So to answer another question, I delved into python + pygame projectile motion. Basically I wanted to create a sprite, then when "launched" with an initial velocity and angle would behave as per gravity and Newtonian physics.
My demo app creates a bunch of random projectiles. For some of the projectiles they fly up, in the correct parabolic path, before landing; perfect!
However:
- No projectiles seem to be able to go left (in the direction 270-360 degrees)
- Some projectiles never land
I suspect this is because of the math.cos()
and math.sin()
functions which will change sign of the result, depending on the quadrant. I think I also have a bad assumption that 0 degrees is "12 o'clock", and that this is really 90 degrees.
Obviously the desired outcome is that particles can go both left and right, and that no particles fly off into orbit.
ball.png:
import pygame
import random
import math
# Window size
WINDOW_WIDTH =1000
WINDOW_HEIGHT = 400
FPS = 60
# background colours
INKY_GREY = ( 128, 128, 128 )
# milliseconds since start
NOW_MS = 0
class ProjectileSprite( pygame.sprite.Sprite ):
GRAVITY = -9.8
def __init__( self, bitmap, velocity=0, angle=0 ):
pygame.sprite.Sprite.__init__( self )
self.image = bitmap
self.rect = bitmap.get_rect()
self.start_x = WINDOW_WIDTH // 2
self.start_y = WINDOW_HEIGHT - self.rect.height
self.rect.center = ( ( self.start_x, self.start_y ) )
# Physics
self.setInitialVelocityRadians( velocity, angle )
def setInitialVelocityRadians( self, velocity, angle_rads ):
global NOW_MS
self.start_time = NOW_MS
self.velocity = velocity
self.angle = angle_rads
def update( self ):
global NOW_MS
if ( self.velocity > 0 ):
time_change = ( NOW_MS - self.start_time ) / 150.0 # Should be 1000, but 100 looks better
if ( time_change > 0 ):
# re-calcualte the velocity
velocity_x = self.velocity * math.cos( self.angle )
velocity_y = self.velocity * math.sin( self.angle ) - ( self.GRAVITY * time_change )
# re-calculate the displacement
# x
displacement_x = velocity_x * time_change * math.cos( self.angle )
# y
half_gravity_time_squared = ( self.GRAVITY * ( time_change * time_change ) ) / 2.0
displacement_y = ( velocity_y * time_change * math.sin( self.angle ) ) - half_gravity_time_squared
# reposition sprite
self.rect.center = ( ( self.start_x + int( displacement_x ), self.start_y - int( displacement_y ) ) )
# Stop at the bottom of the window
if ( self.rect.y >= WINDOW_HEIGHT - self.rect.height ):
self.rect.y = WINDOW_HEIGHT - self.rect.height
self.velocity = 0
#self.kill()
### MAIN
pygame.init()
SURFACE = pygame.HWSURFACE | pygame.DOUBLEBUF | pygame.RESIZABLE
WINDOW = pygame.display.set_mode( ( WINDOW_WIDTH, WINDOW_HEIGHT ), SURFACE )
pygame.display.set_caption("Projectile Motion Example")
# Load resource image(s)
sprite_image = pygame.image.load( "ball.png" )#.convert_alpha()
# Make some sprites
SPRITES = pygame.sprite.Group()
for i in range( 20 ):
speed = random.randrange( 10, 50 )
if ( random.randrange( -100, 101 ) > 0 ):
angle = math.radians( random.randrange( 0, 45 ) ) # 0-45 degrees
else:
angle = math.radians( random.randrange( 315, 360 ) ) # minus 0-45 degrees
new_sprite = ProjectileSprite( sprite_image, speed, angle )
SPRITES.add( new_sprite )
clock = pygame.time.Clock()
done = False
while not done:
NOW_MS = pygame.time.get_ticks()
# Handle user-input
for event in pygame.event.get():
if ( event.type == pygame.QUIT ):
done = True
elif ( event.type == pygame.KEYDOWN ):
if ( event.unicode == '+' or event.scancode == pygame.K_PLUS ):
# Pressing '+' adds a new projectile sprite
speed = random.randrange( 10,100 )
angle = math.radians( random.randrange( -45, 45 ) )
new_sprite = ProjectileSprite( sprite_image, speed, angle )
SPRITES.add( new_sprite )
# Handle continuous-keypresses
keys = pygame.key.get_pressed()
if ( keys[pygame.K_ESCAPE] ):
# [Esc] exits too
done = True
# Repaint the screen
WINDOW.fill( INKY_GREY )
SPRITES.update() # re-position the sprites
SPRITES.draw( WINDOW ) # draw the sprites
pygame.display.flip()
# Update the window, but not more than 60fps
clock.tick_busy_loop( FPS )
pygame.quit()
Formulae for this app were taken directly from the wikipedia article.
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