The next stage in virtual facetting

As I have continued in this virtual lapidary hobby, I have been able to correct earlier mistakes and refine my techniques. I had always been certain that facetting, needing as it does, precision, should prove to be well suited to a computer simulation of it's effects. I studied the available charts for cutting instructions and (finally) have been able to convert the system used.

To begin with, we'll take a look at a common set of cutting instructions such as is found in various lapidary magazines and websites.

Strickland, Robert W;
TFG Newsletter, Oct 92, v13n4p29
Angles for R.I. = 1.76
65 facets + 16 facets on girdle = 81
4-fold, mirror-image symmetry
96 index

1 42.50 02-22-26-46-50-70-74-94
g1 90.00 02-22-26-46-50-70-74-94
2 42.00 96-24-48-72 Meet P1 at girdle
3 41.50 04-20-28-44-52-68-76-92 Meet at girdle
~~~~   (and so on...)

As you can see, a bunch of numbers with little explanation. (Of course, you *could* take a lapidary class and get instructions that way. LOL) But with a little study, and comparison of those numbers to a final product, the explanations come.

The first column (1, g1, 2, 3, etc.) tells which set of facets is to be worked on. Each set will be cut at one angle (the angle found in column two). But it is that group of numbers in the third column which confused me for the longest time. They weren't angles, ---what were they?

The shoe finally dropped when I began to look at all the information in the cutting instructions. I noticed that each set of instructions had something called an *index* number, and the string of numbers in the third column never got bigger than that number. By experimentation, I was able to convert those index numbers into angles which could be used in a modelling program. In the example above, a "96 index" meant that a 360 degree circle is divided into 96 parts, each index unit equal to 3.75 degrees. (There are other index settings, such as 80 index, 60, would merely apply the appropriate conversion factor: Divide 360 by the index number, then multiple each number in the string by that factor.)
The table above could then be re-written like this:

1 42.50 7.5-82.5-97.5-172.5-187.5-262.5-277.5-352.5
g1 90.00 7.5-82.5-97.5-172.5-187.5-262.5-277.5-352.5
2 42.00 0 (360)-90-180-270
3 41.50 15-75-105-165-195-255-285-345
~~~~   (and so on...)

Given the conversions, I could now start the 'cutting' as described in the instructions. First, I created a 'gem rough' and the stand-in for the cutting machine. (Unlike actual facetting, my cutting and polishing occur in the same step--since each cut is exact, there are no *flaws* to smooth out or polish away.)

For ease of visualization, I make the gem rough a cylinder in my model, and the cutting machine stays a cube.

In this side view, the cube (the cutting machine) is rotated on it's Y axis to the amount shown in the first column of the cutting instructions.

Then the gem rough is rotated on it's Z axis to the settings in the third column, and the proces of cutting away the excess begins. (In 3d modelling terms, I use a Boollean subtraction to accomplish this, retaining the cube each time for the next operation.)

The following is a visualization of various steps along the way.


After the pavilion (the bottom) is complete, I rotate the gem rough 180 degrees on the X axis and begin work on the crown (the top). And so on, until the gem is completed.

By this method, I can now create a much more precise model of gemstone cuts, as well as allow for much greater complexity of designs. One of the projects I am working on would have been impossible to contemplate by my older method.

Would you want to do this by hand and eye only?

But the learning goes on. There are still some elements that have to be adjusted by eye and experience. Not all cut designs are as straight-forward as they seem. Stay tuned for further adventures in the virtual lapidary arts.

Unfortunately, I have since learned, from people who do full-time 3d modeling, that this method leads to what are called "inverted normals". This means that when the Boollean cut is made, the 'cutting' block's 3d information takes precedence, and the remaining 'gem' can have display problems when rendered. Fortunately, it's a simple matter in most 3d programs, to specify the command "Invert normals" or "Unify normals" to correct the problem.