Making seamless pattern with tilted lines on rectangle

[ingunnbergferstad]

I need to make a seamless pattern with tilted lines in a rectangle. This is meant for clothing, so I can't just use the patternmaking features in Illustrator, it needs to be a proper seamless pattern.

I found this thread: Creating seamless pattern from slightly tilted lines  and I do believe that I need a similar solution, but I just can't seem to figure out how to do the math myself...

The rectangle's size:

W: 173,202 mm

H: 99,978 mm

There should be only two stripes (preferably), and the tilted lines should (preferably) be about -55 degrees or close to that.

Is this mathematically possible to pull off somehow?

How much distance is needed between the two lines?

And how do I know where to place them in the rectangle?

The only thing I can't change here are the proportions between width and height of the rectangle. If the number of tilted lines or the degree of the tilt must be changed to make this work, I'm absolutely open to that, my mentioned preferences are just approximates, based on what I think would look best on the pattern.

Would be extremely grateful for any help!

Ingunn

[Jacob Bugge · Accepted solution]

Ingunn,

I am afraid the only solution with just two lines is an angle of -40.889 degrees with the lines starting at opposite corners (upper left and lower right) and ending at the midpoint of the opposite (lower/upper) side.

It can be constructed without any calculations as follows, Smart Guides being your friends:

1) Create the rectangle 173.202 x 99.978;

2) Click the Artboard with the Line Segment Tool and set the length to 86.601 (half the width), then deselect and ClickDrag by either end to snap to the relevant end of the top side (Smart Guides say anchor), this gives you the modpoint;

3) With the Line Segment Tool ClickDrag from the lower right corner of the rectangle to snap to the midpoint;

4) Ctrl/Cmd+C+F, then deselect, then ClickDrag with the Selection Tool by the upper end to snap to the left end.

Now you should have the two lines on top of the rectangle; you can delete the line from 2.

You can copy everything (maybe after grouping), then move copies up/left/right/down to snap to see the pattern work.

It can be done differently with three/more lines.

[ingunnbergferstad]

Jacob, thank you very much for the reply.

If I were to try with three or more lines, how should I go about it?

[Jacob Bugge]

Ingunn,

With three lines you will get (very close) to 60 degrees, using the following revised construction:

1) Create the rectangle 173.202 x 99.978;

2) Click the Artboard with the Line Segment Tool and set the length to 57.734 (a third of the width), then deselect and ClickDrag by the right end to snap to the right end of the top side (Smart Guides say anchor), this gives you the thirdendeal point;

3) With the Line Segment Tool ClickDrag from the lower right corner of the rectangle to snap to the thirdendeal point;

4) Object>Transform>Move by 57.734 selecting Copy;

5) Ctrl/Cmd+D to repeat 4).

I have noticed that the proportions of the rectangle correspond very closely to a line between opposite corners of 30 degrees/60 degrees; that proportion is 173.205:100 (or 173.166:99.978 or 173.202:99.998 if either length were to be retained).

Is there any reason to keep the exact original lengths rather than (one of) the exact 30/60 degree equivalent(s)?

[ingunnbergferstad]

Thank you so much again, I'll have to try this out a little later today. The reason I have to stick to the original lengths is because the lines are supposed to be on top of another artwork that has these exact lengths, and I can't make changes to that artwork.

[Jacob Bugge]

Ingunn,

I see your limitation; I believe it may have started out as (an attempt to hit) the 30/60 degree proportions with a slight inaccuracy.

And here is the general answer for any number:

1) Create the rectangle 173.202 x 99.978 or 173.205:100 (or 173.166:99.978 or 173.202:99.998);

2) Click the Artboard with the Line Segment Tool and set the length to the width divided by then number of lines, then deselect and ClickDrag by the right end to snap to the right end of the top side (Smart Guides say anchor), this gives you the first endpoint;

3) With the Line Segment Tool ClickDrag from the lower right corner of the rectangle to snap to the first endpoint;

4) Object>Transform>Move by the length of the line (the width divided by then number of lines) selecting Copy;

5) If the desired number of lines is more than two Ctrl/Cmd+D to repeat 4) until you are done.

As you can see (at least if you try it), the angle of the lines will be:

2 lines: -40.889 degrees

3 lines: -59.995 degrees, closest to the -55

4 lines: -66.583 degrees

I hope you will share your findings.

[ingunnbergferstad]

Screenshots of the patterns. The first one is the end result when making two lines, and the second is the end result when making three lines. Because I made the lines quite thick, I had to add a little bit of black in the corners to make it line up perfectly with the lines that cross in the opposite corners. But that was an easy fix, the difficult part was figuring out everything else, so THANK YOU so much for helping me out!

[Jacob Bugge]

You are welcome, Ingunn.

And thank you for sharing.