I was wondering about the “correctness” of the z-axis movement for the spherical helix. You could pick lots of different functions, including simple linear motion (z = c * t). This would obviously affect the thickness and consistency of the “peels”. The equation used creates a visually appealing result but I’m wondering what a good goal would be in terms of consistency in the distance between the spirals, or evenness…
I think this particular function was selected because it happened to be convenient to program and the visual effect was pleasant enough.
The actual "correct" thing to do would probably be to have the point maintain constant speed in 3D space like a real boat sailing on a globe, right? But that's a rather bigger lift:
const degrees = Math.PI / 180;
const bearing = 5 * degrees; // or it might be 85 degrees? Not sure off the top of my head
const k = Math.tan(bearing);
const v = 0.001 // some velocity, adjust as needed
const phi = (t) => v*t/Math.sqrt(1 + k*k) // the sqrt is not strictly needed
const theta = (t) => k*Math.ln(Math.tan(phi(t)/2)) // this is the annoying one haha
const x = (t) => Math.sin(phi(t)) * Math.cos(theta(t))
const y = (t) => Math.sin(phi(t)) * Math.sin(theta(t))
const z = (t) => Math.cos(phi(t))