A Framework for Self-Intersecting Surfaces (SOS): Symmetric Optimisation for Stability

In this paper, we give a stable and efficient method for fixing self-intersections and non-manifold parts in a given embedded simplicial complex. In addition, we show how symmetric properties can be used for further optimisation. We prove an initialisation criterion for computation of the outer hull of an embedded simplicial complex. To regularise the outer hull of the retriangulated surface, we present a method to remedy non-manifold edges and points. We also give a modification of the outer hull algorithm to determine chambers of complexes which gives rise to many new insights. All of these methods have applications in many areas, for example in 3D-printing, artistic realisations of 3D models or fixing errors introduced by scanning equipment applied for tomography. Implementations of the proposed algorithms are given in the computer algebra system GAP4. For verification of our methods, we use a data-set of highly self-intersecting symmetric icosahedra.