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philconex
Participant
January 14, 2025
Answered

Rotation precision issue (MINDF*** LEVEL = 10/10)

  • January 14, 2025
  • 2 replies
  • 468 views

Hi Guys,

I'm reaching out to you because I'm struggling with a problem. Here's the data:
1. I have a set of three circles (diameter 485 mm, 490 mm and 495 mm) that are dead-on concentric. Ruler has been zeroed on the center.

2. Their sizes are evenly distributed: +5mm in diameter each time, so 0.25mm in radius from one to the next. This means, the space between the inner and outer circles is 5 mm.

3. There's another small circle at 3 o'clock (5mm in diameter) whose center is vertically aligned with the center of the three big circles.

  • THE GOAL: I need the small circle to be positionned 8° above his original 3 o'clock position, following the perimeter of the circles, so that the small circle remains exactly between the inner and outer circles.

  • THE PROBLEM: When i realize a parametric rotation of 8° using the center of the three circles, the small circle is slightly OFF the inner and outer circles (see printscreens). IT DOESN'T MAKE ANY F SENSE: everything is correctly aligned and concentric. All three circles are perfectly round. THIS IS DRIVING ME MAD. This will be laser cut parts that need to be perfectly concentric, that's why I need precision.

 

MY PROCESSS
1)  Overall situation

 

2) Small circle starting point: perfectly aligne between the inner and outer circles.

 

3) I select the small circle, select the rotation tool and ALT-CLIC on the origin of the three circles, set 8 degrees and clic OK.

 

4) the small cercle seems to be at the right location at first glance but when you zoom, you see it's off.

5) the result: I tried everything...

 

Can somebody tell me WHY is it? I just don't understand and I've tried other rotation methods, grouping the small circle with a straight horizontal line etc. Nothing works.

 

My conclusions: either I'm missing something super obvious or there's something wrong with Illustrator.  PLEASE HELP ME!!! Thanks in advance!

 

[abuse removed by moderator]

 

Correct answer Doug A Roberts

I believe this is the bezier circle accuracy problem that comes up from time to time.

The issue is that circles constructed from bezier curves are necessarily inaccurate.

If you copy and repeat that rotation multiple times, you'll find that the small ellipse tends towards the inner of the lines at around 22.5 degrees, then back to centre at 45 degrees. This is because ellipses made from four anchor points bulge slightly compared to a 'true' circle where the red lines are in this example:

The difference is tiny but apparent in situations like yours. This is not strictly an Illustrator problem, but one in any software that uses bezier curves to construct ellipses.

 

You can mitigate it by creating circles from more segments. I use this circle script:

Circle – scripts for designers

 

I replicated your construction with a 32-point circle. This is the small ellipse at the 8 degree point:

 

2 replies

A
Anthony26310869o6wa
Participant
January 14, 2025

Try selecting the three large circles along with the small red one, then rotating them all together.

 

It won't solve the bulge problem mentioned by Doug A Roberts, though, so it depends exactly what tolerances are acceptable for your laser cutting.

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philconexAuthor
Participant
January 15, 2025

Hi Antony, thanks for having taken the time to reply.

That's one of the first things I had tried initially. Didn't work. Although the circles' dimensions were equal in both width and height, I noticed the perimeter was slightly off. As if the 4 main handles were not exactly the same length. And as far as I have understood @Doug A Roberts's answer just above, this might be the manifestation of what he describes.

As for laser cutting tolerances, I haven't measured the offset of circles but I prefer when things follow the number without needing to pray for everything to work as planned.

 

Thanks a lot anyway!

Doug A Roberts
Community Expert
Doug A RobertsCommunity ExpertCorrect answer
Community Expert
January 14, 2025

I believe this is the bezier circle accuracy problem that comes up from time to time.

The issue is that circles constructed from bezier curves are necessarily inaccurate.

If you copy and repeat that rotation multiple times, you'll find that the small ellipse tends towards the inner of the lines at around 22.5 degrees, then back to centre at 45 degrees. This is because ellipses made from four anchor points bulge slightly compared to a 'true' circle where the red lines are in this example:

The difference is tiny but apparent in situations like yours. This is not strictly an Illustrator problem, but one in any software that uses bezier curves to construct ellipses.

 

You can mitigate it by creating circles from more segments. I use this circle script:

Circle – scripts for designers

 

I replicated your construction with a 32-point circle. This is the small ellipse at the 8 degree point:

 

    P
    philconexAuthor
    Participant
    January 15, 2025

    Hi and many thanks for your reply!

     

    The script did work perfectly! Anchor points fall exactly at the tangent of the inner and outer circles, I think that might be the result of the relationship between the number of points of the small circle (32) and the angle of the rotation (8°).


    The funny thing though is that I've never encountered this situation in my career before! I've been working for a long time in the watches industry where - from times to times - I had to design watch dials, with the radial repetition of different elements. I learned something new!

     

    Thanks a lot for your help!

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