A library for unions, intersections, subtractions, and xors of rectangles.
The result of set operations on two rects are shown by the green regions below:
Let's say we have the following rects:
+------------+ +--------+
| | | B |
| +-----------+ |
| A | C | |
| +-----------+----+
| |
+------------+
And we want to represent the region A + B - C:
+------------+ +--------+
| | | |
| +---+ +---+ |
| | | |
| +---+ +----+
| |
+------------+
One method is to divide the area into a series of mutually exclusive horizontal bands:
+------------+ +--------+
| | | |
+--------+---+ +---+----+
| a | b | c | d <- 2nd band with walls at a, b, c, d.
+--------+---+ +----+
| |
+------------+
Each band is a vertical interval and a list of walls. Each contiguous pair of walls indicates a new rect in the band.
A Region is a list of sorted, mutually exclusive bands.
To use rects, construct an initial Region from some rect and iteratively +, -, &, or ^ with other regions:
>>> from rects import *
>>> r = Region.from_rect(Rect(0, 0, 200, 100))
>>> s = Region.from_rect(Rect(25, 10, 75, 40))
>>> t = Region.from_rect(Rect(75, 45, 125, 50))
>>> r
Region(bands=[Band(y1=0, y2=100, walls=[0, 200])])
>>> v = r - s - t
>>> v
Region(bands=[
Band(y1=0, y2=10, walls=[0, 200]),
Band(y1=10, y2=45, walls=[0, 25, 100, 200]),
Band(y1=45, y2=50, walls=[0, 25]),
Band(y1=50, y2=95, walls=[0, 75]),
Band(y1=95, y2=100, walls=[0, 200])
])
>>> list(v.rects())
[
Rect(x=0, y=0, width=200, height=10),
Rect(x=0, y=10, width=25, height=35),
Rect(x=100, y=10, width=100, height=35),
Rect(x=0, y=45, width=25, height=5),
Rect(x=0, y=50, width=75, height=45),
Rect(x=0, y=95, width=200, height=5)
]
>>> v.bbox
Rect(x=0, y=0, width=200, height=100)