This page describes in details how heights of a stone crown, girdle and pavilion are calculated by the system.

Heights Calculation

Points on Girlde Curves

Before calculation, some points should be found:

• Crown bezel point
• Crown bone point
• Pavilion bezel point
• Pavilion bone point
• Pavilion height point
  
• Pavilion upperbone point
  

Where Points are Found

If in the given direction:

• There is no extra facet adjacent to the girdle, the points are found simply on the current model ("on real stone") as described in sections of this page.
• There is an extra facet  adjacent to the girdle, the points are found:
  • For  Crown height and  Pavilion depth - on a virtual model
  • For all girdle heights - on the current model ("on real stone") as described in sections of this page and on a virtual model, see Girdle Heights Calculation Methods

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.

Finding Points

Crown Bezel Point and Point for Calculating  Crown height

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 .

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 .

Pavilion Bezel Point and Point for Calculating  Pavilion depth

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 .

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 

Crown Bone Point and Pavilion Bone point

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.

Pavilion Height Point and Pavilion Uppderbone Point

• Pavilion height point is the universal name for Pavilion bezel point   or    Pavilion bone point   around (+/- 6°)   Crown bezel point or, if they are not presented in the range a point on a lower girdle curve, with the same azimuth as  Crown bezel point .
• Pavilion upperbone point is the universal name for Pavilion bone point  or  Pavilion bezel point  around (+/- 6°)  Crown bone point or, f they are not presented in the range a point on a lower girdle curve, with the same azimuth as  Crown bone point .
  
  See details in the "Calculating ..." sections below.

Calculating  Crown height,  Pavilion depth, and  Girdle bezel

If in the given direction,  there is no extra facet  adjacent to the girdle,

The system:

1. Finds the  Crown bezel point  on the  upper girdle curve, as described in the Points on Girdle Curves section above.
2. The distance, along the diamond's axis, that perpendicular to the table, between the table plane and the Crown bezel point  is called  Crown height .
3. Finds the closest (by azimuth)  Pavilion bezel point  or the  Pavilion bone point  on the  lower girdle curve , as described in the Points on Girdle Curves section above. 
   1. If there are no  Pavilion bezel point or  Pavilion bone point around Crown bezel point , it could be just a point on a lower girdle curve, with the same azimuth as Crown bezel point.
   2. Whatever found may be also called  Pavilion height point .
      
4. The distance, along the diamond's axis, that perpendicular to the table, between maximal distant culet point and the  Pavilion height point is called  Pavilion depth .
   
5. The difference between azimuths of  Crown bezel point and  Pavilion height point is determined. If this difference  is:
   

   1. 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 .

      
      

   2. 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 .

      
      

   3. 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:

      
      

Calculating  Girdle bone

If in the given direction,  there is no extra facet  adjacent to the girdle,

The system:

1. Finds the  Crown bone point  on the upper girdle curve, as described in the Points on Girdle Curves section above.
   
2. Finds the closest (by azimuth)  Pavilion bone point  or the  Pavilion bezel point  on the lower girdle curve, as described in the Points on Girdle Curves section above.
   
   1. If there are no Pavilion bone point  or  Pavilion bezel point  around Crown bone point , it could be just a point on a lower girdle curve, with the same azimuth as  Crown bone point .
   2. Whatever found may be also called   Pavilion upperbone point .
      
3. The distance, along diamond's axis, that perpendicular to the table, between maximal distant culet point and this  Pavilion upperbone point  is called  Pavilion height upperbone (PAVILION_HEIGHT_UPPERBONE bookmarks).
   
4. The difference between azimuths of  Crown bone point  and  Pavilion height point  is determined. If this difference    is:
   

   1. 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 .

      
      

   2. 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

      
      

   3. 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:

      
      

Calculating  Girdle valley

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.

First method, type 1

1) First of all,  Crown heights valley are measured as maximum facet heights on crown wide-facets:

• The wide-facets on the crown are determined. On the picture, wide-facets, like upper girdle facets, marked as orange; wide-facets, like mains facets, marked as green.
  
  
• Maximum height is measured for each crown wide-facet. On the picture marked by arrows. That are  Crown height valleys .
  
  

2) Next, the program finds  zones  for future  Pavilion height valley  and  Girdle valley  measurements:

• The wide-facets on pavilion are determined. On the picture, wide-facets, like upper girdle facets, marked as orange; wide-facets, like mains facets, marked as green.
  
  
• Maximum height is measured for each pavilion wide-facet. On the picture marked by arrows.
  
  
• The zones for pavilion and girdle valley’s measurements are located in the place of intersections of crown wide-facets and opposite pavilion wide-facets. On the picture, wide-facets, like upper girdle facets, marked as orange; wide-facets, like mains facets, marked as green. Borders of facets intersections marked by magenta's dashed lines.
  
  

There are several cases of crown wide-facets and pavilion wide-facet intersections:

1. If there are several pavilion facets opposite the crown wide-facet, the zone for future  Pavilion height valley  and  Girdle valley  measurements is that intersection where pavilion’s wide-facet contains its facet maximum height (marked by red arrow). On the picture the zone for future  Pavilion height valley  and  Girdle valley  marked by gray transparent box.
   
   
2. If there are two pavilion wide-facets opposite crown wide-facet, and if every of these pavilion wide-facets contain its facet maximum height, the only one maximum (marked by red arrow) will be taken into account and defines a zone (marked by gray transparent box) for future  Pavilion height valley  and  Girdle valley  measurements.
   
   
3. In case of no one maximum of the pavilion, the zone for future  Pavilion height valley  and  Girdle valley  measurements will be just full area of crown wide-facet. 
   

3) Estimating  Girdle valley  and  Pavilion height valleys

• Program checks presence of Pavilion wide-facet maximum heights inside zone and considers it as parameters Pavilion height valleys for every zone.

  The difference of azimuths between Crown height valley and Pavilion wide-facet maximum heights is determined for every zone.

  1. If deference is less then 1 degree, the  Girdle valley  will be measured as girdle height between Crown height valley point and Pavilion wide-facet maximum height point.
  2. If deference is more then 1 degree, the Girdle height valley will be measured in a place where girdle height is minimal between their azimuths.
• If there is no one Pavilion wide-facet maximum height inside the zone, the Girdle height valley will be the minimal girdle height on zone interval and the Pavilion height in place with the same azimuth as Girdle height valley considers as Pavilion height valley.

Second method, type 2

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)

Comparison of two systems of measurements, type 1 and type2

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.

Previous Versions

HP Oxygen is an inheritor of the HP Pacor in many aspects including the approach to how stone heights are calculated.

Related Pages

Pavilion depth .