OpenVolumeMesh – A Versatile Index-Based Data Structure for 3D Polytopal Complexes

Abstract

Summary. We present a data structure which is able to represent heterogeneous 3-dimensional polytopal cell complexes and is general enough to also represent nonmanifolds without incurring undue overhead. Extending the idea of half-edge based data structures for two-manifold surface meshes, all faces, i.e. the two-dimensional entities of a mesh, are represented by a pair of oriented half-faces. The concept of using directed half-entities enables inducing an orientation to the meshes in an intuitive and easy to use manner.We pursue the idea of encoding connectivity by storing first-order top-down incidence relations per entity, i.e. for each entity of dimension d, a list of links to the respective incident entities of dimension d−1 is stored. For instance, each half-face as well as its orientation is uniquely determined by a tuple of links to its incident halfedges or each 3D cell by the set of incident half-faces. This representation allows for handling non-manifolds as well as mixed-dimensional mesh configurations. No entity is duplicated according to its valence, instead, it is shared by all incident entities in order to reduce memory consumption. Furthermore, an array-based storage layout is used in combination with direct index-based access. This guarantees constant access time to the entities of a mesh.Although bottom-up incidence relations are implied by the top-down incidences, our data structure provides the option to explicitly generate and cache them in a transparent manner. This allows for accelerated navigation in the local neighborhood of an entity.We provide an open-source and platform-independent implementation of the proposed data structure written in C++ using dynamic typing paradigms. The library is equipped with a set of STL compliant iterators, a generic property system to dynamically attach properties to all entities at run-time, and a serializer/deserializer supporting a simple file format. Due to its similarity to the OpenMesh data structure, it is easy to use, in particular for those familiar with OpenMesh. Since the presented data structure is compact, intuitive, and efficient, it is suitable for a variety of applications, such as meshing, visualization, and numerical analysis. OpenVolumeMesh is open-source software licensed under the terms of the LGPL.

A Generic Implementation of dD Combinatorial Maps in CGAL

“…We again follow the same protocol as in [16,17]: (1) circulator iterates along all vertices incident to all volumes; (2) circulator2 iterates along all vertices adjacent along a common volume; (3) barycenter computes and stores the barycenters of all volumes; (4) smoothing performs a Laplacian smoothing; (5) subdivision does one step of (1 − 4)-subdivision of each tetrahedron; (6) collapse does a series of edge collapses of the shortest edge.…”

“…In 3D, we compare with OpenVolumeMesh [17], which is based on an extension of the halfedge data structure, and with CGoGN [16].…”

“…Several software packages were developed to describe 2D and 3D objects as combinatorial maps [11,16,17,21]. However, to the best of our knowledge, the Combinatorial Maps package, first release as part of CGAL in 2011 [5], was the first software capable of describing and handling subdivided objects in an arbitrary dimension thanks to a generic implementation of combinatorial maps in any dimension.…”

Efficient Computation of Shortest Path-Concavity for 3D Meshes

“…We are grateful to Anca Ivanescu and Torsten Sattler for the valuable discussions, Mike Kremer for help with the OpenVolumeMesh data structure [10], and Jan Möbius for support on OpenFlipper [18]. This work was funded by the DFG Cluster of Excellence UMIC (DFG EXC 89).…”

Distributed Combinatorial Maps for Parallel Mesh Processing

“…Few data structures were defined to represent volumetric meshes, like for example facet-edge [19], handle-face [20], OpenVolumeMesh [21] or AHF [22]. However, these solutions are not able to describe nD meshes.…”