| Table of Contents |
|---|
1. Calculation on first star facet example highlighted with pink
| Note |
|---|
| All calculation are performed in 2D. Model is projected on table facet plane |
1.1 Draw line a through star facet edge belongs to table facet. Line will separate plane into half-planes β and δ:
1.2 Find most distant point (call it B) on star facet from line a. A is point, where perpendicular from point B is crossing line a:
1.3 Find most distant point on girdle (call it D) from line a, point should belong to β half-plane. C is point, where perpendicular from point D is crossing line a:
1.4 Star ratio is |AB| length divided by |CD| length and transferred to percentage view.
1.5 Upper ratio is equal to expression result (100% - Star ratio).
2. Calculation on second star facet example highlighted with pink
| Note |
|---|
| All calculation are performed in 2D. Model is projected on table facet plane |
2.1 Draw line a through star facet edge belongs to table facet. Line will separate plane into half-planes β and δ:
2.2 Find most distant point (call it B) on star facet from line a. A is point, where perpendicular from point B is crossing line a:
2.3 Find most distant point on girdle (call it D) from line a, point should belong to β half-plane. C is point, where perpendicular from point D is crossing line a:
2.4 Star ratio is |AB| length divided by |CD| length and transferred to percentage view.
2.5 Upper ratio is equal to expression result (100% - Star ratio).
3. Star \ Upper ratio parameters in report
3.1 Star \ Upper ratio can be found in Main and Detailed Parameter part of full report, for example:
Main parameters:
Parameter |
| Avg | Min | Max | Dev |
|---|---|---|---|---|---|
Star : Upper ratio | % | 61.39 : 38.61 | 53.29 : 46.71 | 71.25 : 28.75 | 17.96 |
Detailed parameters:
Parameter |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
Star : Upper ratio | % | 59.00 : 41.00 | 63.52 : 36.48 | 71.25 : 28.75 | 58.42 : 41.58 | 61.37 : 38.63 | 64.69 : 35.31 | 59.55 : 40.45 | 53.29 : 46.71 |
3.2 Following bookmark are used for Star ratio:
- STAR_RATIO_PC
- STAR_RATIO_PC_1 - STAR_RATIO_PC_8
- STAR_RATIO_PC_DEV
- STAR_RATIO_PC_MIN
- STAR_RATIO_PC_MAX
3.3 Following bookmark are used for Upper ratio:
- UPPER_RATIO_PC
- UPPER_RATIO_PC_1 - UPPER_RATIO_PC_8
- UPPER_RATIO_PC_DEV
- UPPER_RATIO_PC_MIN
- UPPER_RATIO_PC_MAX
3.4 Star \ Upper ratio can be found in following report types:
- 8-Facet report
- Full report
- Illustrated report
3.5 Star \ Upper ratio is calculated for following cutting types:
- Round brilliant (RBC)
- Round fancies (oval, marquise, heart, pear and etc)
- Cushion
4. Notes
- If you have any question, please ask it in comments or send e-mail to developer.
- If you find mistake, please describe it in comments or send e-mail to developer
In projection on plane XY for each Star facet we find the most distant point from line between Star and Table facets.
Then is the most remote point on the girdle from this line ( in the same half-plane ).
The ratio of this distances is StarUpperRatio.
This algorithm is most consistent case F:E in picture, but here both measurements are in the same line, and in general its can be on parallel lines.
В проекции на плоскость XY для каждой грани звезды вначале ищется самая удалённая точка грани от прямой проходящей через ребро на границе с площадкой.
Затем находится самая удалённая точка на рундисте от этой прямой ( в той же полуплоскости ).
Отношение этих расстояний и есть значение StarUpperRatio.
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