def circular_random_walk(step_options = [0, 0.5, 1], size = 100000):
fig, axs = plt.subplots()
plt.xlabel("Position - x")
plt.ylabel("Position - y")
Radius = 100
step_addition = 0
randomWalk_x= [0]
randomWalk_y= [0]
counter = 1
while counter < (size + 1):
i = counter
angle = np.random.uniform(0, 2*np.pi, size = 1)
distance = np.random.choice(step_options, size = 1)
x_coordinate = distance[0] * np.cos(angle[0])
y_coordinate = distance[0] * np.sin(angle[0])
new_x = randomWalk_x[-1] + x_coordinate
new_y = randomWalk_y[-1] + y_coordinate
distance_from_origin = math.sqrt((new_x)**2 + (new_y)**2)
if distance_from_origin >= (Radius):
new_x = ('%.3f'%(new_x))
new_y = ('%.3f'%(new_y))
old_x = randomWalk_x[-1]
old_y = randomWalk_y[-1]
old_x = ('%.3f'%(old_x))
old_y = ('%.3f'%(old_y))
p1, p2 = Point(old_x, old_y) , Point(new_x, new_y)
if p1.equals(p2):
randomWalk_x.append(old_x)
randomWalk_y.append(old_y)
counter+=1
continue
line = Line(p1, p2)
a, b, c = line.coefficients
x, y = symbols('x,y')
eq1 = Eq((x)**2 + (y)**2 - (Radius)**2, 0, evaluate=False)
eq2 = Eq((a*x) + (b*y) + c, 0, evaluate=False)
sol = solve([eq1, eq2], [x, y])
#find the point on the circumference where our line will touch, call it circpoint
try:
sol1 = Point(sol[0][0], sol[0][1])
sol2 = Point(sol[1][0], sol[1][1])
dist_sol1 = p1.distance(sol1)
dist_sol2 = p1.distance(sol2)
if dist_sol1 > dist_sol2:
circ_point = sol[1]
elif dist_sol1 < dist_sol2:
circ_point = sol[0]
else:
d1 = sol1.distance(p2)
d2 = sol2.distance(p2)
if d1 < d2:
circ_point = sol[0]
else:
circ_point = sol[1]
circ_point = Point(circ_point[0], circ_point[1])
except:
randomWalk_x.append(old_x)
randomWalk_y.append(old_y)
counter+=1
continue
#we know the overflow amount, call that overflowed
overflowed = p2.distance(circ_point)
#get the vector from our curr_pos to circpoint, call it incident
incident = np.array([circ_point[0] - p1[0], circ_point[1] - p1[1]])
#circpoint to origin vector
normal = np.array([circ_point[0], circ_point[1]])
#-find the angle between incident and normal using dot product wali equation, call that theta
if p1.equals(circ_point):
randomWalk_x.append(old_x)
randomWalk_y.append(old_y)
counter+=1
continue
dot = (circ_point[0]*incident[0]) + (circ_point[1]*incident[1])
magnitude1 = (circ_point[0]**2 + circ_point[1]**2)**(0.5)
magnitude2 = (incident[0]**2 + incident[1]**2)**(0.5)
ang = dot / (magnitude1 * magnitude2)
main_ang = math.acos(ang)
Theta = main_ang
if p2[0] < 0 and p2[1] > 0: #second
Theta = -Theta
elif p2[0] > 0 and p2[1] > 0: #first
if incident[1] >= incident[0]:
Theta = (-Theta)
else:
Theta = (Theta)
elif p2[0] > 0 and p2[1] < 0:
if incident[1] > -incident[0]: #fourth
Theta = (-Theta)
elif p2[0] < 0 and p2[1] < 0:
if incident[1] <= incident[0]:
Theta = (-Theta)
#-form a 2x2 rotation matrix, uska format dekh lo aram se mile ga
rotation_matrix = np.array([[np.cos(Theta), -np.sin(Theta)],[np.sin(Theta), np.cos(Theta)]])
#-multiply the rotation matrix by the normal vector to get another 2x1 vector, call it reflected
reflected = np.dot(rotation_matrix, normal)
reflected *= -1
#-find the unit vector in the direction of reflected, call it ref_unit
ref_unit = reflected / math.sqrt(reflected[0]**2 + reflected[1]**2)
#-scalar multiply ref_unit with overflow
ref_point = ref_unit * overflowed
#-us vector ke components ko add to circpoint ke coordinates to get the final coordinates
final = circ_point + ref_point
#-add both circ point (optional but will look better) and final coord to the arrays
randomWalk_x.append(circ_point[0])
randomWalk_y.append(circ_point[1])
distance_from_origin = math.sqrt((final[0])**2 + (final[1])**2)
counter+=1
if distance_from_origin >= Radius:
continue
else:
randomWalk_x.append(final[0])
randomWalk_y.append(final[1])
step_addition += 1
continue
randomWalk_x.append(new_x)
randomWalk_y.append(new_y)
counter += 1
### Uncomment to see plot
#return distance_from_origin
#########################
size = size + step_addition
#########################################################
#UNCOMMENT FOR ANIMATION
# xdata, ydata = [], []
# ln, = plt.plot(xdata,ydata)
# def init():
# #Radius = 5.64189584 when area of circle = 100 unit^2
# axs.set_xlim(-Radius,Radius)
# axs.set_ylim(-Radius,Radius)
# ln.set_data([], [])
# return ln,
# def update(frame):
# xdata.append(randomWalk_x[int(frame)])
# ydata.append(randomWalk_y[int(frame)])
# ln.set_data(xdata, ydata)
# return ln,
# ani = FuncAnimation(fig, update, frames=np.linspace(0, size, size+1, endpoint=True), interval = 20,
# init_func=init, blit=True, repeat=False)
#ANIMATION CODE
########################################################
circle1=plt.Circle((0,0),Radius,color='r', alpha= 0.2)
plt.gcf().gca().add_artist(circle1)
plt.plot(randomWalk_x, randomWalk_y)
plt.show()
def circular_random_walk():
fig, axs = plt.subplots()
plt.xlabel("Position - x")
plt.ylabel("Position - y")
Radius = 100
step_addition_A = 0
step_addition_B = 0
#####
##Choosing initial points
r_A = np.random.uniform(0, Radius)
r_B = np.random.uniform(0, Radius)
thet_A = np.random.uniform(0, 2 * np.pi)
thet_B = np.random.uniform(0, 2 * np.pi)
x_A = r_A * np.cos(thet_A)
y_A = r_A * np.sin(thet_A)
x_B = r_B * np.cos(thet_B)
y_B = r_B * np.sin(thet_B)
####
randomWalk_x_A = [x_A]
randomWalk_y_A = [y_A]
randomWalk_x_B = [x_B]
randomWalk_y_B = [y_B]
flag_A_ref = False
flag_B_ref = False
steps = 0
counter = 0
while True:
angle_A = np.random.uniform(0, 2 * np.pi, size=1)
angle_B = np.random.uniform(0, 2 * np.pi, size=1)
distance_A = np.random.uniform(0, 1, size=1)
distance_B = np.random.uniform(0, 1, size=1)
x_coordinate_A = distance_A[0] * np.cos(angle_A[0])
y_coordinate_A = distance_A[0] * np.sin(angle_A[0])
x_coordinate_B = distance_B[0] * np.cos(angle_B[0])
y_coordinate_B = distance_B[0] * np.sin(angle_B[0])
new_x_A = randomWalk_x_A[-1] + x_coordinate_A
new_y_A = randomWalk_y_A[-1] + y_coordinate_A
new_x_B = randomWalk_x_B[-1] + x_coordinate_B
new_y_B = randomWalk_y_B[-1] + y_coordinate_B
distance_from_origin_A = ((new_x_A)**2 + (new_y_A)**2)**(0.5)
distance_from_origin_B = ((new_x_B)**2 + (new_y_B)**2)**(0.5)
while distance_from_origin_A >= (Radius):
new_x_A = '%.3f' % (new_x_A)
new_y_A = '%.3f' % (new_y_A)
old_x_A = '%.3f' % (randomWalk_x_A[-1])
old_y_A = '%.3f' % (randomWalk_y_A[-1])
p1, p2 = Point(old_x_A, old_y_A), Point(new_x_A, new_y_A)
if p1.equals(p2):
randomWalk_x_A.append(old_x_A)
randomWalk_y_A.append(old_y_A)
flag_A_ref = True
break
line = Line(p1, p2)
a, b, c = line.coefficients
x, y = symbols('x,y')
eq1 = Eq((x)**2 + (y)**2 - (Radius)**2, 0, evaluate=False)
eq2 = Eq((a * x) + (b * y) + c, 0, evaluate=False)
sol = solve([eq1, eq2], [x, y])
#find the point on the circumference where our line will touch, call it circpoint
sol1 = (sol[0][0], sol[0][1])
sol2 = (sol[1][0], sol[1][1])
d1 = ((p2[0] - sol1[0])**2 + (p2[1] - sol1[1])**2)**(0.5)
d2 = ((p2[0] - sol2[0])**2 + (p2[1] - sol2[1])**2)**(0.5)
if d1 <= d2:
circ_point = sol[0]
else:
circ_point = sol[1]
circ_point = Point(circ_point[0], circ_point[1])
#we know the overflow amount, call that overflowed
overflowed = p2.distance(circ_point)
#get the vector from our curr_pos to circpoint, call it incident
incident = np.array([circ_point[0] - p1[0], circ_point[1] - p1[1]])
#circpoint to origin vector
normal = np.array([circ_point[0], circ_point[1]])
#-find the angle between incident and normal using dot product wali equation, call that theta
if p1.equals(circ_point):
randomWalk_x_A.append(old_x_A)
randomWalk_y_A.append(old_y_A)
flag_A_ref = True
break
dot = (circ_point[0] * incident[0]) + (circ_point[1] * incident[1])
magnitude1 = math.sqrt(circ_point[0]**2 + circ_point[1]**2)
magnitude2 = math.sqrt(incident[0]**2 + incident[1]**2)
ang = dot / (magnitude1 * magnitude2)
main_ang = math.acos(ang)
Theta = main_ang
if p2[0] < 0 and p2[1] > 0: #second
Theta = -Theta
elif p2[0] > 0 and p2[1] > 0: #first
if incident[1] >= incident[0]:
Theta = -Theta
elif p2[0] > 0 and p2[1] < 0:
if incident[1] > -incident[0]: #fourth
Theta = -Theta
elif p2[0] < 0 and p2[1] < 0:
if incident[1] <= incident[0]:
Theta = -Theta
#-form a 2x2 rotation matrix, uska format dekh lo aram se mile ga
rotation_matrix = np.array([[np.cos(Theta), -np.sin(Theta)],
[np.sin(Theta),
np.cos(Theta)]])
#-multiply the rotation matrix by the normal vector to get another 2x1 vector, call it reflected
reflected = np.dot(rotation_matrix, normal)
reflected *= -1
#-find the unit vector in the direction of reflected, call it ref_unit
ref_unit = reflected / math.sqrt(reflected[0]**2 + reflected[1]**2)
#-scalar multiply ref_unit with overflow
ref_point = ref_unit * overflowed
#-us vector ke components ko add to circpoint ke coordinates to get the final coordinates
final = circ_point + ref_point
#-add both circ point (optional but will look better) and final coord to the arrays
randomWalk_x_A.append(circ_point[0])
randomWalk_y_A.append(circ_point[1])
distance_from_origin = math.sqrt((final[0])**2 + (final[1])**2)
if distance_from_origin >= Radius:
flag_A_ref = True
break
else:
randomWalk_x_A.append(final[0])
randomWalk_y_A.append(final[1])
step_addition_A += 1
flag_A_ref = True
break
while distance_from_origin_B >= (Radius):
new_x_B = '%.3f' % (new_x_B)
new_y_B = '%.3f' % (new_y_B)
old_x_B = '%.3f' % (randomWalk_x_B[-1])
old_y_B = '%.3f' % (randomWalk_y_B[-1])
p1, p2 = Point(old_x_B, old_y_B), Point(new_x_B, new_y_B)
if p1.equals(p2):
randomWalk_x_B.append(old_x_B)
randomWalk_y_B.append(old_y_B)
flag_B_ref = True
break
line = Line(p1, p2)
a, b, c = line.coefficients
x, y = symbols('x,y')
eq1 = Eq((x)**2 + (y)**2 - (Radius)**2, 0, evaluate=False)
eq2 = Eq((a * x) + (b * y) + c, 0, evaluate=False)
sol = solve([eq1, eq2], [x, y])
#find the point on the circumference where our line will touch, call it circpoint
sol1 = (sol[0][0], sol[0][1])
sol2 = (sol[1][0], sol[1][1])
d1 = ((p2[0] - sol1[0])**2 + (p2[1] - sol1[1])**2)**(0.5)
d2 = ((p2[0] - sol2[0])**2 + (p2[1] - sol2[1])**2)**(0.5)
if d1 <= d2:
circ_point = sol[0]
else:
circ_point = sol[1]
circ_point = Point(circ_point[0], circ_point[1])
#we know the overflow amount, call that overflowed
overflowed = p2.distance(circ_point)
#get the vector from our curr_pos to circpoint, call it incident
incident = np.array([circ_point[0] - p1[0], circ_point[1] - p1[1]])
#circpoint to origin vector
normal = np.array([circ_point[0], circ_point[1]])
#-find the angle between incident and normal using dot product wali equation, call that theta
if p1.equals(circ_point):
randomWalk_x_B.append(old_x_B)
randomWalk_y_B.append(old_y_B)
flag_B_ref = True
break
dot = (circ_point[0] * incident[0]) + (circ_point[1] * incident[1])
magnitude1 = math.sqrt(circ_point[0]**2 + circ_point[1]**2)
magnitude2 = math.sqrt(incident[0]**2 + incident[1]**2)
ang = dot / (magnitude1 * magnitude2)
main_ang = math.acos(ang)
Theta = main_ang
if p2[0] < 0 and p2[1] > 0: #second
Theta = -Theta
elif p2[0] > 0 and p2[1] > 0: #first
if incident[1] >= incident[0]:
Theta = -Theta
elif p2[0] > 0 and p2[1] < 0:
if incident[1] > -incident[0]: #fourth
Theta = -Theta
elif p2[0] < 0 and p2[1] < 0:
if incident[1] <= incident[0]:
Theta = -Theta
#-form a 2x2 rotation matrix, uska format dekh lo aram se mile ga
rotation_matrix = np.array([[np.cos(Theta), -np.sin(Theta)],
[np.sin(Theta),
np.cos(Theta)]])
#-multiply the rotation matrix by the normal vector to get another 2x1 vector, call it reflected
reflected = np.dot(rotation_matrix, normal)
reflected *= -1
#-find the unit vector in the direction of reflected, call it ref_unit
ref_unit = reflected / math.sqrt(reflected[0]**2 + reflected[1]**2)
#-scalar multiply ref_unit with overflow
ref_point = ref_unit * overflowed
#-us vector ke components ko add to circpoint ke coordinates to get the final coordinates
final = circ_point + ref_point
#-add both circ point (optional but will look better) and final coord to the arrays
randomWalk_x_B.append(circ_point[0])
randomWalk_y_B.append(circ_point[1])
distance_from_origin = ((final[0])**2 + (final[1])**2)**(0.5)
if distance_from_origin >= Radius:
flag_B_ref = True
break
else:
randomWalk_x_B.append(final[0])
randomWalk_y_B.append(final[1])
step_addition_B += 1
flag_B_ref = True
break
if flag_A_ref:
pass
else:
randomWalk_x_A.append(new_x_A)
randomWalk_y_A.append(new_y_A)
if flag_B_ref:
pass
else:
randomWalk_x_B.append(new_x_B)
randomWalk_y_B.append(new_y_B)
flag_A_ref = False
flag_B_ref = False
steps += 1
curr_A = (randomWalk_x_A[-1], randomWalk_y_A[-1])
curr_B = (randomWalk_x_B[-1], randomWalk_y_B[-1])
dist_between_particles = ((curr_B[0] - curr_A[0])**2 +
(curr_B[1] - curr_A[1])**2)**(0.5)
counter += 1
if counter % 1000 == 0:
print(counter)
if dist_between_particles <= 1:
break
#return steps
size_A = steps + step_addition_A
size_B = steps + step_addition_B
########################################################
#UNCOMMENT FOR ANIMATION
# xdata, ydata = [], []
# ln, = plt.plot(xdata,ydata)
# def init():
# #Radius = 5.64189584 when area of circle = 100 unit^2
# axs.set_xlim(-Radius,Radius)
# axs.set_ylim(-Radius,Radius)
# ln.set_data([], [])
# return ln,
# def update(frame):
# xdata.append(randomWalk_x[int(frame)])
# ydata.append(randomWalk_y[int(frame)])
# ln.set_data(xdata, ydata)
# return ln,
# ani = FuncAnimation(fig, update, frames=np.linspace(0, size, size+1, endpoint=True), interval = 20,
# init_func=init, blit=True, repeat=False)
#ANIMATION CODE
#######################################################
circle1 = plt.Circle((0, 0), Radius, color='r', alpha=0.2)
plt.gcf().gca().add_artist(circle1)
plt.plot(randomWalk_x_A, randomWalk_y_A)
plt.plot(randomWalk_x_B, randomWalk_y_B)
plt.show()