from math import sin, cos

class beads2d(object):
    """Vector field that describes the approximation of the Beads problem."""

    def __init__(self):
        pass

    # Samples the vector field of the Beads problem
    def sample(self, x, y, t):
        u = -2 * y + (2 * sin(t)) / 3
        v = +2 * x - (2 * cos(t)) / 3
        return u, v;

    # Samples the x-partial of the vector field of the Beads problem
    def sample_dx(self, x, y, t):
        u = 0
        v = 2
        return u, v;

    # Samples the y-partial of the vector field of the Beads problem
    def sample_dy(self, x, y, t):
        u = -2
        v = 0
        return u, v;

    # Samples the t-partial of the vector field of the Beads problem
    def sample_dt(self, x, y, t):
        u = (2 * cos(t)) / 3
        v = (2 * sin(t)) / 3
        return u, v;