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