A Recursive Algorithm to Render Signed Distance Fields

Signed Distance Fields (SDFs) define 3D objects via mathematical functions and can be combined in powerful ways, but rendering them via raymarching is computationally expensive. A novel recursive divide-and-conquer algorithm is proposed and implemented in Rust that subdivides the view frustum into smaller quads, advancing all rays in a patch simultaneously and recursively splitting only when near a surface. This approach achieves 3–4x fewer rays per pixel and triples frame rate on a simple scene. An extension using linear interpolation for flat patches reduces samples to below one per pixel, reaching 100 FPS on a single M1 CPU core. The technique relates to the known but obscure GPU concept of 'cone marching' using multi-pass shaders. The results suggest CPU-based SDF rendering for real-time 3D games may be within reach with further optimization and multi-core usage.