ellipse.py

import sys
import math

DIVISION = 1000.0
CYCLE = 10

def angles(du, a, b):
    """Yeild angles of points on a ellipse.

    @param du - distance of two points which is next to each other
    @param a, b - length of two semi-axes
    """
    phi = 0
    while phi <= 2 * math.pi:
        yield phi
        phi += du / math.sqrt((a * math.sin(phi))**2 + (b * math.cos(phi))**2)

def coordinate(du, a, b):
    """Yeild coordinates of points on a ellipse.

    @param du - distance of two points which is next to each other
    @param a, b - length of two semi-axes
    """
    for angle in angles(du, a, b):
        yield (a * math.cos(angle), b * math.sin(angle))

def circumference(a, b):
    """Return a length of a circumference of an ellipse.

    @param a, b - length of two semi-axes

    reference: http://en.wikipedia.org/wiki/Ellipse#Circumference
    """
    expr = ((a - b)/(a + b))**2
    return math.pi * (a + b) * (1 + (3 * expr)/(10 + math.sqrt(4 - 3 * expr)))

def draw(argv=None):
    if not argv:
        argv = sys.argv
    filename = argv[1]
    a = float(argv[2])
    b = float(argv[3])
    du = circumference(a, b) / DIVISION

    with open(filename, 'w') as out_file:
        print >> out_file, 'plot "-" w l'
        print >> out_file, '#x\ty'
        for i, coord in enumerate(coordinate(du, a, b)):
            i %= CYCLE * 2
            if i < CYCLE:
                print >> out_file, '{0}\t{1}'.format(*coord)
            else:
                print >> out_file, ''
        print >> out_file, 'end'
        print >> out_file, 'pause -1'


if __name__ == '__main__':
    draw(sys.argv)