Lesson 8 of 10 · Ray marching in GLSL

Two shapes

smin(): two spheres melting into one.

Plain min() unions two shapes but leaves a hard crease where they meet. smin() (smooth minimum) fuses them like beads of mercury: in the contact zone it interpolates instead of cutting, and a soft neck appears.

Two spheres, one on each side, fused. This is the magic that makes raymarching feel organic, not built from Lego bricks.

smin(a, b, k)Like min, but k controls how much they melt. Small k = nearly separate; large k = one mass. The neck comes from a quadratic blend, no extra geometry: two spheres and a number.

PruebaRaise the 0.6 in smin(s1, s2, 0.6) and the drops fuse harder. The second slider slides the right sphere (p-vec3(0.6).

The code

precision highp float;
float smin(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 map(vec3 p){
  float s1=length(p-vec3(-0.7,0.0,0.0))-0.85;
  float s2=length(p-vec3(0.6,0.0,0.0))-0.85;
  float blob=smin(s1, s2, 0.6);
  float flo=p.y+1.2;
  return min(blob, flo);
}
vec3 nrm(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)));
}
void main(){
  vec2 uv=(gl_FragCoord.xy*2.0-R)/R.y;
  vec3 ro=vec3(0.0,0.0,3.2);
  vec3 rd=normalize(vec3(uv,-1.5));
  float t=0.0;
  float hit=0.0;
  for(int i=0;i<64;i++){
    vec3 pos=ro+rd*t;
    float d=map(pos);
    if(d<0.001){ hit=1.0; break; }
    t+=d;
    if(t>20.0) break;
  }
  vec3 pos=ro+rd*t;
  vec3 n=nrm(pos);
  vec3 lightDir=normalize(vec3(0.7, 0.9, 0.5));
  float diff=max(dot(n,lightDir),0.0);
  vec3 lit=vec3(0.55,0.65,0.95)*(diff*0.9+0.14);
  vec3 sky=mix(vec3(0.05,0.06,0.12), vec3(0.16,0.22,0.42), uv.y*0.5+0.5);
  float fog=1.0-exp(-t*0.08);
  vec3 col=mix(lit, sky, fog);
  col=mix(sky, col, hit);
  gl_FragColor=vec4(col,1.0);
}