Splines<a href="https://pixelfed.social/discover/tags/3StrandBraids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#3StrandBraids</a><br> <br> <a href="https://pixelfed.social/discover/tags/Braids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Braids</a> are the last of the <a href="https://pixelfed.social/discover/tags/decorative?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#decorative</a> elements on the <a href="https://pixelfed.social/discover/tags/IonicScroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicScroll</a>, but like <a href="https://pixelfed.social/discover/tags/EggsAndDarts?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#EggsAndDarts</a>, they are not specific to the <a href="https://pixelfed.social/discover/tags/IonicOrder?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicOrder</a>.<br> <br> Braids are a popular design motif that find wide currency in modern <a href="https://pixelfed.social/discover/tags/hairstyles?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#hairstyles</a>, <a href="https://pixelfed.social/discover/tags/fashion?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#fashion</a>, and fashion accessories like <a href="https://pixelfed.social/discover/tags/belts?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#belts</a> and <a href="https://pixelfed.social/discover/tags/bracelets?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#bracelets</a>.<br> <br> 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 <a href="https://pixelfed.social/discover/tags/Vignola?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Vignola</a>'s book and previewed in <a href="https://pixelfed.social/p/Splines/792015485979791089" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/792015485979791089</a>. The image here is brightly colored to draw attention to the 3 strands.<br> <br> 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 <a href="https://pixelfed.social/discover/tags/sinusoidal?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#sinusoidal</a> curve.<br> <br> A sinusoidal curve or <a href="https://pixelfed.social/discover/tags/sinusoid?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#sinusoid</a> is a wave form whose function belongs to a family of functions known as <a href="https://pixelfed.social/discover/tags/transcendentalFunctions?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#transcendentalFunctions</a> that also include <a href="https://pixelfed.social/discover/tags/logarithmic?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#logarithmic</a> and <a href="https://pixelfed.social/discover/tags/exponential?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#exponential</a> functions. I mentioned <a href="https://pixelfed.social/discover/tags/logarithmicSpirals?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#logarithmicSpirals</a> in <a href="https://pixelfed.social/p/Splines/792499765146596723" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/792499765146596723</a>, and in a future post I will show how to construct one and compare it with the spirals used in our implementation of <a href="https://pixelfed.social/discover/tags/IonicVolute?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicVolute</a>.<br> <br> 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.<br> <br> Few <a href="https://pixelfed.social/discover/tags/CAD?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#CAD</a> tools have a direct primitive for a sinusoid, but almost all have a primitive for a 3-dimensional round coil shape called a <a href="https://pixelfed.social/discover/tags/helix?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#helix</a> which we can use to create the sinusoids we need for a braid strand. To create s sinusoid, all we need to do is <a href="https://pixelfed.social/discover/tags/project?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#project</a> a helix on a flat surface to convert it into a 2D waveform.