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Celtic Knot

· One min read
Toby Yegian

The Celtic Knot was one of my biggest projects and one of the ones I'm most proud of. It involved taking the Celtic knot from the image below:

img

and turning it into an interactive mathmatical knot. The design followed multiple iterations, first with a set of two b-splines multiplied over each identical quarter of the knot. The effect was very "loopy", and while interesting was not what I had intended.

loopyknot

loopyknot2

I then attempted to make the curve sharper at its points and simpler in construction. Ultimately, with some help from Prof. Sequin, I redefined my knot as a set of four short b-splines (it turns out a new one was needed for each sharp corner) multiplied over each eighth of the knot. The result was quite accurate:

goodknot

And for good measure, I then added a second identical knot and parametrized every dimension I could think of, allowing for manipulation of the design into very fun shapes.

funknot1 funknot2 funknot3

At some point, I hope to export some of these models and 3D print these awesome shapes.