Layered Cylindrical Algebraic Decomposition

D. J. Wilson; M. England

Layered Cylindrical Algebraic Decomposition

D. J. Wilson, M. England

Department of Computer Science

Research output: Book/Report › Other report

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Abstract

In this report the idea of a Layered CAD is introduced: a
truncation of a CAD to cells of dimension higher than a prescribed
value. Limiting to full-dimensional cells has already been
investigated in the literature, but including more levels is shown to
also be beneficial for applications. Alongside a direct algorithm, a
recursive algorithm is provided. A related topological property is
defined and related to robot motion planning. The distribution of cell
dimensions in a CAD is investigated and layered CAD ideas are combined
with other research. All research is fully implemented within a freely
available Maple package, and all results are corroborated with
experimental results.

Original language	English
Place of Publication	Bath, U. K.
Publisher	Department of Computer Science, University of Bath
Publication status	Published - Aug 2013

Publication series

Name	Department of Computer Science Technical Report Series
Publisher	Department of Computer Science, University of Bath
No.	CSBU-2013-05
ISSN (Print)	1740-9497

Access to Document

CSBU-2013-05Final published version, 562 KB

Real Geometry and Connectedness via Triangular Description
Davenport, J. (PI), Bradford, R. (CoI), England, M. (CoI) & Wilson, D. (CoI)
Engineering and Physical Sciences Research Council
1/10/11 → 31/12/15
Project: Research council

Cite this

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title = "Layered Cylindrical Algebraic Decomposition",

abstract = "In this report the idea of a Layered CAD is introduced: atruncation of a CAD to cells of dimension higher than a prescribedvalue. Limiting to full-dimensional cells has already beeninvestigated in the literature, but including more levels is shown toalso be beneficial for applications. Alongside a direct algorithm, arecursive algorithm is provided. A related topological property isdefined and related to robot motion planning. The distribution of celldimensions in a CAD is investigated and layered CAD ideas are combinedwith other research. All research is fully implemented within a freelyavailable Maple package, and all results are corroborated withexperimental results.",

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AB - In this report the idea of a Layered CAD is introduced: atruncation of a CAD to cells of dimension higher than a prescribedvalue. Limiting to full-dimensional cells has already beeninvestigated in the literature, but including more levels is shown toalso be beneficial for applications. Alongside a direct algorithm, arecursive algorithm is provided. A related topological property isdefined and related to robot motion planning. The distribution of celldimensions in a CAD is investigated and layered CAD ideas are combinedwith other research. All research is fully implemented within a freelyavailable Maple package, and all results are corroborated withexperimental results.

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BT - Layered Cylindrical Algebraic Decomposition

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Layered Cylindrical Algebraic Decomposition

Abstract

Publication series

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Real Geometry and Connectedness via Triangular Description

Cite this