[velcrovan]

The linked article references George Bain’s book on Celtic knotwork construction methods, but his son Ian Bain actually found a much, much better method, and argues convincingly that this, not his father’s, was the method used by medieval Celtic illustrators. Ian’s method more easily produces consistent rope widths (when done by hand), and addresses the issue of how to soften these angular turns which ruin the rope effect and produce a robotic grid.

The book is out of print now but it looks like you can borrow it on archive.org: https://archive.org/details/celticknotwork0000bain/mode/2up

[gilleain]

Interested in what Iain's method might be, but the method I like is:

1) Draw the 'skeleton' as a connected (simple?) graph in the plane

2) Place crosses at the midpoint of each edge

3) Connect the crosses with shortest (non-crossing!) connections (bit vague this, but is more obvious by hand)

4) Erase the crosses, and run over the line, assigning under/over as appropriate - you can also thicken at this step

This gives good free-standing knots, although may be more work for the dense knotwork in the OP's examples.

[gilleain]

Actually, this is described well in reverse here :

https://armory-rasa.tumblr.com/post/151872673763/drawing-wit...

[mcphage]

So I do agree with you that Iain Bain's methods is better than his father's, especially for us mere mortals. But George's method for consistent rope widths (step 1: draw them all the same width) did work better for me when I was getting a program to generate knotwork on grid of squares and rhombuses, where following Iain's method led to irregular rope widths because the angles changed.

[quag]

Thank you! I’ll have to take a look.