"""
======================
Tricontour Smooth User
======================

Demonstrates high-resolution tricontouring on user-defined triangular grids
with `matplotlib.tri.UniformTriRefiner`.
"""
import matplotlib.tri as tri
import matplotlib.pyplot as plt
import numpy as np


# ----------------------------------------------------------------------------
# Analytical test function
# ----------------------------------------------------------------------------
def function_z(x, y):
    r1 = np.sqrt((0.5 - x)**2 + (0.5 - y)**2)
    theta1 = np.arctan2(0.5 - x, 0.5 - y)
    r2 = np.sqrt((-x - 0.2)**2 + (-y - 0.2)**2)
    theta2 = np.arctan2(-x - 0.2, -y - 0.2)
    z = -(2 * (np.exp((r1 / 10)**2) - 1) * 30. * np.cos(7. * theta1) +
          (np.exp((r2 / 10)**2) - 1) * 30. * np.cos(11. * theta2) +
          0.7 * (x**2 + y**2))
    return (np.max(z) - z) / (np.max(z) - np.min(z))

# ----------------------------------------------------------------------------
# Creating a Triangulation
# ----------------------------------------------------------------------------
# First create the x and y coordinates of the points.
n_angles = 20
n_radii = 10
min_radius = 0.15
radii = np.linspace(min_radius, 0.95, n_radii)

angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
angles[:, 1::2] += np.pi / n_angles

x = (radii * np.cos(angles)).flatten()
y = (radii * np.sin(angles)).flatten()
z = function_z(x, y)

# Now create the Triangulation.
# (Creating a Triangulation without specifying the triangles results in the
# Delaunay triangulation of the points.)
triang = tri.Triangulation(x, y)

# Mask off unwanted triangles.
triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
                         y[triang.triangles].mean(axis=1))
                < min_radius)

# ----------------------------------------------------------------------------
# Refine data
# ----------------------------------------------------------------------------
refiner = tri.UniformTriRefiner(triang)
tri_refi, z_test_refi = refiner.refine_field(z, subdiv=3)

# ----------------------------------------------------------------------------
# Plot the triangulation and the high-res iso-contours
# ----------------------------------------------------------------------------
fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.triplot(triang, lw=0.5, color='white')

levels = np.arange(0., 1., 0.025)
ax.tricontourf(tri_refi, z_test_refi, levels=levels, cmap='terrain')
ax.tricontour(tri_refi, z_test_refi, levels=levels,
              colors=['0.25', '0.5', '0.5', '0.5', '0.5'],
              linewidths=[1.0, 0.5, 0.5, 0.5, 0.5])

ax.set_title("High-resolution tricontouring")

plt.show()

#############################################################################
#
# .. admonition:: References
#
#    The use of the following functions, methods, classes and modules is shown
#    in this example:
#
#    - `matplotlib.axes.Axes.tricontour` / `matplotlib.pyplot.tricontour`
#    - `matplotlib.axes.Axes.tricontourf` / `matplotlib.pyplot.tricontourf`
#    - `matplotlib.tri`
#    - `matplotlib.tri.Triangulation`
#    - `matplotlib.tri.UniformTriRefiner`
