Creating Animated Toroidal Evolutionary Wavefronts
An “evolute” (short for Toroidal Evolutionary Wavefront Path) is an expression of toroidal geometry and dynamics. The animated path traverses the surface of a torus, defined by the number of “loops” or “turns” around the torus. With the Cosmic Geometry toolkit, you are able to create an “evolute” of any height-ratio, and any number of turns. Clicking the “extrude” button creates 3D printable geometry!
A note about the algorithm… the algorithm was developed to create a “balanced” toroidal path which was equidistant from itself as it cycled about the torus, holding to the rule that a single “turn” of the evolute path will revolve about the lateral plane and radial plane a full 360 degrees respectively, returning to it’s original position. Here’s an example of a single turn evolute built with spheres.
The “evolute” is animated by default, with a full progression around the torus surface, determined by the number of frames in a “cycle”. For a static evolute, set the “cycle” number to 1. You can also animate the radius and height-ratio of the evolute, by clicking the check-box near the top.
You can create “evolutes” constructed from curves, or with these polygonal default primitives: sphere, torus, or plane. Using these settings, uniform geometries are created about the evolute path; not connected with a “curve” but visually represented by the collection of geometries. The “planes” can be toggled to “face camera”, which eases the setup for use as image-planes.
Below are a few examples to create basic Evolute Paths. Click on the image for an actual screen shot with the toolkit settings visible on the right.
And, with a little texturing and lighting magic, something like this is quickly achieved… (batteries not included) 🙂