Develop Reference

How can I connect two points with a series of circles?

I am trying to make realistic water in pygame:
This is till now my code:
from random import randint
import pygame
WIDTH = 700
HEIGHT = 500
win = pygame.display.set_mode((WIDTH, HEIGHT))
WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
AQUA = 'aqua'
RADIUS = 1
x, y = 0, HEIGHT//2
K = 1
FORCE = 100
VELOCITY = 0.5
run = True
class Molecule:
def __init__(self, x, y, radius, force, k):
self.x = x
self.y = y
self.radius = radius
self.force = force
self.k = k
self.max_amplitude = y + force/k
self.min_amplitude = y - force/k
self.up = False
self.down = True
self.restore = False
def draw(self, win):
pygame.draw.circle(win, BLACK, (self.x, self.y), self.radius)
def oscillate(self):
if self.y <= self.max_amplitude and self.down == True:
self.y += VELOCITY
if self.y == self.max_amplitude or self.up:
self.up = True
self.down = False
self.y -= VELOCITY
if self.y == self.min_amplitude:
self.up = False
self.down = True
molecules = []
for i in range(100):
FORCE = randint(10, 20)
molecules.append(Molecule(x, y, RADIUS, FORCE, K))
x += 10
while run:
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
win.fill(WHITE)
for molecule in molecules:
molecule.draw(win)
molecule.oscillate()
for i in range(len(molecules)):
try:
pygame.draw.line(win, BLACK, (molecules[i].x, molecules[i].y), (molecules[i+1].x, molecules[i+1].y))
pygame.draw.line(win, AQUA, (molecules[i].x, molecules[i].y), (molecules[i+1].x, HEIGHT))
except:
pass
pygame.display.flip()
pygame.quit()
But as may expected the water curve is not smooth:
Look at it:
Sample Img1
I want to connect the two randomly added wave points using a set of circles not line like in this one so that a smooth curve could occur.
And in this way i could add the water color to it such that it will draw aqua lines or my desired color line from the point to the end of screen and all this will end up with smooth water flowing simulation.
Now the question is how could i make the points connect together smoothly into a smooth curve by drawing point circles at relative points?

I suggest sticking the segments with a Bézier curves. Bézier curves can be drawn with pygame.gfxdraw.bezier
Calculate the slopes of the tangents to the points along the wavy waterline:
ts = []
for i in range(len(molecules)):
pa = molecules[max(0, i-1)]
pb = molecules[min(len(molecules)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
Use the the tangents to define 4 control points for each segment and draw the curve with pygame.gfxdraw.bezier:
for i in range(len(molecules)-1):
p0 = molecules[i].x, molecules[i].y
p3 = molecules[i+1].x, molecules[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pygame.gfxdraw.bezier(win, [p0, p1, p2, p3], 4, BLACK)
Complete example:
from random import randint
import pygame
import pygame.gfxdraw
WIDTH = 700
HEIGHT = 500
win = pygame.display.set_mode((WIDTH, HEIGHT))
WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
AQUA = 'aqua'
RADIUS = 1
x, y = 0, HEIGHT//2
K = 1
FORCE = 100
VELOCITY = 0.5
class Molecule:
def __init__(self, x, y, radius, force, k):
self.x = x
self.y = y
self.radius = radius
self.force = force
self.k = k
self.max_amplitude = y + force/k
self.min_amplitude = y - force/k
self.up = False
self.down = True
self.restore = False
def draw(self, win):
pygame.draw.circle(win, BLACK, (self.x, self.y), self.radius)
def oscillate(self):
if self.y <= self.max_amplitude and self.down == True:
self.y += VELOCITY
if self.y == self.max_amplitude or self.up:
self.up = True
self.down = False
self.y -= VELOCITY
if self.y == self.min_amplitude:
self.up = False
self.down = True
molecules = []
for i in range(50):
FORCE = randint(10, 20)
molecules.append(Molecule(x, y, RADIUS, FORCE, K))
x += 20
clock = pygame.time.Clock()
run = True
while run:
clock.tick(100)
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
win.fill(WHITE)
for molecule in molecules:
molecule.draw(win)
molecule.oscillate()
ts = []
for i in range(len(molecules)):
pa = molecules[max(0, i-1)]
pb = molecules[min(len(molecules)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
for i in range(len(molecules)-1):
p0 = molecules[i].x, molecules[i].y
p3 = molecules[i+1].x, molecules[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pygame.gfxdraw.bezier(win, [p0, p1, p2, p3], 4, BLACK)
for i in range(len(molecules)-1):
pygame.draw.line(win, AQUA, (molecules[i].x, molecules[i].y), (molecules[i].x, HEIGHT))
pygame.display.flip()
pygame.quit()
If you want to "fill" the water, you must calculate the points along the Bézier line and draw a filled polygon. How to calculate a Bézier curve is explained in Trying to make a Bezier Curve on PyGame library How Can I Make a Thicker Bezier in Pygame? and "X". You can use the following function:
def ptOnCurve(b, t):
q = b.copy()
for k in range(1, len(b)):
for i in range(len(b) - k):
q[i] = (1-t) * q[i][0] + t * q[i+1][0], (1-t) * q[i][1] + t * q[i+1][1]
return round(q[0][0]), round(q[0][1])
def bezier(b, samples):
return [ptOnCurve(b, i/samples) for i in range(samples+1)]
Use the bezier to stitch the wavy water polygon:
ts = []
for i in range(len(molecules)):
pa = molecules[max(0, i-1)]
pb = molecules[min(len(molecules)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
pts = [(WIDTH, HEIGHT), (0, HEIGHT)]
for i in range(len(molecules)-1):
p0 = molecules[i].x, molecules[i].y
p3 = molecules[i+1].x, molecules[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pts += bezier([p0, p1, p2, p3], 4)
Draw the polygon with pygame.draw.polygon():
pygame.draw.polygon(win, AQUA, pts)
Complete example:
from random import randint
import pygame
class Node:
def __init__(self, x, y, force, k, v):
self.x = x
self.y = y
self.y0 = y
self.force = force
self.k = k
self.v = v
self.direction = 1
def oscillate(self):
self.y += self.v * self.direction
if self.y0 - self.force / self.k > self.y or self.y0 + self.force / self.k < self.y:
self.direction *= -1
def draw(self, surf):
pygame.draw.circle(surf, "black", (self.x, self.y), 3)
window = pygame.display.set_mode((700, 500))
clock = pygame.time.Clock()
width, height = window.get_size()
no_of_nodes = 25
dx = width / no_of_nodes
nodes = [Node(i*dx, height//2, randint(15, 30), 1, 0.5) for i in range(no_of_nodes+1)]
def ptOnCurve(b, t):
q = b.copy()
for k in range(1, len(b)):
for i in range(len(b) - k):
q[i] = (1-t) * q[i][0] + t * q[i+1][0], (1-t) * q[i][1] + t * q[i+1][1]
return round(q[0][0]), round(q[0][1])
def bezier(b, samples):
return [ptOnCurve(b, i/samples) for i in range(samples+1)]
run = True
while run:
clock.tick(100)
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
for molecule in nodes:
molecule.oscillate()
ts = []
for i in range(len(nodes)):
pa = nodes[max(0, i-1)]
pb = nodes[min(len(nodes)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
pts = [(width, height), (0, height)]
for i in range(len(nodes)-1):
p0 = nodes[i].x, nodes[i].y
p3 = nodes[i+1].x, nodes[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pts += bezier([p0, p1, p2, p3], 4)
window.fill("white")
pygame.draw.polygon(window, 'aqua', pts)
for molecule in nodes:
molecule.draw(window)
pygame.display.flip()
pygame.quit()
exit()

finding velx, and vely knowing only final x, y and g [duplicate]

So I created this parabola class which can be instantiated with 3 parameters (a, b and c) or with 3 points belonging to the parabola. The punti() function returns all the points belonging to the parabola in a range defined by n and m. Here's the code (Most of this is in Italian, sorry):
class Parabola:
def __init__(self, tipo=0, *params):
'''
Il tipo è 0 per costruire la parabola con a, b, c; 1 per costruire la parabola con
tre punti per la quale passa
'''
if tipo == 0:
self.__a = params[0]
self.__b = params[1]
self.__c = params[2]
self.__delta = self.__b ** 2 - (4 * self.__a * self.__c)
elif tipo == 1:
matrix_a = np.array([
[params[0][0]**2, params[0][0], 1],
[params[1][0]**2, params[1][0], 1],
[params[2][0]**2, params[2][0], 1]
])
matrix_b = np.array([params[0][1], params[1][1], params[2][1]])
matrix_c = np.linalg.solve(matrix_a, matrix_b)
self.__a = round(matrix_c[0], 2)
self.__b = round(matrix_c[1], 2)
self.__c = round(matrix_c[2], 2)
self.__delta = self.__b ** 2 - (4 * self.__a * self.__c)
def trovaY(self, x):
y = self.__a * x ** 2 + self.__b * x + self.__c
return y
def punti(self, n, m, step=1):
output = []
for x in range(int(min(n, m)), int(max(n, m)) + 1, step):
output.append((x, self.trovaY(x)))
return output
Now my little game is about shooting targets with a bow and i have to use the parabola for the trajectory and it passes by 3 points:
The player center
A point with the cursor's x and player's y
A point in the middle with the cursors's y
The trajectory is represented by a black line but it clearly doesn't work and I can't understand why. Here's the code of the game (Don't mind about the bow's rotation, I still have to make it function properly):
import os
import sys
import pygame
from random import randint
sys.path.insert(
1, __file__.replace("pygame-prototype\\" + os.path.basename(__file__), "coniche\\")
)
import parabola
# Initialization
pygame.init()
WIDTH, HEIGHT = 1024, 576
screen = pygame.display.set_mode((WIDTH, HEIGHT))
# Function to rotate without losing quality
def rot_from_zero(surface, angle):
rotated_surface = pygame.transform.rotozoom(surface, angle, 1)
rotated_rect = rotated_surface.get_rect()
return rotated_surface, rotated_rect
# Function to map a range of values to another
def map_range(value, leftMin, leftMax, rightMin, rightMax):
# Figure out how 'wide' each range is
leftSpan = leftMax - leftMin
rightSpan = rightMax - rightMin
# Convert the left range into a 0-1 range (float)
valueScaled = float(value - leftMin) / float(leftSpan)
# Convert the 0-1 range into a value in the right range.
return rightMin + (valueScaled * rightSpan)
# Player class
class Player:
def __init__(self, x, y, width=64, height=64):
self.rect = pygame.Rect(x, y, width, height)
self.dirx = 0
self.diry = 0
def draw(self):
rectangle = pygame.draw.rect(screen, (255, 0, 0), self.rect)
# Target class
class Target:
def __init__(self, x, y, acceleration=0.25):
self.x, self.y = x, y
self.image = pygame.image.load(
__file__.replace(os.path.basename(__file__), "target.png")
)
self.speed = 0
self.acceleration = acceleration
def draw(self):
screen.blit(self.image, (self.x, self.y))
def update(self):
self.speed -= self.acceleration
self.x += int(self.speed)
if self.speed < -1:
self.speed = 0
player = Player(64, HEIGHT - 128)
# Targets init
targets = []
targets_spawn_time = 3000
previous_ticks = pygame.time.get_ticks()
# Ground animation init
ground_frames = []
for i in os.listdir(__file__.replace(os.path.basename(__file__), "ground_frames")):
ground_frames.append(
pygame.image.load(
__file__.replace(os.path.basename(__file__), "ground_frames\\" + i)
)
) # Load all ground frames
ground_frame_counter = 0 # Keep track of the current ground frame
frame_counter = 0
# Bow
bow = pygame.image.load(__file__.replace(os.path.basename(__file__), "bow.png"))
angle = 0
while 1:
for event in pygame.event.get():
if event.type == pygame.QUIT:
sys.exit()
# Spawning the targets
current_ticks = pygame.time.get_ticks()
if current_ticks - previous_ticks >= targets_spawn_time:
targets.append(Target(WIDTH, randint(0, HEIGHT - 110)))
previous_ticks = current_ticks
screen.fill((101, 203, 214))
player.draw()
for i, e in list(enumerate(targets))[::-1]:
e.draw()
e.update()
if e.x <= -e.image.get_rect().width:
del targets[i]
# Calculating the angle of the bow
mouse_pos = pygame.Vector2(pygame.mouse.get_pos())
angle = map_range(mouse_pos.x, 0, WIDTH, 90, 0)
# Rotate the bow
rotated_bow, rotated_bow_rect = rot_from_zero(bow, angle)
rotated_bow_rect.center = player.rect.center
screen.blit(rotated_bow, rotated_bow_rect)
# Animate the ground
if frame_counter % 24 == 0:
ground_frame_counter += 1
if ground_frame_counter >= len(ground_frames):
ground_frame_counter = 0
for i in range(round(WIDTH / ground_frames[ground_frame_counter].get_rect().width)):
screen.blit(
ground_frames[ground_frame_counter],
(
ground_frames[ground_frame_counter].get_rect().width * i,
HEIGHT - ground_frames[ground_frame_counter].get_rect().height,
),
)
# Calculating the trajectory
mouse_pos.x = (
mouse_pos.x if mouse_pos.x != rotated_bow_rect.centerx else mouse_pos.x + 1
)
# print(mouse_pos, rotated_bow_rect.center)
v_x = rotated_bow_rect.centerx + ((mouse_pos.x - rotated_bow_rect.centerx) / 2)
trajectory_parabola = parabola.Parabola(
1,
rotated_bow_rect.center,
(mouse_pos.x, rotated_bow_rect.centery),
(v_x, mouse_pos.y),
)
trajectory = [(i[0], int(i[1])) for i in trajectory_parabola.punti(0, WIDTH)]
pygame.draw.lines(screen, (0, 0, 0), False, trajectory)
pygame.draw.ellipse(
screen, (128, 128, 128), pygame.Rect(v_x - 15, mouse_pos.y - 15, 30, 30)
)
pygame.draw.ellipse(
screen,
(128, 128, 128),
pygame.Rect(mouse_pos.x - 15, rotated_bow_rect.centery - 15, 30, 30),
)
pygame.display.update()
if frame_counter == 120:
for i in trajectory:
print(i)
frame_counter += 1
You can run all of this and understand what's wrong with it, help?

You round the values of a, b and c to 2 decimal places. This is too inaccurate for this application:
self.__a = round(matrix_c[0], 2)
self.__b = round(matrix_c[1], 2)
self.__c = round(matrix_c[2], 2)
self.__a = matrix_c[0]
self.__b = matrix_c[1]
self.__c = matrix_c[2]

Similar to answer above... rounding is the issue here. This is magnified when the scale of the coordinates gets bigger.
However, disagree with other solution: It does not matter what order you pass the coordinates into your parabola construction. Any order works fine. points are points.
Here is a pic of your original parabola function "drooping" because of rounding error:
p1 = (0, 10) # left
p2 = (100, 10) # right
p3 = (50, 100) # apex
p = Parabola(1, p3, p2, p1)
traj = p.punti(0, 100)
xs, ys = zip(*traj)
plt.scatter(xs, ys)
plt.plot([0, 100], [10, 10], color='r')
plt.show()

Turtle subclass doesn't draw a straight line

I am trying to build a subclass that inherited from turtle.Turtle class and want to create a function to automatically draw the polygon. But I find the initial line always tilts a bit.
I don't know where's the problem.
Here's the code:
import turtle
class Polygon(turtle.Turtle):
def __init__(self, point_list):
self.point_list = point_list
def add_point(self, point):
self.point_list.append(point)
return self.point_list
def over_write_points(self, new_points):
self.point_list = new_points
return self.point_list
def perimeter(self):
length_peri = 0
for i in range(len(self.point_list)):
point1 = self.point_list[i-1]
point2 = self.point_list[i]
x1, y1 = point1
x2, y2 = point2
length = ((x1 - x2)**2 + (y1 - y2)**2)*0.5
length_peri += length
return length_peri
def area(self):
area = 0
for i in range(len(self.point_list)):
point1 = self.point_list[i-1]
point2 = self.point_list[i]
x1, y1 = point1
x2, y2 = point2
trapezoid = ((x2 - x1) * (y1 + y2)) / 2
area = area + trapezoid
area = abs(area)
return area
def bound_points(self):
unzip_list = list(zip(*self.point_list))
x_list = unzip_list[0]
y_list = unzip_list[1]
bound1 = max(x_list), min(y_list)
bound2 = max(x_list), max(y_list)
bound3 = min(x_list), max(y_list)
bound4 = min(x_list), min(y_list)
bound_points = [bound1, bound2, bound3, bound4]
return bound_points
def move_poly(self, dx, dy):
new_point_list = []
for i in self.point_list:
x = i[0] + dx
y = i[1] + dy
new_point = (x, y)
new_point_list.append(new_point)
self.point_list = new_point_list
return self.point_list
def draw_poly(self, lineColour="green", fillColour="yellow"):
start = self.point_list[-1]
turtle.pencolor(lineColour)
turtle.fillcolor(fillColour)
turtle.penup()
turtle.pendown()
turtle.begin_fill()
x, y = start
for point in self.point_list: # go through a list of points
dx, dy = point
turtle.goto(x + dx, y + dy)
turtle.end_fill()
turtle.penup()
turtle.mainloop()
return f'The polygon is finished'
test_polygon = Polygon([(50,0), (50,50), (0,50)])
print(test_polygon.add_point((0, 0)))
print(test_polygon.over_write_points([(100,0), (100,100), (0,100), (0,0)]))
print(test_polygon.perimeter())
print(test_polygon.area())
print(test_polygon.bound_points())
print(test_polygon.move_poly(-10,-10))
print(test_polygon.draw_poly())

You've several problems in your code. First, as #martineau notes (+1), you start drawing from the turtle's home position rather than the first position in your list. (And you need to close the polygon by returning back to that first position.)
The math in your perimeter() function seems wrong:
length = ((x1 - x2)**2 + (y1 - y2)**2)*0.5
That should probably be **0.5 to calculate the square root, not half. You forgot to call super() in your __init__ function.
Also, your draw_poly() is calling functions in module turtle instead of invoking methods on self. This is why I do import Screen, Turtle instead of import turtle, just to avoid this error.
Below is a rework of your code with the above and other fixes:
from turtle import Turtle
class Polygon(Turtle):
def __init__(self, point_list):
super().__init__()
self.point_list = point_list
def add_point(self, point):
self.point_list.append(point)
return self.point_list
def over_write_points(self, new_points):
self.point_list[:] = new_points # reload existing list
return self.point_list
def perimeter(self):
length_peri = 0
for i in range(len(self.point_list)):
point1 = self.point_list[i - 1]
point2 = self.point_list[i]
x1, y1 = point1
x2, y2 = point2
length = ((x1 - x2)**2 + (y1 - y2)**2)**0.5
length_peri += length
return length_peri
def area(self):
area = 0
for i in range(len(self.point_list)):
point1 = self.point_list[i - 1]
point2 = self.point_list[i]
x1, y1 = point1
x2, y2 = point2
trapezoid = ((x2 - x1) * (y1 + y2)) / 2
area += trapezoid
return abs(area)
def bound_points(self):
unzip_list = list(zip(*self.point_list))
x_list = unzip_list[0]
y_list = unzip_list[1]
bound1 = max(x_list), min(y_list)
bound2 = max(x_list), max(y_list)
bound3 = min(x_list), max(y_list)
bound4 = min(x_list), min(y_list)
return [bound1, bound2, bound3, bound4]
def move_poly(self, dx, dy):
new_point_list = []
for x, y in self.point_list:
new_point = (x + dx, y + dy)
new_point_list.append(new_point)
return self.over_write_points(new_point_list)
def draw_poly(self, lineColour='green', fillColour='yellow'):
self.pencolor(lineColour)
self.fillcolor(fillColour)
start, *remaining_points = self.point_list
self.penup()
self.goto(start)
self.pendown()
self.begin_fill()
for point in remaining_points: # go through a list of points
self.goto(point)
self.goto(start)
self.end_fill()
self.penup()
return 'The polygon is finished'
if __name__ == '__main__':
from turtle import Screen
screen = Screen()
test_polygon = Polygon([(50, 0), (50, 50), (0, 50)])
print(test_polygon.add_point((0, 0)))
print(test_polygon.over_write_points([(100, 0), (100, 100), (0, 100), (0, 0)]))
print(test_polygon.perimeter(), "pixels")
print(test_polygon.area(), "pixels squared")
print(test_polygon.bound_points())
print(test_polygon.move_poly(-10, -10))
print(test_polygon.draw_poly())
screen.exitonclick()

Spyder; something in our code is causing the kernel to crash

Does Spyder have a good way to detect what is causing a crash?
All the changes we made are in the ArrayPQ class and the node class, the other code works without our changes.
import math
import numpy as np
import numpy.random as rand
import numpy.linalg as linalg
from tkinter import Tk, Frame, Canvas
class ArrayPQ:
def __init__(self, num_balls):
self.collisionNodes = np.array([])
self.pastCollisions = np.zeros(num_balls)
def parent(self, i):
return (i-1) // 2
def right(self, i):
return (i*2) + 1
def left(self, i):
return (i*2) + 2
def insert(self, i, j, value, num_collisions_i, num_collisions_j):
self.pastCollisions[i] = num_collisions_i
self.pastCollisions[j] = num_collisions_j
self.collisionNodes = np.append(self.collisionNodes, node.nodeinit(self, i, j, value, num_collisions_i, num_collisions_j))
self.heapify1(i)
def heapify1(self, i):
l = self.left(i)
r = self.right(i)
end = len(self.collisionNodes)
top = i
if l < end and self.collisionNodes(i) < self.collisionNodes(l):
top = l
if r < end and self.collisionNodes(top) < self.collisionNodes(r):
top = r
if max != i:
self.swap(i, top)
self.heapify1(top)
def heapify2(self, i):
if self.right(i) + len(self.collisionNodes)
def delete(self, i):
self.swap(self, 0, (len(self.collisionNodes) -1))
del self.collisionNodes[len(self.collisionNodes)-1]
self.heapify1(i)
def swap(self, i, j):
self.collisionNodes[i], self.collisionNodes[j] = self.collisionNodes[j],
self.collisionNodes[i]
def get_next(self):
temp = self.collisionsNodes[0]
return temp.BBi, temp.BBj, temp.T, temp.CCi, temp.CCj
class node:
def nodeinit(self, Bi, Bj, T, Ci, Cj):
self.BBi = Bi
self.BBj = Bj
self.TT = T
self.CCi = Ci
self.CCj = Cj
class Painter:
#__init__ performs the construction of a Painter object
def __init__(self, root, scale=500, border=5, refresh_speed=5,
filename='balls.txt', min_radius=5, max_radius=10, num_balls=20):
#width and height are used to set the simulation borders
width = scale + border
height = scale + border
self.time = 0
#setup will set up the necessary graphics window and the ball list
self.setup(root, width, height, border, refresh_speed)
#Check the input parameter 'filename' to load predetermined simulation
#otherwise set up the default simulation
if filename is None:
self.init_balls(max_radius, min_radius, num_balls)
self.num_balls = num_balls
else:
self.num_balls = self.read_balls(scale, filename)
#Create the priority data structure
self.PQ = ArrayPQ(self.num_balls)
#Initialize all possible collision times
self.init_ball_collision_times()
self.init_wall_collision_times()
#draw will draw the graphics to the window
self.draw()
#refresh is a loop method intended to create animations
self.refresh()
#A blank return indicates the end of the function
return
#setup creates the window to display the graphics along with the red border
#of the simulation
def setup(self, root, width, height, border, refresh_speed):
# Draw frame etc
self.app_frame = Frame(root)
self.app_frame.pack()
self.canvas = Canvas(self.app_frame, width = width, height = height)
self.canvas_size = (int(self.canvas.cget('width')),
int(self.canvas.cget('height')))
self.canvas.pack()
self.refresh_speed = refresh_speed
# Work area
self.min_x = border
self.max_x = width - border
self.min_y = border
self.max_y = height - border
#create array to hold the n number of balls
self.balls = []
self.ball_handles = dict()
return
def read_balls(self, scale, filename):
f = open(filename)
num_balls = int(f.readline().strip())
for l in f:
ll = l.strip().split(" ")
x = scale*float(ll[0])
y = scale*float(ll[1])
vx = scale*float(ll[2])
vy = scale*float(ll[3])
radius = scale*float(ll[4])
mass = float(ll[5])
r = int(ll[6])
g = int(ll[7])
b = int(ll[8])
tk_rgb = "#%02x%02x%02x" % (r, g, b)
new_ball = Ball(radius, x, y, vx, vy, mass, tk_rgb)
self.balls.append(new_ball)
return num_balls
def init_balls(self, max_radius, min_radius, num_balls):
for i in np.arange(num_balls):
while(True):
radius = (max_radius - min_radius) * rand.random_sample() +
min_radius
ball_min_x = self.min_x + radius
ball_max_x = self.max_x - radius
x = (ball_max_x - ball_min_x)*rand.random_sample() + ball_min_x
ball_min_y = self.min_y + radius
ball_max_y = self.max_y - radius
y = (ball_max_y - ball_min_y)*rand.random_sample() + ball_min_y
vx = rand.random_sample()
vy = rand.random_sample()
mass = 1.0 # rand.random_sample()
new_ball = Ball(radius, x, y, vx, vy, mass)
if not new_ball.check_overlap(self.balls):
self.balls.append(new_ball)
break
#init_wall_collision_times will set all of the balls' minimum collision time
def init_wall_collision_times(self):
for i in np.arange(len(self.balls)):
bi = self.balls[i]
tix = bi.horizontal_wall_collision_time(self.min_x, self.max_x)
tiy = bi.vertical_wall_collision_time(self.min_y, self.max_y)
self.PQ.insert(i, -1, tix + self.time, self.balls[i].count, -1)
self.PQ.insert(-1, i, tiy + self.time, -1, self.balls[i].count)
return
#init_ball_collision_times will set all of the balls' minimum collision time
#with all other balls and store that time within the ith and jth index of
#PQ.ball_collision_time
def init_ball_collision_times(self):
for i in np.arange(self.num_balls):
bi = self.balls[i]
for j in np.arange(i+1, self.num_balls):
bj = self.balls[j]
tij = bi.ball_collision_time(bj)
self.PQ.insert(i, j, tij + self.time, self.balls[i].count,
self.balls[j].count)
# self.ball_collision_times[i][j] = tij
# self.ball_collision_times[j][i] = tij
return
#walls (horizontal and vertical) and all other balls within the PQ array
def update_collision_times(self, i):
bi = self.balls[i]
tix = bi.horizontal_wall_collision_time(self.min_x, self.max_x)
tiy = bi.vertical_wall_collision_time(self.min_y, self.max_y)
self.PQ.insert(i, -1, tix + self.time,self.balls[i].count, -1)
self.PQ.insert(-1, i, tiy + self.time, -1, self.balls[i].count)
for j in np.arange(self.num_balls):
bj = self.balls[j]
tij = bi.ball_collision_time(bj) + self.time
if i > j:
self.PQ.insert(j, i,
tij,self.balls[j].count,self.balls[i].count)
else:
self.PQ.insert(i, j, tij,self.balls[i].count,
self.balls[j].count)
return
#draw will draw the borders and all balls within self.balls
def draw(self):
#Draw walls
self.canvas.create_line((self.min_x, self.min_y), (self.min_x,
self.max_y), fill = "red")
self.canvas.create_line((self.min_x, self.min_y), (self.max_x,
self.min_y), fill = "red")
self.canvas.create_line((self.min_x, self.max_y), (self.max_x,
self.max_y), fill = "red")
self.canvas.create_line((self.max_x, self.min_y), (self.max_x,
self.max_y), fill = "red")
#Draw balls
for b in self.balls:
obj = self.canvas.create_oval(b.x - b.radius, b.y - b.radius, b.x +
b.radius, b.y + b.radius, outline=b.tk_rgb, fill=b.tk_rgb)
self.ball_handles[b] = obj
self.canvas.update()
#refresh is called to update the state of the simulation
#-each refresh call can be considered one iteration of the simulation
def refresh(self):
#get the next collision
i, j, t, num_collisions_i, num_collision_j = self.PQ.get_next()
#gather the current collisions of the ith and jth ball
current_collisions_i = self.balls[i].count
current_collisions_j = self.balls[j].count
#Check the difference in time between the predicted collision time and
#the current time stamp of the simulation
delta = t - self.time
#If the difference is greater than 1, then just move the balls
if delta > 1.0:
# cap delta to 1.0
for bi in self.balls:
bi.move()
self.canvas.move(self.ball_handles[bi], bi.vx, bi.vy)
self.time += 1.0
#Otherwise a collision has occurred
else:
#Move all balls
for bi in self.balls:
bi.move(delta)
self.canvas.move(self.ball_handles[bi], bi.vx*delta,
bi.vy*delta)
#increment the simulation time stamp
self.time += delta
#Delete the top element within the Priority Queue
self.PQ.delete()
#if i is -1 then this indicates a collision with a vertical wall
#also this if statement checks if the number of collisions recorded
#when the collision returned by PQ.get_next() is equal to the
#number of collisions within the jth ball
#this acts as a test to check if the collision is still valid
if i == -1 and num_collision_j == current_collisions_j:
#compute what happens from the vertical wall collision
self.balls[j].collide_with_vertical_wall()
#update collision times for the jth ball
self.update_collision_times(j)
#if j is -1 then this indicates a collision a horizontal wall
#while also checking if the number of collisions match
#to see if the collision is valid
elif j == -1 and num_collisions_i == current_collisions_i:
#compute what happens from the horizontal wall collision
self.balls[i].collide_with_horizontal_wall()
#update collision times for the ith ball
self.update_collision_times(i)
elif num_collision_j == current_collisions_j and num_collisions_i ==
current_collisions_i:
#Execute collision across the ith and jth ball
self.balls[i].collide_with_ball(self.balls[j])
#update collision times for both the ith and jth ball
self.update_collision_times(i)
self.update_collision_times(j)
#update the canvas to draw the new locations of each ball
self.canvas.update()
self.canvas.after(self.refresh_speed, self.refresh)
def __init__(self, radius, x, y, vx, vy, mass, tk_rgb="#000000"):
self.radius = radius
self.x = x
self.y = y
self.vx = vx
self.vy = vy
self.mass = mass
self.tk_rgb = tk_rgb
#since this ball was just initialized, it hasn't had any collisions yet
self.count = 0
return
#move changes the displacement of the ball by the velocity
def move(self, dt=1.0):
self.x += self.vx*dt
self.y += self.vy*dt
return
#check_overlap checks if this ball is overlapping with any other
#ball, it is used to see if a collision has occurred
def check_overlap(self, others):
for b in others:
min_dist = b.radius + self.radius
center_dist = math.sqrt((b.x - self.x)*(b.x - self.x) + \
(b.y - self.y)*(b.y - self.y))
if center_dist < min_dist:
return True
return False
#collide_with_ball computes collision, changing the Ball's velocity
#as well as the other ball's velocity
def collide_with_ball(self, other):
dv_x = other.vx - self.vx
dv_y = other.vy - self.vy
dr_x = other.x - self.x
dr_y = other.y - self.y
sigma = self.radius + other.radius
dv_dr = dv_x * dr_x + dv_y * dr_y
J = 2.0 * self.mass * other.mass * dv_dr/((self.mass +
other.mass)*sigma)
Jx = J * dr_x/sigma
Jy = J * dr_y/sigma
self.vx += Jx/self.mass
self.vy += Jy/self.mass
other.vx -= Jx/other.mass
other.vy -= Jy/other.mass
#Increment the collision count for both balls
self.count += 1
other.count += 1
return
# Compute when an instance of Ball collides with the given Ball other
# Return the timestamp that this will occur
def ball_collision_time(self, other):
dr_x = other.x - self.x
dr_y = other.y - self.y
if dr_x == 0 and dr_y == 0:
return float('inf')
dv_x = other.vx - self.vx
dv_y = other.vy - self.vy
dv_dr = dv_x * dr_x + dv_y * dr_y
if dv_dr > 0:
return float('inf')
dv_dv = dv_x * dv_x + dv_y * dv_y
dr_dr = dr_x * dr_x + dr_y * dr_y
sigma = self.radius + other.radius
d = dv_dr * dv_dr - dv_dv * (dr_dr - sigma * sigma)
# No solution
if d < 0 or dv_dv == 0:
return float('inf')
return - (dv_dr + np.sqrt(d))/dv_dv
#collide_with_horizontal_wall executes the change in the Ball's
#velocity when colliding with a horizontal wall
def collide_with_horizontal_wall(self):
self.vx = -self.vx
self.count += 1
return
#collide_with_vertical_wall executes the change in the Ball's
#velocity when colliding with a vertical wall
def collide_with_vertical_wall(self):
self.vy = -self.vy
self.count += 1
return
# Compute when the instance of Ball collides with a horizontal wall
# Return the time stamp that this will occur
def horizontal_wall_collision_time(self, min_x, max_x):
if self.vx < 0:
# x + delta_t * vx = min_x + radius
return (min_x + self.radius - self.x)/(1.0*self.vx)
if self.vx > 0:
# x + delta_t * vx = max_x - radius
return (max_x - self.radius - self.x)/(1.0*self.vx)
return float('inf')
# Compute when the instance of Ball collides with a vertical wall
# Return the time stamp that this will occur
# Inputs of min_y and max_y
def vertical_wall_collision_time(self, min_y, max_y):
if self.vy < 0:
# y + delta_t * vy = min_y + radius
return (min_y + self.radius - self.y)/(1.0*self.vy)
if self.vy > 0:
# y + delta_t * vy = max_y - radius
return (max_y - self.radius - self.y)/(1.0*self.vy)
return float('inf')
#show_stats will print out the Ball's data
#specifically the radius, position, velocity, mass, and color
def show_stats(self):
print("radius: %f"%self.radius)
print("position: %f, %f"%(self.x, self.y))
print("velocity: %f, %f"%(self.vx, self.vy))
print("mass: %f"%self.mass)
print("rgb: %s"%self.tk_rgb)
return
#Main script
if __name__ == "__main__":
#Set the parameters for the graphics window and simulation
scale = 800
border = 5
#Set radius range for all balls
max_radius = 20
min_radius = 5
#set number of balls
num_balls = 10
#set refresh rate
refresh_speed = 5
rand.seed(12394)
#create the graphics object
root = Tk()
#Create the painter object
p = Painter(root, scale, border, refresh_speed, None, min_radius,max_radius,
num_balls)
#If you have the commented out files in your directory then
#uncomment them to see what they do
#p = Painter(root, scale, border, refresh_speed, 'wallbouncing.txt')
#p = Painter(root, scale, border, refresh_speed, 'p10.txt')
#p = Painter(root, scale, border, refresh_speed, 'billiards4.txt')
#p = Painter(root, scale, border, refresh_speed, 'squeeze.txt')
#run the Painter main loop function (calls refresh many times)
root.mainloop()

Lennard-Jones potential simulation

import pygame
import random
import numpy as np
import matplotlib.pyplot as plt
import math
number_of_particles = 70
my_particles = []
background_colour = (255,255,255)
width, height = 500, 500
sigma = 1
e = 1
dt = 0.1
v = 0
a = 0
r = 1
def r(p1,p2):
dx = p1.x - p2.x
dy = p1.y - p2.y
angle = 0.5 * math.pi - math.atan2(dy, dx)
dist = np.hypot(dx, dy)
return dist
def collide(p1, p2):
dx = p1.x - p2.x
dy = p1.y - p2.y
dist = np.hypot(dx, dy)
if dist < (p1.size + p2.size):
tangent = math.atan2(dy, dx)
angle = 0.5 * np.pi + tangent
angle1 = 2*tangent - p1.angle
angle2 = 2*tangent - p2.angle
speed1 = p2.speed
speed2 = p1.speed
(p1.angle, p1.speed) = (angle1, speed1)
(p2.angle, p2.speed) = (angle2, speed2)
overlap = 0.5*(p1.size + p2.size - dist+1)
p1.x += np.sin(angle) * overlap
p1.y -= np.cos(angle) * overlap
p2.x -= np.sin(angle) * overlap
p2.y += np.cos(angle) * overlap
def LJ(r):
return -24*e*((2/r*(sigma/r)**12)-1/r*(sigma/r)**6)
def verlet():
a1 = -LJ(r(p1,p2))
r = r + dt*v+0.5*dt**2*a1
a2 = -LJ(r(p1,p2))
v = v + 0.5*dt*(a1+a2)
return r, v
class Particle():
def __init__(self, (x, y), size):
self.x = x
self.y = y
self.size = size
self.colour = (0, 0, 255)
self.thickness = 1
self.speed = 0
self.angle = 0
def display(self):
pygame.draw.circle(screen, self.colour, (int(self.x), int(self.y)), self.size, self.thickness)
def move(self):
self.x += np.sin(self.angle)
self.y -= np.cos(self.angle)
def bounce(self):
if self.x > width - self.size:
self.x = 2*(width - self.size) - self.x
self.angle = - self.angle
elif self.x < self.size:
self.x = 2*self.size - self.x
self.angle = - self.angle
if self.y > height - self.size:
self.y = 2*(height - self.size) - self.y
self.angle = np.pi - self.angle
elif self.y < self.size:
self.y = 2*self.size - self.y
self.angle = np.pi - self.angle
screen = pygame.display.set_mode((width, height))
for n in range(number_of_particles):
x = random.randint(15, width-15)
y = random.randint(15, height-15)
particle = Particle((x, y), 15)
particle.speed = random.random()
particle.angle = random.uniform(0, np.pi*2)
my_particles.append(particle)
running = True
while running:
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False
screen.fill(background_colour)
for i, particle in enumerate(my_particles):
particle.move()
particle.bounce()
for particle2 in my_particles[i+1:]:
collide(particle, particle2)
particle.display()
pygame.display.flip()
pygame.quit()
I wanted to simulate particles by Lennard-Jones potential. My problem with this code is that I do not know how to use the Verlet algorithm.
I do not know where I should implement the Verlet algorithm; inside the class or outside?
How can I use velocity from the Verlet algorithm in the move method?
Is my implementation of the Verlet algorithm correct, or should I use arrays for saving results?
What else should I change to make it work?

You can keep the dynamical variables, position and velocity, inside the class instances, however then each class needs an acceleration vector to accumulate the force contributions. The Verlet integrator has the role of a controller, it acts from outside on the collection of all particles. Keep the angle out of the computations, the forth and back with trigonometric functions and their inverses is not necessary. Make position, velocity and acceleration all 2D vectors.
One way to implement the velocity Verlet variant is (see https://stackoverflow.com/tags/verlet-integration/info)
verlet_step:
v += a*0.5*dt;
x += v*dt; t += dt;
do_collisions(t,x,v,dt);
a = eval_a(x);
v += a*0.5*dt;
do_statistics(t,x,v);
which supposes a vectorized variant. In your framework, there would be some iterations over the particle collection to include,
verlet_step:
for p in particles:
p.v += p.a*0.5*dt; p.x += p.v*dt;
t += dt;
for i, p1 in enumerate(particles):
for p2 in particles[i+1:]:
collide(p1,p2);
for i, p1 in enumerate(particles):
for p2 in particles[i+1:]:
apply_LJ_forces(p1,p2);
for p in particles:
p.v += p.a*0.5*dt;
do_statistics(t,x,v);
No, you could not have done nothing wrong since you did not actually call the Verlet function to update position and velocity. And no, a strict vectorization is not necessary, see above. The implicit vectorization via the particles array is sufficient. You would only need a full vectorization if you wanted to compare with the results of a standard integrator like those in scipy.integrate using the same model to provide the ODE function.
Code with some add-ons but without collisions, desingularized potential
import pygame
import random
import numpy as np
import matplotlib.pyplot as plt
import math
background_colour = (255,255,255)
width, height = 500, 500
aafac = 2 # anti-aliasing factor screen to off-screen image
number_of_particles = 50
my_particles = []
sigma = 10
sigma2 = sigma*sigma
e = 5
dt = 0.1 # simulation time interval between frames
timesteps = 10 # intermediate invisible steps of length dt/timesteps
def LJ_force(p1,p2):
rx = p1.x - p2.x
ry = p1.y - p2.y
r2 = rx*rx+ry*ry
r2s = r2/sigma2+1
r6s = r2s*r2s*r2s
f = 24*e*( 2/(r6s*r6s) - 1/(r6s) )
p1.ax += f*(rx/r2)
p1.ay += f*(ry/r2)
p2.ax -= f*(rx/r2)
p2.ay -= f*(ry/r2)
def Verlet_step(particles, h):
for p in particles:
p.verlet1_update_vx(h);
p.bounce()
#t += h;
for i, p1 in enumerate(particles):
for p2 in particles[i+1:]:
LJ_force(p1,p2);
for p in particles:
p.verlet2_update_v(h);
class Particle():
def __init__(self, (x, y), (vx,vy), size):
self.x = x
self.y = y
self.vx = vx
self.vy = vy
self.size = size
self.colour = (0, 0, 255)
self.thickness = 2
self.ax = 0
self.ay = 0
def verlet1_update_vx(self,h):
self.vx += self.ax*h/2
self.vy += self.ay*h/2
self.x += self.vx*h
self.y += self.vy*h
self.ax = 0
self.ay = 0
def verlet2_update_v(self,h):
self.vx += self.ax*h/2
self.vy += self.ay*h/2
def display(self,screen, aa):
pygame.draw.circle(screen, self.colour, (int(aa*self.x+0.5), int(aa*self.y+0.5)), aa*self.size, aa*self.thickness)
def bounce(self):
if self.x > width - self.size:
self.x = 2*(width - self.size) - self.x
self.vx = - self.vx
elif self.x < self.size:
self.x = 2*self.size - self.x
self.vx = - self.vx
if self.y > height - self.size:
self.y = 2*(height - self.size) - self.y
self.vy = - self.vy
elif self.y < self.size:
self.y = 2*self.size - self.y
self.vy = - self.vy
#------------ end class particle ------------
#------------ start main program ------------
for n in range(number_of_particles):
x = 1.0*random.randint(15, width-15)
y = 1.0*random.randint(15, height-15)
vx, vy = 0., 0.
for k in range(6):
vx += random.randint(-10, 10)/2.
vy += random.randint(-10, 10)/2.
particle = Particle((x, y),(vx,vy), 10)
my_particles.append(particle)
#--------- pygame event loop ----------
screen = pygame.display.set_mode((width, height))
offscreen = pygame.Surface((aafac*width, aafac*height))
running = True
while running:
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False
offscreen.fill(background_colour)
for k in range(timesteps):
Verlet_step(my_particles, dt/timesteps)
for particle in my_particles:
particle.display(offscreen, aafac)
pygame.transform.smoothscale(offscreen, (width,height), screen)
pygame.display.flip()
pygame.quit()