SciPy Central

# License: Creative Commons Zero (almost public domain) http://scpyce.org/cc0

import numpy as np
from pylab import plot, show, grid

def get_ellipse_coords(a=0.0, b=0.0, x=0.0, y=0.0, angle=0.0, nsteps=360):
    """ Draws an ellipse using ``nsteps`` discrete points; based on pseudo code
    given at http://en.wikipedia.org/wiki/Ellipse

    ``a`` = major axis distance,
    ``b`` = minor axis distance,
    ``x`` = offset along the x-axis
    ``y`` = offset along the y-axis
    ``angle`` = clockwise rotation [in degrees] of the ellipse;
        * angle=0  : the ellipse is aligned with the positive x-axis
        * angle=30 : rotated 30 degrees clockwise from positive x-axis
    """
    pts = np.zeros((nsteps, 2)) * np.nan

    beta = -angle * np.pi / 180.0
    sin_beta = np.sin(beta)
    cos_beta = np.cos(beta)

    for idx, alpha in enumerate(np.arange(0.0, 360, 360.0/nsteps)):
        alpha *= np.pi / 180.0
        sin_alpha = np.sin(alpha)
        cos_alpha = np.cos(alpha)
        pts[idx, 0] = x + (a * cos_alpha * cos_beta - b * sin_alpha * sin_beta)
        pts[idx, 1] = y + (a * cos_alpha * sin_beta + b * sin_alpha * cos_beta)

    return pts

if __name__ == '__main__':

    # Plot a unit circle centered at (+2, +3)
    pts = get_ellipse_coords(a=1.0, b=1.0, x=2, y=3)
    ax = plot(pts[:,0], pts[:,1])

    # Set the aspect ratio so it looks like a circle; add a grid as well
    ax[0].get_axes().set_aspect(1)
    grid('on')


    # Ellipse, with major axis length = 4, minor axis = 1, centered at (0,0)
    pts = get_ellipse_coords(a=4.0, b=1.0)
    ax = plot(pts[:,0], pts[:,1])

    # Rotate the above ellipse by 30 degrees:
    pts = get_ellipse_coords(a=4.0, b=1.0, angle=30)
    ax = plot(pts[:,0], pts[:,1])

    # Use all the options:
    pts = get_ellipse_coords(a=2.0, b=0.25, x=-4, y=-2, angle=250)
    ax = plot(pts[:,0], pts[:,1])

    show()