A Novel Approach To (Non-Manifold) Dual Contouring

For the sake of "completness", my first entry is about the very first algorithm I came up when I was thinking about new solutions to procedural meshing / extracting a polygon mesh from implicit geometry (e.g. from a signed distance function, SDF)

You can find out more about it in this thread right here.

At first, I liked the idea. However, the more I worked on the algorithm, the more I found characteristics that I dislike about this approach.
You can read about the pro's in the thread linked above, so here is the stuff that I dislike now:

• The algorithm is a typical "voxel" algorithm. It relies on a 3D grid.
• It may suffer from floating-point imprecision
• It lost it's simpleness. The idea behind the algorithm was to find a simple alternative to DC. This is still very true for the 2D version of the algorithm, but for the 3D version, not so much...
  I had to account for more & more "special cases" during the development of the algorithm, resulting in an algorithm that wasn't simple enough anymore for my taste.