import numpy as np
from numpy.polynomial.polynomial import Polynomial
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider, Button


# The parametrized function to be plotted
def mantle(rfrac, n=1000):
    theta = np.linspace(-np.pi, np.pi, n)
    rmaj = 1
    rmin = rmaj*rfrac
    u = theta * rmin
    func = (np.pi)*(rmaj - rmin*np.cos(theta))
    data = np.array([func, u])
    data2 = np.array([-func, u[::-1]])

    data = np.append(data, data2, axis=1)
    data = np.append(data, data[:, 0:1], axis=1)
    return data


def crossection(rfrac, n=1000):
    theta = np.linspace(0, 2*np.pi, n)
    rmaj = 1
    rmin = rmaj * rfrac
    x = rmaj + rmin*np.cos(theta)
    y = rmin*np.sin(theta)
    data = np.array([x, y])
    data2 = np.array([-x, y])
    data = np.append(data, [[np.nan,], [np.nan,]], axis=1)
    data = np.append(data, data2, axis=1)
    return data


def sunpath_side(rfrac, n=1000):
    theta = np.linspace(0, 2*np.pi, n)
    rmaj = 1
    x = rmaj + rmaj*np.cos(theta)
    y = rmaj*np.sin(theta)
    return np.array([x, y])


def sunpath_top(rfrac, n=1000):
    theta = np.linspace(0, np.pi, n)
    rmaj = 1
    x = rmaj + rmaj*np.cos(theta)
    y = np.zeros_like(theta)
    return np.array([x, y])


def sun_side(rfrac, sunpos):
    rmaj = 1
    x = rmaj - rmaj*np.cos(sunpos)
    y = rmaj*np.sin(sunpos)
    return [x, y]


def sun_top(rfrac, sunpos):
    rmaj = 1
    x = rmaj - rmaj*np.cos(sunpos)
    y = 0
    return [x, y]


def sun_map(rfrac, sunpos):
    rmaj = 1
    rmin = rmaj*rfrac
    y = sunpos * rmin
    x = 0
    return [x, y]


def topview(rfrac, n=1000):
    theta = np.linspace(0, np.pi, n)
    rmaj = 1
    rmin = rmaj*rfrac
    x1 = (rmaj + rmin) * np.cos(theta)
    y1 = -1 * (rmaj + rmin) * np.sin(theta)
    data1 = np.array([x1, y1])
    x2 = (rmaj - rmin) * np.cos(theta)
    y2 = -1 * (rmaj - rmin) * np.sin(theta)
    data2 = np.array([x2, y2])

    data = np.append(data1, [[np.nan,], [np.nan,]], axis=1)
    data = np.append(data, data2, axis=1)
    return data


def contour_map(rfrac, sunpos, n=100):
    rmaj = 1
    rmin = rmaj*rfrac
    phi = np.linspace(-np.pi, np.pi, n)
    theta = np.linspace(-np.pi, np.pi, int(n*rfrac))

    y = np.array([[w]*n for w in rmin*theta])
    func = (np.pi)*(rmaj - rmin*np.cos(theta))
    x = np.array([np.linspace(-f, f, n) for f in func])
    # x, y = np.meshgrid(np.linspace(-func[0], func[0], n), rmin*theta)

    sun = [rmaj - rmaj*np.cos(sunpos), 0, rmaj*np.sin(sunpos)]

    def raytraced(ph, th):
        def r(ph, th):
            rx = (rmaj - rmin*np.cos(th)) * np.cos(ph)
            ry = (rmaj - rmin*np.cos(th)) * np.sin(ph)
            rz = rmin * np.sin(th)
            return rx, ry, rz

        def n(ph, th):
            rx, ry, rz = r(ph, th)
            cx = rmaj * np.cos(ph)
            cy = rmaj * np.sin(ph)
            cz = 0
            retx, rety, retz = rx-cx, ry-cy, rz-cz
            return -1*np.array([retx, rety, retz])/np.linalg.norm([retx, rety, retz])

        def b(ph, th):
            rx, ry, rz = r(ph, th)
            sx, sy, sz = sun
            retx, rety, retz = rx-sx, ry-sy, rz-sz
            return np.array([retx, rety, retz])/np.linalg.norm([retx, rety, retz])
        o = sun
        d = b(ph, th)
        s = r(ph, th)

        pol = Polynomial(coef(rmaj, rmin, d, o))
        roots = uproot(pol.roots())

        if len(roots) == 0:
            return 0
        poi = o + roots[0]*d
        return (1 if np.allclose(s, poi) else -1)

    z = np.array([[raytraced(ph, th) for ph in phi] for th in theta])
    # z = np.array([[np.dot(b(ph, th), n(ph, th)) for ph in phi] for th in theta])

    return x, y, z


def coef(rmaj, rmin, d, o):
    k1 = np.inner(d, d)
    k2 = np.inner(o, d)
    k3 = np.inner(o, o) - (rmin**2 + rmaj**2)

    c4 = k1**2
    c3 = 4*k1*k2
    c2 = 2*k1*k3 + 4*k2**2 + 4*(rmaj*d[2])**2
    c1 = 4*k3*k2 + 8*(rmaj**2)*o[2]*d[2]
    c0 = k3**2 - 4*(rmaj**2)*(rmin**2 - o[2]**2)
    return [c0, c1, c2, c3, c4]


def uproot(arr):
    mask = np.logical_and(arr > 0, np.isreal(arr))
    masked = arr[mask]
    return np.real(sorted(masked))


r_fraction = 0.5
sun_pos = np.pi/2

# Create the figure and the line that we will manipulate
fig, (ax_side, ax_top, ax_map) = plt.subplots(3, 1, gridspec_kw={'height_ratios': [1, 1, 1]})

circles_top, = ax_top.plot(*topview(r_fraction), 'k')
path_top, = ax_top.plot(*sunpath_top(r_fraction), 'k:')
pos_top, = ax_top.plot(*sun_top(r_fraction, sun_pos), marker='o', color='r', markersize=10,)
ax_top.set_xlim(-2.05, 2.05)
ax_top.set_ylim(-2.05, None)
ax_top.set_aspect('equal')

ax_top.axis('off')

circles_side, = ax_side.plot(*crossection(r_fraction), 'k')
path_side, = ax_side.plot(*sunpath_side(r_fraction), 'k:')
pos_side, = ax_side.plot(*sun_side(r_fraction, sun_pos), marker='o', color='r', markersize=10,)
ax_side.set_xlim(-2.05, 2.05)
ax_side.set_aspect('equal')
# ax_side.set_ylim(-r_min, None)
ax_side.axis('off')

map_border, = ax_map.plot(*mantle(r_fraction), 'k')
pos_map, = ax_map.plot(*sun_map(r_fraction, sun_pos), marker='o', color='r', markersize=10,)
dawnline_map = [ax_map.contourf(*contour_map(r_fraction, sun_pos), [-1, 0, 1], cmap='YlOrBr_r')]
ax_map.set_aspect('equal')
ax_map.set_ylabel('Longitude')
ax_map.set_xlabel('Lattitude')
ax_map.axis('off')
# cbar = fig.colorbar(dawnline_map[0])

# adjust the main plot to make room for the sliders
fig.subplots_adjust(left=0.25, bottom=0.25)

# Make a horizontal slider to control the frequency.
axsun = fig.add_axes([0.25, 0.1, 0.65, 0.03])
slider_sun = Slider(
    ax=axsun,
    label='Angle of Sun',
    valmin=-np.pi,
    valmax=np.pi,
    valinit=sun_pos,
)

# Make a vertically oriented slider to control the amplitude
axrad = fig.add_axes([0.1, 0.25, 0.0225, 0.63])
slider_rf = Slider(
    ax=axrad,
    label="Fraction of Radii (r/R)",
    valmin=0,
    valmax=1,
    valinit=r_fraction,
    orientation="vertical"
)


# The function to be called anytime a slider's value changes
def update_torus(val):
    def update(ax, line, func):
        u, m = func(slider_rf.val)
        line.set_ydata(m)
        line.set_xdata(u)
        ax.relim()
        ax.autoscale_view()

    update(ax_map, map_border, mantle)
    update(ax_side, circles_side, crossection)
    update(ax_side, path_side, sunpath_side)
    update(ax_top, circles_top, topview)
    update(ax_top, path_top, sunpath_top)

    for coll in dawnline_map[0].collections:
        coll.remove()
    dawnline_map[0] = ax_map.contourf(*contour_map(slider_rf.val, slider_sun.val), [-1, 0, 1], cmap='YlOrBr_r')

    fig.canvas.draw_idle()


# The function to be called anytime a slider's value changes
def update_sun(val):
    def update(ax, line, func):
        u, m = func(slider_rf.val, slider_sun.val)
        line.set_ydata(m)
        line.set_xdata(u)

    update(ax_map, pos_map, sun_map)
    update(ax_side, pos_side, sun_side)
    update(ax_top, pos_top, sun_top)

    for coll in dawnline_map[0].collections:
        coll.remove()
    dawnline_map[0] = ax_map.contourf(*contour_map(slider_rf.val, slider_sun.val), [-1, 0, 1], cmap='YlOrBr_r')

    fig.canvas.draw_idle()


# register the update function with each slider
slider_sun.on_changed(update_sun)
slider_rf.on_changed(update_torus)

# Create a `matplotlib.widgets.Button` to reset the sliders to initial values.
resetax = fig.add_axes([0.8, 0.025, 0.1, 0.04])
button = Button(resetax, 'Reset', hovercolor='0.975')


def reset(event):
    slider_sun.reset()
    slider_rf.reset()


button.on_clicked(reset)

plt.show()