billiards.py

# Write a program simulating "billiards on a circle". More precisely: inside the unit circle,
# a particle (point) moves on the plane, maintaining a constant speed, until it hits the edge
# i.e. the circle, then it reflects according to the principle that the angle of incidence equals
# the angle of reflection; it is about the angle between the velocity vector and the radius of
# the unit circle at the point where the path intersects with the circle, after reflection it is
# the same in value but on the other side of the radius. The program should draw the unit circle
# and the path of the particle inside this circle, depending on from the initial position,
# the direction of the initial velocity (the velocity value is irrelevant as it is constant),
# and the observation time.

# %%
import numpy as np
import matplotlib.pyplot as plt

# %%

r = 1.0                         # circle radius

p = np.array([0.5,  0.7])       # initial position (x, y)
v = np.array([1.0, -0.4])       # initial velocity (vx, vy)

T = 20.                         # total simulation time

# %%

# Your code here


# %%
plt.show()