Python求两个矩形相交的面积

Question

我一直在尝试使用shapely来寻找给定两个点的两个矩形的交点，然后我可以将其扩展到四个点，所以我现在有类似这样的东西……

from shapely.geometry import Polygon

polygon = Polygon([(-3, 2), (1, 2), (-3, -2), (1, -2)])
other_polygon = Polygon([(2, 1), (-1, 1), (2, 4), (-1, 4)])

if polygon.overlaps(other_polygon):
  print( polygon.intersection(other_polygon).area )
else:
  print(0)

这些点通常存储为变量，但为了减少我在这里抛出的代码量，我去掉了所有的逻辑和多余的信息，但本质上这就是传递的内容。但它一直在抛出这个错误，我不明白shapely为什么生气……

TopologyException: Input geom 0 is invalid: Self-intersection at or near point -1 0 at -1 0
Traceback (most recent call last):
  File "main.py", line 66, in <module>
    print( polygon.intersection(other_polygon).area )
  File "/opt/virtualenvs/python3/lib/python3.8/site-packages/shapely/geometry/base.py", line 676, in intersection
    return geom_factory(self.impl['intersection'](self, other))
  File "/opt/virtualenvs/python3/lib/python3.8/site-packages/shapely/topology.py", line 70, in __call__
    self._check_topology(err, this, other)
  File "/opt/virtualenvs/python3/lib/python3.8/site-packages/shapely/topology.py", line 35, in _check_topology
    raise TopologicalError(
shapely.errors.TopologicalError: The operation 'GEOSIntersection_r' could not be performed. Likely cause is invalidity of the geometry <shapely.geometry.polygon.Polygon object at 0x7f49b40b2ee0>

如果你真的想看到一些非常丑陋的代码，我已经尝试了一段时间了……

class Point:
    def __init__(self, x, y):
        self.x = int(x)
        self.y = int(y)

ax1,ay1,ax2,ay2, = input().split()
bx1,by1,bx2,by2 = input().split()

ATL = Point(ax2, ay2)
ATR = Point(ax1, ay2)
ABL = Point(ax2, ay1)
ABR = Point(ax1, ay1)
if ax1 < ax2:
  if ay1 > ay2:
    ATL = Point(ax1, ay1)
    ATR = Point(ax2, ay1)
    ABL = Point(ax1, ay2)
    ABR = Point(ax2, ay2)
  else:
    ATL = Point(ax1, ay2)
    ATR = Point(ax2, ay2)
    ABL = Point(ax1, ay1)
    ABR = Point(ax2, ay1)
else:
  if ay1 > ay2:
    ATL = Point(ax2, ay1)
    ATR = Point(ax1, ay1)
    ABL = Point(ax2, ay2)
    ABR = Point(ax1, ay2)

BTL = Point(bx2, by2)
BTR = Point(bx1, by2)
BBL = Point(bx2, by1)
BBR = Point(bx1, by1)
if bx1 < bx2:
  if by1 > by2:
    BTL = Point(bx1, by1)
    BTR = Point(bx2, by1)
    BBL = Point(bx1, by2)
    BBR = Point(bx2, by2)
  else:
    BTL = Point(bx1, by2)
    BTR = Point(bx2, by2)
    BBL = Point(bx1, by1)
    BBR = Point(bx2, by1)
else:
  if by1 > by2:
    BTL = Point(bx2, by1)
    BTR = Point(bx1, by1)
    BBL = Point(bx2, by2)
    BBR = Point(bx1, by2)

# polygon = Polygon([(ATL.x, ATL.y), (ATR.x, ATR.y), (ABL.x, ABL.y), (ABR.x, ABR.y)])
# other_polygon = Polygon([(BTL.x, BTL.y), (BTR.x, BTR.y), (BBL.x, BBL.y), (BBR.x, BBR.y)])

# -3 2 1 -2
# 2 1 -1 4


from shapely.geometry import Polygon

polygon = Polygon([(-3, 2), (1, 2), (-3, -2), (1, -2)])
other_polygon = Polygon([(2, 1), (-1, 1), (2, 4), (-1, 4)])

if polygon.overlaps(other_polygon):
  print( polygon.intersection(other_polygon).area )
else:
  print(0)

Answer 1

您的多边形无效：

>>> polygon.is_valid
False
>>> other_polygon.is_valid
False

这是因为您没有按正确的顺序指定顶点。如果你自己跟踪它们，你会看到一个Z字形的模式。要解决此问题，请切换最后两个顶点：

>>> polygon = Polygon([(-3, 2), (1, 2), (1, -2), (-3, -2)])
>>> polygon.is_valid
True
>>> other_polygon = Polygon([(2, 1), (-1, 1), (-1, 4), (2, 4)])
>>> other_polygon.is_valid
True

你的交集计算也会起作用：

>>> polygon.overlaps(other_polygon)
True
>>> polygon.intersection(other_polygon).area
2.0