The Tomoe Symbol
After designing the triquetra and posting on RampantPixel I started thinking about other ancient symbols. The tomoe is an ancient Asian symbol. I thought that there may be some folks out there that may want a little help with the construction so I worked out some geometry to post.
The design looks something like two commas formed into a circle. There are other geometries that can be used to make tomoe. I chose this as fairly easy to create and it is attractive. There is an article on tomoe on Wikipedia http://en.wikipedia.org/wiki/Tomoe.
Tomoe Construction Geometry
I started with three different sizes of circle, made copies and aligned them.
As you can see, all of the circles are centered using Vertical Align Center. They are also all grounded to the top or bottom points of the largest circle. The large red circle is about 620 pt in diameter. The blue circles are about 460 pt and the smallest circles are 300 pt.
Tomoe Construction Steps
- Draw five circles: 1 circle 620 points in diameter; 2 circles 460 points in diameter; 2 circles 300 points in diameter
- Select the large circle and one of each of the other sizes.
- Click the largest circle again to make it “most selected.” (This prevents it from moving during alignment.)
- Click Vertical Align Center
- Click Horizontal Align Bottom
- Deselect everything (click on empty artboard or click Select > Deselect)
- Select the largest circle.
- Select the two remaining circles not aligned.
- Click the largest circle again (most selected).
- Click Vertical Align Center.
- Click Horizontal Align Top.
- Now you should have the construction in Figure 2.
- Make a copy of your construction and work on the copy.
- Select the entire construction.
- Choose the Shape Builder Tool.
- Set the fill color to black or another dark color.
- Move the Shape Builder cursor to one of the small circles (I started on the lower shape).
- Click and drag the cursor over the areas that make up the “comma shape.”
- Release the mouse to see the newly formed area.
- Repeat the Shape Builder action on the upper comma shape.
- Ungroup the construction by clicking Object > Ungroup (Shift + Ctrl/Cmd + G).
- Click one of the commas and shift-click the other so that they are both selected.
- Move them away from the remaining construction lines.
- Group the Tomoe design by clicking Object > Group (Ctrl/Cmd + G)
- Remove the stroke by setting it to None.
A Little More About the Geometry
The circle sizes I chose give the design these relationships.
- The small circle is about 48% of the size of the large circle.
- The medium circle is about 74% of the size of the large circle.
I have noticed that in constructions where the smallest circle must be moved away from the outer circle (see the next section) that the join between the small and medium circles makes an abrupt change in direction. This join needs some manual smoothing. It doesn’t need the extra work in the form presented here, in my opinion, Because the tail of the next shape balances the transition and makes it pleasing to the eye. When that tail bypasses the head of the comma it starts to look uneven.
Different Tomoe Geometries
This is only one of many possible geometries for making a tomoe. The comma tails can run either direction. They were commonly made with three and four comma shapes in the circle. The thiple form of the tomoe is called mitsudomoe in Japanese. The construction becomes a bit more complex because the comma shapes begin to overlap their neighbors. When this happens the circle that makes the head of the comma shape must be moved away from the outer circle to make room for the tail of the next comma shape.