dividing a circle into equal n blocks and then generate one point inside each block

how can I dividing a circle into equal n blocks and then generate only one point inside each block the circle radius is R and the blocks represent the users distribution inside the circle eg. if the circle radius 1 km and each block 1m by 1m (the border block may less than the block size)

If anyone can help me to do this, thanks in advance.

[John D'Errico]

Why would you not just use polar coordinates?

[Image Analyst]

Please upload a diagram of what you consider to be equal sized blocks.

[Walter Roberson]

What exactly is to happen at the border? Are the blocks to get smaller and smaller? Are you to use fixed-size blocks, but any block that has a presence inside the circle is to be allocated a point that must be inside the circle, thereby packing points closer together at the border?

[Walter Roberson]

Is the specification by length of the side of the blocks? or is the specification by number of blocks? Specifying by the number of blocks makes the calculation more difficult.

For example if the user specified that the circle of radius 1000 was to be divided into 57 square blocks, then it would not be possible to do that by dividing into squares in a way that was symmetric around the origin, as such a division would have at least 2-fold symmetry (typically more), which would leave you with an even number of blocks when an odd number was called for.

See http://www2.stetson.edu/~efriedma/squincir/ for examples of how complex it can be to optimally divide a circle into a fixed number of squares.

Answer 1

[Walter Roberson]

You cannot get exactly equal areas with any finite precision calculation system.

You can do "not so badly" by working in polar coordinates, and dividing up by angle.

sector_angle = 2*Pi/N;

rand_angle = ((0:N-1) + rand(1,N)) * sector_angle;
rand_rad = sqrt(rand(1,N)) * R;          %sqrt compensates for area getting larger away from center

[rand_x, rand_y] = pol2cart(rand_angle, rand_rad);