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#belts

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#3StrandBraids

#Braids are the last of the #decorative elements on the #IonicScroll, but like #EggsAndDarts, they are not specific to the #IonicOrder.

Braids are a popular design motif that find wide currency in modern #hairstyles, #fashion, and fashion accessories like #belts and #bracelets.

Braids come in infinite varieties with varying number of strands, thickness of strands, roundness or flatness of strands, and how tightly or loosely they are wound together. Here, I focus on the 3-strand variant mentioned in #Vignola's book and previewed in https://pixelfed.social/p/Splines/792015485979791089. The image here is brightly colored to draw attention to the 3 strands.

The geometry of braid strands is not at all obvious despite how familiar they look. Also, a braid strand is the only feature in the entire iconic order whose geometry cannot be captured with straight lines and circular arcs. Instead, a strand geometry must be defined in a series of steps starting with a basic #sinusoidal curve.

A sinusoidal curve or #sinusoid is a wave form whose function belongs to a family of functions known as #transcendentalFunctions that also include #logarithmic and #exponential functions. I mentioned #logarithmicSpirals in https://pixelfed.social/p/Splines/792499765146596723, and in a future post I will show how to construct one and compare it with the spirals used in our implementation of #IonicVolute.

They are called transcendental functions because they transcend the math of finite algebraic polynomials and go beyond geometry into trigonometry. Fortunately, we don't have to go there.

Few #CAD tools have a direct primitive for a sinusoid, but almost all have a primitive for a 3-dimensional round coil shape called a #helix which we can use to create the sinusoids we need for a braid strand. To create s sinusoid, all we need to do is #project a helix on a flat surface to convert it into a 2D waveform.

Here's a bit of how I #work .

I make my patterns myself - the ones I use to cut out pieces for #leather #goods and the ones I use for a #handcarved #decoration .

Two of these #leather #belts are decorated by a pattern that are inspired by #Estonian #folkart .

The other two are decorated by a sort of pattern that makes them #unique as they're cut onto the leather without any prepared drawing.

So as there is no #written #proof of the making process - are they #real or are they #myth ?

Je suis hyper content de ma ceinture en jute minimaliste, avec que des noeuds, du tressage, du torsadage.
Très efficace, une des meilleures ceintures que j'ai jamais eues!!
J'ai dû à l'instant rajuster mon nœud de huit, ça a dû un peu travailler !
Du coup j'aimerai en faire une plus large, un peu plus technique, mais toujours avec le même principe, qui déchire.
Merci Clifford W Ashley!!