#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.