"""Fill four compatible Bezier boundary curves with a Coons patch."""
import numpy as np
import matplotlib.pyplot as plt
import nurbspy as nrb

nrb.set_plot_options()

# South and north run west to east; west and east run south to north.
south = nrb.NurbsCurve(np.array([[0., 1., 2., 3.],
                                 [0., 0., 0., 0.],
                                 [0., -0.4, -0.4, 0.]]))
north = nrb.NurbsCurve(np.array([[0., 1., 2., 3.],
                                 [2., 2., 2., 2.],
                                 [0.5, 1.4, 1.4, 0.5]]))
west = nrb.NurbsCurve(np.array([[0., 0., 0., 0.],
                                [0., 2/3, 4/3, 2.],
                                [0., 0.8, 1.1, 0.5]]))
east = nrb.NurbsCurve(np.array([[3., 3., 3., 3.],
                                [0., 2/3, 4/3, 2.],
                                [0., -0.3, 0.2, 0.5]]))
surface = nrb.NurbsSurfaceCoons(
    C_south=south, C_north=north, C_west=west, C_east=east,
).NurbsSurface

t = np.linspace(0., 1., 61)
boundaries = [
    ("south", south, t, np.zeros_like(t)),
    ("north", north, t, np.ones_like(t)),
    ("west", west, np.zeros_like(t), t),
    ("east", east, np.ones_like(t), t),
]
print("Control net shape:", surface.P.shape)
print(f"Degrees: ({surface.p}, {surface.q})")
for name, curve, u, v in boundaries:
    error = np.max(np.abs(surface.get_value(u, v) - curve.get_value(t)))
    print(f"Maximum {name} boundary error: {error:.2e}")

fig, ax = surface.plot(surface_color=nrb.COLORS_MATLAB[0],
                       boundary=False, isocurves_u=9, isocurves_v=9)
for _, curve, _, _ in boundaries:
    curve.plot_curve(fig, ax, color=nrb.COLORS_MATLAB[1], linewidth=2.5)
ax.set_title("Coons patch bounded by four curves")
ax.view_init(elev=30, azim=-55)
# Leave room for the 3D axis labels when displaying or exporting the figure.
fig.set_size_inches(7, 6)
fig.subplots_adjust(left=0.05, right=0.85, bottom=0.15, top=0.9)
ax.set(xlabel="$x$", ylabel="$y$", zlabel="$z$")
for axis in (ax.xaxis, ax.yaxis, ax.zaxis):
    axis.labelpad = 4
plt.show()