VCG - Rotating Center

Description

Single rotating Coreline around the z-axis. Coreline is diagonal in all 3 dimensions.

Details


The Rotating 3D Center flow [Günther] consists of a vortex with its core line through the points $(1,0,0)^T$ $(0,1,1)^T$ at $t=0$, which is globally rotated around the center in the z-axis. The resulting equation is:
$v(x,y,z,t)= \frac{\sqrt{3}}{3}*\begin{pmatrix}z*\cos(t)+z*\sin(t)-\cos(t)-y\\z*\cos(t)-z*\sin(t)+\sin(t)+x\\-(x*\cos(t)+y*\cos(t)+x*\sin(t)-y*\sin(t)-2)\end{pmatrix}$
Operating in in the space of $\rm I\!R^3\times T = [-5,5]^3 \times [0,2\pi]$

Input

Output

vtkImageData

Parameters

Name
Description
 Values/Default
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. 32
Samples Number of samples in each dimension. 32 32 32
Origin Point of origin for the samples window. -5. -5. -5.
Scale Scale of sample distance in each dimension. 10 10 10

Installation Instructions

Authors

Lutz Hofmann

References

T. Günther, H. Theisel:
Objective Vortex Corelines of Finite-sized Objects in Fluid Flows
IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE Scientific Visualization 2018), 2018.

Acknowledgements