Raymarched 3D shapes

How it works

Most 3D graphics start from triangles. Raymarching starts from a function instead. The scene is a 3D signed distance field: give it any point and it returns how far that point is from the nearest surface. A sphere is length(p) - r; a box, a torus or a capsule each take a line or two; and the operators from 2D composition work unchanged, so min joins shapes and a smooth minimum melts them together.

To see the scene, a fragment shader over a full-screen quad shoots one ray per pixel from a virtual camera. It steps along the ray by the scene’s distance, which is always a safe step because nothing is closer, until the distance is almost zero: the ray has hit. The surface normal comes from the field’s gradient, a few more samples around the hit, and from there lighting is the same dot product as on any mesh.

What you get is a kind of geometry triangles can’t easily give: shapes that blend smoothly, repeat to infinity with a mod on the point, bend and twist, all exact at any zoom and changing every frame with no mesh to rebuild. What it costs is a loop in every pixel, each step evaluating the whole scene. That makes it the tool for full-screen demos, backgrounds, title cards and effects inside a box, and the wrong tool for a game’s main geometry.

In an engine it runs on a full-screen rectangle (Godot’s ColorRect, a quad in front of the camera elsewhere). Mixing it with the engine’s own meshes needs the hit’s depth written out, which each engine handles differently.