Healed marching cubes algorithm for non-manifold implicit surfaces

We present an algorithm, called Healed Marching Cubes (HMC), which is capable of triangulating non-manifold implicit surfaces with the help of healing techniques based on differential geometry tools. The leading idea of HMC algorithm is to leverage data generated by the standard Marching Cubes (MC) algorithm for manifold surfaces, healing the sub-triangulation inside each critical cube, i.e., a cube inside which the surface self-intersects along a (straight or curved) line. The healing process starts with the identification of such critical cubes, continues with the identification of endpoints of the intersection line segment across each critical cube, and terminates with re-triangulation inside each critical cube. As far as we know, this geometric healing process has never been used as an extension of MC algorithm for non-manifold implicit surfaces.