Bezier.py

    def __repr__(self):
        return self.__class__.__name__ + '({0._p0}, {0._p1}, {0._p2})'.format(self)

    ##############################################

    def to_bezier(self):
        basis = np.dot(self.BASIS, QuadraticBezier2D.INVERSE_BASIS)
        points = np.dot(self.geometry_matrix, basis).transpose()
        return QuadraticBezier2D(*points)

    ##############################################

    def point_at_t(self, t):

        # Q(t) = (
        #          P0 *  (1-t)**3                      +
        #          P1 * (  3*t**3 - 6*t**2       + 4 ) +
        #          P2 * ( -3*t**3 + 3*t**2 + 3*t + 1 ) +
        #          P3 *      t**3
        #        ) / 6
        #
        #     = P0*(1-t)**3/6 + P1*(3*t**3 - 6*t**2 + 4)/6 + P2*(-3*t**3 + 3*t**2 + 3*t + 1)/6 + P3*t**3/6

        return (self._p0/6 + self._p1*2/3 + self._p2/6 +
                (-self._p0/2 + self._p2/2)*t +
                (self._p0/2 - self._p1 + self._p2/2)*t**2 +
                (-self._p0/6 + self._p1/2 - self._p2/2 + self._p3/6)*t**3)

####################################################################################################

class QuadraticSpline2D(Primitive2DMixin, PrimitiveNP):

    """Class to implements 2D Quadratic Spline Curve."""

    # control points define the curve shape
    # knots are part extremities on the curve

    __number_of_points__ = 3
    __part_cls__ = QuadraticSplinePart2D

    #######################################

    def __init__(self, *points):

        points = self.handle_points(points)
        PrimitiveNP.__init__(self, points)
        if len(self) < self.__number_of_points__:
            raise ValueError('Require at least 4 points')

    ##############################################

    def number_of_parts(self):
        return self.number_of_points - self.__number_of_points__

    ##############################################

    def iter_on_parts(self):
        for points in self.iter_on_nuplets(self.__number_of_points__):
            print(points)
            yield self.__part_cls__(*points)

    ##############################################

    def get_part(self, i):
        points = self._points[i:i+self.__number_of_points__]
        return self.__part_cls__(*points)

####################################################################################################

class CubicSplinePart2D(Primitive2DMixin, Primitive4P):

    """Class to implements 2D Cubic Spline Curve."""

    # T = (1 t t**2 t**3)
    # P = (Pi Pi+2 Pi+2 Pi+3)
    # Q(t) = T M Pt
    #      = P Mt Tt
    # Basis = Mt
    BASIS = np.array((
        (1, -3,  3, -1),
        (4,  0, -6,  3),
        (1,  3,  3, -3),
        (0,  0,  0,  1),
    )) / 6

    INVERSE_BASIS = np.array((
        (  1,    1,    1,     1),
        ( -1,    0,    1,     2),
        (2/3, -1/3,  2/3,  11/3),
        (  0,    0,    0,     6),
    ))

    #######################################

    def __init__(self, p0, p1, p2, p3):
        Primitive4P.__init__(self, p0, p1, p2, p3)

    ##############################################

    def __repr__(self):
        return self.__class__.__name__ + '({0._p0}, {0._p1}, {0._p2}, {0._p3})'.format(self)

    ##############################################

    def to_bezier(self):
        basis = np.dot(self.BASIS, CubicBezier2D.INVERSE_BASIS)
        points = np.dot(self.geometry_matrix, basis).transpose()
        return CubicBezier2D(*points)

    ##############################################

    def point_at_t(self, t):

        # Q(t) = (
        #          P0 *  (1-t)**3                      +
        #          P1 * (  3*t**3 - 6*t**2       + 4 ) +
        #          P2 * ( -3*t**3 + 3*t**2 + 3*t + 1 ) +
        #          P3 *      t**3
        #        ) / 6
        #
        #     = P0*(1-t)**3/6 + P1*(3*t**3 - 6*t**2 + 4)/6 + P2*(-3*t**3 + 3*t**2 + 3*t + 1)/6 + P3*t**3/6

        return (self._p0/6 + self._p1*2/3 + self._p2/6 +
                (-self._p0/2 + self._p2/2)*t +
                (self._p0/2 - self._p1 + self._p2/2)*t**2 +
                (-self._p0/6 + self._p1/2 - self._p2/2 + self._p3/6)*t**3)

####################################################################################################

class CubicSpline2D(QuadraticSpline2D):

    """Class to implements 2D Cubic Spline Curve."""

    __number_of_points__ = 4
    __part_cls__ = CubicSplinePart2D