Theoretical and empirical analysis of a fast algorithm for extracting polygons from signed distance bounds

We investigate an asymptotically fast method for transforming signed distance bounds into polygon meshes. This is achieved by combining sphere tracing (also known as ray marching) and one of the traditional polygonization schemes (e.g., Marching cubes). Let us call this approach Gridhopping. We provide theoretical and experimental evidence that it is of the $O(N^2\log N)$ computational complexity for a polygonization grid with $N^3$ cells. The algorithm is tested on both a set of primitive shapes as well as signed distance fields generated from point clouds by machine learning. Given its speed, simplicity and portability, we argue that it could prove useful during the modelling stage as well as in shape compression for storage. The code is available here: https://github.com/nenadmarkus/gridhopping