You are here: MIMS > EPrints
MIMS EPrints

2008.53: A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane.

2008.53: Jia Liu, W. T. Hewitt, W.R.B. Lionheart, J Montaldi and M. Turner (2008) A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane.

There is a more recent version of this eprint available. Click here to view it.

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
2410 Kb

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 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 58 Global analysis, analysis on manifolds
MSC 2000 > 68 Computer science
MIMS number:2008.53
Deposited By:Prof WRB Lionheart
Deposited On:27 April 2008

Available Versions of this Item

Download Statistics: last 4 weeks
Repository Staff Only: edit this item