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| HOME : FORUM : EDUCATION : GEMSTONES : Lapidary : Changing Facet Slopes |
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Post#1 @
11-26-02
, 03:31 PM
. If you want to retain the geometric proportions of a cut but change the slope of certain facets, it is necessary to change the slope of the other facets accordingly. This is done by changing the tangents of all facet slopes by the same ratio. . WORRY PAS! Any old-fashioned slide-rule will do this for you. Here I provide a circular one that you can cut out and use with a pin or grommet in the middle. . I also made other slide-rules to adjust index and slope if stretching a round into an oval or a square into a rectangle (I made my own index wheels). . These were made in 1975 but the cost of getting them made in production exceeded what I expected to receive by sales, so I didn't do it. I gave a set to John Sinkankas; now I am giving this one to everyone. I hope that some will benefit - perhaps those pumping different combinations into Octonus' DiamCalc. . Here is the simple FACET SLOPE CONVERSION slide-rule for you to cut out. You can get a better copy by SASE or by CAD file if you have AutoCAD 2000. |
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Last edited by beryl : 11-26-02 at 03:47 PM.
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Changing Pavilion Slopes
Post#2 @
11-26-02
, 03:39 PM
. This ratio trick is applied separately to the parts of the gem above and below the girdle. . In the example below, we are making the cut shown in "Girdle Scallops" - Fig.1 with 40° pavilion mains instead of 40.75°. By reading from the break slope of 41.9° (actually 41.89° but who can measure or control it?) we get a new break slope of approx. 41.14°, which it is sufficient to call 41.1° |
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Last edited by beryl : 11-26-02 at 03:48 PM.
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Changing Crown Slopes
Post#3 @
11-26-02
, 03:43 PM
. And below we show how to derive the crown break and star slopes for that same cut if we change the crown mains from 34.5° to 36°. |
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Post#4 @
11-27-02
, 06:23 AM
Dear Bruce, We found these slide-rules very ingenious. However, with the DiamCalc one can see any angle of any facet and all angles and proportions are calculated automatically, so there is no need to calculate any angles or proportions for the DiamCalc owners. Here is screenshot showing beryl’s example in the DiamCalc. I open the DiamCalc and set parameters of initial diamond: 34.5°, 54%, and 50% Star (approximately gives your 2/3 high crown breaks). By moving the mouse over desired facet I can see all these angles: 40.7° crown breaks and 22.7° stars. Then I enter the new crown mains angle: 36°. The model is immediately recalculated and here we have it (The picture shows the 42.3° slope on the selected crown break facet). So we do not understand how it should be used with the DiamCalc. Please explain if you meant any specific use. Sincerely yours, Vladimir, DiamCalc team. |
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Post#5 @
11-27-02
, 08:18 AM
. I do not see crown break and star slopes in your illustration. The pavilion slopes do not affect them. . I understand that DiamCalc must do this; however, it is limited to generic cuts which have been programmed into it. . Perhaps it will not accept new cuts for which there is no programmed master form, such as the 'zircon cut' proportions I sent to Serg recently (since entered in DiamCalc library) or the modified brilliant I showed in Fig.4 or 4a of "Girdle Scallops" last week (Serg and Garry have asked for the AutoCAD data for Fig.4, which I sent to them last week). Garry says that he wants to look at this in DiamCalc; can he do it with just the data or does he need a generic form programmed into the library? . If DiamCalc cannot accept data without a master program for the generic cut, I think this would be a nice addition, which, I am sure, you could achieve very easily. Obviously the fundamentals are already there. . Anton Vasiliev's 'GEMSHAPE' software approached from the cut-creation viewpoint, probably because he is also a colored-stone cutter, not limited to the concepts associated with diamond. I hope that there are some other colored-stone cutters reading this forum who would benefit from this slide-rule as well. Furthermore, this enables people who do not have DiamCalc to make the adjustments. . I am startled at the small response. Apparently the effort is not justified to redo my cut-distortion slide-rules for DT - for converting indexes and slopes from round and square cuts to oval and rectangular ones. Perhaps DiamCalc does this; as you know, I had to delete DiamCalc from my computer, and so cannot comment intelligently. |
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Last edited by beryl : 11-27-02 at 08:35 AM.
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Post#6 @
11-27-02
, 10:34 AM
Hi Beryl, The facet angle is at the bottom row in diamcalc. S |
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Post#7 @
11-27-02
, 12:20 PM
Sibelius: . Thank you; I did not see it. . Just above this it says 'angle 11.1'; that is why I don't use the word 'angle' = too ambiguous in gem talk. I call it 'index 1/32', which is 11.25°. On the bottom line you cite, they show 'azimuth 78.8', which is the military term and = index 7/32 = 78.75°. Note that they cite a different value in the two places: not incorrect but inconsistent. ******************* Other: . I have just received private communication from a well-known colored-stone cutter, so there are interested folks hiding in the wings. . The world of colored-stones is FAR more interesting and complex than diamonds; note that diamonds are just one RI group in "Faceting Limits", which applies to ALL gemstones. . My friend suggested that this is the wrong forum for such things, but where else is there? I want to share this stuff while I can. |
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Last edited by beryl : 11-27-02 at 12:42 PM.
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Post#8 @
11-27-02
, 01:08 PM
Dear Bruce, as you know there is no problem to install the DiamCalc again. Vladimir, DiamCalc Team. |
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Post#9 @
11-27-02
, 01:29 PM
Bruce, Quote:
You post hasty. You write about the window where the user can put arbitrary angle to rotate model with the "rotation buttons". If I want to rotate model by 2° to the left then I instruct the program to rotate it 2° and there is no good reason why should know even anything about the indexes when I want to rotate diamond. You should consider a possibility to learn the DiamCalc capacities deeper before posting inconsiderate critics. |
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Post#10 @
11-27-02
, 05:22 PM
Vladimir: Well said. I apologize. ************ Others: Happy Thanksgiving Day. |
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Last edited by beryl : 11-27-02 at 05:24 PM.
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Post#11 @
11-27-02
, 06:31 PM
Garry: . I did not mean my comments as 'criticism' but should have realized they would be interpreted that way. . From what I showed in "Girdle Scallops", and commented at one point, and as I have said to you offline, I think that the shifted breaks were not made by 'clicks' but rather by use of another index wheel or a specially-made one - which is what any cutter would do for production. However, that discussion does not belong in this thread (why did you say nothing about Fig.4a? Answer in that thread, please). |
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Last edited by beryl : 11-27-02 at 06:33 PM.
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Post#12 @
03-01-03
, 11:07 AM
. Here are straight-line slide rules for those who did not like the round one - just cut along the mid-line and slide them. The advantage of the round one is that you get a longer scale in a smaller space. . You probably will not get good resolution by copying this. I can send you a scanner copy free by e-mail, or a print with 10-inch long scales if you send self-addressed stamped envelope for 8½"x11" paper. . This solves the 'ratio of tangents' often discussed among faceters. |
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Post#13 @
03-01-03
, 08:30 PM
. Without knowledge of logarithms, I could not have made these slide rules. These are better than a calculator because they don't give you absurdly accurate results. . Sadly, some things have been lost by the advent of computers. I hope that students still learn to think. . What will you do with these, Garry? You are not a gem-cutter? |
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Post#14 @
03-01-03
, 09:21 PM
You guys make me think about an article I saw recently in the Wall Street Journal about one of the leading sellers of slide rules as "antiques" or collectibles, "Slide Rule Universe" at http://www.sphere.bc.ca/test/sruniverse.html. I'm a few years behind you guys, made my way through school with an HP calculator  .
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Post#15 @
03-02-03
, 04:46 AM
. What would you do without electricity - AC and batteries? I am so far in the boonies that I have an LP gas-operated computer. |
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Post#16 @
03-02-03
, 11:47 AM
Beryl: Those slides rules work for diamonds that are cut with "regular" (even) girdles. Very cool, btw. When I was in Highschool, we still had to learn how to use slide rules to calculate logarithms etc. However, there are cuts such as EightStar or A Cut above that have irregular or "tweaked" girdles ("irregular" by design that is), for which those slide rules do not apply. The same holds true with the DiamCalc standard round brilliant model. For these tweaked girdle stones, other star facet/ crown break slope combinations apply. Do you have any slide rules for those cuts as well? Parsifal |
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Post#17 @
03-02-03
, 08:15 PM
Parsifal: . Logarithms are the basis of slide rules, not the opposite. I make them by plotting the logarithms of the factors in the formulas they solve (this also applies to nomographs). . The "Facet Slope Change Slide-Rules" of this thread solve the tangent-ratio formula. That is, given a set of reference slopes, stretching the stone vertically changes all slope tangents by the same ratio. . Because there are so many 'angles' in a faceted gem, I use the term 'slope' to describe a facet's angle from the girdle plane (like gunnery 'elevation'), and I use 'index' to describe the rotational angle of facets about the gem axis (like gunnery 'azimuth'). . With these slide rules I am changing the slopes only; the indexes stay the same, whether standard or 'tweaked'. The top and bottom view of the stone are unaffected by this change. . This has nothing to do with 'tweaking', or 'cheating', which is a modification of standard indexes; such 'tweaking' will be the same in both stones; only the slopes are changed. . There is another thread "Cutting Ovals", which involves changing standard indexes of a round to new indexes of an oval, using slide rules also. This does not include 'tweaking'. Bruce Harding, winner EFMLS Lapidary Award 1975. |
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Post#18 @
03-02-03
, 09:06 PM
Beryl: Ahh.. I see. Thank you for the explanation. As far as the slide rules are concerned: It was a long time ago in my life, but I'm pretty sure we used them to calculate logarithms, exp. powers, if I'm not mistaken, trigonometric functions. I should still have a couple of those, but they are probably stashed away in storage. Maybe I can dig them out someday... Greetings, Parsifal |
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. All the calculations of "Faceting Limits" were done with a slide rule (except, of course, addition and subtraction). The formulas at the end were easy to solve by slide-rule but must be transposed to solve other ways (see my notes if you have one of my copies). In 1975 there were no home computers and I did not have a calculator. In 1956 a calculator that would do square roots cost $1200! In 1981 I bought a computer that cost $100! . My slide rule was stolen in 1986 and I miss it when I have to design gear or pulley ratios for machines - just set the "1" on the ratio you want and look along the scale for available numbers that match. Nothing else is so easy. . In 1953 I won the contest to design the emblem (pin) for JETS (organization for high-school students who wanted to be engineers); it was a slide-rule because that was the common identifier of all types of engineering students. A girl on campus had said "I knew you were an engineer because you wore a slide-rule." (they hung from our belts). . Perhaps the greatest advantage of the slide rule (and nomograph) is that it does not give absurd precision, like angles discussed to two or more decimal places in some DT discussions. |
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Last edited by beryl : 03-03-03 at 06:35 AM.
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