40.6 vs 41.0 pavilion angle

[Serg]

Here is the original photo I took in the hotel room after dinner with Peter Yantzer and several others including John Pollard and maybe Wink Jones from memory?
Along with the original Ideal-scope reference chart from more than 20 years ago.



And I know you will love to point out the error in the shallow ray path stone - because it goes straight back to the observers head.

But as you know - for earrings the observer is much further away and so that argument does not hold unless the observer is like these two:

For diamonds with larger tables, as I recommend with shallow stones, there is a much larger area of minor pavilion facet than for diamonds with the Firey proportions and smaller tables.

And finally, larger tables mean 90% of the light "seen" by an observer from the crown facets on big table diamond is also entering the stone from an oblique angle.
Why not make a DiamCalc model with a pavilion with 1.4-1.5 RI Sergey?

But as you know - for earrings the observer is much further away and so that argument does not hold unless the observer is like these two:

If the outgoing ray is exactly parallel to the incoming ray, a Dead Zone is formed. This zone always appears black because the ray enters the observer's pupil, regardless of the distance to the observer and the size of their head. The size of the observer's head and the distance only determine how wide the range of crown and pavilion angles is when this effect is observed.

The Dead Zone phenomenon is well-known, often referred to as NailHead for round diamonds with a pavilion angle of around 44 degrees.

In this case, the ray entering the table, after reflecting off Pavilion Halves, exits the table perfectly parallel to it. The effect is clearly visible even at a 43-degree angle when observed from short distances. This is because the ray entering the diamond, for example, from the right eye, reaches the left eye (according to Tolkowsky's parameters, the ray entering the diamond from the right eye exits towards the right ear .


More about this you can find here https://docs.cutwise.com/blog/ray-path-in-round-diamond). Therefore, Head Obscuration for such proportions is 3-5 times smaller than for diamonds with a pavilion angle of 42.5 degrees.

Of course, the effect can also be observed for a pavilion angle of 45 degrees when the incoming ray to the table reflects perfectly parallel to the incoming ray after reflecting off the Main Facet Pavilion.

However, diamonds with a 45-degree pavilion angle are never cut, unlike diamonds with a pavilion angle of 42.5-43 degrees, which are extremely rare but can be found on the market.

It is less known that a similar effect can be achieved for Shallow Pavilion diamonds. In this case, for example, with a Pavilion angle of 40.25 and a Crown Angle of 30.3, the ray entering the table, after reflecting off the Main Facets, exits the crown perfectly parallel to the incoming ray.

At these proportions, the Main Facets will appear black at any viewing distance, under any lighting conditions, and when the diamond is rocked. When viewed from close distances, the effect is also observed for larger pavilion angles. Unlike the NailHead Table Table, which is very rare in the current market, NailHead Table Crown is quite common. This is because, in the case of height-restricted diamonds (typical for LGD like CVD), diamond cutters cut diamonds with smaller crown and pavilion angles. This effect is often found in fancy cuts like Oval, Pear, Marquise, where it is called the BowTie effect.

It is important to note that a Round Brilliant Cut (RBC) with a Steep Pavilion (NailHead Table Table) can be recut to Tolkowsky parameters with minimal mass loss. On the other hand, to eliminate NailHead Table Crown in diamonds with a Shallow Pavilion, significant mass loss in the diamond would be necessary.

Additionally, NailHead is often seen in emeralds, where the range of angle parameters for all crown and pavilion tiers, when this effect is not observed on a certain facet tier of the Pavilion, is extremely narrow. A change of just 1 degree can create a Dead Zone in an Emerald Cut, and this is very common. Cutting a good Emerald is very, very challenging

 

[Garry H (Cut Nut)]

If the outgoing ray is exactly parallel to the incoming ray, a Dead Zone is formed. This zone always appears black because the ray enters the observer's pupil, regardless of the distance to the observer and the size of their head. The size of the observer's head and the distance only determine how wide the range of crown and pavilion angles is when this effect is observed.

The Dead Zone phenomenon is well-known, often referred to as NailHead for round diamonds with a pavilion angle of around 44 degrees.

In this case, the ray entering the table, after reflecting off Pavilion Halves, exits the table perfectly parallel to it. The effect is clearly visible even at a 43-degree angle when observed from short distances. This is because the ray entering the diamond, for example, from the right eye, reaches the left eye (according to Tolkowsky's parameters, the ray entering the diamond from the right eye exits towards the right ear .


More about this you can find here https://docs.cutwise.com/blog/ray-path-in-round-diamond). Therefore, Head Obscuration for such proportions is 3-5 times smaller than for diamonds with a pavilion angle of 42.5 degrees.

Of course, the effect can also be observed for a pavilion angle of 45 degrees when the incoming ray to the table reflects perfectly parallel to the incoming ray after reflecting off the Main Facet Pavilion.

However, diamonds with a 45-degree pavilion angle are never cut, unlike diamonds with a pavilion angle of 42.5-43 degrees, which are extremely rare but can be found on the market.

It is less known that a similar effect can be achieved for Shallow Pavilion diamonds. In this case, for example, with a Pavilion angle of 40.25 and a Crown Angle of 30.3, the ray entering the table, after reflecting off the Main Facets, exits the crown perfectly parallel to the incoming ray.

At these proportions, the Main Facets will appear black at any viewing distance, under any lighting conditions, and when the diamond is rocked. When viewed from close distances, the effect is also observed for larger pavilion angles. Unlike the NailHead Table Table, which is very rare in the current market, NailHead Table Crown is quite common. This is because, in the case of height-restricted diamonds (typical for LGD like CVD), diamond cutters cut diamonds with smaller crown and pavilion angles. This effect is often found in fancy cuts like Oval, Pear, Marquise, where it is called the BowTie effect.

It is important to note that a Round Brilliant Cut (RBC) with a Steep Pavilion (NailHead Table Table) can be recut to Tolkowsky parameters with minimal mass loss. On the other hand, to eliminate NailHead Table Crown in diamonds with a Shallow Pavilion, significant mass loss in the diamond would be necessary.

Additionally, NailHead is often seen in emeralds, where the range of angle parameters for all crown and pavilion tiers, when this effect is not observed on a certain facet tier of the Pavilion, is extremely narrow. A change of just 1 degree can create a Dead Zone in an Emerald Cut, and this is very common. Cutting a good Emerald is very, very challenging

None of that has anything to do with the shallow crown 40.6 pavilion diamond in question Sergey.
The nailhead shallow stone effect is only concerning the main facets and they are smaller in this case.
I explained the main Ideal-Scope dark zones are in the lower girdle zones. The main facets are less prominent in large table stones both in table and in crown.
Why the diversion?
And the 8 stars that 'experts' like are exactly what you are describing.
?????

 

[Garry H (Cut Nut)]

Can we go back to the question I asked before Sergey, please?
Diamonds get dirty.
I started a pol her on PS - and even here amongst the most likely people on earth to keep their diamonds clean- we can see that earrings aren't getting cleaned more than once a week on average. i.e. they are dirty most of the time!
I see clients jewelry daily and my clients are also mostly passionate about their diamonds. We even give more than half of them little ultrasonic cleaners. For 30 years I have given them bottles of our cleaner we use in our workshop ultrasonic cleaners.
Diamonds are dirty 99% of their life.
Pavilion RI 1.4 or 1.5 please

How often do you clean your diamonds?

This will be interesting. And I am asking the converted hahaha

www.pricescope.com

 

[Serg]

Can we go back to the question I asked before Sergey, please?
Diamonds get dirty.
I started a pol her on PS - and even here amongst the most likely people on earth to keep their diamonds clean- we can see that earrings aren't getting cleaned more than once a week on average. i.e. they are dirty most of the time!
I see clients jewelry daily and my clients are also mostly passionate about their diamonds. We even give more than half of them little ultrasonic cleaners. For 30 years I have given them bottles of our cleaner we use in our workshop ultrasonic cleaners.
Diamonds are dirty 99% of their life.
Pavilion RI 1.4 or 1.5 please

How often do you clean your diamonds?

This will be interesting. And I am asking the converted hahaha

www.pricescope.com

I have answered you in detail several times why I will not create a diamond model specifically for you, with the refractive index of the pavilion facets like glass and the crown facets like diamonds. For example please reread my posts on the first page of this chat.

If that is not enough, I will add that in the case of earrings with diamonds, it is not correct to assume that dirt accumulates only on the pavilion. Your photos of Drena's earrings clearly show that dirt mainly accumulates on both the pavilion and the crown in the area of the girdle, where Drena touched the diamonds to remove or put on the earrings. Therefore, a model where dirt is only on the Pavilion( whole Pavilion) and the whole crown is clean does not correspond to reality.

On this photo of earrings in IS lighting, it is clear that leakage due to contamination occurs in the girdle area, and the pavilion area under the table is clean.


So I will not spend tens of thousands of dollars and the time of Octonus developers on creating a completely inadequate model of the path of light in a diamond just to help you justify your mistake in promoting Shallow Diamonds.

Your survey about the frequency of diamond cleaning shows that approximately one-third of consumers clean their diamonds every day because they understand that dirty diamonds are not beautiful. So, it is important to them that clean diamonds are beautiful, which shallow diamonds with the NailHead effect cannot be.



But once again, in your survey, you only see what you want to see, dismissing everything else, no matter how valuable it may be.

 

[Serg]

None of that has anything to do with the shallow crown 40.6 pavilion diamond in question Sergey.
The nailhead shallow stone effect is only concerning the main facets and they are smaller in this case.
I explained the main Ideal-Scope dark zones are in the lower girdle zones. The main facets are less prominent in large table stones both in table and in crown.
Why the diversion?
And the 8 stars that 'experts' like are exactly what you are describing.
?????

None of that has anything to do with the shallow crown 40.6 pavilion diamond in question Sergey.

This statement is only true for diamonds with crown angles of 35-37 degrees. If the crown angle is less than 33 degrees, then approximately half of the virtual facets under the table become dark and practically stop creating brilliance and fire. If the crown angle is less than 32, diamonds with a pavilion of P40.6 develop a pronounced NailHead effect under the table.

example the diamond with P40.53Cr31.2

VG Round, 1.00ct, G, VS2, EX, VG, NON, -3.6%

VG Round, 1.00ct, G, VS2, EX, VG, NON, -3.6%

cutwise.com

And it is incorrect to claim that the effect is insignificant because the main facets have a smaller area than the Pavilion haves .
Even though the area of the main facets under the table is 2-3 times smaller than the area of the pavilion halves, the black areas created by the main facets are connected one common pattern and have a significantly stronger negative impact on the perception of the diamond. This negative effect of visually connected Dead zones is much stronger than if these areas of the same total size were isolated and evenly distributed, as is the case with Princess cuts.

The black arrows visible in lighting conditions like IS and ASET for diamonds with parameters close to Tolkowsky's create a strong brilliance effect for stereo observers. This is because when one eye sees the pavilion facet as black under the table, the other eye sees it as white. This conflict of brightness in one area (Stereo Rivalry) creates a strong illusion of a sparkling diamond (Brilliance).


However, if you reduce the pavilion angle, both eyes see dark areas simultaneously in the location of the main facets under the table, and the illusion disappears, making the diamond look dark.

 

[Garry H (Cut Nut)]

Extend the closest distance to earring and pendant viewing and your theory crumbles Sergey. Extend it to other side of the dining table and the slightest movement makes 6 of the 8 dark facets bright.
If you are sitting at the heads of the table the contrast during mouth movements chewing or talking causes loads of scintillating sparkle.

 

[Serg]

Extend the closest distance to earring and pendant viewing and your theory crumbles Sergey. Extend it to other side of the dining table and the slightest movement makes 6 of the 8 dark facets bright.
If you are sitting at the heads of the table the contrast during mouth movements chewing or talking causes loads of scintillating sparkle.

If the incoming and outgoing rays are strictly parallel, then the facet will appear black no matter how far away you look at it. Are you disputing this mathematical statement?

For the shallow diamond, I provided a set of crown and pavilion angles in which the outgoing ray is strictly parallel to the incoming ray in the Table-Main facet-Main facet-Crown tracing scenario.

Of course, if you are sitting at a 3-5 meters dining table and looking at a 0.5-carat diamond on the other side of the table, you won't see individual black facets because their angular size is smaller than the resolving power of the human eye. However, you may still see distinct bright flashes, especially if you are dining in a dimly lit restaurant with candles.

 

[Garry H (Cut Nut)]

If the incoming and outgoing rays are strictly parallel, then the facet will appear black no matter how far away you look at it. Are you disputing this mathematical statement?

Absolutely Sergey. If anything this diamond will have too little star contrast.
This is the stone in DiamCalc (at ideal 1ct diameter it can weigh only 0.92ct!)
Here is the stone face on as seen with a virtual ideal-scope from 1M (a bit more than a yard. Close viewing distance. Each next image has 1 degree of tilt:

By 3 degrees of tilt there is almost no dark zone - and certainly a lot less than a Tolkwosky's 'ideal' leakage zones at tilted angles. Superior light return and superior spread. Plus less affect from grease and dirt.

 

[Garry H (Cut Nut)]

At 3M viewing e.g. dining table:

 

[Karl_K]

40.6 is not a shallow pavilion its the lower end of the normal range so of course your not going to find huge issues with the mains nor gain a lot of dirt tolerance.
The long stars also mute the effects of the mains angle.
The 31.3 CA is going to negatively effect fire and life(scintillation)
Drop the PA to 40.4 and the lgf to 75% then look at the different distances again.

 

[Garry H (Cut Nut)]

40.6 is not a shallow pavilion its the lower end of the normal range so of course your not going to find huge issues with the mains nor gain a lot of dirt tolerance.
The long stars also mute the effects of the mains angle.
The 31.3 CA is going to negatively effect fire and life(scintillation)
Drop the PA to 40.4 and the lgf to 75% then look at the different distances again.

Thanks Karl,
Sergey has fixated on the shallow stone in Drena's earring.
I would prefer to focus on the shallowest wierd combo in my recomended proportion chart
Here is the result and there is little if any change through small ranges of tilt from 1M:

 

[Karl_K]

I actually get what Serg is talking about he hates internal contrast aka obstruction contrast pattern aka arrows.
I know a couple people like that.
They like princess cuts and crushed ice stones that do not have the obstruction zones.
The also dislike many types of pattern designs like EC and SE.
Changing the mrb to something its not is not the answer.

 

[Serg]

At 3M viewing e.g. dining table:

1. In the field of creating your own lighting schemes in Diamcalc, the interface is quite complex, and it's easy to make a mistake. If you changed the distance from the diamond to the observer's head in the "Observer head Shading and view distance" panel, you needed to either use Photorealistic (Standard render) or change the Panorama radius in the HDR settings/Panorama panel from 24 mm to 3001m. In your lighting setup, there was no Head Obscuration because you were observing the diamond from a distance of 3 m through IS, which was next to the diamond.
2. To observe the Nail Head Table Crown, you need to use the proportions P40.25Cr31.4.

 

[Garry H (Cut Nut)]

1. In the field of creating your own lighting schemes in Diamcalc, the interface is quite complex, and it's easy to make a mistake. If you changed the distance from the diamond to the observer's head in the "Observer head Shading and view distance" panel, you needed to either use Photorealistic (Standard render) or change the Panorama radius in the HDR settings/Panorama panel from 24 mm to 3001m. In your lighting setup, there was no Head Obscuration because you were observing the diamond from a distance of 3 m through IS, which was next to the diamond.
2. To observe the Nail Head Table Crown, you need to use the proportions P40.25Cr31.4.

This is for the diamond Drena was wearing - actually quite a lot of sparkle - more than I would expect!



3 degrres of tilt to the right


5 dergees tilt

30 degrees tilt - which is about the angle the diamonds are at when the wearer is facing you:

 

[Serg]

Garry, from your last post, I didn't understand whether you changed your response to my question:

"If the incoming and outgoing rays are strictly parallel, then the facet will appear black no matter how far away you look at it. Are you disputing this mathematical statement?"

Are you still disputing it, or are you in agreement with it after you corrected your lighting design mistake?

Discussing other complex issues doesn't make sense when even on such simple questions, opinions fundamentally differ.

 

[Garry H (Cut Nut)]

Garry, from your last post, I didn't understand whether you changed your response to my question:

"If the incoming and outgoing rays are strictly parallel, then the facet will appear black no matter how far away you look at it. Are you disputing this mathematical statement?"

Are you still disputing it, or are you in agreement with it after you corrected your lighting design mistake?

Discussing other complex issues doesn't make sense when even on such simple questions, opinions fundamentally differ.

Sergey I am simply showing that cyclops looking at someone wearing a shallow diamond (that was first discussed) would see from the other side of the table.

I am sure you can agree that the dark zones (stars) are not showing as an ugly feature?
If I get time I will do the shallow pavilion stone (off to HK show today).

 

[Serg]

Sergey I am simply showing that cyclops looking at someone wearing a shallow diamond (that was first discussed) would see from the other side of the table.

I am sure you can agree that the dark zones (stars) are not showing as an ugly feature?
If I get time I will do the shallow pavilion stone (off to HK show today).

Garry,

1. Observing one diamond at distances of 3m and 0.3m differs approximately the same as observing 1ct and 0.001ct diamonds from a distance of 0.3m. Of course, HeadObscuration behaves quite differently at distances of 0.3m and 3m. Do you believe that consumers can perceive a difference in Optical Performance for solitary 0.001ct diamonds from a distance of 0.3m if these diamonds only differ in the pavilion facet angle by:a) 0.5 degrees?b) 1 degree?If consumers cannot distinguish between such 0.001ct diamonds from a distance of 0.3m, why would they notice differences between 1ct diamonds with the same proportions from a distance of 3m?
2. As the distance to the diamond increases, not only does the angular size of the head decrease, but the stereo angle at which the facets of the diamond are seen by the left and right eyes also decreases proportionally. Therefore, Stereo Head Obscuration does not decrease rapidly with increasing distance to the diamond.
3. I will remind you that Brilliancy is created through three types of Brightness Rivalry (Spatial, Temporal, Stereo). Brightness Spatial Rivalry is widely known as contrast and can be considered higher in Shallow diamonds due to stronger Head Obscuration. However, Brightness Stereo Rivalry is much more important for Brilliancy, and it decreases for Shallow diamonds. Therefore, over a wide range of viewing distances, Shallow Diamonds have weaker Brilliancy than diamonds with proportions P40.8Cr34.5.
4. Brightness Temporal Rivalry depends on the angular speed at which the exiting ray from the diamond scans the space of light sources. At the end of the page https://docs.cutwise.com/blog/ray-path-in-round-diamond it is shown how this speed changes with the pavilion angle for rays reflected from the main pavilion facets. If the pavilion angle for a P40.8Cr34.5 diamond is increased/decreased by 1 degree, the scanning angle speed of the exiting rays increases/decreases by approximately a factor of 3. In other words, for P40.6Cr34.5 and P41Cr34.5 diamonds, the scanning speed of the exiting rays from the main pavilion facets will be approximately 1.5-2 times faster. This leads to a significant difference in the probability of capturing a light source when the diamond is tilted. This is why stones with a slightly larger pavilion angle than a round brilliant with classic proportions have more "life" than those with a slightly smaller pavilion angle. Of course, if the pavilion angle is increased significantly, the path of the ray will fundamentally change for many facets, leading to many negative effects. However, when we are talking about small changes in the pavilion angle, such as 0.2 degrees, increasing the angle enhances Optical Performance, while decreasing the angle reduces Optical Performance in clean stones. Dirty stones with P40.6Cr34.5 and P41Cr34.5 will look equally bad, and the dirt will wash away any differences between these cuts.
   
   

The effects of Brightness Temporal and Stereo rivalry cannot be analyzed based on static photographs or instruments such as IS, ASET, FS, etc. If we were cyclopses examining static diamonds, then, of course, the difference between P40.6Cr34.5 and P41Cr34.5 diamonds would be much smaller. However, we are not cyclopses, and consumers can independently verify that when viewing without a loupe, IS, ASET, and other mono tools, a P41Cr34.5 diamond has more "life," Fire, and Brilliancy than P40.6Cr34.5 diamonds. Of course, the visible difference also depends greatly on the size of the diamond, and in the past, when most diamonds were no more than 0.5 ct, few could see this difference. However, now, with the widespread availability of 3-5ct LGD, many consumers will be able to see this difference.

 

[Karl_K]

As Bruce H. once told me that response to obstruction is not a fixed value its a range.
It is a range both in distance and degrees.

Using that information you can look at the range from dark to bright pavilion mains in distance both cyclops and stereo.
P40.6Cr34.5 and P41Cr34.5(same table and minor%) have a huge amount of overlap on that range.
The 40.6 combo would have a slightly longer distance between the 2 points as it is slightly more directional.
However it is close enough that I would not call one better.

 

[Garry H (Cut Nut)]

Dear Sergey,
You seem fixated on some things that I am not.
1. main facets.
2. 40.6 pavilion angle with a shallow crown in Drenas earrings.

1. I would like you to please focus on the proportions I recommend to all.
Here is the chart:

You can see the pavilion angles on the earring recommended diamonds (the second most common diamond usage) are 41.2 to 41.4 degrees.
It is also obvious that the main facets in these proportions make up a very small part of the light entering and exiting in the same plane (as all your narrow examples).
2. because the pavilion angle is greater than Tolkowsky or 40.6 - what you are focused on is not relevant to anything other than the extreme stone that I used for Drena's earring (which fails HCA anyway because overall it is too shallow).

Because in these proportions most of the light is coming from oblique angles the fan and speed of changes is huge.
The proportions are on the 'sweet line'.

What is the problem?
I know you enjoy a good argument, but this one seems to have become irrelevant?
But happy to keep responding as at least Karl is entertained

 

[Serg]

Dear Sergey,
You seem fixated on some things that I am not.
1. main facets.
2. 40.6 pavilion angle with a shallow crown in Drenas earrings.

1. I would like you to please focus on the proportions I recommend to all.
Here is the chart:

You can see the pavilion angles on the earring recommended diamonds (the second most common diamond usage) are 41.2 to 41.4 degrees.
It is also obvious that the main facets in these proportions make up a very small part of the light entering and exiting in the same plane (as all your narrow examples).
2. because the pavilion angle is greater than Tolkowsky or 40.6 - what you are focused on is not relevant to anything other than the extreme stone that I used for Drena's earring (which fails HCA anyway because overall it is too shallow).

Because in these proportions most of the light is coming from oblique angles the fan and speed of changes is huge.
The proportions are on the 'sweet line'.

What is the problem?
I know you enjoy a good argument, but this one seems to have become irrelevant?
But happy to keep responding as at least Karl is entertained

Garry,

As far as I recall, there used to be a rule on Pricescope that discouraged changing the original discussion topic. Am I correct in remembering this rule, or has it already been revoked?

This chat was initiated with a question about whether P40.6Cr34.5 or P41Cr34.5 is better. I find this question highly important and interesting. The question can be formulated without numbers as follows: What happens to performance when we take a modern Tolkowsky cut and start increasing or decreasing the pavilion angle while keeping other parameters constant? Which direction should we move in?

An even more intriguing question is whether it's possible to achieve a more beautiful round diamond than one with P40.8Cr34.5 proportions?

I'm trying to address these questions in this chat, while it seems like you constantly try to change the topic, either by requesting tools for evaluating dirty diamonds or suggesting comparing diamonds on SweetLine. The essence of Sweetline is that the optics of diamonds along this direction change very weakly, unlike the perpendicular direction or when we change only the pavilion angle (or only the crown angle).

I urge you to keep the discussion within the framework of the original question.

Which is a 40.6 or 41.0 better pavilion angle works better with a 34.5 crown angle? (I know 40.8 is optimal..) just curious what’s the better combo if 40.8 is another an option.

If someone doesn't see the difference between P40.6Cr34.5 and P41Cr34.5, they can compare P40.4Cr34.5 and P41.2Cr34.5. It's also interesting to compare all these combinations with P40.8Cr34.5.

The most important question is not how large the difference is between P40.6Cr34.5 and P41Cr34.5, but whether P40.8Cr34.5 indeed provides the maximum performance when all other parameters, including LGF%, remain unchanged.

 

[Karl_K]

but whether P40.8Cr34.5 indeed provides the maximum performance when all other parameters, including LGF%, remain unchanged.

With reasonable table sizes and lowers it does provide a good balance of many areas of performance.

It does not give max performance in any one measure of performance. Never has.
Brightest? nope
Most fire? nope
Low light performance? nope
Flat light performance? - nope
Direct light performance? Its strong but nope
best scintillation? - nope
Best balanced contrast at different distances - It is very strong in this category. You could argue a tie.
so on and so forth.

 

[Garry H (Cut Nut)]

Garry,

As far as I recall, there used to be a rule on Pricescope that discouraged changing the original discussion topic. Am I correct in remembering this rule, or has it already been revoked?

This chat was initiated with a question about whether P40.6Cr34.5 or P41Cr34.5 is better. I find this question highly important and interesting. The question can be formulated without numbers as follows: What happens to performance when we take a modern Tolkowsky cut and start increasing or decreasing the pavilion angle while keeping other parameters constant? Which direction should we move in?

An even more intriguing question is whether it's possible to achieve a more beautiful round diamond than one with P40.8Cr34.5 proportions?

I'm trying to address these questions in this chat, while it seems like you constantly try to change the topic, either by requesting tools for evaluating dirty diamonds or suggesting comparing diamonds on SweetLine. The essence of Sweetline is that the optics of diamonds along this direction change very weakly, unlike the perpendicular direction or when we change only the pavilion angle (or only the crown angle).

I urge you to keep the discussion within the framework of the original question.

If someone doesn't see the difference between P40.6Cr34.5 and P41Cr34.5, they can compare P40.4Cr34.5 and P41.2Cr34.5. It's also interesting to compare all these combinations with P40.8Cr34.5.

The most important question is not how large the difference is between P40.6Cr34.5 and P41Cr34.5, but whether P40.8Cr34.5 indeed provides the maximum performance when all other parameters, including LGF%, remain unchanged.

OK Sergey, I guess then I need to state the divergence was to state that Drena's shallow pavilion diamond showed less dirt (but to be fair that was mainly because of the crown angle).
You could not deny that below the sweet line combo's will show less dirt - agreed?

Now given there is many times more non main to non main and non main to main and main interactions than purely main to main, I contend your main to main focus is bogus.
In almost every interaction the other than main to main light is drawn from a higher angle as in this example below:
As we all agree higher angle light, that is not obscured by a potential observer of a ring, is an advantage, this is a demonstrable fact with a few minutes of firing rays through many iterations in DiamCalc.

 

[Serg]

OK Sergey, I guess then I need to state the divergence was to state that Drena's shallow pavilion diamond showed less dirt (but to be fair that was mainly because of the crown angle).
You could not deny that below the sweet line combo's will show less dirt - agreed?

Now given there is many times more non main to non main and non main to main and main interactions than purely main to main, I contend your main to main focus is bogus.
In almost every interaction the other than main to main light is drawn from a higher angle as in this example below:
As we all agree higher angle light, that is not obscured by a potential observer of a ring, is an advantage, this is a demonstrable fact with a few minutes of firing rays through many iterations in DiamCalc.

Garry,
You are once again seeing (or showing) only what you want to see, ignoring the essential facts.

The facts are as follows:
A slight increase in the pavilion angle results in a significant increase in both the dispersion of the outgoing ray and the scanning speed of the space illuminated by this ray for almost all zones of the diamond, with exceptions like the Star-Pavilion and halve-Pavilion halve-Table rays. In other words, this leads to a substantial increase in the visible Fire and the overall "Life" of the diamond.

You can verify this through ray tracing and Cutwise metrics, as I've previously shared. If you enable the second reflection visualization mode in DiamCalc, you'll see areas with identical ray paths for the first two reflections, which play a crucial role in creating the image of a round cut. Let's focus on these areas under the main crown facet. Three of them, together, account for 80-90% of the area of the main crown facet.

How could you have missed these areas?



It's easy to see that the ray path responds to changes in the pavilion angle, just as in the case of the Table-Main Facet-Main Facet-Crown ray. Specifically, the dispersion of the outgoing ray increases, as does the speed at which it scans the space illuminated by the diamond during motion. Furthermore, the outgoing ray becomes closer to vertical, which increases the risk of Head and Body Obscuration.

These three areas are formed by reflections from both the main pavilion facets and the Pavilion halves.

The same effect applies to roughly half of the Crown Halves area.



I previously used the Table-Main-Main-Crown ray for illustration, not because this effect only occurs in this case, but because it's easier to see and understand with this ray.

The fact is that a slight increase in the pavilion angle (0.2-0.4 degrees) has a positive impact on the Fire and "Life" of a diamond. This can be observed by analyzing clean diamonds or videos of clean diamonds. Cutwise metrics, which calculate the number of flashes, their duration, brightness, and saturation, also show a significant increase in Fire when the pavilion goes from 40.8 to 41 degrees.

Pa variation for Ca34.5

cutwise.com

Importantly, these metrics do not consider the proportions of the cut or the path of the ray.

The specific pavilion and crown angles of dirty diamonds are almost irrelevant because nearly all dirty diamonds look equally poor. Therefore, I am discussing only clean diamonds.

 

[Serg]

Often, you can come across the statement that Pavilion Halves have a stronger influence on the optics of a Round Brilliant Cut (RBC) diamond than Pavilion Main Facets because their surface area is much larger. I colored one Pavilion Main Facet green and the adjacent Halves red.

When looking at the pavilion facets, it seems obvious that the Halves have a significantly greater impact on the diamond's optics.

However, if you view these facets from the crown side after refraction, a completely different picture emerges.

Under the table, although the surface area of the Halves is larger, it's not by much. In the Main Crown Facets, we see many more images of Pavilion Facets than Pavilion Halves. Pavilion Halves certainly dominate when viewed through Crown Halves, but even in this case, the percentage of their surface area appears significantly smaller than the percentage of the surface area of Pavilion Halves on the Pavilion facets.

So, the assertion that Pavilion Halves have a significantly stronger impact on the optics of a round diamond than Pavilion Main Facets is unlikely to be accurate because after refraction, their visible surface areas are very close. Of course, it's also necessary to consider images of facets not only after refraction but at least after the first reflection. However, I need to wait for a new version of Diamcalc that allows me to see this.

 

[Garry H (Cut Nut)]

Often, you can come across the statement that Pavilion Halves have a stronger influence on the optics of a Round Brilliant Cut (RBC) diamond than Pavilion Main Facets because their surface area is much larger. I colored one Pavilion Main Facet green and the adjacent Halves red.

When looking at the pavilion facets, it seems obvious that the Halves have a significantly greater impact on the diamond's optics.

However, if you view these facets from the crown side after refraction, a completely different picture emerges.

Under the table, although the surface area of the Halves is larger, it's not by much. In the Main Crown Facets, we see many more images of Pavilion Facets than Pavilion Halves. Pavilion Halves certainly dominate when viewed through Crown Halves, but even in this case, the percentage of their surface area appears significantly smaller than the percentage of the surface area of Pavilion Halves on the Pavilion facets.

So, the assertion that Pavilion Halves have a significantly stronger impact on the optics of a round diamond than Pavilion Main Facets is unlikely to be accurate because after refraction, their visible surface areas are very close. Of course, it's also necessary to consider images of facets not only after refraction but at least after the first reflection. However, I need to wait for a new version of Diamcalc that allows me to see this.

Your comparison is for direct view, but the two eye angular divergence for even 5M away makes such an argument null and Void.
Not to mention the speed of angular movement from minor facets which seems to be far faster with more change from main to minor facets.
Also my recomended proportions for 40.6 degree pavilion are up to 35 and 36 degree which creates a more rapid angular reaction.

 

[Serg]

Your comparison is for direct view, but the two eye angular divergence for even 5M away makes such an argument null and Void.
Not to mention the speed of angular movement from minor facets which seems to be far faster with more change from main to minor facets.
Also my recomended proportions for 40.6 degree pavilion are up to 35 and 36 degree which creates a more rapid angular reaction.

Garry,

What is the connection of your message to my post about the ratio of the visible surface areas of Pavilion Main Facet and Pavilion Halves through the crown facets? This ratio is not dependent on distance.

Furthermore, I wouldn't use the word "Even" when referring to distances of around 5 meters. This is a very long distance for viewing diamonds, at which they appear smaller than Melee from a viewing distance of 0.5 meters.

 

[Serg]

When I make statements about the beauty of diamonds, I usually do so under the condition of observing clean diamonds from a distance of 0.4-0.5 meters. If I make any statements for other observation conditions, I specify that deliberately.

I am not an expert in evaluating the beauty of dirty diamonds from several meters away, and I do not plan to spend time becoming an expert in these observation conditions because I consider this knowledge entirely useless at the moment. Currently, there are many more important and interesting tasks in the field of evaluating the beauty of clean diamonds than trying to assess which diamonds look better when they are dirty from a distance of 5 meters. Perhaps in a few decades, when more pressing issues are resolved, it might become important to evaluate dirty diamonds from a distance of 5 meters.

 

[Karl_K]

At 5m the diamond even a 5ct is a tiny dot, the contrast between that dot and what is behind determines if it stands out or not. Since the eye will not pick up fine details the brightness is a blurred average of the dot relative to the background.
Obstruction will play little part in it.
However shallow pavilions are more directional, there could be an advantage there.
LGD is not that expensive, Garry consider having some cut and play with them?
You could even send them to others to look at.
That was not practical with mined but 4-6 1ct LGD might make it affordable?

 

[Serg]

Not to mention the speed of angular movement from minor facets which seems to be far faster with more change from main to minor facets.

Indeed, for the P40.8 Cr34.5 cut, the rays reflected from the Pavilion Halves exhibit higher dispersion and angular velocity than the rays reflected from the Pavilion Mains.However, Pavilion slope 0.2 degree variations have a much smaller percentage impact on these rays compared to the rays reflected from the Mains.
If the speed of the Pavilion Main-Main rays differs by 2-3 times for angles P40.6 and P41, the same ratio for the Halves rays is much smaller.

This is why the difference between the P40.6 Cr34.5 and P41 Cr34.5 cuts is primarily determined by the changes in Main-Main rays, rather than the changes in Halve-Halve (Minor-Minor) rays.

In other words, the Halves facets for the P40.8 Cr34.5 cut operate within a stable plateau zone, and their performance changes very little with slight variations in the pavilion angle, whereas the Pavilion Mains facets, P40.8 Cr34.5, are on a steep slope, and even a small change in the pavilion angle significantly alters the contribution of these facets to Fire and "Life."

 

[Rfisher]

You could even send them to others to look at.
That was not practical with mined but 4-6 1ct LGD might make it affordable?

I would LOVE to participate in this pay (shipping?) to play this lab grown different cut diamond game, if it ever fruits.

Especially if it included Garry’s shallower is better for earrings cut (extreme and moderate version), a good but typical gia xxx, a nice 60/60, and a super ideal.