Cutting the Cushport—Design L/W

Here is my Cushport design from my previous post for L/W=1.356, as downloaded from www.facetdiagrams.org.

Note the diagonal dimension:
 (2 2)/W=1.058
To get GemCad to display this diagonal dimension in the table of dimensions, label opposing facets on the girdle with the same name. See in the bottom view where there are two facets labeled 2? Anytime GemCad sees two parallel girdle facets at the same mast height labeled the same, it will add this diagonal dimension to the table of dimensions. It is important to note that this is not the distance from the tips of the arrows but is the distance you would measure if you put the jaws of your caliper flat against both the indicated facets. It's the distance between the planes of the two facets.

So how to we use these diagonal dimensions? Let's say, for the sake of discussion that we are cutting a piece of rough and we think we can get a stone of length 13 mm. The width for this pattern would be 13/1.356=9.59 mm. First off, make sure that the rough is at least this size. When cutting, we could cut step 1 facets alternately until we get to 9.59 mm (allowing an additional half to one mm to grind away when prepolishing). Then cut step 3 facets until we get our length 13 mm (plus some extra). Then cut step 2 facets alternately. But how deep? The diagonal dimension gives us a clue. Cut them alternately until the diagonal dimension measures 1.058*W=1.058*13/1.356=10.14 mm. Again, this dimension is not the distance between the tips of the arrows but is instead be measured with the jaws of the caliper measured flat to the girdle facets.

How to proof-cut the outline in GemCad? The trick is to type in some coordinate points in GemCad's Points field in the 90° New Facet Info box. First a review of GemCad's coordinate system. GemCad's x axis increases to the right, and the y axis coordinate increases down in GemCad's top view. The z coordinate increases up out of the screen. GemCad's coordinate system is in arbitrary units, not millimeters. A cube of two units on a side is about as big as will fit on the screen. Our stone needs to extend from -1 to 1 on the x axis and from -W/L to W/L on the y axis. For our example, W/L=1/1.356=0.7375.

Set the Symmetry to 2-fold, mirror-image. Next, enter the point (0, 0.7375, 0) on any of the 3 lines of the Points field of the New Facet Info box by typing "0 0.7375 0" without the quotes. Whenever the mouse focus changes, GemCad will reformat it, adding in decimal point and some zeroes. Then enter an Angle of 90° and an Index of 96. Click the Apply/Cut button, and GemCad will cut the pair of girdle facets at 96-48. 

Next, enter the point (1,0,0) by typing "1 0 0" without the quotes on any of the 3 lines in the Points field. Then enter an Angle of 90° and an Index of 20. GemCad will cut four more girdle facets, and our girdle outline should be a long hexagon. You should see L/W=1.356 at the bottom status line. You might have noticed that the z coordinates were zero. Why zero? Well, the z coordinate is arbitrary since girdle facets are parallel to the line of sight in the top view, so our z coordinates could have been anything, and 0 is easy to type.

To get the other girdle facets, we have to make use of the diagonal dimension. We will use the concept of Center-to-Facet Distance. This is the distance from the center of the stone, the point (0, 0, 0) to the plane of the facet. When your protractor is set at 90°, this is the distance from the axis of the dop to the plane of the lap. On some faceting machines, you can read off this distance on a calibrated ruler. In GemCad, we'll have to do a bit of math. Recall that our stone's length, the x coordinate goes from -1 to 1, so L=2 GemCad units. Our width W is 2 divided by L/W. W=2/1.356. Our diagonal dimension is 1.058W = 1.058*2/1.356. The center-to-facet distance is exactly half this distance, so it is 1.058/1.356=0.7802.

Enter 0.7802 in the Center-to-Facet Distance box, an Angle of 90° and an Index of 4, and GemCad will  finish the girdle outline. From here on, the design is pure meetpoint.

In my next post, we'll look at how to adapt this design for other L/W, even adapting it "on the fly."