2 m = mat2(c, -s, s, c);
  vec3 q = vec3(m * p.xy, p.z);
  return sdBox(q, vec3(0.5));
}

Onion (Hollow)

float opOnion(float d, float thickness) {
  return abs(d) - thickness;
}

Round

float opRound(float d, float r) {
  return d - r;
}

2D Rendering Techniques

Anti-aliased Edge

float aa = fwidth(d) * 1.5;
float mask = smoothstep(aa, -aa, d);

Outline

float outline = smoothstep(thickness + aa, thickness - aa, abs(d));

Glow

float glow = exp(-d * falloff);

Drop Shadow

float shadow = smoothstep(0.0, blur, sdShape(p - shadowOffset));

3D Raymarching (Basic)

float map(vec3 p) {
  float d = sdSphere(p, 1.0);
  d = opSmoothUnion(d, sdBox(p - vec3(1.0, 0.0, 0.0), vec3(0.5)), 0.2);
  return d;
}

vec3 calcNormal(vec3 p) {
  vec2 e = vec2(0.001, 0.0);
  return normalize(vec3(
    map(p + e.xyy) - map(p - e.xyy),
    map(p + e.yxy) - map(p - e.yxy),
    map(p + e.yyx) - map(p - e.yyx)
  ));
}

float raymarch(vec3 ro, vec3 rd) {
  float t = 0.0;
  for (int i = 0; i < 100; i++) {
    vec3 p = ro + rd * t;
    float d = map(p);
    if (d < 0.001) break;
    if (t > 100.0) break;
    t += d;
  }
  return t;
}

void mainImage(out vec4 fragColor, in vec2 fragCoord) {
  vec2 uv = (fragCoord - 0.5 * iResolution.xy) / iResolution.y;

  vec3 ro = vec3(0.0, 0.0, 3.0);  // Ray origin
  vec3 rd = normalize(vec3(uv, -1.0));  // Ray direction

  float t = raymarch(ro, rd);

  vec3 color = vec3(0.0);
  if (t < 100.0) {
    vec3 p = ro + rd * t;
    vec3 n = calcNormal(p);
    vec3 light = normalize(vec3(1.0, 1.0, 1.0));
    float diff = max(dot(n, light), 0.0);
    color = vec3(diff);
  }

  fragColor = vec4(color, 1.0);
}

File Structure

shader-sdf/
├── SKILL.md
├── references/
│   ├── 2d-primitives.md      # All 2D shapes
│   ├── 3d-primitives.md      # All 3D shapes
│   └── operations.md         # All operations
└── scripts/
    ├── primitives/
    │   ├── 2d.glsl           # 2D shape functions
    │   └── 3d.glsl           # 3D shape functions
    ├── operations.glsl       # Boolean & domain ops
    └── examples/
        ├── logo.glsl         # 2D logo example
        └── raymarch.glsl     # 3D raymarching example

Reference

• references/2d-primitives.md — Complete 2D shape library
• references/3d-primitives.md — Complete 3D shape library
• references/operations.md — All boolean and domain operations