This page describes in details how heights of a stone crown, girdle and pavilion are calculated by the system.
All the information below considers stone orientation "Table on the top." |
Before calculation, some points should be found:
If in the given direction:
Building a virtual model when calculating Crown height
If there are extra facets on the girdle, a virtual model without these facets is created and used for the measurement. To build the virtual model, the extra facets are removed and the neighboring facets are continued until they intersect.
Building a virtual model when calculating Pavilion depth
If there are extra facets on the girdle, a virtual model without these facets is created and used for the measurement. To build the virtual model, the extra facets are removed and the neighboring facets are continued until they intersect.
In a simple case, a vertex of the crown main facet that belongs to the girdle upper curve will be a crown bezel point. It will also be used for calculating the Crown height .
In case, when the crown main facet does not meet the girdle, the lowest vertex (main facet edge point) forms +/- 6° range, the highest in this range point on the girdle upper curve will be a crown bezel point. It will also be used for calculating the Crown height .
The case "does not meet the girdle" includes an extra facet case. |
In case, when the crown main facet reaches the girdle and has one or more common vertices with it, the lowest vertex (main facet edge point) forms +/- 6° range, the highest in this range point on the girdle upper curve will be a crown bezel point. It will also be used for calculating the Crown height .
In a simple case, a vertex of the pavilion main facet that belongs to the girdle lower curve will be a pavilion bezel point. It will also be used for calculating the Pavilion depth .
In case, when the pavilion main facet does not meet the girdle, the highest vertex (main facet edge point) forms +/- 6° range, the lowest in this range point on the girdle lower curve will be a pavilion bezel point. It will also be used for calculating the Pavilion depth .
The case "does not meet the girdle" includes an extra facet case. |
In case, when the pavilion main facet reaches the girdle and has one or more common vertices with it, the highest vertex (main facet edge point) forms +/- 6° range, the lowest in this range point on the girdle lower curve will be a pavilion bezel point. It will also be used for calculating the
On the edge between the crown upper facets, a vertex that belongs to the upper girdle curve is a crown bone point.
On the edge between the pavilion lower facets, a vertex that belongs to the lower girdle curve is a pavilion bone point.
In case, when the edge between the crown upper facets does not meet the girdle (extra facet case), the points are found using the same logic as for bezel points.
If in the given direction, there is no extra facet adjacent to the girdle,
The system:
Less than 4 degrees, the Girdle bezel is measured as the difference between z-coordinates of the Crown bezel point and the opposite Pavilion height point .
Enlarged view: |
|
O - Crown bezel point and Pavilion height point . |
From 4 to 10 degrees, the Girdle bezel is measured as the local maximum among several values of the girdle height, which are measured between the Crown bezel point and the Pavilion height point with a step of 0.5 degrees by azimuth.
Enlarged view: |
O - Two range of points located on the girdle lower curve and girdle upper curve. Every range has 720 points with step 0.5 degree by azimuth. O - Crown bezel point and Pavilion height point O - Girdle points at a local maximum of Girdle height on the segment between Crown bezel point and Pavilion height point . |
More than 10 degrees, the Girdle bezel is measured at one azimuth, that is equal to the girdle height along the Crown bezel point azimuth.
Enlarged view: |
If in the given direction, there is no extra facet adjacent to the girdle,
The system:
Less than 4 degrees, the Girdle bone is measured as the difference between z-coordinates of the Crown bone point and the opposite Pavilion upperbone point.
Enlarged view: |
O - Crown bone point and Pavilion upperbone point . |
From 4 to 10 degrees, the Girdle bone is measured as local maximum among several values of the girdle height, which are measured between the Crown bone point and the Pavilion upperbone point with a step of 0.5 degrees by azimuth.
Enlarged view: |
O - Two range of points located on the girdle lower curve and girdle upper curve. Every range has 720 points with step 0.5 degree by azimuth. O - Crown bone point and Pavilion upperbone point . O - Girdle points at a local maximum of Girdle height on the segment between Crown bone point and Pavilion upperbone point |
More than 10 degrees, the Girdle bone is measured at one azimuth, that is equal to the girdle height along the Crown bone point azimuth.
Enlarged view: |
If in the given direction, there is no extra facet adjacent to the girdle,
There is a variety of stones and a variety of states for each particular stone during its polishing. Thus a model may have a different number of facets for the crown and pavilion and different positioning of them relative to each other. The HP Oxygen system aims to provide a universal approach allowing precise calculating of Girdle valley in all cases. It considers that zones for calculating the Girdle valley are always presented in spite of different facet sets of a crown and pavilion. The wide-facet term is used to define those zones. The wide-facet is a facet on crown or pavilion that could be any type: main facets, upper, lower facets and any other, if it has the longest width in a place where it touches girdle (marked as yellow on the picture below). Usually, the upper and lower girdle facets are wide-facets. Main facets could be wide-facets in semi-polished diamonds, while upper and lower girdle facets are not made yet.
There are two methods of calculating the Girdle valley :
First method, type 1 , is based on parameter Crown height valley . The Crown height valley parameter can be measured on any wide-facet on the crown. The Crown height valley parameter defines measurement for Pavilion height valley and Girdle valley parameters. As a result, we have the same quantities of Crown height valleys , Pavilion height valleys and Girdle valleys , in spite of having different quantities of crown and pavilion facets.
Second method, type 2, is based on Pavilion wide-facet maximum heights. The Pavilion height valley type 2 parameter measures maximum height for any wide-facet on the pavilion (lower girdle facets, wide-facet main facets), as well. Pavilion height valley type 2 defines Girdle height valley type 2.
1) First of all, Crown heights valley are measured as maximum facet heights on crown wide-facets:
2) Next, the program finds zones for future Pavilion height valley and Girdle valley measurements:
There are several cases of crown wide-facets and pavilion wide-facet intersections:
3) Estimating Girdle valley and Pavilion height valleys
The difference of azimuths between Crown height valley and Pavilion wide-facet maximum heights is determined for every zone.
This method uses Pavilion wide-facet maximum heights for definition Pavilion height valley type 2 and Girdle height valley type 2 parameters.
The measurement for parameter Pavilion height valley type 2 (black arrows on the picture) are the same as Pavilion wide-facet maximum heights that described above (see description for Fist method, type 1, section 2).
The Pavilion height valley type 2 parameter measures maximum heights for all wide-facets on the pavilion.
Girdle height valley type 2 parameter defines the same way as Girdle height valley type 1 (see description for Fist method, type 1, section 3)
The difference between Pavilion heights valley and Pavilion height valley type 2 are shown on the picture below. Left picture illustrates measurements of Pavilion heights valley , by first method (blue arrows), and right picture illustrates measurements of Pavilion heights valley type 2 , by second method (green arrows). Crown height valley are shown by black arrows. The Pavilion height valley type 2 parameter is used not to lose measurements are shown on the right picture.
HP Oxygen is an inheritor of the HP Pacor in many aspects including the approach to how stone heights are calculated.
Version | Link | Comment |
---|---|---|
Version 1 | Girdle thickness | In the documentation of HP Pacor, description of how a girdle thickness is defined. |
Version 2 | New measurements of Heights for Pavilion and Girdle | In the release notes of HP Pacor v.5.4, the section containing a detailed description of how stone heights are calculated. Contains examples. |