# (c) Vsevolod Solovyov, 2009

class curve(object):
    """
    Cubic Bezier curve.

    >>> c1 = curve((0,0), (0,1), (1,0), (1,1))
    >>> curve((0,0), (0,1), (1,0))
    Traceback (most recent call last):
        ...
    ValueError: Cubic Bezier curve must have 4 points, but 3 provided

    You can use index to get points::

    >>> c1[0]
    (0, 0)

    >>> list(c1.calc(steps=4))
    [(0.0, 0.0), (0.15625, 0.4375), (0.5, 0.5), (0.84375, 0.5625), (1.0, 1.0)]

    """
    def __init__(self, *points):
        if len(points) != 4:
            raise ValueError("Cubic Bezier curve must have 4 points, but %d provided" % len(points))
        self.points = points

    def __getitem__(self, item):
        return self.points[item]

    def calc(self, steps=20, last_step=True):
        (x1, y1), (x2, y2), (x3, y3), (x4, y4) = self.points
        step = 1./steps
        for i in xrange(steps + last_step):
            b = step * i
            a = 1 - b
            kab = 3*a*b
            ka, ka2b, kab2, kb = a**3, kab*a, kab*b, b**3
            yield (x1 * ka + x2 * ka2b + x3 * kab2 + x4 * kb,
                   y1 * ka + y2 * ka2b + y3 * kab2 + y4 * kb)

class spline(object):
    """
    Spline constructs from cubic Bezier curves.

    If we just add calculated points from both curves we get duplicating
    entries::

    >>> c1 = curve((0,0), (0,1), (1,0), (1,1))
    >>> c2 = curve((1,1), (1,2), (2,1), (2,2))
    >>> list(c1.calc(steps=2)) + list(c2.calc(steps=2))
    [(0.0, 0.0), (0.5, 0.5), (1.0, 1.0), (1.0, 1.0), (1.5, 1.5), (2.0, 2.0)]

    But spline avoids that by using `last_step` argument of curve.calc()::

    >>> s = spline(c1, c2)
    >>> list(s.calc(steps=2))
    [(0.0, 0.0), (0.5, 0.5), (1.0, 1.0), (1.5, 1.5), (2.0, 2.0)]

    Additionaly, it checks for arguments order::

    >>> spline(c2, c1)
    Traceback (most recent call last):
        ...
    ValueError: Corresponding end and begin points are not equal.
    """
    def __init__(self, *curves):
        self.curves = []
        map(self.add_curve, curves)

    def add_curve(self, curve):
        if self.curves and self.curves[-1][-1] != curve[0]:
            raise ValueError("Corresponding end and begin points are not equal.")
        else:
            self.curves.append(curve)

    def calc(self, steps=20):
        last_num = len(self.curves) - 1
        for i, curve in enumerate(self.curves):
            for p in curve.calc(steps, i == last_num):
                yield p

if __name__ == "__main__":
    import doctest
    doctest.testmod()