python - Projectile motion and gravity in pygame only sometimes working

Question

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.

Answer 1

Set a random angle in range [-45, 45].

NOW_MS = pygame.time.get_ticks()
SPRITES = pygame.sprite.Group()   
for i in range( 20 ):
   speed = random.randrange( 10, 50 )
   angle = math.radians( random.randrange( -45, 45 ) )
   new_sprite = ProjectileSprite( sprite_image, speed, angle )
   SPRITES.add( new_sprite )

This angle defines the outgoing direction in relation to the upward direction of the window. Thus displacement_x depends on math.sin(self.angle) and displacement_y depends on math.cos(self.angle). Note half_gravity_time_squared has to be added, because self.GRAVITY is a negative value:

half_gravity_time_squared = self.GRAVITY * time_change * time_change / 2.0
displacement_x = self.velocity * math.sin(self.angle) * time_change 
displacement_y = self.velocity * math.cos(self.angle) * time_change + half_gravity_time_squared

See the example, where I applied the suggestions to your original code:

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
                half_gravity_time_squared = self.GRAVITY * time_change * time_change / 2.0
                displacement_x = self.velocity * math.sin(self.angle) * time_change 
                displacement_y = self.velocity * math.cos(self.angle) * time_change + 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 
NOW_MS = pygame.time.get_ticks()
SPRITES = pygame.sprite.Group()   
for i in range( 20 ):
    speed = random.randrange( 10, 50 )
    angle = math.radians( random.randrange( -45, 45 ) )
    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 )
            if event.key == pygame.K_n:
                for s in SPRITES:
                    s.start_time = NOW_MS
                    s.velocity = random.randrange( 10, 50 )

    # 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()