geom.py

def point_on_arc(radius, start_x, start_y, end_x, end_y):
    """
    Returns set of possible points on arc given by start and end points and
    circle radius.
    Return value is dictionary with keys 'center' and 'points'.
    Center is associated with list of tuples with possible center coordinates.
    Points is associated with list of tuples with possible points on the arc.
    """
    X = start_x - end_x
    Y = start_y - end_y
    D = X ** 2 + Y ** 2

    Q = sqrt(4 * radius ** 2 / D - 1)
    K1 = 0.5 * (Y + X * Q)
    K2 = 0.5 * (Y - X * Q)

    H1 = 0.5 * (X + Y * Q)
    H2 = 0.5 * (X - Y * Q)

    x01, y01 = H1 + end_x, K1 + end_y
    x02, y02 = H2 + end_x, K2 + end_y

    xc1 = 0.5 * (start_x + end_x)

    Q1 = sqrt(radius ** 2 - (xc1 - x01) ** 2)
    Q2 = sqrt(radius ** 2 - (xc1 - x02) ** 2)

    return {
        'center': [
            (x01, y01),
            (x02, y02)
        ],
        'points': [
            (xc1, y01 + Q1),
            (xc1, y01 - Q1),
            (xc1, y02 + Q2),
            (xc1, y02 - Q2)
        ]
    }