Parallel Deviation

Parallel deviation is computed using the following steps:

1. Ignoring midside nodes, unit vectors are constructed in 3D space along each element edge, adjusted for consistent direction, as demonstrated in the figure below.

   Parallel deviation unit vectors

   

2. For each pair of opposite edges, the dot product of the unit vectors is computed, then the angle (in degrees) whose cosine is that dot product is computed. The parallel deviation is the larger of these two angles. (In the illustration above, the dot product of the two horizontal unit vectors is 1, and acos (1) = 0 degrees. The dot product of the two vertical vectors is 0.342, and acos (0.342) = 70 degrees. Therefore, this element’s parallel deviation is 70 degrees.)
3. The best possible deviation, for a flat rectangle, is 0 degrees. The figure below shows quadrilaterals having deviations of 0 degrees, 70 degrees, 100 degrees, 150 degrees, and 170 degrees.

   Parallel deviations for quadrilaterals