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()

How do I add a score tracker?

So I want it to count the score every time the snake eats a candy.
I haven't tried much, but I tried to find existing codes and adding them to mine but that just broke the game. I also tried to make my own score board by watching a tutorial, but I don't know where the code should go like at the beginning or end.
import pygame
import random
score = 0
welcome = ("Welcome to our snake game")
print(welcome)
class cube:
height = 20
w = 500
def __init__(movee,start,x=1,y=0,color=(0,0,0)):
movee.pos = start
movee.x = 1
movee.y = 0
movee.color = color
def move(movee, x, y):
movee.x = x
movee.y = y
movee.pos = (movee.pos[0] + movee.x, movee.pos[1] + movee.y)
def draw(movee, surface, eyes=False):
leng = movee.w // movee.height
i = movee.pos[0]
j = movee.pos[1]
pygame.draw.rect(surface, movee.color, (i*leng+1,j*leng+1, leng-2, leng-2))
class snake:
body = []
turns = {}
def __init__(movee, color, pos):
movee.color = color
movee.head = cube(pos)
movee.body.append(movee.head)
def move(movee):
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
keys = pygame.key.get_pressed()
for key in keys:
if keys[pygame.K_LEFT]:
movee.x = -1
movee.y = 0
movee.turns[movee.head.pos[:]] = [movee.x, movee.y]
elif keys[pygame.K_RIGHT]:
movee.x = 1
movee.y = 0
movee.turns[movee.head.pos[:]] = [movee.x, movee.y]
elif keys[pygame.K_UP]:
movee.x = 0
movee.y = -1
movee.turns[movee.head.pos[:]] = [movee.x, movee.y]
elif keys[pygame.K_DOWN]:
movee.x = 0
movee.y = 1
movee.turns[movee.head.pos[:]] = [movee.x, movee.y]
for i, c in enumerate(movee.body):
p = c.pos[:]
if p in movee.turns:
turn = movee.turns[p]
c.move(turn[0],turn[1])
if i == len(movee.body)-1:
movee.turns.pop(p)
else:
if c.x == -1 and c.pos[0] <= 0: c.pos = (c.height-1, c.pos[1])
elif c.x == 1 and c.pos[0] >= c.height-1: c.pos = (0,c.pos[1])
elif c.y == 1 and c.pos[1] >= c.height-1: c.pos = (c.pos[0], 0)
elif c.y == -1 and c.pos[1] <= 0: c.pos = (c.pos[0],c.height-1)
else: c.move(c.x,c.y)
def add(movee):
tail = movee.body[-1]
dx, dy = tail.x, tail.y
if dx == 1 and dy == 0:
movee.body.append(cube((tail.pos[0]-1,tail.pos[1])))
elif dx == -1 and dy == 0:
movee.body.append(cube((tail.pos[0]+1,tail.pos[1])))
elif dx == 0 and dy == 1:
movee.body.append(cube((tail.pos[0],tail.pos[1]-1)))
elif dx == 0 and dy == -1:
movee.body.append(cube((tail.pos[0],tail.pos[1]+1)))
movee.body[-1].x = dx
movee.body[-1].y = dy
def draw(movee, surface):
for i, c in enumerate(movee.body):
if i ==0:
c.draw(surface, True)
else:
c.draw(surface)
def drawingAGrid(w, height, surface):
sizein = w // height
x = 0
y = 0
for l in range(height):
x = x + sizein
y = y + sizein
def redrawGrid(surface):
global height, width, s, snack
surface.fill((255,255,255))
s.draw(surface)
snack.draw(surface)
drawingAGrid(width, height, surface)
pygame.display.update()
def Candy(height, item):
positions = item.body
while True:
x = random.randrange(height)
y = random.randrange(height)
if len(list(filter(lambda z:z.pos == (x,y), positions))) > 0:
continue
else:
break
return (x,y)
def gameloop():
global width, height, s, snack, x_pos, y_pos, reset
width = 500
height = 20
win = pygame.display.set_mode((width, width))
s = snake((255, 0, 0), (10, 10))
snack = cube(Candy(height, s), color=(0, 0, 0))
flag = True
clock = pygame.time.Clock()
x_pos, y_pos = s.body[0].pos
while flag:
pygame.time.delay(50)
clock.tick(7)
s.move()
x, y = s.body[0].pos
if not -1 <= x - x_pos <= 1 or not -1 <= y - y_pos <= 1:
movee.reset((10,10))
x_pos, y_pos = s.body[0].pos
if s.body[0].pos == snack.pos:
s.add()
snack = cube(Candy(height, s), color=(0, 0, 0))
redrawGrid(win)
gameloop()
I just want like a scoreboard in any of the corners counting the score.

Use pygame.freetype to render text. e,g, crated a pygame.freetype.SysFont object:
import pygame.freetype
pygame.init()
font = pygame.freetype.SysFont('Times New Roman', 30)
The score is the number of body parts. Use str to convert a number to a text and .render() to render a text to a pygame.Surface object:
score = len(s.body)
text_surf, text_rect = font.render(str(score), (255, 0, 0), size=30)
Define a margin to the border of the window, calculate the text position (e.g. bottom right) and .blit the text to the window surfrace:
margin = 10
text_pos = (width - text_rect.width - margin, width - text_rect.height - margin)
surface.blit(text_surf, text_pos)
Function redrawGrid:
def redrawGrid(surface):
global height, width, s, snack
surface.fill((255,255,255))
s.draw(surface)
snack.draw(surface)
drawingAGrid(width, height, surface)
score = len(s.body)
text_surf, text_rect = font.render(str(score), (255, 0, 0), size=30)
margin = 10
text_pos = (width - text_rect.width - margin, width - text_rect.height - margin)
surface.blit(text_surf, text_pos)
pygame.display.update()

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()

How do I import a gif in Tkinter?

So I have this maze code, and it's really cool but when you play you move around a red square. Is there a way that I can change this red square that moves around into an image, instead of where it says return "red" I want to put this personaje.gif file so a little person can appear moving through the maze.
this is my code:
import random
import Tkinter as tk
import sys
from PIL import Image, ImageTk
class Application(tk.Frame):
def __init__(self, width=600, height=600, size=600):
tk.Frame.__init__(self)
self.maze = Maze(width, height)
personaje = Image.open("personaje.gif")
photo = ImageTk.PhotoImage(personaje)
self.size = size
self.steps = 0
self.grid()
self.create_widgets()
self.draw_maze()
self.create_events()
def create_widgets(self):
width = self.maze.width * self.size
height = self.maze.height * self.size
self.canvas = tk.Canvas(self, width=width, height=height)
self.canvas.grid()
self.status = tk.Label(self)
self.status.grid()
def draw_maze(self):
for i, row in enumerate(self.maze.maze):
for j, col in enumerate(row):
x0 = j * self.size
y0 = i * self.size
x1 = x0 + self.size
y1 = y0 + self.size
color = self.get_color(x=j, y=i)
id = self.canvas.create_rectangle(x0, y0, x1, y1, width=0, fill=color)
if self.maze.start_cell == (j, i):
self.cell = id
self.canvas.tag_raise(self.cell) # bring to front
self.status.config(text='Movidas mínimas: %d' % self.maze.steps)
def create_events(self):
self.canvas.bind_all('<KeyPress-Up>', self.move_cell)
self.canvas.bind_all('<KeyPress-Down>', self.move_cell)
self.canvas.bind_all('<KeyPress-Left>', self.move_cell)
self.canvas.bind_all('<KeyPress-Right>', self.move_cell)
def move_cell(self, event):
if event.keysym == 'Up':
if self.check_move(0, -1):
self.canvas.move(self.cell, 0, -self.size)
self.steps += 1
if event.keysym == 'Down':
if self.check_move(0, 1):
self.canvas.move(self.cell, 0, self.size)
self.steps += 1
if event.keysym == 'Left':
if self.check_move(-1, 0):
self.canvas.move(self.cell, -self.size, 0)
self.steps += 1
if event.keysym == 'Right':
if self.check_move(1, 0):
self.canvas.move(self.cell, self.size, 0)
self.steps += 1
args = (self.steps, self.maze.steps)
self.status.config(text='Movimientos %d/%d' % args)
self.check_status()
def check_move(self, x, y):
x0, y0 = self.get_cell_coords()
x1 = x0 + x
y1 = y0 + y
return self.maze.maze[y1][x1] == 0
def get_cell_coords(self):
position = self.canvas.coords(self.cell)
x = int(position[0] / self.size)
y = int(position[1] / self.size)
return (x, y)
def check_status(self):
if self.maze.exit_cell == self.get_cell_coords():
args = (self.steps, self.maze.steps)
self.status.config(text='Resuelto en %d/%d movidas!' % args)
def get_color(self, x, y):
if self.maze.start_cell ==(x,y):
return "red"
if self.maze.exit_cell == (x, y):
return 'green'
if self.maze.maze[y][x] == 1:
return 'black'
class Maze(object):
def __init__(self, width=21, height=21, exit_cell=(1, 1)):
self.width = width
self.height = height
self.exit_cell = exit_cell
self.create()
def create(self):
self.maze = [[1] * self.width for _ in range(self.height)] # full of walls
self.start_cell = None
self.steps = None
self.recursion_depth = None
self._visited_cells = []
self._visit_cell(self.exit_cell)
def _visit_cell(self, cell, depth=0):
x, y = cell
self.maze[y][x] = 0 # remove wall
self._visited_cells.append(cell)
neighbors = self._get_neighbors(cell)
random.shuffle(neighbors)
for neighbor in neighbors:
if not neighbor in self._visited_cells:
self._remove_wall(cell, neighbor)
self._visit_cell(neighbor, depth+1)
self._update_start_cell(cell, depth)
def _get_neighbors(self, cell):
x, y = cell
neighbors = []
# Left
if x - 2 > 0:
neighbors.append((x-2, y))
# Right
if x + 2 < self.width:
neighbors.append((x+2, y))
# Up
if y - 2 > 0:
neighbors.append((x, y-2))
# Down
if y + 2 < self.height:
neighbors.append((x, y+2))
return neighbors
def _remove_wall(self, cell, neighbor):
x0, y0 = cell
x1, y1 = neighbor
# Vertical
if x0 == x1:
x = x0
y = (y0 + y1) / 2
# Horizontal
if y0 == y1:
x = (x0 + x1) / 2
y = y0
self.maze[y][x] = 0 # remove wall
def _update_start_cell(self, cell, depth):
if depth > self.recursion_depth:
self.recursion_depth = depth
self.start_cell = cell
self.steps = depth * 2 # wall + cell
def show(self, verbose=False):
MAP = {0: ' ', # path
1: '#', # wall
2: 'B', # exit
3: 'A', # start
}
x0, y0 = self.exit_cell
self.maze[y0][x0] = 2
x1, y1 = self.start_cell
self.maze[y1][x1] = 3
for row in self.maze:
print ' '.join([MAP[col] for col in row])
if verbose:
print "Steps from A to B:", self.steps
if __name__ == '__main__':
from optparse import OptionParser
parser = OptionParser(description="Random maze game")
parser.add_option('-W', '--width', type=int, default=43)
parser.add_option('-H', '--height', type=int, default=43)
parser.add_option('-s', '--size', type=int, default=11,
help="cell size")
args, _ = parser.parse_args()
for arg in ('width', 'height'):
if getattr(args, arg) % 2 == 0:
setattr(args, arg, getattr(args, arg) + 1)
print "Warning: %s must be odd, using %d instead" % (arg, getattr(args, arg))
sys.setrecursionlimit(5000)
app = Application(args.width, args.height, args.size)
app.master.title('Maze game')
app.mainloop()