Port of Pavel Sountsov's DrawCircle to python. Basic idea -- avoid using sin/cos a lot (like a naive implementation) when drawing a circle.

draw_circle.py

import math
def estimate_segments(radius, segment_length=0.25): 
    """ Basically want segments that are about the size of .25 pixel for the given radius. 
        Derive as follows:
            segment_length as a function of theta: 
                segment_length = (1 - cos(theta)) * radius 
        Solving for theta given segment_length:
                theta = math.acos(1 - (float(segment_length) / radius))
    """
    
    # How many thetas in a circle?
    return 2*math.pi / math.acos(1 - (float(segment_length) / radius))


def fast_estimate_segments(radius):
    """From P. Sountsov. Approximates the more precise result without resorting to acos"""
    return 10 * math.sqrt(radius)


def circle_points(cx, cy, r, segments, theta_start=0):
    """from here: http://slabode.exofire.net/circle_draw.shtml"""
    theta = 2 * pi / segments
    # precalculate sin/cos
    c = cos(theta)
    s = sin(theta)

    # If we don't need to accept theta_start, hardcoding
    # to x = 0, y = r would be faster.
    x = r*cos(theta_start)
    y = r*sin(theta_start)
    
    pts = [None] * (segments + 1)
    for i in xrange(segments+1):
        pts[i] = (cx + x, cy + y)
        
        # apply the rotation matrix
        x, y = (c * x - s * y, s * x + c * y)

    return pts