# Reference Plane for Quadrilateral Element or Face

In order to measure the distortion of the quadrilateral face of a solid element, a unique reference plane is defined by two auxiliary plane vectors.

The plane vectors are calculated as:(1)
${\mathit{PL}}_{\mathit{1}}\mathit{=}\mathit{\left(}{V}_{\mathit{3}}\mathit{+}{V}_{\mathit{2}}\mathit{\right)}\mathit{-}\mathit{\left(}{V}_{\mathit{1}}\mathit{+}{V}_{\mathit{4}}\mathit{\right)}$
(2)
${\mathit{PL}}_{\mathit{2}}=\mathit{\left(}{V}_{\mathit{3}}\mathit{+}{V}_{\mathit{4}}\mathit{\right)}\mathit{-}\mathit{\left(}{V}_{\mathit{1}}\mathit{+}{V}_{\mathit{2}}\mathit{\right)}$
where, ${V}_{1}$ , ${V}_{2}$ , ${V}_{3}$ , and ${V}_{4}$ are the vectors that connect the four corner nodes with the centroid of the quadrilateral. These two plane vectors and the centroid are then used to construct the reference plane.