Generating non-overlapping rectangle test sets - testing

Question

Alas this is a university type question, but one im struggling with none the less.
I need to generate large test sets of rectangles, non-overlapping, that can then be used to test an algorithm that finds the adjacencies between them. The test sets will need to probably have upwards of 10000 - 100000 rectangles in them. Ive been searching the net for examples of how to generate test sets like this, but have come up with nothing. Im aware that I could use a purely brute force method, and every time a random rectangle is generated, check whether or not it overlaps with any of the other rectangles, but this seems like generating the test sets will end up taking days if not longer!
Any one know how to go about doing this, or at least where I should start looking?

Answer 1

I found your idea fun and challanging and therefore tried a solution by using a matrix.
Basicly, the idea is (when talking in pixels) to create a matrix of booleans of the same width and height as the square root of MaxWidthOfRectangle * (NumberOfRectangles) (just for simplicity the same width and height).
Next, for each entry in the matrix, generate a random rectangle between min and max bounds. and set all the bools in the matrix for the specific rectangle. Now when generating the next rectangle, you can simply check "around" the desired location to determine how much space you can occupy rather then having to estimate a size and compare with each other rectangle if it conflicts.
My code:
class RectangleGenerator
{
readonly bool[,] _matrix;
readonly int _size;
readonly int _minimalBoxSize;
readonly int _maximumBoxSize;
readonly Random _random = new Random(1);
readonly List<Point> _offsets;
public bool[,] Matrix { get { return _matrix; } }
public RectangleGenerator(int size, int minimalBoxSize, int maximumBoxSize)
{
_matrix = new bool[size, size];
_size = size;
_minimalBoxSize = minimalBoxSize;
_maximumBoxSize = maximumBoxSize;
_offsets = new List<Point>(size * size);
Reset();
}
public IEnumerable<Rectangle> Calculate()
{
while (_offsets.Count > 0)
{
Point currentPoint = _offsets[_offsets.Count - 1];
_offsets.RemoveAt(_offsets.Count - 1);
if (!_matrix[currentPoint.X, currentPoint.Y])
{
Rectangle rectangle;
if (TryCreateNextRectangle(currentPoint.X, currentPoint.Y, out rectangle))
{
// fill the matrix with the rectangle + padding
int startFillX = Math.Max(0, rectangle.Left);
int startFillY = Math.Max(0, rectangle.Top);
int endFillX = Math.Min(_size, rectangle.Right);
int endFillY = Math.Min(_size, rectangle.Bottom);
for (int fillX = startFillX; fillX < endFillX; fillX++)
for (int fillY = startFillY; fillY < endFillY; fillY++)
{
_matrix[fillX, fillY] = true;
}
yield return rectangle;
}
}
}
}
private bool TryCreateNextRectangle(int x, int y, out Rectangle rectangle)
{
int maxWidth = DetermineMaxWidth(x, y, _minimalBoxSize);
int maxHeight = DetermineMaxHeight(y, x, maxWidth);
if (maxWidth < _minimalBoxSize || maxHeight < _minimalBoxSize)
{
rectangle = Rectangle.Empty;
return false;
}
int width = _random.Next(_minimalBoxSize, maxWidth);
int height = _random.Next(_minimalBoxSize, maxHeight);
rectangle = new Rectangle(x, y, width, height);
return true;
}
private int DetermineMaxWidth(int x, int y, int height)
{
int result = Math.Min(_maximumBoxSize, _size - x);
for (int offsetX = 0; offsetX < result; offsetX++)
for (int offsetY = 0; offsetY < height; offsetY++)
{
if (_matrix[x + offsetX, y + offsetY])
{
result = offsetX;
break;
}
}
return result;
}
private int DetermineMaxHeight(int y, int x, int width)
{
int result = Math.Min(_maximumBoxSize, _size - y);
for (int offsetY = 0; offsetY < result; offsetY++)
for (int offsetX = 0; offsetX < width; offsetX++ )
{
if (_matrix[x + offsetX, y + offsetY])
{
result = offsetY;
break;
}
}
return result;
}
public void Reset()
{
// append for padding:
for (int x = 0; x < _size; x++)
for (int y = 0; y < _size; y++)
{
_matrix[x, y] = false;
if (_size - x >= _minimalBoxSize && _size - y >= _minimalBoxSize)
{
_offsets.Add(new Point(x, y));
}
}
_offsets.Sort((x, y) => x == y ? 0 : _random.Next(-1, 1));
}
}