Next problem:
This is an arbitrary polygon. It should be covered with 100% minimum number of circles of a given radius.
Note:
1) Naturally, the circles must intersect. 2) I am trying to solve the problem for ARBITRARY polygons. But decisions are also being made for CONVEX landfills. 3) As far as I know, this problem is NP-hard (an algorithm for finding the minimum cover size for a problem with installation coverage ) Choose: U = polygon and S1 ... Sk = circles with arbitrary centers.
My solution:
I already read several articles and tried several things myself. The most promising idea that I came up with was actually already mentioned in Covering an arbitrary area with circles of equal radius .
So, I think that best of all I will quickly try to describe my own idea, and then I will clarify my questions.
The image gives you a pretty good idea of what I'm doing.
1. R2, .. ; - . (... , , )
2. - , .
Im, N, , , , "" N.
:
, ( ). , , .
:
, :
1. 3 * r ( = r) .
2. y r ^ 2 + r ^ 2-2 * rrcos (2/3 * pi) .
3. phi 2/3 * pi.
, .
, stepize (x, y, phi) , .
1) ? , , .
2) ?
3) : , , , . , - , .
, , , , .
, , .
PS matlab