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import itertools as IT
def scale_polygon(path,offset):
    center = centroid_of_polygon(path)
    for i in path:
        if i[0] > center[0]:
            i[0] += offset
        else:
            i[0] -= offset
        if i[1] > center[1]: 
            i[1] += offset
        else:
            i[1] -= offset
    return path


def area_of_polygon(x, y):
    """Calculates the signed area of an arbitrary polygon given its verticies
    http://stackoverflow.com/a/4682656/190597 (Joe Kington)
    http://softsurfer.com/Archive/algorithm_0101/algorithm_0101.htm#2D%20Polygons
    """
    area = 0.0
    for i in xrange(-1, len(x) - 1):
        area += x[i] * (y[i + 1] - y[i - 1])
    return area / 2.0

def centroid_of_polygon(points):
    """
    http://stackoverflow.com/a/14115494/190597 (mgamba)
    """
    area = area_of_polygon(*zip(*points))
    result_x = 0
    result_y = 0
    N = len(points)
    points = IT.cycle(points)
    x1, y1 = next(points)
    for i in range(N):
        x0, y0 = x1, y1
        x1, y1 = next(points)
        cross = (x0 * y1) - (x1 * y0)
        result_x += (x0 + x1) * cross
        result_y += (y0 + y1) * cross
    result_x /= (area * 6.0)
    result_y /= (area * 6.0)
    return (result_x, result_y)