Vertex Azimuth

Vertex Azimuth is the angular deviation of the vertices' azimuth angles from ideal values.

Calculation

For all groups of symmetrically equivalent vertices (see the picture), all pairwise azimuth differences are calculated and compared to the ideal values. The deviation from the ideal value is the Vertex Azimuth. See the details below.

1. To locate the vertices of each type, the following procedure is performed with each of the corresponding facets:

   Type	1	2	3	4	5
   Facet	Star	Bezel	Upper girdle	Lower girdle	Pavilion
   Pivot point	Bottommost	Bottommost	Topmost	Bottommost	Bottommost

   1. The pivot point of the facet is found (topmost or bottommost point of the facet, depending on the type, see the table above).
   2. A line is passed through that point and the facet's center of mass.

   3. Two point furthest from the line on each side are located.
      

      Whether or not the vertices of one facet coincide with the vertices of the same type belonging to the neighboring facets (as they should in an ideal stone), is irrelevant at the moment

2. Pairwise azimuth differences between the points of each type are considered, separately for the "left" and "right" sub-arrays. Each difference is compared to the ideal value and the absolute deviation is taken. For each point (blue arrow on the picture below) the deviations for the adjacent and opposite points (bold red arrows on the picture) are put in the Array A, and the rest (thin arrows) in the Array B.
   
3. The final value is calculated as
   Vertex Azimuth = max(A_i) + 1/2 max(B_i)