Are there alternatives to inversion for finding these equations?

Why do we want to rewrite theta as 2 * pi * xi here? (What does xi_1 and xi_2 represent here?)

Could we sample on a square who have the same area and then convert it to the circle?

Why do we change r to be the square root of xi_2?

Are there generalizations of this for other shapes (e.g. in higher dimensions)?

Can we get the corresponding pdf from inversed Monte Carlo sampling?

Can we use it in a sphere?

I think we can use it in a sphere, by adding a dimensionality.

can this be applied to spherical objects

Are there alternatives to inversion for finding these equations?

Why do we want to rewrite theta as 2 * pi * xi here? (What does xi_1 and xi_2 represent here?)

Could we sample on a square who have the same area and then convert it to the circle?

Why do we change r to be the square root of xi_2?

Are there generalizations of this for other shapes (e.g. in higher dimensions)?

Can we get the corresponding pdf from inversed Monte Carlo sampling?

Can we use it in a sphere?

I think we can use it in a sphere, by adding a dimensionality.

can this be applied to spherical objects