How do I create symmetrical curves on vector shapes in Photoshop?

Question

Let's say I want to make a mark representing the shape of a rotor in a rotary engine:

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This shape is similar to a Reuleaux triangle:

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I know how to create equilateral polygons in Photoshop, but I do not know how to create curves that have the same curve handle (is that the right term?) on both ends.

• How do I modify lines into curves and keep them symmetrical?

• By the same token, how can I then make other lines symmetrical to the first line, especially when they are at odd (non-right-or-45° angles)?

• In general, what is the best way to keep elements of shapes symmetrical when modifying them? Right now, I resort to lots of copying, pasting, flipping, and combining.

Note: I realize there are instructions on the Wiki-page for constructing a Reuleaux triangle using circles, but that only applies to an exact Reuleaux triangle where it is a curve of constant width. I am interested in creating a shape that may have shallower curves and is therefore no longer a curve of constant width. In addition, this is a principle I've run into more than once, so I'm interest in general principles for creating and working with symmetrical vector lines.

Answer 1

I drop lots of guides.

Create your triangle. Add an anchor point somewhere in the middle of the left-hand side, then use the Convert Point tool to drag it out and set up the Bézier handles where you want them. Drop guides on the anchor point and the end points of both handles.

On the right-hand side, add an anchor point. Drag it out until it matches the guide, and tweak the handles until they match up with the second and third guides.

You may have to rotate it 60 degrees to do the third side, but it beats copy-paste-join paths.