A Lemon is not a Monstar: Visualization of Singularities of Symmetric Second Rank Tensor Fields in the Plane

Liu, J.; Hewitt, W. T.; Lionheart, W. R. B.; Montaldi, J.; Turner, M.

A Lemon is not a Monstar: Visualization of Singularities of Symmetric Second Rank Tensor Fields in the Plane

Files

099-106.pdf (554.99 KB)

Date

2008

Authors

Liu, J.
Hewitt, W. T.
Lionheart, W. R. B.
Montaldi, J.
Turner, M.

Publisher

The Eurographics Association

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.

        @inproceedings{:10.2312/LocalChapterEvents/TPCG/TPCG08/099-106
,
booktitle = {Theory and Practice of Computer Graphics
},
editor = {Ik Soo Lim and Wen Tang
},
title = {{A Lemon is not a Monstar: Visualization of Singularities of Symmetric Second Rank Tensor Fields in the Plane
}},
author = {Liu, J. and 
Hewitt, W. T. and 
Lionheart, W. R. B. and 
Montaldi, J. and 
Turner, M.
},
year = {2008
},
publisher = {The Eurographics Association
},
ISBN = {978-3-905673-67-8
},
DOI = {/10.2312/LocalChapterEvents/TPCG/TPCG08/099-106
}
}