Abstract
This work investigates data structures for representing and manipulatingd-dimensional geometric objects for arbitraryd ≥ 1. A class of geometric objects is defined, the “subdividedd-manifolds,” which is large enough to encompass many applications. A new representation is given for such objects, the “cell-tuple structure,” which provides direct access to topological structure, ordering information among cells, the topological dual, and boundaries.
The cell-tuple structure gives a simple, uniform representation of subdivided manifolds which unifies the existing work in the field and provides intuitive clarity in all dimensions. The dual subdivision, and boundaries, are represented consistently.
This work has direct applications in solid modeling, computer graphics, and computational geometry.
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This work was supported by the National Science Foundation, under Grant CCR-8657562, and Digital Equipment Corporation. An early version of this work appeared in theProceedings of the Fifth Annual ACM Symposium on Computational Geometry.
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Brisson, E. Representing geometric structures ind dimensions: Topology and order. Discrete Comput Geom 9, 387–426 (1993). https://doi.org/10.1007/BF02189330
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DOI: https://doi.org/10.1007/BF02189330