I am attempting to distrubute objects evenly in concentric circles according to the following rules.
- There will always be 1 object at the centre of the plane at $(0,0)$.
- Each circle will have n elements which need to be distributed.
- The number of each element in the circle is known as k.
- The circles level, known as h, starts at 1 at the center object.
- Every element has a parent, of which it has a direct relation. Each element should be at one level more than its parent.
- No element shall have more than 1 parent, or be its own parent.
- A parent may have 0 to many children.
- With the exception of the first circle, each element should be distributed in respect to the elements parent to no more than half of its parent's angle.
- This image gives more context here but a way of explaining this is if each parent has a pie wedge, which is half way between it and k-1 and k+1, then each child element should sit between these two points.
- The radius of the circles is known as r.
The purpose of this is to generate a hierarchy of people and who they report to in an organisation.
I can currently generate the second circle's distribution via the formula:
- x = Parent_x + r cos(2kπ/n)
- y = Parent_y + r sin(2kπ/n)
However, I am unsure as to how to proceed for h >= 3