Aspect Ratio
Calculation for Triangles
The aspect ratio for a triangle is computed in the following manner, using only the corner nodes of the element:
Triangle aspect ratio calculation
- A line is constructed from one node of the element to the midpoint of the opposite edge, and another through the midpoints of the other two edges. In general, these lines are not perpendicular to each other or to any of the element edges.
- Rectangles are constructed centered about each of these two lines, with edges passing through the element edge midpoints and the triangle apex.
- These constructions are repeated using each of the other two corners as the apex.
- The aspect ratio of the triangle is the ratio of the longer side to the shorter side of whichever of the six rectangles is most stretched, divided by the square root of 3.
The best possible aspect ratio, for an equilateral triangle, is 1. A triangle having an aspect ratio of 20 is shown in the figure below.
Aspect ratio for triangles
Calculation for Quadrilaterals
The aspect ratio for a quadrilateral is computed by the following steps, using only the corner nodes of the element:
Quadrilateral aspect ratio calculation
- If the element is not flat, the nodes are projected onto a plane passing through the average of the corner locations and perpendicular to the average of the corner normals. The remaining steps are performed on these projected locations.
- Two lines are constructed that bisect the opposing pairs of element edges and which meet at the element center. In general, these lines are not perpendicular to each other or to any of the element edges.
- Rectangles are constructed centered about each of the two lines, with edges passing through the element edge midpoints. The aspect ratio of the quadrilateral is the ratio of a longer side to a shorter side of whichever rectangle is most stretched.
The best possible aspect ratio, for a square, is 1. A quadrilateral having an aspect ratio of 20 is shown in the figure below.
Aspect ratio for quadrilaterals
