VCG - Four Centers

Description

Flow containing 4 vortices in each quadrant, rotating around the center either by rotating the reference frame or the actual cores.

Details

The Four Centers Flow [Günther] is a 2D velocity field with four vortices in each quadrant rotating around the center. The parameter PathLineCores controls wether the vortices actually perform a translation or only appear to do so as the observer is the one rotating. With rotation of the observer the flows equation is $v(x,y,t)=\begin{pmatrix}\frac{\partial}{\partial y} s(x',y') \\-\frac{\partial}{\partial x} s(x',y')\end{pmatrix}$
with $s(x,y)=3xy*e^{-x^2-y^2}$ and $\begin{pmatrix}x'\\y'\end{pmatrix} = \begin{pmatrix} \cos(t) & \sin(t) \\-\sin(t) & \cos(t)\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}$

Input

Output

vtkImageData

Parameters

Name
Description
 Values/Default
PathLineCores If set, will rotate the the Vortex Cores instead of the reference frame, turning them to Pathline Cores. 1
OutputSpaceTime Add time dimension to output dimenstions. 0
TimeRange Time range of samples. 0.0 6.28318530718
TimeSteps Number of time steps for the samples. 64
Samples Number of samples in each dimension. 64 64
Origin Point of origin for the samples window. -2.0 -2.0
Scale Scale of sample distance in each dimension. 4.0 4.0

Installation Instructions

Authors

Lutz Hofmann

References

T. Günther, M. Schulze, H. Theisel:
Rotation Invariant Vortices for Flow Visualization
IEEE Transactions on Visualization and Computer Graphics, vol. 22, no. 1, pp. 817-826, 2016.

Acknowledgements