"""Driven string + free-end ring standalone script."""
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from matplotlib.patches import Arc, Circle

L = 4.203704897601963
mu = 0.08286859421653214
T = 3.847738932370455
A = 0.13663233607116249
f_drive = 1.5370326125642633
gamma_w = 0.8047650381905198
N = 200
n_per_frame = 16
duration = 12
fps = 30

omega = 2*np.pi*f_drive
c = np.sqrt(T/mu)
dx = L/N
x_grid = np.linspace(0.0, L, N+1)
dt = 1.0/(fps*n_per_frame)
factor = (c*dt/dx)**2
damp_n = 1.0/(1.0+gamma_w*dt)
damp_p = 1.0 - gamma_w*dt
assert factor < 1.0, f"CFL violated: factor={factor:.3f}"

u_curr = np.zeros(N+1); u_prev = np.zeros(N+1)
n_frames = int(duration*fps)+1
U_frames = np.zeros((n_frames, N+1))
U_frames[0] = u_curr.copy()
for frame in range(1, n_frames):
    for sub in range(n_per_frame):
        t_curr = (frame-1)/fps + (sub+1)*dt
        u_next = np.empty_like(u_curr)
        lap_int = u_curr[2:] - 2*u_curr[1:-1] + u_curr[:-2]
        u_next[1:-1] = damp_n*(2*u_curr[1:-1] - damp_p*u_prev[1:-1] + factor*lap_int)
        lap_right = 2*(u_curr[-2] - u_curr[-1])
        u_next[-1] = damp_n*(2*u_curr[-1] - damp_p*u_prev[-1] + factor*lap_right)
        u_next[0] = A*np.sin(omega*t_curr)
        u_prev, u_curr = u_curr, u_next
    U_frames[frame] = u_curr.copy()

fig_w, fig_h = 12.0, 4.0
fig_aspect = fig_w/fig_h
x_lo_d, x_hi_d = -0.40, L+0.40
y_lo_d, y_hi_d = -4.5*A, 4.5*A
dx_d, dy_d = x_hi_d-x_lo_d, y_hi_d-y_lo_d
if dx_d/dy_d < fig_aspect:
    extra = (fig_aspect*dy_d - dx_d)/2.0
    x_lo, x_hi = x_lo_d-extra, x_hi_d+extra
    y_lo, y_hi = y_lo_d, y_hi_d
else:
    extra = (dx_d/fig_aspect - dy_d)/2.0
    x_lo, x_hi = x_lo_d, x_hi_d
    y_lo, y_hi = y_lo_d-extra, y_hi_d+extra

fig = plt.figure(figsize=(fig_w,fig_h), facecolor="#1a1a2e")
ax = fig.add_axes([0,0,1,1]); ax.set_facecolor("#16213e")
ax.set_xlim(x_lo,x_hi); ax.set_ylim(y_lo,y_hi)
ax.set_aspect("equal"); ax.axis("off")
ax.axhline(0.0, color="#3a4357", lw=1, ls="--", zorder=0)
ax.plot([0,0],[y_lo,y_hi], color="#4a4e69", lw=1.5, ls=":", zorder=1)
driver_dot = Circle((0,0), 0.04, facecolor="#e63946",
                    edgecolor="#adb5bd", lw=1.0, zorder=5)
ax.add_patch(driver_dot)
r_x = 0.22; r_y = 0.11
back_arc = Arc((L,0), 2*r_x, 2*r_y, theta1=0, theta2=180,
               edgecolor="#e63946", lw=10, zorder=2)
ax.add_patch(back_arc)
ax.plot([L,L],[y_lo,y_hi], color="#adb5bd", lw=14, solid_capstyle="butt", zorder=3)
front_arc = Arc((L,0), 2*r_x, 2*r_y, theta1=180, theta2=360,
                edgecolor="#e63946", lw=10, zorder=5)
ax.add_patch(front_arc)
n_cut = int(round(r_x/dx))
n_inside = (N+1) - n_cut
str_x_plot = x_grid[:n_inside]
str_line, = ax.plot([],[], color="#a8dadc", lw=2.4, zorder=4)

def update(f):
    u = U_frames[f]; yy = u[-1]
    str_y = u[:n_inside].copy(); str_y[-1] = yy
    str_line.set_data(str_x_plot, str_y)
    driver_dot.center = (0, u[0])
    back_arc.set_center((L, yy))
    front_arc.set_center((L, yy))
    return str_line, driver_dot, back_arc, front_arc

ani = animation.FuncAnimation(fig, update, frames=n_frames,
                              interval=1000.0/fps, blit=False)
ani.save("video.mp4", writer=animation.FFMpegWriter(fps=fps, bitrate=1800), dpi=120)
plt.close()
print("Saved video.mp4")