Florie Florie - 1 year ago 138
Python Question

Counting points inside an ellipse

I'm trying to count given data points inside each ring of ellipse:

enter image description here

The problem is that I have a function to check that:
so for each ellipse, to make sure whether a point is in it, three inputs have to be calculated:

def get_focal_point(r1,r2,center_x):
# f = square root of r1-squared - r2-squared
focal_dist = sqrt((r1**2) - (r2**2))
f1_x = center_x - focal_dist
f2_x = center_x + focal_dist
return f1_x, f2_x

def get_distance(f1,f2,center_y,t_x,t_y):
d1 = sqrt(((f1-t_x)**2) + ((center_y - t_y)**2))
d2 = sqrt(((f2-t_x)**2) + ((center_y - t_y)**2))
return d1,d2

def in_ellipse(major_ax,d1,d2):
if (d1+d2) <= 2*major_ax:
return True
return False

Right now I'm checking whether or not it's in an ellipse by:

for i in range(len(data.latitude)):
t_x = data.latitude[i]
t_y = data.longitude[i]
d1,d2 = get_distance(f1,f2,center_y,t_x,t_y)
if in_ellipse(major_ax,d1,d2) == True:
core_count += 1
# if the point is not in core ellipse
# check the next ring up
for i in range(loop):

But I would then have to calculate each pairs of focal points of the outside loops..
is there any more efficient and or clever way to do this?

Answer Source

This may be something similar to what you are doing. I'm just looking to see if f(x,y) = x^2/r1^2 + y^2/r2^2 = 1.

When f(x,y) is larger than 1, the point x,y is outside the ellipse. When it is smaller, then it is inside the ellipse. I loop through each ellipse to find the one when f(x,y) is smaller than 1.

The code also does not take into account an ellipse that is centered off the origin. It's a small change to include this feature.

import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np

def inWhichEllipse(x,y,rads):
    With a list of (r1,r2) pairs, rads, return the index of the pair in which
    the point x,y resides. Return None as the index if it is outside all 
    xx = x*x
    yy = y*y

    count = 0
    ithEllipse =0
    while True:
        rx,ry = rads[count]
        ellips = xx/(rx*rx)+yy/(ry*ry)
        if ellips < 1:
            ithEllipse = count
        if count >= len(rads):
            ithEllipse = None

    return ithEllipse

rads = zip(np.arange(.5,10,.5),np.arange(.125,2.5,.25))

fig = plt.figure()
ax = fig.add_subplot(111)

# plot Ellipses
for rx,ry in rads:
    ellipse = patches.Ellipse((0,0),rx*2,ry*2,fc='none',ec='red')    

idx = inWhichEllipse(x,y,rads)
rx,ry = rads[idx]
ellipse = patches.Ellipse((0,0),rx*2,ry*2,fc='none',ec='blue')    

if idx != None:
    circle = patches.Circle((x,y),.1)


This code produces the following figure: enter image description here

Keep in mind, this is just a starting point. For one thing, you can change inWhichEllipse to accept a list of the square of r1 and r2, ie (r1*r1,r2*r2) pairs, and that would cut the computation down even more.

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