Generalizing a yin-yang for the nth degree
Continuing my brief foray into things yin and things yang, I have decided to do some generalization.
My earlier yin-yang works are rotating a yin-yang in 2 planes and rotating a triple yin-yang in three planes.
When working on my triple yin-yang, I spent a bit of time calculating the correct positions of the circles that this shape is drawn from. I tried approaching it from various directions, and eventually found something that worked for three parts.
When I made the three part yin-yang three-dimensional, I noticed that it would clip into itself. And even after my best efforts to mitigate this, I couldn't get it to rotate cleanly without clipping.
I decided to try "higher-order" yin-yangs (with more than three parts) to see if there was a point at which the clipping would no longer be an issue, but I wanted to first develop a simpler method of creating the things; one that would be generalized to any value of n.
After about a hour's work, here is the result.
• r_1 is the radius of each yin "head"
• n is the number of pieces in the ying-yang-+ (for any value greater than 2)
• a is the angle (rotation) of the whole thing
• The gradient can be customized in the "color" folder.
I have yet to try any of these higher order yin-yangs in 3d, but this alone is pretty fun to play with.