A Hierarchical Representation and Computation Scheme of Arbitrary-dimensional Geometrical Primitives Based on CGA

A Hierarchical Representation and Computation Scheme of Arbitrary-dimensional Geometrical... Resolving the conflicts between the high dimensionality of geometry representation and the linear organization and storage of geometrical objects in computer memories plays a key role in spatial data structure constructions. In this paper, a new data structure MVTree is developed based on geometric algebra to support the unified organization and computation of geometrical primitives. The MVTree is a tree-like data structure which has a dimensional hierarchical structure generated by outer product. Multidimensional geometrical primitives is represented as the combination of blades stored in the nodes of MVTrees. The geometric computation between different geometrical objects is operated with GA operators with a judgement-based hierarchical computation. Applications of the MVTree are demonstrated by a topological relation computation and a Delaunay-TIN intersection. The results suggest that the MVTree structure can support unified representation of arbitrary-dimensional geometrical primitives, and can integrate data organization and computation in a unitary structure as well. The application of the new MVTree data structure can not only reduce the complexity of data architectures but also inherit the power of geometric algebra computing to improve the processing ability of computer graphic software. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

A Hierarchical Representation and Computation Scheme of Arbitrary-dimensional Geometrical Primitives Based on CGA

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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
D.O.I.
10.1007/s00006-016-0697-3
Publisher site
See Article on Publisher Site

Abstract

Resolving the conflicts between the high dimensionality of geometry representation and the linear organization and storage of geometrical objects in computer memories plays a key role in spatial data structure constructions. In this paper, a new data structure MVTree is developed based on geometric algebra to support the unified organization and computation of geometrical primitives. The MVTree is a tree-like data structure which has a dimensional hierarchical structure generated by outer product. Multidimensional geometrical primitives is represented as the combination of blades stored in the nodes of MVTrees. The geometric computation between different geometrical objects is operated with GA operators with a judgement-based hierarchical computation. Applications of the MVTree are demonstrated by a topological relation computation and a Delaunay-TIN intersection. The results suggest that the MVTree structure can support unified representation of arbitrary-dimensional geometrical primitives, and can integrate data organization and computation in a unitary structure as well. The application of the new MVTree data structure can not only reduce the complexity of data architectures but also inherit the power of geometric algebra computing to improve the processing ability of computer graphic software.

Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Jun 24, 2016

References

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