Friday, July 16, 2004

Triangular Blocks and EQ5

Time to vent a little frustration at EQ5. It turns out to be extremely difficult to design a quilt that uses triangular blocks in a regular layout. The typical recommendation is to use a Variable Point layout and use a block with a pair of triangles into the two block halves, separated by the diagonal of the square. Yeah, this works, sort of, but the process can be made much easier.

Of course, the first problem you run into is how large should I size the blocks in the layout? Unfortunately, this requires the use of the dreaded "M" word. That's right, MATH!

A little geometry is in order here. The ideal shape for a triangular block is an equilateral triangle (one where all 3 sides are the same length). If you take an equilateral triangle, stand it up on one side, and draw a line from the middle of the base up to the top point, you have divided the equilateral triangle into a pair of tiangles called 30-60-90 triangles. A 30-60-90 triangle has some special properties, geometrically speaking. The hypotenuse (the slanty part as you are looking at it), is twice as long as the short leg (the one it is standing on....the part you split in half drawing the line). So, if you start with an equilateral triangle with 8 inch sides, and do the split like I said, the short leg will be 4 inches. That only makes sense, since you created it by splitting an 8 inch side in half!

Well, that's mildly interesting, and mostly useless . However, the other property is the length of the long leg (the one you drew). This leg will always be the square root of 3 times the length of the short leg. Huh? Ok, let's simply this, and use a magic number. The square root of 3 is 1.73205080756588772935274463415059....,
but for practical purposes, you can use the value 1.73, and, frankly, for many quilting purposes, you can use the value 1.75. That is "close enough" for real life applications.

Anyway, back to our equilateral triangle. If we want to create a triangle that is 8 inches on a side, we divide the length by 2, and multiply by 1.73. This gives us a height of 6.92 inches for the block. If you use the value 1.75, rather than the more accurate 17.3, the size becomes 7 inches. Note that this is only off by .08 inches. that is less than 1/12 of an inch, or 1/3 of 1/4 of an inch. Most quilters vary their quarter inche seam allowances by more than that margin, so the 1.75 number works very well.

Ok, back to my quilt layout. To create a variable point layout, I need to give the width and height of a diamond shape, not a triangle or square. So what size to I need? Well, the diamond is two of my equilateral triangles stacked base-to-base. We already know that this is 8 inches across the base, so my block width should be 8 inches. We've already calculated the triangle height at 7 inches, so my block height needs to be 14 inches. Voila, that part is done.

Of course, now we ask the obvious question: Why doesn't EQ allow me to ask for this automatically! Think about this a second....I had to use a calculator to tell the computer how to figure out something very common. Why doesn't EQ do this for me?

Ok, that is the easy part. The hard part of this process is yet to come. In order to get this to work, I need to create a block that contains a pair of triangles. when this block is set into the variable point layout with the proper rotation, EQ will distort the block into a diamond, making look like you actually using triangles. You can find an example of how to do this here.

This works "ok" if your block is very regular and is constructed mostly from straight lines or boxes. It can be somewhat mind boggling trying to picture the distortions, but the partition tools come in very handy for figuring out where nodes can be positioned. It gets even worse if you want to use curves.

Ok, time for another rant: Why can't I partition the edges of the blocks into nodes? I can parition any line I draw in the block properly, but I can't do this along the edges, which makes positioning very difficult. If you try to draw a line along the edge, it disappears so you can't select it....I've also found this to be an invitation to cause EQ5 to hang or crash when you save to the sketch book :-(

I have tried drawing a triangle block, to get the proper shape (using my magic 1.73 times the base formula). Once you have a triangle that looks the way you want, select all of the lines, duplicate the lines. Rotate the duplicated block by 180 degrees, and position it against the base of the first block to create a diamond.

Now you have a diamond, which we need to convert into a square block. This is where the process becomes painful, since I've found that you really need to use a secondary tool like CorelDraw to help in the process.

I made an attempt at doing this entirely in EQ5, with fairly disastrous results. In thoery, you should be able select all of the lines in the diamond, "squeeze" the top and bottom into a square, rotate 45 degrees to line up with edges, and then stretch the square out to the size of the block. In theory, practice and theory are the same. In practice, practice and theory are never the same! Without fail, saving this created block to the sketch book crashed EQ5. It was also very difficult to get the first "squeezing" process to create a correct square.

For this part of the process, I turned to CorelDraw. By drawing this block in CorelDraw, it proved possible to draw the diamond and created the skewed block drawing. I then saved the CorelDraw drawing as a bitmap, imported the bitmap into EQ5 as a tracing bitmap. Once it was resized to the block size, I then traced over the lines of the square to created my block.

In the case of the block I was trying to create, I needed to have some curved pieces in the block. When reshaped into a square, the curves ended up quite distorted from the orginal curves, so the tracing process in EQ5 required a bit of poking and prodding to edit the curves into the shape I was trying to trace over. However, when this was set into the variable point layout, these nicely warped back into the smooth curves I started with.

Time for another rant: Why doesn't EQ5 directly support creating triangle blocks or a diamond shaped drawing board setup?