CODEWITHSUNDEEP
pythonmathgeometry
Jacek Potapczuk
Jacek Potapczuk

Reputation: 29

How to draw the best ellipse given number of points?

Given the vectors p,q and number of points n I want to approximate shape of the ellipse with these n points as best as possible. To do this I use parametric equation of ellipse and change radius and angle in a double for loop:

n = 10000
points = []
p = [300, 0]
q = [0, 200]
root = int(math.sqrt(n))
for a in range(root):
    for b in range(root):
        x = 400 + (a/root)*(p[0] - q[0])*math.cos(2*math.pi*b/root)
        y = 300 - (a/root)*(p[1] - q[1])*math.sin(2*math.pi*b/root)
        points.append([x, y])
for w in points:
    pygame.draw.circle(screen, (200, 50, 75), (int(w[0]), int(w[1])), 1)

Here I'm using pygame to draw but it doesn't really matter. Given these parameters my ellipse looks like this:

ellipse 1

with n = 100000. It looks like this: ellipse 2

Given the nature of the ellipse there are more points in the middle using basic parametrization of the radious and angle. Because of that I need very large n to get good picture. How can I change parameterization to make points better spread on the whole area?

Upvotes: 1

Views: 446

Answers (1)

Nick Martin
Nick Martin

Reputation: 729

Perhaps create the points uniformly and then filter out the ones outside the ellipse?

import numpy as np
from math import sqrt
import matplotlib.pyplot as plt

def filter_points(h, k, a, b, x, y): 
  mask = ((x-h)**2)/(a**2) + ((y-k)**2)/(b**2) <= 1
  return x[mask], y[mask]

h = 0
k = 0
a = 4
b = 5
N = 10000
n = int(sqrt(N))

X, Y = np.meshgrid(
  np.linspace(-a,a,n),
  np.linspace(-b,b,n)
)

X, Y = filter_points(h, k, a, b, X[:], Y[:])
points = np.asarray([X, Y]).T

plt.figure
plt.plot(X,Y,'.')

enter image description here

Upvotes: 1

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