How to calculate the average stretch of a Quad?

Not sure if I formulate the correct answer but basically I need to know how to calculate the average size of a stretch quad, or something like taking the 2 diagonals AC and BD how can I calculate the average of them

The blue square show its origina开发者_JS百科l size and the pink lines shows when its deform, I need to calculate some sort of average so I can change its color in relation to how is deform if expands change to a lighter color if contracts change to darker color, hope that makes sense

Not quite sure what the question here is.

If you're asking how to find the average diagonal length, just find the length of each diagonal, add them together and divide by two.

If you're asking how to determine the area of the resultant shape, here are several formulas for finding the area of an arbitrary quadrilateral. They are all equivalent to the formula

Area = 1/2 * |AC x BD|

Where x means the cross-product.

A quadrilateral will have a 2nd order symmetric strain tensor:

| Exx Exy |
| Exy Eyy |

Exx is the strain in the x-direction; Eyy is the strain in the y-direction; Exy is the shear strain that occurs when one of the angles that is originally 90 degrees changes its value.

If you have large strains, you'll need a Lagrangian point of a view and a Green-Lagrange large strain measure.

See Malvern's Continuum Mechanics for definitions of each term. I'd give you the formulas, but I don't have LaTeX available here.