Polygonization of non-homogeneous non-manifold implicit surfaces with tentative topological guarantees

Previous work on implicit surfaces has almost exclusively focused on homogeneously 2-dimensional surfaces, regardless of whether they are manifold or not. Consequently, current geometric and graphical systems, and even commercial mathematical software packages, cannot generate non-homogeneous implicit surfaces such as, for example, the Steiner surface or the Whitney surface correctly. This paper overcomes these difficulties by introducing a new uniform space partitioning-based algorithm that generates a polygonization for implicit surfaces possibly with self-intersections and isolated 0-and 1-dimensional singularities.