# Regular Curve on Parallel Lines in Illustrator

Hi Community!

I'm trying to draw a liberty-style image frame in Illustrator. You can see what I've made so far in the first image.

I am trying to always maintain the two parallel lines that compose the frame at the same distance and the curves as smooth as possible. I'm trying to do everything geometrically. However to obtain the curves I circled in my second image I just approximatively dragged the path handles and I'm not satisfied working that way.

Can somebody suggest me how to make those curves geometrically so that the two parallel lines are always at the same distance and the curves are as smooth as possible?

I suspect the solution involes drawing some circles, but haven't figured it out 100% just yet.

• Does this answer your question? Illustrator. Spacing between parallel lines of art brush Commented Mar 4 at 19:31
• If you cut lies at each intersection (or elsewhere to be honest) you can also offset the stroke in 2 directions, or expand it Commented Mar 4 at 20:06
• Commented Mar 4 at 20:11

Draw 1 stroke.. a centerline, if you will.

Expand the stroke.. and you then have a shape. Use Shape Builder to combine portions, then swap the fill and stroke...

I would also merely draw 1 corner this way - clean up any superfluous anchors - copy/reflect it for the other other corners, then connect the verticals/horizontals.

• thanks for the reply, great little graph! learning a lot from all of you. Commented Mar 5 at 9:31

Nearly the same is already shown, but here's a variation which uses numbers:

Image 1: The dashed circle has the same diameter (=D) as the 3/4 circle in the bottom left corner. The green line is rotated -45 degrees from the straight vertical. The red curves are 135 degrees parts of circles. Apply Object > Path > Add Anchor Points to a circle to get the needed intermediate anchors for splitting.

The smaller circles have diameters 0,41421*D. Actually the factor is irrational number sqrt(2)-1. If the bigger circle was 100 mm wide, the smaller circle should be 41,421 mm wide. The diameter is calculated for tangency in all points where a line meets an arc. The right arcs could be also made with the corner widget. (See note 1)

Image 2: The extras are removed, a straight line segment is added between the red arcs, all parts are joined (Ctrl+J)

Image 3: make an art brush - it's a horizontal line duplicated and moved downwards

Image 4: the art brush is applied. make the paths free by applying Object > Expand Appearance.

Image 5: the crossing is cleaned with the shape builder in remove mode (hold the Alt key)

Something else

Joining tangentially a circular arc and a straight line isn't smooth for everyone. Why? I do not know any psychological explanation, but in elementary mechanics a very obvious reason exists. If such joints are used for example in a railroad the passengers would sense violent thumps when the centrifugal force suddenly starts or stops. In that sense a Bezier curve could be a smoother transition between 2 straight lines. It's tangential and the curvature changes smoothly, there's no discontinuous curvature changes:

The lower one is a 180 degrees rotated copy. But just in this case using the shown Bezier curve would be a stylistic breakage, because you had already decided the bigger loops are circular arcs. Also they should be smoothed. It's done in the next image:

The blue curve is drawn in Inkscape, because there the pen has an easy to use spline drawing mode. The spline control points for the curved sections are the corners of the red squares.

These result has continuously changing curvature, which makes it also to look consistent, but that's, of course, only an opinion. Check yourself, if it could be used as a frame corner in your application

Another route to visual regularity is to use only one kind of curved sections. The next one with sharp corners in the left may be difficult to understand but it becomes trivial in the right when the legacy round corners effect is added and the black drawing jig ( 2 lines, 2 squares) is removed:

This is in Illustrator, but it's as easy in Inkscape. Thee path becomes free for other edits after applying Object > Expand Appearance (=Object to Path in Inkscape).

Note 1: This one could be constructed exactly (=parts snap) also without trigonometric calculations or the corner widget by starting from the small circles. The bigger circle is easy to draw after the rounded Z is made. The whole thing can be scaled afterwards to the wanted size.

Calculations and snapping are not a must in artistic work. The most important thing is to see what's the right look for certain purpose. The parts can then be made to fit acceptably as well by zooming in and eyeballing. Engineering is a different case.

• This is exactly what I was looking for! sorry if my question was a very basic, but learning a lot from your reply Commented Mar 5 at 9:22

You could use the Corner Widgets for this.

1. Draw everything as straight lines with a thick stroke like as shown below, and add an extra anchor in the long vertical stroke, and cut it here using the Scissors. Send the top piece to the back.

I've used the graphic you shared as a guide here, but you could use a grid and snap to grid to create everything.

1. Then select the corners and drag the Corner Widgets to create the curves

1. Finally add an extra stroke in the appearance panel, set the bottom stroke black and increase the width to form a black outline. Apply the same to the other vertical piece.

Obviously I've used pink strokes here so you can see everything clearly. You could of course set it to white afterwards.

• Thank you so much for the reply. I was looking for the kind of precise math @EricWillis gave me, but this also improves my skills at getting similar results very fast@ Commented Mar 5 at 9:30
• @BrokenFreeLancer You're welcome. I'm not sure you are aware of this, but the Corner Widget functionality enables you to create circular arcs without having to actually draw circles. see an example demonstrating this. It's basically a mathematical approach, but Illustrator is doing the maths. Commented Mar 5 at 20:45
• Yeah, I get it. I just like to have a better grasp on the math, it feels like that way I can build on the skill more later on :) Maybe it's just a bias I have to get over Commented Mar 6 at 13:49
• Rioght now to work fast I'm using your solution :) but I really appreciate having the other two to be able to break down in detail the steps of how the shapes are made/function Commented Mar 6 at 14:15