Partition a rectangle into near-squares of given areas

Posted by Marko Dumic on Stack Overflow See other posts from Stack Overflow or by Marko Dumic
Published on 2010-03-28T14:32:29Z Indexed on 2010/03/28 15:23 UTC
Read the original article Hit count: 195

Filed under:

algorithm

|

rectangles

I have a set of N positive numbers, and a rectangle of dimensions X and Y that I need to partition it in N smaller rectangles such that:

the surface area of each smaller rectangle is proportional to it's corresponding number in given set
all space of big rectangle is occupied and there is no leftover space between smaller rectangles
each small rectangle should be shaped as close to square as feasible
the execution time should be reasonably small

I need directions on this. Do you know of such algorithm described on the web? Do you have any ideas (pseudo-code is fine)?

Thanks.

© Stack Overflow or respective owner

Related posts about algorithm

Jpeg Algorithm vs BMP Algorithm?

as seen on Super User - Search for 'Super User'
I'm just wonder, what the differences are between creating a BMP file algorithm and JPG file algorithm ? If you know the others images' format algorithm, please post them. Thanks. >>> More
word disambiguation algorithm (Lesk algorithm)

as seen on Stack Overflow - Search for 'Stack Overflow'
Hii.. Can anybody help me to find an algorithm in Java code to find synonyms of a search word based on the context and I want to implement the algorithm with WordNet database. For example, "I am running a Java program". From the context, I want to find the synonyms for the word "running", but the… >>> More
Search algorithm (with a sort algorithm already implemented)

as seen on Stack Overflow - Search for 'Stack Overflow'
Hello, Im doing a Java application and Im facing some doubts in which concerns performance. I have a PriorityQueue which guarantees me the element removed is the one with greater priority. That PriorityQueue has instances of class Event (which implements Comparable interface). Each Event is associated… >>> More
Is there any algorithm for finding LINES by PIXEL COLORS on picture?

as seen on Stack Overflow - Search for 'Stack Overflow'
So I have Image like this I want to get something like this (I hevent drawn all lines I want but I hope you can get my idea) I need algorithm for finding all straight lines on it by just reading colors of pixels. No hard math, no Haar, no Hough. Some algorithm which would be based on points… >>> More
collsion issues with quadtree [on hold]

as seen on Game Development - Search for 'Game Development'
So i implemented a Quad tree in Java for my 2D game and everything works fine except for when i run my collision detection algorithm, which checks if a object has hit another object and which side it hit.My problem is 80% of the time the collision algorithm works but sometimes the objects just go… >>> More

Related posts about rectangles

Move 3 rectangles up in their X but keep order of rectangles

as seen on Stack Overflow - Search for 'Stack Overflow'
I have 3 rectangles being rendered here. Let's say i wanted to move them all above the line yet keep their order, how would i go about that? I tried subtracting the Y and height rather than adding the Y it but as expected, the lower rectangle goes at the top, middle stays in the middle and top goes… >>> More
Triangle - Rectangle Intersection in 2D

as seen on Game Development - Search for 'Game Development'
I had previously asked this for 3D but now I changed my strategy and would like to do the intersection in 2D. The Rectangle is axis aligned and will always be in a fixed position, and has a constant shape and size, basically I want to clip the red areas of the triangles that extend outside the bounds… >>> More
Ray-plane intersection to find the Z of the intersecting point

as seen on Game Development - Search for 'Game Development'
I have a rectangle in 3d space (p1, p2, p3, p4) and when the mouse rolls over it I need to calculate the exact Z of the point on the rect, given the mouse coordinates (x, y). Would a Ray-plane intersection find the Z of the intersecting point? Edit: Would this one-liner work? .. it returns the… >>> More
Algorithm to reduce a bitmap mask to a list of rectangles?

as seen on Game Development - Search for 'Game Development'
Before I go spend an afternoon writing this myself, I thought I'd ask if there was an implementation already available --even just as a reference. The first image is an example of a bitmap mask that I would like to turn into a list of rectangles. A bad algorithm would return every set pixel as a 1x1… >>> More
Algorithms for positioning rectangles evenly spaced with unknown connecting lines

as seen on Game Development - Search for 'Game Development'
I'm new to game development, but I'm trying to figure out a good algorithm for positioning rectangles (of any width and height) in a given surface area, and connecting them with any variation of lines. Two rectangles will never have more than one line connecting them. Where would I begin working… >>> More