Question

I am writing an application which subdivides an N-dimensional axis aligned bounding box into smaller N-dimensional bounding boxes, I need an algorithm which will do this.

For example:

in 1 dimension a “bounding box” is simply a length
e.g. { Min=0, Max=100 }
which would be subdivided into
{Min=0, Max=50} and {Min=50, Max=100}

in 2 dimensions a “bounding box” is a square
e.g. {Min=[0,0], Max=[100,100]}
would be divided into
{Min=[0,0], Max=[50,50]}
{Min=[0,50], Max=[50,100]}
{Min=[50,0], Max=[100,50]}
{Min=[50,50], Max=[100,100]}

And so on, all I need is a description of an algorithm for doing this, language doesn’t particularly matter, since once I know how to do it I can translate it into the language of choice (C# in this case)

EDIT:: In response to questions in comments:

• subdivisions must always be equal (as
  in the examples)
• boundaries are
  floating points, so divisibility by two isn’t a problem

Answer 1

Break it into two problems: iterating over the grid of “Min” points, and constructing a small box for a Min point.

For your second case, {[0,0], [100,100]}, deltaX=50 and deltaY=50. The grid is

[0,   0]
[0,  50]
[50,  0]
[50, 50]

and it is trivial to construct the second column from the first:

[ 0,  0] [ 50,  50]
[ 0, 50] [ 50, 100]
[50,  0] [100,  50]
[50, 50] [100, 100]

Here’s a three-dimensional case {[0,0,0], [100,100,60]}, delta = [50, 50, 30]

[ 0,  0,  0] [ 50,  50, 30]
[ 0,  0, 30] [ 50,  50, 60]
[ 0, 50,  0] [ 50, 100, 30]
[ 0, 50, 30] [ 50, 100, 60]
[50,  0,  0] [100,  50, 30]
[50,  0, 30] [100,  50, 60]
[50, 50,  0] [100, 100, 30]
[50, 50, 30] [100, 100, 60]