zirkus

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Splines<a href="https://pixelfed.social/discover/tags/Milestone8?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone8</a> - <a href="https://pixelfed.social/discover/tags/SimpleIntercolumniation?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#SimpleIntercolumniation</a> Floor Plan of archetypal Greek Temple <a href="https://pixelfed.social/p/Splines/803021258359555093" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/803021258359555093</a> Front and back <a href="https://pixelfed.social/discover/tags/intercolumniation?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#intercolumniation</a> <a href="https://pixelfed.social/p/Splines/803076419096100108" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/803076419096100108</a> Side intercolumniation <a href="https://pixelfed.social/p/Splines/803089629244302486" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/803089629244302486</a> <a href="https://pixelfed.social/discover/tags/Milestone7?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone7</a> - Complete <a href="https://pixelfed.social/discover/tags/IonicOrder?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicOrder</a> <a href="https://pixelfed.social/p/Splines/800050647761776920" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/800050647761776920</a> <a href="https://pixelfed.social/discover/tags/Milestone6?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone6</a> — <a href="https://pixelfed.social/discover/tags/Braids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Braids</a> <a href="https://pixelfed.social/discover/tags/3StrandBraids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#3StrandBraids</a> <a href="https://pixelfed.social/p/Splines/799602946527813102" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/799602946527813102</a> <a href="https://pixelfed.social/discover/tags/Milestone5?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone5</a> — <a href="https://pixelfed.social/discover/tags/EggsAndDarts?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#EggsAndDarts</a> https://pixelfed.social/p/Splines/797069447808333887 <a href="https://pixelfed.social/discover/tags/Milestone4?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone4</a> — <a href="https://pixelfed.social/discover/tags/IonicScroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicScroll</a> https://pixelfed.social/p/Splines/795361973789834465 <a href="https://pixelfed.social/discover/tags/Milestone3?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone3</a> — <a href="https://pixelfed.social/discover/tags/IonicColumn?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicColumn</a> https://pixelfed.social/p/Splines/792803978865652429 <a href="https://pixelfed.social/discover/tags/Milestone2?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone2</a> — Classic <a href="https://pixelfed.social/discover/tags/IonicEntablature?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicEntablature</a> https://pixelfed.social/p/Splines/791021871062069787 <a href="https://pixelfed.social/discover/tags/Milestone1?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone1</a> — <a href="https://pixelfed.social/discover/tags/IonicPedestal?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicPedestal</a> https://pixelfed.social/p/Splines/790752092700055739

Splines<a href="https://pixelfed.social/discover/tags/Milestone7?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone7</a> - Complete <a href="https://pixelfed.social/discover/tags/IonicOrder?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicOrder</a> with fluted and unadorned <a href="https://pixelfed.social/discover/tags/IonicColumn?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicColumn</a> with details of <a href="https://pixelfed.social/discover/tags/decorativeElements?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#decorativeElements</a> <a href="https://pixelfed.social/discover/tags/Milestone6?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone6</a> — <a href="https://pixelfed.social/discover/tags/Braids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Braids</a> <a href="https://pixelfed.social/discover/tags/3StrandBraids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#3StrandBraids</a> <a href="https://pixelfed.social/p/Splines/799602946527813102" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/799602946527813102</a> <a href="https://pixelfed.social/discover/tags/Milestone5?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone5</a> — <a href="https://pixelfed.social/discover/tags/EggsAndDarts?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#EggsAndDarts</a> <a href="https://pixelfed.social/p/Splines/797069447808333887" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/797069447808333887</a> <a href="https://pixelfed.social/discover/tags/Milestone4?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone4</a> — <a href="https://pixelfed.social/discover/tags/IonicScroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicScroll</a> <a href="https://pixelfed.social/p/Splines/795361973789834465" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/795361973789834465</a> <a href="https://pixelfed.social/discover/tags/Milestone3?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone3</a> — <a href="https://pixelfed.social/discover/tags/IonicColumn?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicColumn</a> <a href="https://pixelfed.social/p/Splines/792803978865652429" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/792803978865652429</a> <a href="https://pixelfed.social/discover/tags/Milestone2?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone2</a> — Classic <a href="https://pixelfed.social/discover/tags/IonicEntablature?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicEntablature</a> <a href="https://pixelfed.social/p/Splines/791021871062069787" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/791021871062069787</a> <a href="https://pixelfed.social/discover/tags/Milestone1?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone1</a> — <a href="https://pixelfed.social/discover/tags/IonicPedestal?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicPedestal</a> https://pixelfed.social/p/Splines/790752092700055739

Splines<a href="https://pixelfed.social/discover/tags/Milestone6?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone6</a> — <a href="https://pixelfed.social/discover/tags/Braids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Braids</a> <a href="https://pixelfed.social/discover/tags/3StrandBraids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#3StrandBraids</a> <a href="https://pixelfed.social/discover/tags/Sinusoid?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sinusoid</a> from <a href="https://pixelfed.social/discover/tags/Helix?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Helix</a> <a href="https://pixelfed.social/p/Splines/797893262102038801" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/797893262102038801</a> Braid Geometry <a href="https://pixelfed.social/p/Splines/797916882329430160" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/797916882329430160</a> Braid Strand <a href="https://pixelfed.social/p/Splines/798252244743520392" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/798252244743520392</a> Braid Assembly <a href="https://pixelfed.social/p/Splines/799340150182400358" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/799340150182400358</a> Braid <a href="https://pixelfed.social/discover/tags/FlowOnSurface?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#FlowOnSurface</a> <a href="https://pixelfed.social/p/Splines/799514176049543252" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/799514176049543252</a> <a href="https://pixelfed.social/discover/tags/Milestone5?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone5</a> — <a href="https://pixelfed.social/discover/tags/EggsAndDarts?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#EggsAndDarts</a> https://pixelfed.social/p/Splines/797069447808333887 <a href="https://pixelfed.social/discover/tags/Milestone4?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone4</a> — <a href="https://pixelfed.social/discover/tags/IonicScroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicScroll</a> https://pixelfed.social/p/Splines/795361973789834465 <a href="https://pixelfed.social/discover/tags/Milestone3?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone3</a> — <a href="https://pixelfed.social/discover/tags/IonicColumn?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicColumn</a> https://pixelfed.social/p/Splines/792803978865652429 <a href="https://pixelfed.social/discover/tags/Milestone2?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone2</a> — Classic <a href="https://pixelfed.social/discover/tags/IonicEntablature?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicEntablature</a> https://pixelfed.social/p/Splines/791021871062069787 <a href="https://pixelfed.social/discover/tags/Milestone1?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone1</a> — <a href="https://pixelfed.social/discover/tags/IonicPedestal?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicPedestal</a> https://pixelfed.social/p/Splines/790752092700055739

Splines<a href="https://pixelfed.social/discover/tags/3StrandBraids?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#3StrandBraids</a> <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>. 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>. 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. 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. 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>. 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 <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.

Splines<a href="https://pixelfed.social/discover/tags/Milestone5?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone5</a> — <a href="https://pixelfed.social/discover/tags/EggsAndDarts?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#EggsAndDarts</a> Egg 2D <a href="https://pixelfed.social/p/Splines/796857354690493749" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/796857354690493749</a> Dart 2D <a href="https://pixelfed.social/p/Splines/796961505955555432" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/796961505955555432</a> Egg and Dart 3D <a href="https://pixelfed.social/p/Splines/797038670230603707" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/797038670230603707</a> Flow on ovolo surface <a href="https://pixelfed.social/p/Splines/797060809462854953" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/797060809462854953</a> <a href="https://pixelfed.social/discover/tags/Milestone4?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone4</a> — <a href="https://pixelfed.social/discover/tags/IonicScroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicScroll</a> <a href="https://pixelfed.social/p/Splines/795361973789834465" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/795361973789834465</a> <a href="https://pixelfed.social/discover/tags/Milestone3?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone3</a> — <a href="https://pixelfed.social/discover/tags/IonicColumn?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicColumn</a> https://pixelfed.social/p/Splines/792803978865652429 <a href="https://pixelfed.social/discover/tags/Milestone2?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone2</a> — Classic <a href="https://pixelfed.social/discover/tags/IonicEntablature?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicEntablature</a> https://pixelfed.social/p/Splines/791021871062069787 <a href="https://pixelfed.social/discover/tags/Milestone1?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Milestone1</a> — <a href="https://pixelfed.social/discover/tags/IonicPedestal?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#IonicPedestal</a> https://pixelfed.social/p/Splines/790752092700055739

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