[FIXED] How can I count number of points between 2 contours in Python

Issue

I am using matplotlib.pyplot to interpolate my data and create contours. Following this answer/example (about how to calculate area within a contour), I am able to get the vertices of a contour line. Is there a way to use that information, i.e., the vertices of a line, to count how many points fall between two given contours? These points will be different from the data used for deriving the contours.

Solution

Usually, you do not want to reverse engineer your plot to obtain some data. Instead you can interpolate the array that is later used for plotting the contours and find out which of the points lie in regions of certain values.

The following would find all points between the levels of -0.8 and -0.4, print them and show them in red on the plot.

import numpy as np; np.random.seed(1)
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
from scipy.interpolate import Rbf

X, Y = np.meshgrid(np.arange(-3.0, 3.0, 0.1), np.arange(-2.4, 1.0, 0.1))
Z1 = mlab.bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
Z2 = mlab.bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
Z = 10.0 * (Z2 - Z1)

points = np.random.randn(15,2)/1.2
levels = [-1.2, -0.8,-0.4,-0.2]

# interpolate points
f = Rbf(X.flatten(), Y.flatten(), Z.flatten()) 
zi = f(points[:,0], points[:,1])
# add interpolated points to array with columns x,y,z
points3d = np.zeros((points.shape[0],3))
points3d[:,:2] = points
points3d[:,2] = zi
# masking condition for points between levels
filt = (zi>levels[1]) & (zi <levels[2])
# print points between the second and third level
print(points3d[filt,:])

### plotting
fig, ax = plt.subplots()

CS = ax.contour(X, Y, Z, levels=levels)
ax.clabel(CS, inline=1, fontsize=10)
#plot points between the second and third level in red:
ax.scatter(points[:,0], points[:,1], c=filt.astype(float), cmap="bwr" )

plt.show()

Answered By - ImportanceOfBeingErnest