# Medina

Medina-specific checks used to calculate element quality for 2D and 3D elements.

Additional element checks not listed here are not part of the solver’s normal set of checks, and therefore use HyperMesh check methods.

## 2D and 3D Element Checks

These checks apply to both types of elements, but when applied to 3D elements they
are generally applied to each face of the element. The value of the worst face is
reported as the 3D element’s overall quality value.

- Aspect Ratio (Edge Ratio)
- Edge Ratio is calculated as the ratio between an element’s shortest edge and its longest edge; For the sake of consistency, HyperMesh inverts this result, effectively making it the ratio of longest to shortest, and reports the result as the element’s aspect ratio.
- Interior Angles
- Maximum and minimum values are evaluated independently for triangles and quadrilaterals.
- Jacobian
- Deviation of an element from its ideal or "perfect" shape, such as a triangle’s deviation from equilateral. The Jacobian value ranges from 0.0 to 1.0, where 1.0 represents a perfectly shaped element. The determinant of the Jacobian relates the local stretching of the parametric space which is required to fit it onto the global coordinate space.
- Length (min)
- Minimum element lengths are calculated using one of two methods:
- The shortest edge of the element. This method is used for non-tetrahedral 3D elements.
- The shortest distance from a corner node to its opposing edge (or face, in the case of tetra elements); referred to as "minimal normalized height".

- Maximum Angle
- Largest angle between adjacent edges of the element is reported.
- Minimum Angle
- Smallest angle between adjacent edges of the element is reported.
- Skew
- Element’s interior corner angles are compared to 90 degrees (for quads) or 60 degrees (for trias). The absolute values of these deviations are summed and reported.
- Taper
- Quadrilateral elements are split into two triangles.The area of the smaller of the two triangles is compared to the
total area of the quadrilateral. In Figure 2,
$taper=\frac{{A}_{b}}{{A}_{quad}}$
.Note: To improve consistency with other taper checks, HyperMesh displays a value of 0.5 minus this value so that 0 implies no taper. However, this is not completely consistent with other taper checks, because in this case taper ranges from 0 (no taper) to 0.5 (full taper), whereas HyperMesh’s own taper check reports a 1.0 for full taper.
- Warpage
- Elements with more than three nodes are split into triangles. The largest angle between the normals of triangle pairs is reported as the warpage.

## 3D Element Only Checks

Medina does not use any 3D specific checks. HyperMesh uses its own checks instead.