procedural-mathematics-expert

Define SDF primitive functions like sdSphere and sdBox that return the shortest distance to a surface, combine them with smooth CSG operators, then march rays by stepping the returned distance each iteration. Bound iterations and use epsilon offsets for stable convergence.

Domain warping distorts input coordinates with noise or flow fields before evaluating geometry, using methods like FBM warp, curl warp, or recursive warp. It makes procedural scenes appear fluid and organic rather than static.

Yes, geometry, lighting, fog, and materials can be computed entirely in fragment shaders, with Three.js only compiling shaders, uploading uniforms, and presenting framebuffers. This suits raymarched and fractal scenes but not asset-heavy pipelines.

Long-running shaders degrade from floating-point drift, division by zero, and exploding recursion. Guard normalize, length, and division operations, clamp values, use epsilon offsets, and prefer highp precision for raymarching.

Use Voronoi for cellular structures like crystals, coral, rock, and biological patterns. Use FBM for continuous phenomena like terrain, clouds, and atmospheric density, keeping octave counts minimal to control GPU cost.