Classify dihedral angles

Classification of boundary edges by the vexity of their dihedral angles is the basic heuristic for automatic feature recognition.

In a valid boundary representation, the outer contour of each face should be oriented counterclockwise looking from the direction of the face normal. This property of the shape representation is used in Analysis Situs for computation of dihedral angles.

The computed dihedral angles may have one the following types:

1. Convex.
2. Concave.
3. Smooth (with a prescribed angular precision).

The smooth angles can be precised by additional analysis of the interior points on the adjacent faces (such recomputation uses Newton iterations and is more expensive when the basic check). It is a common practice to use the computed angles as the attributes for constructing an Attributed Adjacency Graph (AAG).