Sphere tracing
A way to trace rays against implicit surfaces by stepping forward exactly as far as the distance field says is safe.
When a surface is described by a distance field (an SDF) — a function that returns, for any point, the distance to the nearest surface — you can trace a ray without solving any equations. At each step you ask the field how far the surface is and jump exactly that far. Because the distance is the shortest in every direction, the step can never pass through the surface. You approach asymptotically until the distance is negligible.
The method was formulated by John C. Hart in 1996, precisely for implicit surfaces. It underpins modern SDF rendering: the demoscene's 64 kB productions, Shadertoy, Inigo Quilez's distance functions and Media Molecule's Dreams. Compared with naive fixed-step raymarching it is both faster and exact — but only as good as the distance field is accurate.