Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Primitives for the manipulation of three-dimensional subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
Introduction to Solid Modeling
Introduction to Solid Modeling
Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Structured topological complexes: a feature-based API for non-manifold topologies
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Handbook of discrete and computational geometry
Winged edge polyhedron representation.
Winged edge polyhedron representation.
A bézier-based approach to unstructured moving meshes
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
CHF: A Scalable Topological Data Structure for Tetrahedral Meshes
SIBGRAPI '05 Proceedings of the XVIII Brazilian Symposium on Computer Graphics and Image Processing
Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments
IEEE Computer Graphics and Applications
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
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A new topological representation of surfaces in higher dimensions, “cell-chains” is developed. The representation is a generalization of Brisson's cell-tuple data structure. Cell-chains are identical to cell-tuples when there are no degeneracies: cells or simplices with identified vertices. The proof of correctness is based on axioms true for maps, such as those in Brisson's cell-tuple representation. A critical new condition (axiom) is added to those of Lienhardt's n-G-maps to give “cell-maps”. We show that cell-maps and cell-chains characterize the same topological representations.