Unconstrained isosurface extraction on arbitrary octrees

This paper presents a novel algorithm for generating a watertight level-set from an octree. We show that the levelset can be efficiently extracted regardless of the topology of the octree or the values assigned to the vertices. The key idea behind our approach is the definition of a set of binary edge-trees derived from the octree’s topology. We show that the edge-trees can be used define the positions of the isovalue-crossings in a consistent fashion and to resolve inconsistencies that may arise when a single edge has multiple isovalue-crossings. Using the edge-trees, we show that a provably watertight mesh can be extracted from the octree without necessitating the refinement of nodes or modification of their values.