3D Modeling and Carving Celtic Knots

I came up with a relatively simple workflow for modeling Celtic knots in 3D with Nomad Sculpt on the iPad and, took it through to doing vary power 3D carving on the Glowforge (as well as carving on a desktop CNC, resin printing and making single image stereograms). This is something I have wanted to be able to do for a long time but, my 3D modeling skills were not up to it and, every approach I had seen seemed like a slog. This probably requires some basic familiarity with Nomad Sculpt and Blender but, I came up with a trick to make the modeling easier than I expected. I can now knock out a simple knot model in about 20 minutes.

This is all very visual. So, I made a video on how to do it. I know some people don’t love those. I tried to keep it concise and, there are chapter markers for each section. TL;DW below the images.

Here are some photos of the carved pieces and one of the models. I did the Glowforge carvings on 1/4” basswood using the settings @MakerTales worked out. Char reduced with a toothbrush and water. Dried back out under heavy cement pavers to defeat curling. Shown next to CNC-carvings of the same designs.

More photos and stereograms with my blog post: Celtic Knots in 3D

The basic idea for building the knot in Nomad Sculpt is to lay it out with the tube tool between two surfaces. Then, make the top surface translucent, lock editing to the tube, use the tube tool’s snap to get the points to jump to the translucent upper surface.

Here is the terse version of how to create a depth map from the 3D model in Blender:

  1. Start with an empty scene
  2. Import model at origin
  3. Move camera to origin, point at origin
  4. Move camera to Z level just above model
  5. No lights
  6. Orthographic camera
  7. If necessary, use orthographic scale to fit in view
  8. Scene: Cycles rendering engine
  9. Scene: Film: check Transparent
  10. Scene format 2000px square
  11. 16-bit color depth
  12. View Layer: check the Z box under Data (and Combined)
  13. Render (?)
  14. In Compositing tab, check “Use Nodes” box
  15. Add Viewer
  16. Connect Depth from Render Layers to Normalize, to invert, to Gamma, to Viewer
  17. Adjust Gamma to get a good range of grays
  18. Connect Alpha from Render Layers to Viewer Alpha for transparent background
  19. In Render result window, center drop-down, pick “Viewer Node”
  20. Image → Save

You can also use RGB curve node in place of Gamma.

Edit: There is now a way to get a depth map straight out of blender. Details and a walkthrough video below.

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Very cool! Totally bookmarking this post for when I get far enough along building my house to need decorative elements! :slight_smile:

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I have a partial set of books on how to do knotwork and Celtic style calligraphy written by Aidan Meehan. They are really helpful when designing knotwork.

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Thank you so much for sharing the fruits of your labor. This will help and inspire others. Great job.

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I may have seen the Aidan Meehan books somewhere. They are very good.

George/Ian Bain’s Celtic Art: the Methods of Construction is also pretty great.

Adam Tetlow’s Celtic Pattern: Visual Rhythms of the Ancient Mind is less systematic and requires more study to decode but, has some clever observations.

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I used to have the whole set. An ex stole some of them, including The Dragon and the Griffin. I was a little upset. When I get a larger house and have room to set up my calligraphy work again I will replace the ones I am missing.

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I feel your pain. I had a similar experience with the George Bain book during a time when it was out of print.

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George and Ian Bain I had thought were the ones who first figured it out. Inkscape has a trick to break a single overlapping line, but Artcam had the really best I have seen able to layout all sorts of things. Originally it was thousands of dollars and needed a dongle but now is kaput I think, but there are broken copies about.

The math is very interesting and I think it is an easy thing to program if anyone with the skill would care to try. As long as it is only two lines crossing a single spot the math will always work out. The Ian Bain method of laying out an array of “X” shapes and connecting them works very well.

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I think the original Ian Bain stuff is c. 1951, IIRC. I have seen some other approaches that I don’t think are derived from the Bains’ work.

You can do a lot with simple grids, a few rules and, some aesthetic sense.

I use the Inkscape knot path effect in the video as a quick way to make the example knot. I have also done it the long way with more complicated knots.

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Those are phenomenal! I don’t understand how you got the rounded edges on the knots, but kudos!

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I don’t know about going around corners but rounding the shape is not hard. A sharp black and white division when engraved will make a sharp drop-off but a gaussian blur will be rounded.

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Your Celtic work is terrific! Thanks for the detailed depth map instructions. I will have to try again sometime—I did not get good results when I tried it in Blender with somebody else’s tutorial. Had to use Meshlab or https://3dp.rocks/lithophane/.

Off to watch the video!

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Thank you for sharing. I have been wanting to figure out how these 3d images are done… I’m headed into the rabbit hole, if you don’t hear from me in a day or two, please send a rescue team.

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New book on historical knotwork design techniques:

I haven’t seen it yet but, looks promising from the table of contents.

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I don’t have anywhere to store that book or work on knotwork right now so I am safe! LOL

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Alas, I have no such deterrent. I haven’t had time to look at it yet but, my copy arrived this afternoon.

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I got a chance to look through Knotwork By Hand and Eye a bit. It looks to be a pretty comprehensive treatment of the ‘five dot grid” method for creating Celtic knots. That is something you have likely seen described in much less detail elsewhere, if you have already done any knotwork. Carroll’s approach seems to be very systematized. He provides a list of a dozen rules that summarize the method. There is some coverage of fitting knots into circles, arcs and, irregular non-rectangular shapes.

The book is about 100 pages and, covers just this one method for making knots. It doesn’t cover key patterns, spirals or, any of the figurative stylistic flourishes (zoomorphics, human forms, floral forms). While it is solid and, would likely be a good limited introduction for someone interested specifically in making their own knots, it is a bit spendy for the scope.

As discussed above, there are some other excellent books by George Bain, Ian Bain and Aidan Meehan that are worth your consideration if you are considering getting into Celtic art.

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I think you just saved me the purchase. If it only covers that knotwork, I have Meehan’s work that I consider to be more than adequate for all my designs.

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About covers it as George gets into all the other stuff (spirals, zoomorphs etc) and his father Ian in the OG on it. The one thing worth looking at by someone with the programming chops is the math that makes it work. It would be amazing to have a Festi type program applying that math. Artcam has done that but it was outrageously expensive and now dead in any case.

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Array this however you wish and connect the ends and you have knotwork…
knot one