This method simulates a random polygon. We choose random angles until . The coordinates of points are then given by where are independent random radii between 0 and 150.
(Note that the intervals of and are arbitrarily chosen.)
Uniform distribution of points on the unit sphere
This method simulates random points on the unit sphere by sampling random angles theta in . The coordinates of points are then given by . The parameter defines the number of points and the radius of the sphere.
Random beta polygon
This method simulates a beta polygon created by independent identically distributed random points with density
For more details, see https://arxiv.org/pdf/1805.01338.pdf.
Here a short description of the simulation of the model:
* Choose the number of points
* Choose a parameter
* Sample random angles
* Sample radii that follow the probability density:
by using the inverse transform sampling:
– simply draw a random number uniformly from
* Coordinates of points are then given by r*(cos(theta), sin(theta))