It seems like whether or not this simple strategy works depends on which coordinate system we decide to use. Is there a general way to tell if the strategy will work for a given coordinate system?
enzyme
I think this isn't uniform because the sampling distribution is denser towards the center of the circle.
bepis
This does not produce a uniform sampling because the number of points on a circle increase by a power of 2 as radius increases, so if we pick the angle and radius uniformly the sampling will be denser in the center and become less dense towards the outer edges of the circle.
It seems like whether or not this simple strategy works depends on which coordinate system we decide to use. Is there a general way to tell if the strategy will work for a given coordinate system?
I think this isn't uniform because the sampling distribution is denser towards the center of the circle.
This does not produce a uniform sampling because the number of points on a circle increase by a power of 2 as radius increases, so if we pick the angle and radius uniformly the sampling will be denser in the center and become less dense towards the outer edges of the circle.