As I've played around with my soft and hard transition ideas, I've found it helpful to move around the hand and poi paths of some popular moves in Illustrator and other graphics editing programs, but my technique for doing so has left a lot to be desired. Essentially, I've been putting the proper variables into an online spirograph program (located at http://wordsmith.org/anu/java/spirograph.html and mirrored below), taking a screencapture of the result, and importing it into Illustrator using the livetrace function.
Needless to say, it's not perfect. For one thing the graphics are too small for Illustrator to get all the detail it needs to create perfect vector drawings. For another the results are slightly pixelated, so the intersections of lines tend to get fudged a bit.
So, to try and create better antispin flowers and more importantly CAPs (because this program won't create them), I built these figures by hand in Illustrator using a more precise method. So, if anybody else out there is interesting in drawing your own poi charts, these are tools you can use if you're so inclined. I have each diagram in AI, EPS, JPG, and GIF format. For a full accounting of the method used for rendering these shapes, see below.
Also, for anyone who would like to monkey with the source file, here it is:
Granted, this may be a primitive approach, but it worked in an albeit time consuming kind of way. For the distance between any two flower petals, I'm operating on the assumption that the poi will complete a complete period or cycle of rotation (360 degrees in other words) and that the number of petals dictates how many degrees of arm rotation must be completed for each period of poi head rotation. In other words, for a three-petal flower the poi completes a rotation relative to hand position every 120 degrees (1/3 of 360). I decided on an arbitrary level of detail that there would be 8 positions tracked between the completion of each petal. Ergo, for a triquetra between each petal I would track 8 positions that would rotate the hand position a total of 120 degrees for every 360 degrees of change in poi head position.
To track this difference, I created hand circles of both two poi lengths across and three poi lengths across to scale the triquetra and four-petal antispin flowers respectively given that my own poi lengths represent 1/3 of my armspan from thumb to thumb. I then added a single line using the line tool in Illustrator to represent the poi leash and made it a single poi length in comparison to the hand path circles and began tracking by way around each circle. I made an additional line for purposes of rotational symmetry in Illustrator to ensure one end of the line would always be on the hand path.
For the 4-petal antispin flower, I tracked distances of 11.25 degrees (1/8 of the 90 degrees between each flower petal) and inclined the line by 40 degrees at each position (360 degrees of a complete circle divided by the 8 steps of detail) and used Illustrator's snap to grid function to place one end directly at the point of intersection with the hand path circle. I performed this operation as many times as was necessary to have a complete series representing all 36 positions of detail for the poi orientation around the hand path circle.
The procedure for the triquetra was identical except that I tracked distances of 15 degrees (1/8 of the 120 degrees between each petal, 1/3 the distance around the circle) for every 40 degrees of rotation by the poi head.
Once I had a complete series of individual snapshots of poi position around the hand path circle, I used the create path tool to add a point of intercept on a new layer near each point that would be occupied by the poi head. Illustrator would occasionally assume I meant to join the path to the preexxisting line, so I had to draw them slightly off, then individually re place the points as hear as I could to the end of the line for each point of intercept.
Finally, I converted each point to a curve using Illustrator's built-in tools. The curve is not perfect, however, and I may attempt this method again later with a higher degree of detail, such as 12 or 16 points between petals.
To derive the CAP, I took the 4-petal flower and removed half the intercept points before adding an additional point near the sole remaining petal and connecting the path once again. I used a circle drawn within Illustrator itself to match the curve properties of the extension to make it as round as possible.
Enjoy playing with these!
Here is the original spirograph program I used:The Spirograph applet is written using Java. You must turn on Java or have a Java-enabled browser such as Firefox or Microsoft IE to see this applet.