A series of points are plotted on a unit radius sphere, see image above.
Each point represents a vector coming from the origin.
First, points on XY and XZ planes are created using a certain equal angle increment for fi and theta respectively.
Then the rest of the points are built, one at a time, row by row, based on condition that angles between the resulting four points are the same.
The point circled in while is created first, preserving angles marked by white lines, then the point circled by red is created preserving angles marked by red lines and so on.
This is done by solving proper equations for each group of four points (3 of which are always known) numerically.
There is no need to cover the whole sphere with this pattern, only a part of it, as shown on the image.
My questions are:
Is this type of plot well known? If so, does it have a name?
Is there (a way to come up with) an analytical formula for this distribution?
What is the fastest (preferably analytical) way to "map" a given point on a sphere, shown as a green spot on the image, to its respective "row" and "column" of the distribution?
Thank you!