使用matplotlib重叠2个椭圆的区域

Question

有谁知道是否可以使用matplotlib.patches.Ellipse.

计算两个椭圆的重叠面积

我必须这样省略：

我想计算重叠面积与各个椭圆面积之间的比率。这是否可能仅使用 matplotlib.patches

中的 Ellipse

Answer 1

您无法计算与 matplotlib 相交的面积（至少据我所知），但您可以使用 shapely 计算然后使用 matplotlib 可视化 结果。这里有一个快速演示：

from matplotlib import pyplot as plt
from shapely.geometry.point import Point
from shapely import affinity
from matplotlib.patches import Polygon
import numpy as np

def create_ellipse(center, lengths, angle=0):
    """
    create a shapely ellipse. adapted from
    https://gis.stackexchange.com/a/243462
    """
    circ = Point(center).buffer(1)
    ell = affinity.scale(circ, int(lengths[0]), int(lengths[1]))
    ellr = affinity.rotate(ell, angle)
    return ellr

fig,ax = plt.subplots()

##these next few lines are pretty important because
##otherwise your ellipses might only be displayed partly
##or may be distorted
ax.set_xlim([-5,5])
ax.set_ylim([-5,5])
ax.set_aspect('equal')

##first ellipse in blue
ellipse1 = create_ellipse((0,0),(2,4),10)
verts1 = np.array(ellipse1.exterior.coords.xy)
patch1 = Polygon(verts1.T, color = 'blue', alpha = 0.5)
ax.add_patch(patch1)

##second ellipse in red    
ellipse2 = create_ellipse((1,-1),(3,2),50)
verts2 = np.array(ellipse2.exterior.coords.xy)
patch2 = Polygon(verts2.T,color = 'red', alpha = 0.5)
ax.add_patch(patch2)

##the intersect will be outlined in black
intersect = ellipse1.intersection(ellipse2)
verts3 = np.array(intersect.exterior.coords.xy)
patch3 = Polygon(verts3.T, facecolor = 'none', edgecolor = 'black')
ax.add_patch(patch3)

##compute areas and ratios 
print('area of ellipse 1:',ellipse1.area)
print('area of ellipse 2:',ellipse2.area)
print('area of intersect:',intersect.area)
print('intersect/ellipse1:', intersect.area/ellipse1.area)
print('intersect/ellipse2:', intersect.area/ellipse2.area)


plt.show()

结果图如下所示：

计算出的面积（打印到终端）是：

area of ellipse 1: 25.09238792436751
area of ellipse 2: 18.81929094327563
area of intersect: 13.656608779925698
intersect/ellipse1: 0.5442530547945023
intersect/ellipse2: 0.7256707397260032

请注意，我修改了代码以从 this post 生成 ellipse-shaped 多边形。希望这会有所帮助。

使用matplotlib重叠2个椭圆的区域

Overlap area of 2 ellipses using matplotlib

python

matplotlib

geometry

ellipse