def test_plot_obstacles():
obs = [
billiards.obstacles.Disk((0, 0), 10),
billiards.obstacles.InfiniteWall((-1, -20), (1, -20)),
]
bld = billiards.Billiard(obstacles=obs)
fig, ax = visualize.default_fig_and_ax()
artists = visualize.plot_obstacles(bld, ax)
assert len(artists) == len(bld.obstacles)
def _create_newtons_cradle(num_balls=5, with_walls=True):
if with_walls:
left = -4
right = 2 * num_balls + 3
obs = [
InfiniteWall((left, -2), (left, 2), "right"),
InfiniteWall((right, -2), (right, 2)),
]
else:
obs = []
bld = billiards.Billiard(obstacles=obs)
bld.add_ball((-3, 0), (1, 0), 1)
for i in range(1, num_balls):
bld.add_ball((2 * i, 0), (0, 0), radius=1)
return bld
def make_data(obs):
ics = []
Xs = []
Ys = []
tss = []
angle = np.random.uniform(low=0, high=(2 * pi), size=(10,))
vels = 0.2 * np.vstack(([np.cos(angle), np.sin(angle)])).T
positions = np.vstack(([np.random.uniform(low=-2, high=2, size=(10,)),
np.random.uniform(low=-2, high=2, size=(10,))])).T
for i in positions:
for j in vels:
ic = []
ts = [0]
bld = billiards.Billiard(obstacles=obs)
#print(i.shape, j.shape)
bld.add_ball(i, j, radius=0)
for k in range(10):
[(fl, _)] = bld.obstacles_toi
bld.evolve(fl)
p, v = bld.balls_position, bld.balls_velocity
#print(p.shape, v.shape, fl.shape)
ic.append(np.hstack((p, v)))
ts.append(fl.reshape(1, 1))
tss.append(ts)
#print(np.asarray(ic).shape)
ics.append(ic)
for i in ics:
X = i[:-1]
Y = i[1:]
Xs.append(X)
Ys.append(Y)
Xs , Ys = np.asarray(Xs).reshape((100, 9, 4)), np.asarray(Ys).reshape((100, 9, 4))
Ts = np.asarray(tss)
np.save("time_steps.npy", Ts, allow_pickle=True)
np.save("input.npy", Xs, allow_pickle=True)
np.save("output.npy", Ys, allow_pickle=True)
print(Ts)
print(Xs.shape)
print(Ys.shape)
from math import cos, pi, sin
from pathlib import Path
import matplotlib.pyplot as plt
import numpy as np
from tqdm import tqdm
import billiards
from billiards import visualize
here = Path(__file__).parent.resolve() # should be docs folder
# Quickstart - Setup
obstacles = [billiards.obstacles.InfiniteWall((0, -1), (0, 1), inside="right")]
bld = billiards.Billiard(obstacles)
bld.add_ball((3, 0), (0, 0), radius=0.2)
bld.add_ball((6, 0), (-1, 0), radius=1, mass=100 ** 5)
fig = visualize.plot(bld)
fig.savefig(here / "_images/quickstart_1.svg")
v_squared = (bld.balls_velocity ** 2).sum(axis=1)
print(f"Kinetic energy before: {(v_squared * bld.balls_mass).sum() / 2}")
print()
# Quickstart - Iteration
print(bld.toi_next)
total_collisions = 0
for i in [1, 2, 3, 4, 5]:
total_collisions += len(bld.evolve(i))
Reference:
Gregory Galperin, "Playing pool with π (the number π from a billiard point of view)",
Regular and Chaotic Dynamics, 2003, 8 (4), 375-394
"""
from math import isinf, pi
import matplotlib.pyplot as plt
import billiards
from billiards import visualize
digits = 6 # number of digits of pi
# setup the billiard table: Wall -- mass -<- MASS
obstacles = [billiards.obstacles.InfiniteWall((0, -1), (0, 1), inside="right")]
bld = billiards.Billiard(obstacles)
bld.add_ball((3, 0), (0, 0), radius=0.2)
bld.add_ball((6, 0), (-1, 0), radius=1, mass=100 ** (digits - 1))
# simulate until there are no more collisions and print the total number of collisions
total_collisions = 0
while not isinf(bld.toi_next[0]) or not isinf(bld.obstacles_next[0]):
num_collisions = len(bld.evolve(bld.time + 1))
print(f"From t = {bld.time - 1:4} to t = {bld.time:4}: {num_collisions} collisions")
total_collisions += num_collisions
print(f"Total number of collisions: {total_collisions}")
print(f"Value of pi: {pi}")
# reset billiard
bld = billiards.Billiard(obstacles)
from billiards import visualize
# global settings
disk_radius = 0.5 # radius of the disk in the middle
num_balls = 300 # increase this if your computer can handle it
np.random.seed(0) # fix random state for reproducibility
# construct the billiard table
obs = [
billiards.InfiniteWall((-1, -1), (1, -1)), # bottom side
billiards.InfiniteWall((1, -1), (1, 1)), # right side
billiards.InfiniteWall((1, 1), (-1, 1)), # top side
billiards.InfiniteWall((-1, 1), (-1, -1)), # left side
billiards.Disk((0, 0), radius=disk_radius), # disk in the middle
]
bld = billiards.Billiard(obstacles=obs)
# distribute particles uniformly in the square, moving in random directions but
# with the same speed
for _i in range(num_balls):
pos = np.random.uniform((-1, -1), (1, 1))
angle = np.random.uniform(0, 2 * pi)
vel = [cos(angle), sin(angle)]
bld.add_ball(pos, vel, radius=0)
bld.balls_velocity /= 5 # slow down
# start the animation
anim = visualize.animate(bld, end_time=10)
anim._fig.set_size_inches((6, 6))
#!/usr/bin/env python3 # -*- coding: utf-8 -*- import os import billiards print(os.getcwd()) # print current working directory # Quickstart bld = billiards.Billiard() fig_name = "_images/quickstart_1.svg" bld.add_ball((2, 0), (4, 0), radius=1) bld.evolve(end_time=10.0) fig = billiards.visualize.plot(bld) fig.savefig(fig_name) print(fig_name) fig2_name = "_images/quickstart_2.svg" bld.add_ball((50, 18), (0, -9), radius=1, mass=2) bld.evolve(14.0) fig2 = billiards.visualize.plot(bld) fig2.savefig(fig2_name) print(fig2_name) # Usage: Newton's cradle anim_name = "_static/newtons_cradle.mp4" bld = billiards.Billiard() bld.add_ball((0, 0), (1, 0), 1)