The class Alpha_status is a small data structure to store the critical alpha values of faces of an alpha shape.

Each face has three critical alpha values, called alpha_min, alpha_mid and alpha_max in increasing order. The face will be exterior for any $\alpha <$ alpha_min, singular for alpha_min $\leq \alpha <$ alpha_mid, regular for alpha_mid $\leq \alpha <$ alpha_max and interior for alpha_max $\leq \alpha$. The value alpha_min is undefined for faces which are not Gabriel faces and therefore do not appear in the alpha complex without any of their including face. The value alpha_max is undefined for convex hull faces which can never be interior. The data structure also includes two Boolean to mark if the face is a Gabriel face or a convex hull face.

The class Alpha_status is parameterized by a number type NT.

See Also

AlphaShapeCell_3

AlphaShapeVertex_3