# VCG Vortex Core Lines

### Description

The VortexCores filter computes vortex core lines of point (node) data. This filter requires unstructured grid data and produces geometry output.

### Details

Vortices are an important construct in fluid flow (represented as a vector field $u(x)$). They represent the possibly curved "axis" line of a vortex, i.e., curves around which particles swirl. A typical phenomenon, we instinctively imagine when dealing with vortices, would be tornadoes.
Vortex core lines aim to extract the center of such a vortex and, thus, give important insight about the data at hand.
This plugin implements two methods to identify vortex core lines.

The Sujudi-Haimes algorithm {reference}{/reference} and the Levy criterion {reference}{/reference}.
Sujudi and Haimes define a point $x$ as being part of a core line if $u(x)$ is parallel (or anti-parallel, used in this context as a synonym) to the real eigenvector of the Jacobian $\nabla u(x)$, with the additional criterion that the two other eigenvalues are complex.

The approach by Levy also defines core lines by means of points where two vectors are parallel, but in this case the two vectors are the vorticity vector $\nabla \times u(x)$ and velocity.

Since the approach is local, one typically obtains spurious core line parts, which need to be filtered. A primary means for suppressing unimportant core line parts is to increase the required vortex strength MinStrength . The vortex strength is the absolute imaginary part of the Jacobian of the projected velocity (projected to a plane perpendicular to the core), scaled such that the quantity get problem-independent. It is a measure for how fast the flow rotates around the core line. An other important approach (which is typically employed subsequently) is to suppress them by the maximum angle MaxAngle between their tangent and the vector of the underlying field. Well-defined vortex core lines are consistent with stream lines, and therefore exhibit low angles. However, this angle should not be set to values higher than $45^{\circ}$. Remaining, typically small, core line fragments are rejected by requiring a minimum number of vertices MinimumNumberOfVertices per vortex line.

### Input

vtkUnstructuredGrid

vtkPolyData

### Parameters

###### Description
Values/Default
Method Method for vortex core line extraction.
• Levy
• Sujudi-Haimes
Variant Non-planar faces are either decomposed into triangles and the intersections with the core lines are determined directly, or the intersections with the non-planar faces are determined using Newton iterations.
• triangle
MinimumNumberOfVertices Core line segments with fewer vertices will be discarded. 10
MaximumNumberOfExceptions Core line segments with more exceptions will be discarded. Increasing this value suppresses disruptions of core lines. 3
MinStrength The minimal required vortex strength. Segments with lower strength will be discarded. 1.0
MaxAngle The maximal allowed angle between the vector and the core line tangent. This angle serves as a quality measure, i.e., low angles indicate consistency with streamlines. Segments with larger angles will be discarded. 30.0

### Authors

Martin Roth, Ronald Peikert, Filip Sadlo

[BibTeX]