Say you have a triangular mesh on a flat plane. This has been drawn to eventually solve some problem in mechanics, for example.
A mesh of equilateral triangles is the best inasmuch as the distances between the vertices and between the centroids are the same all over. This makes interpolations and the calculation of gradients an easy and accurate task. However, because of constraints and circumstances, it is not always possible to work on a mesh of all equilateral triangles.
So, the questions regard a mesh of triangular elements of arbitrary shape.
Concerning individual mesh elements. Which metrics are commonly used to quantify the dissimilarity of one generic triangle from some underlying ideal equilateral shape?
Concerning the whole mesh. Which metrics are in use to quantity the irregularity of a mesh of arbitrary triangles on the whole? These metrics should indicate how scrambled the mesh is.
Thanks for thinking along.
Note All contributions from the finite-element community have been greatly appreciated. For this question, please note that the interest is to quantify differences purely in the geometry (arbitrary vs equilateral triangles). The subsequent effect on the interpolation and conditioning errors are outside scope. Granted these can be insightful and relevant, they complicate the mathematical handling.