

THAT WAS THEN,
THIS IS NOW
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.
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, 120...you would merely apply the appropriate conversion
factor: Divide 360 by the index number, then multiple each number
in the string by that factor.)
For ease of
visualization, I make the gem rough a cylinder in my model, and the
cutting machine stays a cube. 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 straightforward as they seem. Stay tuned for further adventures in the virtual lapidary arts. Unfortunately, I have since learned, from people who do fulltime 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. 
