Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Geometry of subanalytic and semialgebraic sets
Geometry of subanalytic and semialgebraic sets
Proceedings of the sixth ACM symposium on Solid modeling and applications
Performance Evaluation of Boundary Data Structures
IEEE Computer Graphics and Applications
Winged edge polyhedron representation.
Winged edge polyhedron representation.
AIF: a data structure for polygonal meshes
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Euler operators for stratified objects with incomplete boundaries
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Representing non-manifold geometric objects in n dimensions: incidence, order, and shape
ISCGAV'06 Proceedings of the 6th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
Oversimplified euler operators for a non-oriented, non-manifold b-rep data structure
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
Q-Complex: Efficient non-manifold boundary representation with inclusion topology
Computer-Aided Design
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Current geometric kernels suffer from poor abstraction and design of their data structures. In part, this is due to the lack of a general mathematical framework for geometric modelling and processing. As a result, there is a proliferation of ad hoc solutions, say external data structures, whenever new problems arise in industry, causing serious difficulties in software maintenance. This paper proposes such a framework based on subanalytic geometry and theory of stratifications, as well as a concise data structure for it, called DiX (Data in Xtratus). Basically, this is a non-manifold b-rep (boundary representation) data structure without oriented cells (e.g. half-edges, coedges or so). Thus, it is more concise than the traditional b-rep data structures provided that no oriented cells (e.g. half-edges, half-faces, etc.) are used at all. Nevertheless, all the adjacency and incidence data we need is retrieved by a single operator, called mask operator. Besides, the DiX data structure includes shape descriptors, as generalizations of loops and shells, to support shape reasoning as needed in the design and implementation of shape operators such as, for example, Euler operators.