## 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.*

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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 |
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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

- A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane. (deposited 13 June 2008)
- A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane. (deposited 27 April 2008)
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- A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane. (deposited 27 April 2008)

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