Grading the Princess Cut by Bruce Harding

[beryl]

. Here's Fig.1 of the article turned for direct side view (some lines on left are missing because they were removed from wire-frame drawing for the other illustration).
. Note the closeness of 'point P'; I saw this sticking out of the crystal in an OGI demonstration. I think it can be a problem if radial dimension to 'point P' is too great or if side angle Pav1 is too steep.
. Red outline is projection of diagonals and so represents shape at corners. Bulge between corners does not show, so proximity of 'point P' at mid-side is not as bad as it appears here.

 

[strmrdr]

thank you for the pictures.

They make it clear what you are talking about with indexes and click wheels.

 

[michaelgem]

RE: I think that some missed the point: the computer definitions in different software (such as OGI and DiamCalc) may not match each other, they may not match what AGS tested, and they may not match what the cutter does. So, if you're trying to grade a Princess cut by computer-simulated images, don't put excess faith in light-leak patterns or the color grade of the AGS grading charts. Bruce L. Harding


Great piece of work, Bruce. As always. Your insights from your faceting, mathematics, mechanical, and autocad background and knowledge are unique and of great value.


And I agree with your above point.

The complexity of the princess cut combined with the error inherent in the Sarin and OGI measurements make it difficult to believe that prediction of optical performance can be adequately done from computer modeling using these measurements.

I fall in the group that favor 'direct assessment' from images of the diamond being judged.

We believe most aspects of optical performance or diamond beauty may be more accurately observed, (or predicted), and evaluated from stationary images of a diamond , (face-up and tilted), under a representation of typical illumination and viewing circumstances.

Michael Cowing

 

[beryl]

Michael:
. Thanks for compliments.
. It sounds like your last paragraph, highlighted, is a quote from something. If so, what?

 

[JohnQuixote]

Date: 8/17/2005 9:59:10 AM
Author: michaelgem

RE: I think that some missed the point: the computer definitions in different software (such as OGI and DiamCalc) may not match each other, they may not match what AGS tested, and they may not match what the cutter does. So, if you''re trying to grade a Princess cut by computer-simulated images, don''t put excess faith in light-leak patterns or the color grade of the AGS grading charts. Bruce L. Harding


Great piece of work, Bruce. As always. Your insights from your faceting, mathematics, mechanical, and autocad background and knowledge are unique and of great value.


And I agree with your above point.
The complexity of the princess cut combined with the error inherent in the Sarin and OGI measurements make it difficult to believe that prediction of optical performance can be adequately done from computer modeling using these measurements.

I fall in the group that favor ''direct assessment'' from images of the diamond being judged.

We believe most aspects of optical performance or diamond beauty may be more accurately observed, (or predicted), and evaluated from stationary images of a diamond , (face-up and tilted), under a representation of typical illumination and viewing circumstances.

Michael Cowing

Welcome Michael.

It is great to see you posting on PS.

 

[beryl]

Checked-out a lot of things today and found the errors I noted on the 2nd half of tabulated data (page 1).
Also found the best set of azimuths, shown below in Fig.39C, for equal angles between faces (see at right). I think this may be important and look forward to checking it out on DiamCalc. The azimuth angles look odd - not whole degrees - but this makes no difference to the click-wheel manufacturer, they are easy for him to make with a 'dividing head'. Actually, these are notches on a 96-tooth index wheel, as noted, which is common for many colored-stone cutters. Note that this resulted from a 3-4-5 progression of notch intervals.
From the Cutting Data shown, you can determine the corresponding slopes for any other chosen slope by the 'tangent ratio' method commonly used by advanced amateur colored-stone cutters. Tables are not necessary. If I get time I will make a simple straight slide-rule for this conversion. I had one but I lost it transferring files (maybe I have a hard copy I can scan).

Edit Sep.03: Slope at 11.25° azimuth (3/96 index) is 49.60°, as shown in picture (not 49.80° in Cutting Data list - clerical error). This is verified by EXCEL calc in tabular data presented here on Sep.01.

 

[beryl]

The azimuths below, in Fig.39D, are whole degrees and teeth of a 120-tooth index wheel. This is almost as good as Fig.39C with regard to even-distribution of the angles between faces. Note that these indexes are also spaced by a smooth progression - of 4,5,6 teeth = seems like a rule lurking here.
Got the call to go back to work tomorrow = end of time for intensive effort on gems (I was also out-of-work when I wrote "Faceting Limits" and "'Diamond Design' Revisited" in 1975). Will be away from Aug.20-25.

 

[michaelgem]

"We believe most aspects of optical performance or diamond beauty may be more accurately observed, (or predicted), and evaluated from stationary images of a diamond , (face-up and tilted), under a representation of typical illumination and viewing circumstances." Michael D. Cowing

Re: Michael:
. Thanks for compliments.
. It sounds like your last paragraph, highlighted, is a quote from something. If so, what? Bruce L. Harding

This is my wording of the concept that I have been promoting for 6 plus years beginning in print in my 2000 Journal article and, among other ideas, elaborated upon in the 2005 Journal article: "Describing diamond beauty - assessing the optical performance of a diamond". A four page digest version, which you would better appreciate for its brevity,

, appears in the latest NY Diamonds Magazine and Israel Diamonds Magazine.

I have found a number of people that promote or are sympathetic to this idea or concept. I believe we can adequately handle the objections that have been posed concerning ''direct assessment'' from diamond imaging. For example, I have made the camera lens adequately ''see'' what my asymmetrically placed eye sees in typical illumination (including the diamond''s fire).

I like direct assessment from images of diamonds under a representation of typical viewing and illumination circumstances, because it can clear away for the consumer the mystery, smoke and mirrors, and allows for clear and easy-to-understand explanations of what constitutes the best, (or do I dare say Ideal?), diamond cutting.

Michael Cowing

http://www.acagemlab.com

 

[beryl]

I repeat, having changed the word grade to judge .....
I think that some missed the point: the computer definitions in different software (such as OGI and DiamCalc) may not match each other, they may not match what AGS tested, and they may not match what the cutter does. So, if you're trying to judge a Princess cut by computer-simulated images, don't put excess faith in light-leak patterns or the color grade of the AGS grading charts.

 

[Paul-Antwerp]

I just returned from holidays (being completely offline for 2 weeks), and I find this wonderful article of Bruce. Good work, my friend. I could not agree with you more.

To put it Bruce''s article and comments into a different light, here is what we found using Diamcalc, OGI, Sarin and of course cutting the princess-cuts.

Very often, the measuring machines (OGI and Sarin) gave totally different predictions of the final weight of the stones than Diamcalc did. That difference could amount to 8%. To make it clear, while using the same basic proportions in both stones, as far as we could. After cutting the stones, we found that neither (nor Sarin, OGI, nor Diamcalc) were correct in their predictions, and that the real finished weight was generally somewhere in between.

This difference is partly due to the effects described in Bruce''s article.

Another resulting effect: in our first trials of AGS-0 princess-cuts, we tried to explore the limits of the AGS-0 cutting-guideline-charts, because we knew that working on the edge would give us the best feedback. We learned that working in those areas greatly reduced the chance of obtaining the 0-grade, and based upon this learning curve, we now ''master'' the ideal light performance-grade.

And finally, this article stresses another point that I raised before: the cutting guidelines of AGS are exactly that, and they should not be used as grading charts. They provide a wealth of information for the well-informed professional, but one cannot decide which cut-grade a stone will get, even if one has all the info needed to read the charts.

Finally, a last word: It feels good to be back here.

Live long,

 

[beryl]

. My efforts came as the result of a visit with Paul, watching the OGI software during a visit with his cutter, and meeting with ADRI, which makes cutting equipment; I hope that they will all benefit from this effort. I am still working with AGS on this and similar projects to make them more usable by cutters.
. Thanks, Paul and Lieve, for a wonderful and educational visit and your hospitality. Certainly, no one has had a more enjoyable trip to Belgium. We are also just back from Nevada, but eager to return.

 

[Garry H (Cut Nut)]

For those that know a little about DiamCalc, but maybe do not understand the point that Beryl is raising, I have made this example.

Taking a real stone, and opening the Advanced tab, and reading off all the actual angles and averaging them for this stone, I have then made a model using the standard DiamCalc Princess cut.

1. note the real model on the right has 3 chevrons each side (7 pavilion facets per corner), where as the standard DC model only has 2 chevrons (5 per corner).

2. This leads to errors in weight.

3. the chevrons all have different facet angles from the 2 models

4. The ASET images are different (although both are very nice)

5. the DiamCalc light performance is different

Model: 0.81 and 0.84 for light return mono and stereo. 1.15 Contrast
Real stone: 0.86 and .89 for Light return mono and stereo. 1.33 Contrast

Of course none of this effects the accurate 3D scan of a real stone, which is how the AGS system works.

Hope this helps

 

[beryl]

2-, 3-, and 4-chevron stones each have their own AGS ''grading'' charts and will have their own cutting info soon. It is not fair to compare them - they are different ''species''.
The point of my article was the difference between the AGS charts, simulated images, actual cutting, and real-world appearance for any of these ''species''; that is, 2-chevron cuts vary as do 3- and 4-chevron cuts.
AGS is redefining these cuts more logically; hopefully the image-generators and cutters will use these guidelines for agreement of their outputs. I have already forwarded 2-chevron data to Octonus, as presented in this thread. AGS will follow with 3- and 4-chevron standards; I do not want to ''steal their thunder''.

 

[beryl]

As promised a few days ago, here are the cutting data for the Princess pavilion of Fig.39C, which is my choice as the best-proportioned and most practical variety Princess to cut. For whole values of corner facet slope, from 25° to 50°, it gives the slopes of the other facets.
Note the 'tan ratio' at the bottom: for each chosen value for slope at the corner you can calculate the other slopes. For example, with a corner slope of 42.5° you can multiply its tangent by these ratios to get the tangents of the other slopes = 44.57°, 50.12°, and 58.62°.
For those of you who wish to avoid math, I am preparing slide rules. These will appear in a few days; they are less accurate, but good to one decimal place, which is adequate in the real world of faceting.

Edit Sep.03: Note that, for 42° slope at corner, slope at 11.25° is 49.60°, revealing clerical error in Cutting Data list of Fig.39C in post of Aug.18.

 

[beryl]

Here is the slide rule for changing slopes without changing proportions. Copy the upper picture and cut it down the dividing line; then slide the two scales against each other.
Consider Fig.39C (above): with corner slope of 42° the side slope is 58.17° and the chevrons are 44.07° and 49.60°. Suppose you want the side slope to be 60°: line-up the 60 on the upper scale with the 58.2 on the lower (approximately 58.17); the upper scale shows 44.0 for the corner (opposite 42 on lower scale) and 46.1 and 51.7 for the chevrons (opposite 44.1 and 49.6, respectively).
Note that you must round-off the numbers to one decimal place with this device. That is no problem: you can''t cut or measure the facets any better than this, anyway.
Now you can specify the slope you want at any one facet, and the others are defined accordingly without changing the azimuths or the proportions of the cut. This is a standard method used by advanced amateur colored-stone cutters to adapt given designs to materials with different refractive indexes (a problem unfamiliar to diamond cutters).

 

[beryl]

Brian Gavin brought up a very important point. Some of the Princess designs we have discussed have slopes near 55° at the side mains; these are virtually impossible to polish because the shear planes of diamond are at a slope of 54.7° along the sides of the octahedral crystal. The material would slough-off as you tried to polish it. Thank you, Brian, for pointing this out.
AGS: take note of this when you publish your Princess cutting recommendations.
In colored stones this happens with topaz: when cutting in the direction for best color the perfect cleavage across the crystal axis is parallel to the table. We tip the stone about 7° off this orientation and polish 'downhill' only (like sanding wood with the grain).
Spodumene (kunzite, etc.) is another problem - its easy cleavages are parallel to the direction of best color, thus across the girdle (in 2 planes). Setting it is risky and wearing it in a ring is foolish.
However, the problem is much more severe with diamond because this condition exists on all 4 sides of the crystal. It would be a nightmare with the Princess cut.
It is educational to note that diamond faceting-heads have an extra axis = vertical, above the others, so you can change the orientation of the stone relative to the lap for each facet - because of the 'grain' - without changing the azimuth and slope of the facets relative to the dop.

 

[Garry H (Cut Nut)]

That is an important point because it can be very difficult to achieve a high polish in such a case (I am told).

This link http://www.designsbyindigo.co.uk/i/diamondhouse/natural_rough_diamond.JPG shows a nic octahedra. In an ''ideal world'' - if the 4 big triangular pavilion facets are polished as close as possible to these crystal faces, then the highest attainable yeild can be achieved, and there are indeed many possible proportions sets in the AGS cutters guideline candidates that have angles around 55%.
In fact the most common angles for these 4 pavilion mains that get good AGS results are between the mid 60''s and the low 50s. The 54.7 problem area is just below many of the optimum candidate ranges.

 

[beryl]

Date: 9/8/2005 3:30:59 AM
Author: Garry H (Cut Nut)
That is an important point because it can be very difficult to achieve a high polish in such a case (I am told).

This link http://www.designsbyindigo.co.uk/i/diamondhouse/natural_rough_diamond.JPG shows a nic octahedra. In an ''ideal world'' - if the 4 big triangular pavilion facets are polished as close as possible to these crystal faces, then the highest attainable yeild can be achieved, and there are indeed many possible proportions sets in the AGS cutters guideline candidates that have angles around 55%.
In fact the most common angles for these 4 pavilion mains that get good AGS results are between the mid 60''s and the low 50s. The 54.7 problem area is just below many of the optimum candidate ranges.

- which means that ''recommendations'' near this angle are unrealistic.
There are two illustrations of a typical octahedral crystal in this thread. I am embarrassed that I did not recall the cleavage planes parallel to these surfaces.

 

[Garry H (Cut Nut)]

Does this help Beryl?
The eight crystal faces are also cleavage planes. This is how you would like to cut a nice crystal - the yeild can be near 70-80%