  Recently there has been renewed interest in signed distance bound
representations due to their unique properties for 3D shape modelling. This is
especially the case for deep learning-based bounds. However, it is beneficial
to work with polygons in most computer-graphics applications. Thus, in this
paper we introduce and investigate an asymptotically fast method for
transforming signed distance bounds into polygon meshes. This is achieved by
combining the principles of sphere tracing (or ray marching) with traditional
polygonization techniques, such as Marching Cubes. We provide theoretical and
experimental evidence that this approach 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 bounds generated
from point clouds by machine learning (and represented as neural networks).
Given its speed, implementation 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
