r"""
Comparing All Five Billiards
=============================

Every billiard here is a point particle moving in a straight line at
constant speed inside a closed boundary, undergoing specular reflection

.. math::

    \mathbf{v}' = \mathbf{v} - 2(\mathbf{v}\cdot\mathbf{n})\,\mathbf{n}

whenever it strikes the boundary; the five shapes below differ only in that
boundary's geometry: a disk :math:`x^2+y^2=r^2` (Circle), a rectangle
:math:`|x|\le w/2,\ |y|\le h/2` (Rectangle), a disk with a flat chord cut
off (Truncated Circle), a square cell with a circular scatterer removed from
its center (Sinai), and two semicircular caps joined by straight edges
(Bunimovich Stadium). This is a side-by-side comparison of the Poincare
section for every billiard shape ``physicskit.chaos`` ships, from fully
integrable (Circle, Rectangle) through mixed (Truncated Circle) to fully
chaotic (Sinai, Bunimovich Stadium).
"""

import matplotlib.pyplot as plt

from physicskit.chaos.systems.billiards import (
    BunimovichStadium,
    CircleBilliard,
    RectangleBilliard,
    SinaiBilliard,
    TruncatedCircleBilliard,
)
from physicskit.chaos.visualizers.phase_space import plot_poincare_section

# %%
# Build one instance of each billiard and plot its Poincare section into its
# own subplot, using the ``ax=`` parameter of
# :func:`physicskit.chaos.visualizers.phase_space.plot_poincare_section` to draw into
# a shared figure.
billiards = {
    "Circle (integrable)": CircleBilliard(radius=1.0),
    "Rectangle (integrable)": RectangleBilliard(width=2.0, height=1.0),
    "Truncated Circle (mixed)": TruncatedCircleBilliard(radius=1.0, cut=0.3),
    "Sinai (chaotic)": SinaiBilliard(cell_size=2.0, scatterer_radius=0.5),
    "Bunimovich Stadium (chaotic)": BunimovichStadium(radius=1.0, straight_length=2.0),
}

fig, axes = plt.subplots(2, 3, figsize=(15, 9))
for ax, (name, billiard) in zip(axes.flat, billiards.items()):
    plot_poincare_section(billiard, n_rays=25, n_bounces=150, ax=ax, s=1.0)
    ax.set_title(name)
axes.flat[-1].axis("off")
fig.tight_layout()

plt.show()