Matlab：如何在特定半径的圆上生成不均匀且不重叠的圆/矩形

Question

I want to generate a series of points as building in simulation.

Points density is 1/1000m^3

The points have its shape just like the real buildings(circle or rectangle or something else) In order to reach the reality, these shapes should not be overlapped. The question is how to generate the center point of these 'buildings'?

I tried this

clusterNumber = round((pi*areaRadius^2)/1000); 

radius = unifrnd (0,areaRadius,clusterNumber,1);
angle = unifrnd (-pi,pi,clusterNumber,1);

for i=1:clusterNumber
Coordinate(i,1) = cos(angle(i))*radius(i); % x
Coordinate(i,2) = sin(angle(i))*radius(i); % y

and the result showed as what I expected... it did'nt work When I used scatter it showed

So, my question is how to generate non-uniform and non-overlap circles or rectangles in a specific circle.

Answer 1

If you want your buildings not to intersect, you must check for intersections with already created buildings before creating one at your random position.

Of course, if you create many buildings, collision detection will be costly. You can speed it up with an efficient nearest neighbour search, for example with kd-trees or by creating a fine grid in the building space so that you have only a few neighbour cells to check.

Imposing the condition that buildings must not intersect will also alter your distribution. You will no longer have the marked clustering in the circle's centre. You still generate morre random positionsthere, but as your area gets more populated, most of them will be rejected.

Here's an example distribution:

Enforcing the criterion may also affect your algorithm: It might be a good idea to limit the number of randomly gerenated positions, so that you don't run into an infinite loop when no more buildings can be placed or when the probability to find a suitable space is very low.