A framework for symmetric self-intersecting surfaces

Graphical Models, vol. 145, pp. 101329

Abstract

3D modelling using triangular complexes, i.e. meshes consisting of triangles, has become an established method for prototyping, visualisation and manufacturing. However, such meshes often contain certain degenerations, such as self-intersecting triangles or singular parts, which pose serious problems in further workflows. Therefore, it is necessary to examine these degenerations beforehand. The main contribution of this work is to give a full framework for fixing 3D models employing the combinatorial language of simplicial surfaces, exploiting symmetries and removing non-manifold parts. We provide algorithms that make minimal changes to the original model, allowing the printing of meshes that were previously impossible or difficult to process with existing software. For example, exploitation of the symmetry of the underlying triangular complex leads to a notable speed-up when computing a retriangulation. Implementations of the proposed methods are made available as an open-source GAP4 package. To verify our methods, we use a dataset of self-intersecting symmetric icosahedra and a selection of standard degenerate STL files.

Authors 2

1. Christian Amend Aachen Lehrstuhl für Algebra und Darstellungstheorie

   RWTH Aachen University · University of Twente

   Affiliation as printed

   RWTH Aachen University, Lehrstuhl für Algebra und Darstellungstheorie, Aachen, Germany

   University of Twente, Department of Applied Mathematics, Enschede, Netherlands

2. Tom Goertzen corresponding Aachen Lehrstuhl für Algebra und Darstellungstheorie

   RWTH Aachen University · The University of Sydney

   Affiliation as printed

   RWTH Aachen University, Lehrstuhl für Algebra und Darstellungstheorie, Aachen, Germany

   University of Sydney, School of Mathematics and Statistics, Sydney, Australia