On Periodic Tilings with Regular Polygons

The Periodic Table for Spatial Analysis - GIS Geography

The Periodic Table for Spatial Analysis lists 90 tools for quantifying, finding patterns, and predicting outcomes in a geographic context.

Splines (@[email protected])

#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 #spiral 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 a sinusoid, all we need to do is #project a helix on a flat surface to convert it into a 2D waveform.