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Generating Surface Geometry in Higher Dimensions using Local Cell Tilers

Hill, Steve and Roberts, Jonathan C. (1998) Generating Surface Geometry in Higher Dimensions using Local Cell Tilers. Technical report. , Computing Laboratory, University of Kent, Canterbury, Kent CT2 7NF (KAR id:21680)


In two dimensions contour elements surround two dimensional objects, in three dimensions surfaces surround three dimensional objects and in four dimensions hypersurfaces surround hyperobjects. These surfaces can be represented by a collection of connected simplices, hence, continuous n dimensional surfaces can be represented by a lattice of connected n-1 dimensional simplices. The lattice of connected simplices can be calculated over a set of adjacent n-dimensional cubes, via for example the Marching Cubes Algorithm. These algorithms are often named local cell tilers. We propose that the local-cell tiling method can be usefully-applied to four dimensions and potentially to N-dimensions. We present an algorithm for the generation of major cases (cases that are topologically invariant under standard geometrical transformations) and introduce the notion of a sub-case which simplifies their representations. Each sub-case can be easily subdivided into simplices for rendering and we describe a backtracking tetrahedronization algorithm for the four dimensional case. An implementation for surfaces from the fourth dimension is presented and we describe and discuss ambiguities inherent within this and related algorithms.

Item Type: Reports and Papers (Technical report)
Uncontrolled keywords: Higher Dimensions, Surface Mesh, Cell Tilers, Marching Cubes, Major Cases,
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Mark Wheadon
Date Deposited: 28 Aug 2009 16:40 UTC
Last Modified: 16 Nov 2021 10:00 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Roberts, Jonathan C..

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