Formula to calculate the coordinates of some points on a circle Given the following variables * $a$ : the number of points proportionally spread on a circle * $(O_x, O_y)$ : the origin of the circle * $\theta$ : the angle separating the points i.e. $360/a$ * $r$ : the radius of the circle how to get the coordinates of each point? Here is an illustration with three points, i.e. $a = 3$ and $\theta = 120$ **NOTE:** The $(x, y)$ axis is clockwise. * * * ![Illustration of equally spread points on a circle in a clockwise axis]( * * *

The angle separating point has to be $\frac{2\pi}{a}$ (using radians). Using the definition of $\sin$ and $\cos$ (and assuming that the first point has $\theta=0$), translating the points from the origin to the centre of the circle and applying a simmetry on the x-axis, we get the following:

Given the number $a$, you have: $p_i=\left(O_x+r\cos\left(\frac{2i\pi}{a}\right),O_y-r\sin\left(\frac{2i\pi}{a}\right)\right)$, where $p_i$ is the i-th point, and $0\leq i
I assumed that the passages should be easily understandable without the explicit calculation, if it is not the case I will insert them