create various topologies of a structure

hello guys. I want to plot various positions of coordinates, inside a given rectangle. In other words, a rectangle is given and I have to mark various positions in the rectangle such that each position is at a distance of at least 3 units from its surrounding positions.

For example, if I have a rectangle of 10X15 units , then one of the set of configurations of positions will be points marked at all the four vertices . The other set of configuration can be all vertices and the midpoints of sides.

Similarly certain finite configurations will result. The positions marked can be inside of rectangle.

[Guillaume]

The more barrier you put in understanding your question, the less likely are people to read it, and the less likely you'll get an answer.

Using proper grammar and punctuation and formatting your post into paragraphs makes it easier to read. I for one, couldn't read your post to the end without my eyes glazing over.

[Ace_ventura]

I am sorry for my bad english. I have edited the question. I hope it helps.Please look into it.

[Guillaume]

Your post is certainly much clearer now.

Isn't the most efficient way of packing your rectangle with vertices to create a diamond pattern?

[Ace_ventura]

I want all the ways in which it can be packed. The points might lie inside of it not just vertices. I will then employ genetic algorithm to find, one of the optimums. But for this case, I just want the various configurations that may result when we try to impose above said conditions_(points not less than 3 unit distance). I hope it is clear

[Guillaume]

I must be missing something, because isn't there an infinity of possible vertice position?

For example, suppose your locate your first vertice on a corner. A second vertice can then be located at distance [3 to length of rectangle] side onto the side of the rectangle. That interval includes an infinity of points.