# VTK/mesh quality

# Definition

In finite element analysis, the shape of individual elements (cells in VTK parlance) can significantly affect the accuracy of a simulation. Mesh quality metrics compute a positive real number related to the shape of each cell in a VTK mesh for inspection during both pre- and post-processing. There are several metrics for each cell type (shape); which one is most closely related to the accuracy of a simulation is application-specific.

# Implementation

VTK now includes the Verdict quality library. Routines from this library are used by the vtkMeshQuality filter to compute per-cell quality. Quality measures for triangular, quadrilateral, tetrahedral, and hexahedral cells are available. The filter will compute the value of one quality metric per cell and allows you to choose this metric on a per-cell-type basis. For example, you might compute the radius ratio for triangular cells and the Frobenius aspect for tetrahedral cells. The results are stored in a new cell array named "Quality". The filter also computes summary information for the entire mesh including

- the average value of some quality metric per cell type (e.g., the average over all tetrahedral cells)
- the variance of some quality metric per cell type
- the minimum and maximum quality metric values per cell type
- the number of cells of each type.

The summary information is stored in the output mesh's field data.

# Documentation

In addition to the Doxygen documentation for the vtkMeshQuality class, Verdict has a user's manual which you may download from this page:

- Verdict Manual, rev. A (3 MB)

This document contains the mathematical definition of each quality metric as well as implementation details.