import math as mth
import cmath as cmt
import numpy as npy
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from itertools import product, combinations
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d


class Arrow3D(FancyArrowPatch):

    def __init__(self, xs, ys, zs, *args, **kwargs):
        FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
        self._verts3d = xs, ys, zs

    def draw(self, renderer):
        xs3d, ys3d, zs3d = self._verts3d
        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
        FancyArrowPatch.draw(self, renderer)


def kugel(historie):
    fig = plt.figure()
    ax = fig.gca(projection='3d')

    # draw sphere
    u, v = npy.mgrid[0:2*npy.pi:20j, 0:npy.pi:10j]
    x = npy.cos(u)*npy.sin(v)
    y = npy.sin(u)*npy.sin(v)
    z = npy.cos(v)
    ax.plot_wireframe(x, y, z, color="r")

    # draw a time evolution
    for blochpunkt in historie:
        x = mth.cos(blochpunkt[1]) * mth.cos(blochpunkt[0])
        y = mth.cos(blochpunkt[1]) * mth.sin(blochpunkt[0])
        z = mth.sin(blochpunkt[1])
        a = Arrow3D([0, x], [0, y], [0, z], mutation_scale=20,
                    lw=1, arrowstyle="-|>", color="k")
        ax.add_artist(a)
    plt.show()

def phi(phi):
    ax = plt.axes()
    plt.grid()

    x = mth.cos(phi[0])
    y = mth.sin(phi[0])

    ax.arrow(0, 0, 0.5, 0.5, head_width=0.05, head_length=0.07)
    plt.title('Zeitentwicklung von phi')

    plt.xlim(-1.1,1.1)
    plt.ylim(-1.1,1.1)
    plt.show()