Advanced SDF geometry: curves, implicit forms, and material channels

This module is where your raymarched visuals stop looking like demo-scene sphere soup and start carrying identity. In a live set, the shapes on screen are your typography: a logo glyph, a signature curve, a textured planet that recurs across the night. The capstone is exactly that whole task — a Bezier-curve glyph grown from an implicit equation, wired into a scene that reports material IDs and auxiliary channels so the shading pass can texture a sphere with proper spherical UVs, all running at projector framerate.

The arc starts supported: take a known implicit curve and convert it to a distance field using the deriving-SDFs-from-implicit-equations procedure, then swap in IQ’s three-control-point quadratic Bezier field and animate its control points — these two are your part-task drills, because mid-performance you will sketch curves faster than you can look them up. Next you confront why the glyph flickers or crawls: the exact-versus-approximate distinction explains your step sizes, and abs()-based signed backtracking is the JIT fix when a displaced field overshoots. Finally you plumb the data path — extending map() to a vec4 so UVs and occlusion travel with the winning material, then mapping latitude/longitude onto the sphere.

The required atoms gate the capstone directly: without the implicit-equation and Bezier techniques there is no glyph; without exactness reasoning and backtracking it won’t render stably; without vec4 channels and spherical UVs there is nothing to texture. Supporting atoms deepen the craft — polynomial smooth-min rigidity for when you later blend glyphs, ray differentials for antialiased edges, and Perlin noise as a UV-free alternative texture source.

Runnable examples

Generated from the context/ instrument corpus by concept (redistributable idioms only). Do not edit — regenerate with gen-module-examples.mjs.

sdf-shape

circle [0,0] 0.4 >> add

_{punctual-0018 · CC0-1.0}

float d = length(uv) - r;

_{glsl-0003 · public-domain}

noise-field

noise(4, 0.1).out()

_{hydra-0002 · CC0-1.0}

float h21(vec2 p){return fract(sin(dot(p,vec2(12.9898,78.233)))*43758.5453);}

_{glsl-0013 · public-domain}

raymarch-sdf

vec3 nrm(vec3 p){vec2 e=vec2(.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)));}

_{glsl-0033 · public-domain}