random rectangle partitioning

[upbeat glade]

I need a method of generating a random partitioning of a rectangle into sub rectangles. This method must have a chance of generating any potential rectangle partitioning. Here is an example.

[sinful dust]

are the coordinates integers?

[upbeat glade]

yes

subpartitioning a w by h rectangle with everything integer coordinates

[sinful dust]

any other conditions?

like the number of rectangles?

[upbeat glade]

atleast n rectangles

thats it

it can be a little more

the naive solution is recursively splitting rectangles along the x or y axis

but that can't generate a lot of partitions

that are more complex

[sinful dust]

imma call

!xy

[split relic]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sinful dust]

maybe a bit more context behind this? i assume this is a programming task

[upbeat glade]

?

yes

I am making a puzzle game played on a rectangular partitioning grid

[sinful dust]

i found some answers for this online

https://cs.stackexchange.com/a/68645

https://stackoverflow.com/questions/71777511/divide-rectangle-in-random-sized-smaller-rectangles
here, a p5.js solution is provided

[upbeat glade]

thats the naive solution

i believe

ill read the first one

[sinful dust]

in the first one the answer was specifically avoiding it

[upbeat glade]

yeah... neither the second or first one can generate this

the first one implemented one specific case

but there's more than one of these rectangular partitioning that aren't just made by horizontal/vertical splits

i did some research on this

[sinful dust]

weird idea: what if you do the naive solution but then repartition some rectangles that are along the same axis?

like this

turn the orange and part of a purple rectangle into one (blue outline) and the rest of the purple one just keep as another rectangle

although i cannot guarantee that this will generate every pattern ever

[upbeat glade]

hm

this is the most basic one that can't be generated by the naive solution

i wonder if its possible with that technique

hm

ok yes it is possible cause what you would do is

have vertical lines at x=1 and x=3

have horizontal lines at y = 1 and y = 3

then merge some stuff

and you get that

not a bad solution but I feel like there has to be something more elegant

[proper ocean]

.close