Monday, August 25, 2014

Adapting the Cushport On the Fly for L/W=1.25

This post builds on the previous one, so please read that post first. The length-to-width given in the header of the diagram is L/W=1.356, but let's say we want to cut it for L/W=10 mm by 8 mm=1.25 instead.

How to get started? When cutting on your faceting machine, you could start by cutting the stone to width. Cut the two step 1 facets at 90° at index settings 96 and 48. Alternate until the width is about 8.5 or 9 mm (to allow for progressing to finer laps). Then cut the four step 2 facets at 90° at 20-28-68-76. Alternate until length is 10.5 or 11 mm again allowing you to "sneak up" on the final 10 mm width when you pre-polish.

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 8 by 10 stone needs to extend from -1 to 1 on the axis and from -0.8 to 0.8 on the axis.

Set the Symmetry to 2-fold, mirror-image. Next, enter the point (0, 0.8, 0) on any of the 3 lines of the Points field of the New Facet Info box by typing "0 0.8 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=1.250 at the bottom status line. You might have noticed that the 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.

OK. Now we need to cut our last set of four girdle facets. On the faceting machine, cut facets at 90°at 04-44-52-92. How deep? Cut until the outline shape looks pleasing and until you cut away any flaws and you get 4 good corners.

In GemCad, you can just set a point by eye to cutting depth. Another way is to enter the 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 with a scale. I found that for this L/W, a center-to-facet distance of 0.85 gave a pleasing outline, to my eye. Type in 0.85 in the Center-to-Facet Distance box. Enter an Angle of 90°and an Index of 4, and GemCad will cut the last 4 girdle facets.

On the faceting machine, for our 8 by 10 mm stone, another way to reproduce this shape is to cut until the opposing facets are 8.5 mm apart (rough cut to 9 or 9.5 mm apart) with the calipers flat to the opposing facets.

Here is our girdle outline:




Now let's cut the rest of the pavilion using our diagram at the end of the last program--the one with the wrong L/W.




Not too bad, considering. Now we have some decisions to make. If I were cutting a valuable piece of rough, I probably wouldn't worry too much about the bad meets at 3 and 5. After all, in a commercial appraisal, good meets don't add to the value of the stone. If the poor meets bother you, you can make them meet by using your cheater when pre-polishing or even polishing. In GemCad, you can fix them by giving GemCad 3 points and letting it figure out the index and angle. Note that we could get facet labeled Y to meet by lowering its angle and leaving its index alone. However, if you click on points 4 and 6, put your cursor inside facet Y, click and select Uncut/Recut, you will find that the angle needed is below the critical angle for quartz. It would be fine for corundum, though. If you click on points 4, 5 and 6, selecting Use to Cut each time, then click in Y and click Uncut/Recut, and click the Apply/Cut button, GemCad will change mostly the index instead of angle. Similarly you can do the same thing for points 1, 2, and 3 and facet X. Here is the result:




Facet X ended up at 56.5 at index 6.7. Facet Y ended up 42.2 at index 21.2.

at With GemCad, you can label the opposite girdle facets with the same number, and GemCad will show that flat-to-flat dimension in the table of dimensions. Here, I labeled both of them 3, and it shows (3 3)/W=1.062 in the table of dimensions. For our stone, with W=8 mm, this dimension is 1.0625 x 8 = 8.50 mm. This corresponds to our 0.85 center-to-facet distance that we typed in.

Now we can transfer and cut the crown. When we use the angles and indices for the wrong L/W, we get the following:



Facet Z can be re-cut, cheating to meet points 1, 2, and 3. Here is the result:

While not the prettiest arrangements of facets, everything meets up, and the resulting stone will be pleasing. For reference, facet Z ended up at 27.6° at index 18.6.

Another possibility for this design is the idea of cutting to constant mast height instead of constant angle. Notice that this design has several sets of facets cut to the same angle but at different mast heights. Since this is a generic design, we could equally well cut adjacent steps using the same mast height but slightly different angles without changing the general look of the design. Depending on which adjustment is easier, it might make sense to leave the mast height alone and adjust the angle instead.

So, what have we learned? Meetpoint faceting is not always the best approach--adapting on the fly to the shape of the rough, eliminating flaws as you go is a valuable skill. By proof-cutting with GemCad, you can work out ideas for how to adapt on the fly. With this design, you can save all of the adjustments to the very end by cheating in one or two key sets of facets. If you want to make this design fully meetpoint for your L/W of choice, GemCad gives you the tools to do this. Diagonal measurements can be a useful preforming technique.

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