I use matplotlib 1.15.1 and I try to generate scattergrams like this:
The ellipses have fixes s
This approach should test if a point is within an ellipse, given the ellipse's centre, width, height and angle. You find the point's x and y coordinates relative to the ellipse centre, then transform those using the angle to be the coordinates along the major and minor axes. Finally, you find the normalised distance of the point from the cell centre, where a distance of 1 would be on the ellipse, less than 1 is inside, and more than 1 is outside.
import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
fig,ax = plt.subplots(1)
ax.set_aspect('equal')
# Some test points
x = np.random.rand(500)*0.5+0.7
y = np.random.rand(500)*0.5+0.7
# The ellipse
g_ell_center = (0.8882, 0.8882)
g_ell_width = 0.36401857095483
g_ell_height = 0.16928136341606
angle = 30.
g_ellipse = patches.Ellipse(g_ell_center, g_ell_width, g_ell_height, angle=angle, fill=False, edgecolor='green', linewidth=2)
ax.add_patch(g_ellipse)
cos_angle = np.cos(np.radians(180.-angle))
sin_angle = np.sin(np.radians(180.-angle))
xc = x - g_ell_center[0]
yc = y - g_ell_center[1]
xct = xc * cos_angle - yc * sin_angle
yct = xc * sin_angle + yc * cos_angle
rad_cc = (xct**2/(g_ell_width/2.)**2) + (yct**2/(g_ell_height/2.)**2)
# Set the colors. Black if outside the ellipse, green if inside
colors_array = np.array(['black'] * len(rad_cc))
colors_array[np.where(rad_cc <= 1.)[0]] = 'green'
ax.scatter(x,y,c=colors_array,linewidths=0.3)
plt.show()
Note, this whole script takes 0.6 seconds to run and process 500 points. That includes creating and saving the figure, etc.
The process of setting the colors_array using the np.where
method above takes 0.00007s for 500 points.
Note, in an older implementation shown below, setting the colors_array in a loop took 0.00016 s:
colors_array = []
for r in rad_cc:
if r <= 1.:
# point in ellipse
colors_array.append('green')
else:
# point not in ellipse
colors_array.append('black')