Authors:
David Canino
and
Leila De Floriani
Affiliation:
University of Genova, Italy
Keyword(s):
Geometric Modeling, Topological Data Structures, Simplicial Complexes, Non-manifold Shapes, Decomposition, Structural Representation.
Related
Ontology
Subjects/Areas/Topics:
CAGD/CAD/CAM Systems
;
Computer Vision, Visualization and Computer Graphics
;
Geometry and Modeling
;
Modeling and Algorithms
;
Surface Modeling
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.