Edge distribution points evenly distributed on circle

Question

We have a circle of radius R on which we evenly spread points. We are interested in the distribution of points by radius and polar angle that you get after transforming the even distribution of $f_X(x, y) = 1/\pi R^2$, from cartesian coordinates (x, y) to polar coordinates (r, φ) and specify the edge distributions sought. Check if the edge distributions are normalized.

I do not want solution the the problem, beacause i know that this is agains the policy on this platform, but i want hints how to tacle this problem.

score 0 · Accepted Answer · answered Jun 12 '21 at 11:31

0

Think about the area made by increasing the radius from $r$ to $r+dr$. The number of points will be in proportion to the area.

answered Jun 12 '21 at 11:31

John Hunter

13,700

What does $f_X(x,y) = \frac{1}{\pi R^2}$ actually represent here. – Edward Henry Brenner Jun 12 '21 at 12:01

score 0 · Answer 2 · answered Jun 12 '21 at 15:15

If your points are evenly spread around a circle, they are separated by an angle of $360^o$/N, where N is the number of points. Choose a starting point, and if needed, convert from polar to Cartesian coordinates. If you want the points spread over the area within the circle, it is a much more complex problem. Do you want them at the corners of squares or triangles, and then, how do you deal with the curved boundaries? Do you require symmetry?

Edge distribution points evenly distributed on circle

2 Answers2