Drawing semi-randomly placed squares of various size and rotation

Programming Questions

bigbugbuzz

Drawing semi-randomly placed squares of various size and rotation

in Programming Questions • 2 years ago

Hi Everyone,

I wonder if someone can help me here. I am new to Processing. The following is a subset of a problem I am working on, and I hope that if someone can show me how to solve it, then I can work out the solution to the whole problem.

* I need to draw N squares on the screen (where N may be 1 to 25).
* The centre a given square is one of the corners of a 4 by 4 grid.
* The length of each square in this grid is G, so that the total length of the grid is 4G.
* To ensure non-overlapping squares, the maximum length of a given square is L = G/sqrt(2)
* The actual length of each drawn square is a random number from 0 to L.
* The rotation of each square drawn is random.
* No square may share the same centre (grid point).

Please see the diagram below for a visual aid.

Replies(7)

martin846

Re: Drawing semi-randomly placed squares of various size and rotation

2 years ago

I am not quite sure what the problem is here... given that the maximum length L ensures that squares cannot overlap, can't we simply pick N random points on the grid and lay down the squares? In other words, this is not an algorithmic problem, but simply one of drawing the squares?

bigbugbuzz

Re: Re: Drawing semi-randomly placed squares of various size and rotation

2 years ago

Hi Martin,

The formula for maximum square size L = G/sqrt(2) only ensures none-overlapping squares if squares have a centre at one of the 25 points on the grid. If the centres were much closer together, as might happen if centres were placed at random, then L = G/sqrt(2) would cause an overlap somewhere if 25 squares were drawn.

//BigBugBuzz

martin846

Re: Drawing semi-randomly placed squares of various size and rotation

2 years ago

The formula for maximum square size L = G/sqrt(2) only ensures none-overlapping squares if squares have a centre at one of the 25 points on the grid.

I thought that this was the case, given the constraint in your original question:

* The centre a given square is one of the corners of a 4 by 4 grid.

Does this actually mean that only one square (out of the N) has its centre at a yellow dot?

bigbugbuzz

Re: Re: Drawing semi-randomly placed squares of various size and rotation

2 years ago

The centre a given square is one of the corners of a 4 by 4 grid.

This means that any square drawn, must have a centre at one of the 25 dots in the diagram. Now, squares drawn cannot have the same centre. This is why there are 25 dots and N is at most 25. In other words, squares drawn have different dots as their centre.

martin846

Re: Drawing semi-randomly placed squares of various size and rotation

2 years ago

OK, lets look at some code. This is my interpretation of the problem:

http://www.openprocessing.org/visuals/?visualID=27591

Do I have it correct?

bigbugbuzz

Re: Re: Drawing semi-randomly placed squares of various size and rotation

2 years ago

Hi Martin, that is exactly right! Thank you very much for your excellent help!

martin846

Re: Drawing semi-randomly placed squares of various size and rotation

2 years ago

Cool, glad I got it right :-) I think I was a bit confused when I started reading the description, because it sounded like one of those classic algorithmic programming problems - you know, like how to fit as many squares on a grid as possible without overlaps - so I thought it was more complicated than it really was!

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