如何使用 Matplotlib 在 Python 中计算轮廓内的面积?

问题描述

我想找出一种方法来获得特定轮廓线内的区域?
我使用 matplotlib.pyplot 来创建我的轮廓.
有没有人有经验为此?

I am trying to figure out a way to get the area inside a specific contour line?
I use matplotlib.pyplot to create my contours.
Does anyone have experience for this?

非常感谢.

推荐答案

从contour函数返回的contour集合的collections属性，你可以获取描述每个轮廓的路径.路径的 vertices 属性包含轮廓的有序顶点.

From the collections attribute of the contour collection, which is returned by the contour function, you can get the paths describing each contour. The paths' vertices attributes then contain the ordered vertices of the contour.

使用顶点可以近似轮廓积分 0.5*(x*dy-y*dx)，通过应用 格林定理给出了封闭区域的面积.

Using the vertices you can approximate the contour integral 0.5*(x*dy-y*dx), which by application of Green's theorem gives you the area of the enclosed region.

但是，轮廓必须完全包含在绘图中，否则轮廓会被分解为多个不一定相连的路径并且方法会崩溃.

However, the contours must be fully contained in the plot, because otherwise the contours are broken up into multiple, not necessarily connected paths and the method breaks down.

这里是用来计算半径函数包围面积的方法，即r = (x^2 + y^2)^0.5，对于r=1.0, r=2.0, r=3.0.

Here's the method used to compute the area enclosed of the radius function, i.e. r = (x^2 + y^2)^0.5, for r=1.0, r=2.0, r=3.0.

import numpy as np
import matplotlib.pylab as plt

# Use Green's theorem to compute the area
# enclosed by the given contour.
def area(vs):
    a = 0
    x0,y0 = vs[0]
    for [x1,y1] in vs[1:]:
        dx = x1-x0
        dy = y1-y0
        a += 0.5*(y0*dx - x0*dy)
        x0 = x1
        y0 = y1
    return a

# Generate some test data.
delta = 0.01
x = np.arange(-3.1, 3.1, delta)
y = np.arange(-3.1, 3.1, delta)
X, Y = np.meshgrid(x, y)
r = np.sqrt(X**2 + Y**2)

# Plot the data
levels = [1.0,2.0,3.0]
cs = plt.contour(X,Y,r,levels=levels)
plt.clabel(cs, inline=1, fontsize=10)

# Get one of the contours from the plot.
for i in range(len(levels)):
    contour = cs.collections[i]
    vs = contour.get_paths()[0].vertices
    # Compute area enclosed by vertices.
    a = area(vs)
    print "r = " + str(levels[i]) + ": a =" + str(a)

plt.show()

输出:

r = 1.0: a = 2.83566351207
r = 2.0: a = 11.9922190971
r = 3.0: a = 27.3977413253

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