Ray Marching and Signed Distance Fields

Polygon rasterization won the real-time race for decades. But in shader land, a fullscreen quad and a for loop can render infinite detail no meshes, no UV unwrapping, no LOD chains.

The setup

Cast a ray from the camera through each pixel. Step along the ray until you hit a surface. That's ray marching but naive stepping is slow.

Sphere tracing uses signed distance functions (SDFs): at any point in space, the SDF returns the distance to the nearest surface. You can safely advance by that distance without overshooting.

float map(vec3 p) {
  float sphere = length(p) - 1.0;
  float box = sdBox(p - vec3(2,0,0), vec3(0.5));
  return min(sphere, box);
}
 
float rayMarch(vec3 ro, vec3 rd) {
  float t = 0.0;
  for (int i = 0; i < 128; i++) {
    vec3 p = ro + rd * t;
    float d = map(p);
    if (d < 0.001) return t;
    t += d;
    if (t > 100.0) break;
  }
  return -1.0;
}

Primitive SDFs

CSG operations combine shapes with min (union), max (intersection), and smooth variants.

Normals and lighting

No vertex normals exist estimate via gradient:

vec3 calcNormal(vec3 p) {
  vec2 e = vec2(0.001, 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)
  ));
}

Then standard Phong/Blinn lighting applies.

Where it shines

• Demoscene and ShaderToy art
• Procedural planets and terrain
• UI effects and transitions
• Teaching 3D math without engine overhead

The tradeoff

Ray marching is CPU/GPU brute force. Modern games hybridize SDFs for volumetrics, meshes for characters. But understanding SDFs unlocks a different way to think about geometry entirely.