A Compact Representation for Topological Decompositions of Non-manifold Shapes

David Canino, Leila De Floriani

2013

Abstract

Simplicial complexes are extensively used for discretizing digital shapes in several applications. A structural description of a non-manifold shape can be obtained by decomposing the input shape into a collection of meaningful components with a simpler topology. Here, we consider a unique decomposition of a non-manifold shape into nearly manifold parts, known as the \emph{Manifold-Connected decomposition}, that we extend in arbitrary dimension. We present the \emph{Compact MC-Graph}, an efficient and graph-based representation for this decomposition, which can be combined with any topological data structure for encoding the underlying components. We present the main properties of this representation as well as algorithms for its generation. We also show that this representation may be more compact than many topological data structures, which do not explicitly describe the non-manifold structure of a shape.

Paper Citation

in Harvard Style

Canino D. and De Floriani L. (2013). A Compact Representation for Topological Decompositions of Non-manifold Shapes . In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013) ISBN 978-989-8565-46-4, pages 100-107. DOI: 10.5220/0004294501000107

in Bibtex Style

@conference{grapp13,
author={David Canino and Leila De Floriani},
title={A Compact Representation for Topological Decompositions of Non-manifold Shapes},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)},
year={2013},
pages={100-107},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004294501000107},
isbn={978-989-8565-46-4},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)
TI - A Compact Representation for Topological Decompositions of Non-manifold Shapes
SN - 978-989-8565-46-4
AU - Canino D.
AU - De Floriani L.
PY - 2013
SP - 100
EP - 107
DO - 10.5220/0004294501000107