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

J. Liu, W. T. Hewitt, W. R. B. Lionheart, J. Montaldi, M. Turner
2008 Computer Graphics and Visual Computing  
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  ...  ), lemon and monstar.  ...  The introduction Symmetric second rank tensor data is central to many applications in both physics and engineering.  ... 
doi:10.2312/localchapterevents/tpcg/tpcg08/099-106 dblp:conf/tpcg/LiuHLMT08 fatcat:hur47fj7djhnrpqmrsua3hwcti

An intuitive explanation of third-order surface behavior

Pushkar Joshi, Carlo Séquin
2010 Computer Aided Geometric Design  
We present a novel parameterization-independent exposition of the third-order geometric behavior of a surface point.  ...  We extract four parameters that provide a quick and concise understanding of the third-order surface behavior at any given point.  ...  The first-order analysis adds the tangent plane, the second-order the curvature tensor, and the third-order a rank-3 tensor that describes the derivatives of curvature.  ... 
doi:10.1016/j.cagd.2009.11.003 fatcat:jezqvch3gnaudo3s3lbvydljta

Optical Möbius strips in three-dimensional ellipse fields: I. Lines of circular polarization

Isaac Freund
2010 Optics Communications  
The major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips.  ...  Statistical probabilities are presented for the most important index combinations in random fields.  ...  David A. Kessler, and an important email from Dr. Mark R. Dennis (Bristol).  ... 
doi:10.1016/j.optcom.2009.09.042 fatcat:ff4d4begovca5az3hrjja2rpgy

Umbilic Lines in Orientational Order

Thomas Machon, Gareth P. Alexander
2016 Physical Review X  
Here we show that such lines can be identified as a set of natural geometric singularities in a unit vector field, the generalisation of the umbilic points of a surface.  ...  We characterise these lines in terms of the natural vector bundles that the order defines and show that they give a way to localise and identify Skyrmion distortions in chiral materials -- in particular  ...  reduce when the Q tensor is written in terms of the director field.  ... 
doi:10.1103/physrevx.6.011033 fatcat:aob5tqnnyzcppdkut3ouw33h4a

Medial axis of regions bounded by b-spline curves and surfaces

Suraj Ravi Musuvathy
2012
Suppose γ(u) lies in the XY plane without loss of generality. Then γ u = [γ (x) u γ (y) u 0] T is a vector in the XY plane.  ...  Since J F has the full rank, F is differentiable. Let F (1) and F (2) represent the first and second vector components of F . F (1) = 0 and F (2) = 0 represent hypersurfaces in R 3 u,û,t .  ... 
doi:10.26053/0h-ax2d-rxg0 fatcat:woahkidztzff5e5tissnyp4hwq