A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane.

Liu, Jia and Hewitt, W. T. and Lionheart, W.R.B. and Montaldi, J and Turner, M. (2008) A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane. [MIMS Preprint]

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Abstract

In the visualization of the topology of second rank symmetric tensor fields in the plane one can extract some key points (degenerate points), and curves (separatrices) that characterize the qualitative behaviour of the whole tensor field. This can provide a global structure of the whole tensor field, and effectively reduce the complexity of the original data. To construct this global structure it is important to classify those degenerate points accurately. However, in existing visualization techniques, a degenerate point is only classified into two types: trisector and wedge types. In this work, we will apply the theory from the analysis of binary differential equations and demonstrate that, topologically, a simple degenerate point should be classified into three types: star (trisector), lemon and monstar. The later two types were mistakenly regarded as a single type in the existing visualization techniques.

Item Type: MIMS Preprint
Uncontrolled Keywords: visualization, tensor field, singularity theory
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User: Prof WRB Lionheart
Date Deposited: 27 Apr 2008
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1092

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