## Math Time

Feel free to skip all of this.

### Changing the Grid

You can use any set of numbers you want, but if you want an even grid you have to follow a formula. For four layers, pick any number between 0 and 89 for the first layer. For the second layer, add 90. This gives you two sets of stitches at right angles to each other. For the third layer, add 45 to your first number. Finally, for the last layer add 135 to your first number.

If you use a different number of layers, you will need to change the numbers. Four layers seems to be a pretty good base for the FSL earrings, but you could get a nice triangle grid with 0, 60 and 120.

### Lining Things Up

Unfortunately, any time diagonal lines are involved, the lines will not intersect the way you probably want them to. This is because the density is measured as a perpendicular distance between the two lines of stitches, and the distance between pairs of diagonal lines on a grid is different than the distance between pairs of horizontal or vertical lines on the same grid. (Remember Pythagoras?) In the picture below, the distance between the red lines is greater than the distance between the green lines. (This is what we want, not what Generations is doing.)

How do we fix this? Do we even want to? Is there a reason we shouldn’t?

I don’t usually worry about it, because anyone close enough to see it is way too close for comfort.

However, the math teacher that still lives in my heart wants to figure this out.

The numbers in the following discussion apply to a 0, 90, 45, 135 configuration.

As far as I can tell, the only way to fix it would be to adjust the density of the 45 and 135 layers. According to the manual, the density numbers are set to control the distance between points of a satin stitch. 0.4 means the points on each side will be 0.4 mm apart. It doesn’t seem to correlate quite so nicely for filled areas.

If the density is set to 1.0, the lines are .51 mm apart as best I can measure (with magnification set to 1600% using the ruler tool). At 2.0, the lines are .99 mm apart. 3.0 gives lines 1.5 mm apart. I think we can say that the distance apart = density ÷ 2. Sure enough, density 10.0 measures 5.01 mm apart.

Another aside — I finally figured out what that second number on the ruler is. (Yes, I know — I could have just looked in the manual.) It’s the angle of the line the ruler is following. I’ve been careful to keep that angle at 90 as I measured between the two lines. You can also use the ruler as a protractor by moving the ruler and watching the second number instead of the first.

When the direction is set to 45, the lines are the same distance apart **measured along a line perpendicular to the two lines**. However, we want to to measure along the vertical or horizontal line, which gives a number that is longer. (This is the hypotenuse of an isosceles right triangle, so it’s about 1.41 times the perpendicular distance.)

As you can see in the picture, the two black lines are the same length. The two blue lines need to be the same length for the grid to line up so the diagonal lines need to be closer together.

If we reduce the density of the two diagonal layers, we’ll make the squares formed by the diagonal lines smaller. Using a density of 2 for the first two layers and 1.41 (the square root of 2) for the diagonal layers gets us pretty close.

However, they still don’t intersect where we want them to, even when we start with a square.

In this picture, the densities are set to 4.0 and 2.82. You can see that the two diagonal lines and the vertical lines intersect pretty well, but the horizontal lines are off.

Hmm. This sounds very familiar. Remember the Flower Font? In Motifs 1 I discussed adding a bump to the top of each letter to force the blooms to move up above the stems. The same procedure works here.

The grid is finally aligned. I still need to finish this up, and when I add the border, I need to be careful not to select the heart with the bump or my border will also have a bump.

If I needed to adjust the vertical lines, I suspect the bump should go on the left side of the heart.

Something to consider: If the lines all cross at the same points, will those points become too thick and cause issues when embellishments are added?

Each earring is about 2 1/4″ in each direction, not including the wires.

You are welcome to use these file to make objects for personal use or for sale. You may not resell or distribute the embroidery files. Be sure to test first.

When you remove the WSS, only wet the earrings enough to dissolve the WSS, but not to remove it completely. The residual WSS will stiffen the earrings. Save your scraps. If your earrings aren’t stiff enough, you can dissolve the scraps in water to make a stiffening liquid.

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Categories: Earrings, Freestanding Lace

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