What ‪@shawnrainbow.bsky.social‬ said: a geodesic on a sphere is an arc of a great circle (the shortest distance between two points on the sphere, measured on the surface of the sphere).

This contrasts with great-circle navigation, which feels natural on the sphere, but is non-trivial on a flat projection map.

This trajectory is NOT the shortest path between the start and destination points, but the simplicity of navigation far outweighs the extra distance in practical cases.

That spiral trajectory is called LOXODROME (or rhumb line) and is the reason why Mercator projection got so popular: Sailors could plot a course by drawing a straight line and following a constant compass bearing.

Thank you. For the time being, this is just a small private prototype. Not meant to be distributed or bundled in a way that would be useful outside my project's needs.

Related links:

healpix.sourceforge.io/index.php

And @redblobgames (always!) observablehq.com/@redblobgame...

This system provides O(1) angle<->patchID queries (no spatial trees required), and is fairly low-distortion and reasonable-looking when unfolded.

I struggled with the implementation a little more than I anticipated, but here it is!

Feng-Shui, Zen decoration with cute/warm visuals. I bet that many people would dig that setting/aesthetic.

Useful related links:

@redblobgames -> www.redblobgames.com/x/1842-delau...
and -> github.com/Fil/d3-geo-v...

- Stereograhically-project all other points.
- Add 3 auxiliary points creating a triangle large enough to contain all other 2D points.
- Do classic 2D Delaunay on the projected point set.
- The 3 aux points map to the point we picked as pole. The rest of points map to themselves. Done!

- For better stability, take the point that is the furthest from its nearest neighbor in the sphere (I am using euclidean kdtree k=2) here.
- Rotate the pointset so said point becomes the top pole to send its projection to infinity while all other points will have a finite projection.

If you take points on a sphere, project them on the floor from the top pole with stereographic proj., and compute the (2D) Delaunay there, you get the exact same triangle connectivity as if you'd triangulated directly on the sphere. Stereographic proj. preserves DT's "empty circumcircle" property.

I know, right?

In layman’s terms: distributions of samples that are roughly equally spaced, yet do not exhibit any noticeable pattern (as a regular lattice would). In more formal terms: distribs of samples whose spectrum lacks low-frequency components => they are devoid of low frequencies in the spectral domain.

Congrats! The demo release is coming closer and closer!