School of Computing

Generating Surface Geometry in Higher Dimensions using Local Cell Tilers

Steve Hill and Jonathan C. Roberts

Technical Report 4-98, University of Kent at Canterbury, Computing Laboratory, University of Kent, Canterbury, Kent CT2 7NF, March 1998.

Abstract

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.

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Bibtex Record

@techreport{577,
author = {Steve Hill and Jonathan C. Roberts},
title = {{Generating Surface Geometry in Higher Dimensions using Local Cell Tilers}},
month = {March},
year = {1998},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/1998/577},
    address = {Computing Laboratory, University of Kent, Canterbury, Kent CT2 7NF},
    institution = {University of Kent at Canterbury},
    number = {4-98},
}

School of Computing, University of Kent, Canterbury, Kent, CT2 7NF

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