Parallel Deviation

The Parallel Deviation metric is computed for quadrilateral surface elements, or quad faces of volume elements, using the following steps:

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

   

2. For each pair of opposite edges, the angle between the vectors is computed using their dot product. In the illustration above, the dot product of the 2 horizontal unit vectors is 1, and angle between the vectors is acos (1) = 0°. The dot product of the 2 vertical vectors is 0.342, and the angle is acos (0.342) = 70°.

3. The parallel deviation is the larger of these 2 angles. In the illustration above, with angles of 0° and 70°, this element's parallel deviation is 70°.

The best possible parallel deviation is 0° and occurs for a flat rectangle. The image below shows quadrilaterals having parallel deviations of 0°, 70°, 100°, 150°, and 170°.