# The Python Game Book

code games. learn Python.

### Site Tools

en:pygame:step017

# Step 017 - Rotating, shooting, inheritance, physics

Time to play! The source code example below is an actual playable game, demonstrating several different concepts:

1. Trigonometric_functions to rotate objects
2. Inheritance to build classes out of existing classes.
3. Elastic collision between to physical objects (birds, but reduced to physical disc's). <note important>Horst: what are physical discs?</note>

# gameplay With the source code example below you can shoot down little penguins (again). This time, you steer a fat penguin and can rotate and move him with the <key>w</key>,<key>a</key>,<key>s</key>,<key>d</key> keys. The movement is relative to the facing of the fat penguin; by pressing <key>w</key> he will not move upwards, but instead forward depending on his actual rotation. You can still move sidewards by pressing <key>q</key> and <key>r</key>.

To calculate the forward movement of a rotated object in a cartesian (x,y) coordinate system some Trigonometric_functions are used. To make the game more interesting, some small penguins are also in the game. The player can shoot at them (using the <key>SPACE</key> key) and collide with them but should avoid the fragments when a small penguin explodes.

If a small penguin reaches the ground, he get some random “fuel”1) and moves upward (negative dy) until the “fuel” runs out. Gravity, that the player can turn on and off with the <key>g</key>, will suck penguins, shots and fragments down.

The small objects (penguins, shots) are pushed around by forces (boost, gravity, impact of shots and fragments or other penguins), leading to diagonal movement (dx and dy). While the rotation of the fat penguin dedicate it's movement, the movement of the small objects dedicate their rotation.

The goal of the game is too shoot down as many small penguins while trying to reach a 100% hit ratio. Each time one small penguin is killed a new one is created. The ratio of hits / misses will be calculated by the computer. The game ends if the `gametime` runs out or the player was hit by too much red fragments.

#### to tinker

• change the constants (all in CAPITAL LETTER) like GRAVITY, FRICTION etc.
• uncomment out-commented lines in `Bird.areacheck` to let birds bounce off walls
• uncomment out-commented lines in `Bird.speedcheck` to introduce a general speed limit
• give the small birds more “fuel” to fly higher: change `self.boostmax` in `Bird.__init__`

# code discussion

## some trigonometry for pygame  How to calculate sine and cosine for angle x Radiand vs. Grad: 360° = 2 * π π (Pi) = 3.1418….

While python will take care of most mathematics involved in rotating sprites for you, it may be a good to refresh some school wisdom. In this example games, those trigometric functions are used:

• The sine: takes an angle (in radiant) as argument, returns the y coordinate
• The cosine: takes an angle (in radiant) as argument, returns the x coordinate
• The arctangent: takes a fraction as argument, returns an angle (in radiant)

As you can see in the drawing at the right side, sine is the vertical coordinate of a given point ( D in the diagram) on a unit circle2) while the cosine is the horizontal coordinate of the same point. The relation between those coordinates (vertical / horizontal) equals the tangent of the angle. The arctangent function is the inverse function of the tangent: arctangent takes the relation (y/x) as argument and returns the angle.

There are several methods to measure the angle:

• divide a full circle into 360 degrees (grad) or
• divide a full circle into 2 times Pi 3)

While python's pygame module can handle basic rotation of sprites and surfaces using the 360 degree method, for calculating sine, cosine and arctangent, you need python's math module. Math functions use radians.

Two small functions help here:

```import math
return (radians / math.pi) * 180.0
return degrees * (math.pi / 180.0)
```

## calculating direction for a given rotation

The player's class, BigBird knows the rotation of the sprite and need the movement vectors `dx` and `dy` to calculate. Here is the code, not-so important bits are omitted:

```import math
class BigBird(pygame.sprites.Sprites):
#...
def __init__(self):
pressedkeys = pygame.key.get_pressed()
self.ddx = 0.0
self.ddy = 0.0
if pressedkeys[pygame.K_w]: # forward
if pressedkeys[pygame.K_s]: # backward
if pressedkeys[pygame.K_e]: # right side
if pressedkeys[pygame.K_q]: # left side
#...
self.dx += self.ddx * self.speed
self.dy += self.ddy * self.speed
#...
self.pos += self.dx * seconds
self.pos += self.dy * seconds
#...
```

## calculating rotation for a given direction

On the other hand, if you know dx and dy and need the fitting angle, you can use this code:

```class Bullet(pygame.sprite.Sprite):
#...
def update(self, time):
#...
#--------- rotate into direction of movement ------------
#--- calculate with math.atan ---
#if self.dx != 0 and self.dy!=0:
#        ratio = self.dy / self.dx
#        if self.dx > 0:
#            self.angle = -90-math.atan(ratio)/math.pi*180.0 # in grad
#        else:
#            self.angle = 90-math.atan(ratio)/math.pi*180.0 # in grad
#--- or calculate with math.atan2 ---
self.angle = math.atan2(-self.dx, -self.dy)/math.pi*180.0
self.image = pygame.transform.rotozoom(self.image0,self.angle,1.0)
```
Using math.atan2 function instead of math.atan save some code lines. You can view the documentation for the math module online at http://docs.python.org/library/math.html : <note> math.atan(x)

`  Return the arc tangent of x, in radians.`

math.atan2(y, x)

```  Return atan(y / x), in radians. The result is between -pi and pi.
The vector in the plane from the origin to point (x, y) makes
this angle with the positive X axis.

The point of atan2() is that the signs of both inputs are known
to it, so it can compute the correct quadrant for the angle. For
example, atan(1) and atan2(1, 1) are both pi/4,
but atan2(-1, -1) is -3*pi/4.```

</note>

## using class inheritance In this code example exist 2 kinds of birds: The big (fat) BigBird and many smalle SmallBird's. Both have a common parent class Bird. Bird in turn is a child class of the pygame.sprite.Sprite class.

The very useful Fragment class serves as a parent class for the BlueFragment class, the RedFragment class, the Smoke class and the Shot class.

## elastic collision

Inside the game's mainloop is a tiny “physic engine” in use: It checks with a crashgroup if one bird is actually crashing into another bird. If so, both birds move away from each other.

This could be done with less sophisticated code like in the previous examples, like by simply giving the crashbird's new random values for dx and dy. However Lenoard Michlmayr was so nice to help me out here with some code for an elastic collision:

Note that to simplify the calculation, each bird is calculated as a disc. Also in the very special case that there is no speed (like if one bird is “beamed” into another bird) some random values for dx and dy are created.

```# ...
def elastic_collision(sprite1, sprite2):
"""elasitc collision between 2 sprites (calculated as disc's).
The function alters the dx and dy movement vectors of both sprites.
The sprites need the property .mass, .radius, .pos, .pos, .dx, dy
pos is the x postion, pos the y position"""
# here we do some physics: the elastic
# collision
#
# first we get the direction of the push.
# Let's assume that the sprites are disk
# shaped, so the direction of the force is
# the direction of the distance.
dirx = sprite1.pos - sprite2.pos
diry = sprite1.pos - sprite2.pos
#
# the velocity of the centre of mass
sumofmasses = sprite1.mass + sprite2.mass
sx = (sprite1.dx * sprite1.mass + sprite2.dx * sprite2.mass) / sumofmasses
sy = (sprite1.dy * sprite1.mass + sprite2.dy * sprite2.mass) / sumofmasses
# if we sutract the velocity of the centre
# of mass from the velocity of the sprite,
# we get it's velocity relative to the
# centre of mass. And relative to the
# centre of mass, it looks just like the
# sprite is hitting a mirror.
#
bdxs = sprite2.dx - sx
bdys = sprite2.dy - sy
cbdxs = sprite1.dx - sx
cbdys = sprite1.dy - sy
# (dirx,diry) is perpendicular to the mirror
# surface. We use the dot product to
# project to that direction.
distancesquare = dirx * dirx + diry * diry
if distancesquare == 0:
# no distance? this should not happen,
# but just in case, we choose a random
# direction
dirx = random.randint(0,11) - 5.5
diry = random.randint(0,11) - 5.5
distancesquare = dirx * dirx + diry * diry
dp = (bdxs * dirx + bdys * diry) # scalar product
dp /= distancesquare # divide by distance * distance.
cdp = (cbdxs * dirx + cbdys * diry)
cdp /= distancesquare
# We are done. (dirx * dp, diry * dp) is
# the projection of the velocity
# perpendicular to the virtual mirror
# surface. Subtract it twice to get the
# new direction.
#
# Only collide if the sprites are moving
# towards each other: dp > 0
if dp > 0:
sprite2.dx -= 2 * dirx * dp
sprite2.dy -= 2 * diry * dp
sprite1.dx -= 2 * dirx * cdp
sprite1.dy -= 2 * diry * cdp
```

The function is called with 2 sprites as arguments during the mainloop. Note that the elastic_collision function has no return values but instead manipulates the .dx and .dy properties (the movement vectors) of both sprites.

```# ... inside mainloop
# ------ collision detection
for bird in birdgroup:  # test if a bird collides with another bird
bird.crashing = False # make bird NOT blue
# check the Bird.number to make sure the bird is not crashing with himself
if not bird.waiting: # do not check birds outside the screen
crashgroup = pygame.sprite.spritecollide(bird, birdgroup, False )
for crashbird in crashgroup:  # test bird with other bird collision
if crashbird.number > bird.number: #avoid checking twice
bird.crashing = True # make bird blue
crashbird.crashing = True # make other bird blue
if not (bird.waiting or crashbird.waiting):
elastic_collision(crashbird, bird) # change dx and dy of both birds
```

## source code on github

To run this example you need:

017_turning_and_physic.py `pygame` Download the whole Archive with all files from Github:
https://github.com/horstjens/ThePythonGameBook/archives/master
babytux.png `pygame/data`
babytux_neg.png `pygame/data`
claws.ogg
from Battle of Wesnoth
`pygame/data`
wormhole.ogg `pygame/data`
bomb.ogg `pygame/data`
shoot.ogg `pygame/data`
beep.ogg `pygame/data`

```#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
017_turning_and_physic.py
pygame sprites primitive physic (elastic collision)
url: http://thepythongamebook.com/en:part2:pygame:step017
author: horst.jens@spielend-programmieren.at
physic by Leonard Michlmayr

move the big bird around with the keys w,a,s,d  and q and e
fire with space, toggle gravity with g

works with pyhton3.4 and python2.7
"""
#the next line is only needed for python2.x and not necessary for python3.x
from __future__ import print_function, division

def game(folder = "data"):
import pygame
import os
import random
import math
#------ starting pygame -------------
pygame.mixer.pre_init(44100, -16, 2, 2048) # setup mixer to avoid sound lag
pygame.init()
screen=pygame.display.set_mode((640,480)) # try out larger values and see what happens !
#winstyle = 0  # |FULLSCREEN # Set the display mode
print("pygame version", pygame.ver)
# ------- game constants ----------------------
BIRDSPEEDMAX = 200
FRAGMENTMAXSPEED = 200
FRICTION =.991  # between 1 and 0. 1 means no friction at all (deep space)
FORCE_OF_GRAVITY = 2.81 # pixel per second square earth: 9.81 m/s²
# ----------- functions -----------
def write(msg="pygame is cool", color=(0,0,0)):
"""write text into pygame surfaces"""
myfont = pygame.font.SysFont("None", 32)
mytext = myfont.render(msg, True, color)
mytext = mytext.convert_alpha()
return mytext
def getclassname(class_instance):
"""this function extract the class name of a class instance.
For an instance of a XWing class, it will return 'XWing'."""
text = str(class_instance.__class__) # like "<class '__main__.XWing'>"
parts = text.split(".") # like ["<class '__main__","XWing'>"]
return parts[-1][0:-2] # from the last (-1) part, take all but the last 2 chars

def elastic_collision(sprite1, sprite2):
"""elasitc collision between 2 sprites (calculated as disc's).
The function alters the dx and dy movement vectors of both sprites.
The sprites need the property .mass, .radius, .pos, .pos, .dx, dy
pos is the x postion, pos the y position"""
# here we do some physics: the elastic
# collision
#
# first we get the direction of the push.
# Let's assume that the sprites are disk
# shaped, so the direction of the force is
# the direction of the distance.
dirx = sprite1.pos - sprite2.pos
diry = sprite1.pos - sprite2.pos
#
# the velocity of the centre of mass
sumofmasses = sprite1.mass + sprite2.mass
sx = (sprite1.dx * sprite1.mass + sprite2.dx * sprite2.mass) / sumofmasses
sy = (sprite1.dy * sprite1.mass + sprite2.dy * sprite2.mass) / sumofmasses
# if we sutract the velocity of the centre
# of mass from the velocity of the sprite,
# we get it's velocity relative to the
# centre of mass. And relative to the
# centre of mass, it looks just like the
# sprite is hitting a mirror.
#
bdxs = sprite2.dx - sx
bdys = sprite2.dy - sy
cbdxs = sprite1.dx - sx
cbdys = sprite1.dy - sy
# (dirx,diry) is perpendicular to the mirror
# surface. We use the dot product to
# project to that direction.
distancesquare = dirx * dirx + diry * diry
if distancesquare == 0:
# no distance? this should not happen,
# but just in case, we choose a random
# direction
dirx = random.randint(0,11) - 5.5
diry = random.randint(0,11) - 5.5
distancesquare = dirx * dirx + diry * diry
dp = (bdxs * dirx + bdys * diry) # scalar product
dp /= distancesquare # divide by distance * distance.
cdp = (cbdxs * dirx + cbdys * diry)
cdp /= distancesquare
# We are done. (dirx * dp, diry * dp) is
# the projection of the velocity
# perpendicular to the virtual mirror
# surface. Subtract it twice to get the
# new direction.
#
# Only collide if the sprites are moving
# towards each other: dp > 0
if dp > 0:
sprite2.dx -= 2 * dirx * dp
sprite2.dy -= 2 * diry * dp
sprite1.dx -= 2 * dirx * cdp
sprite1.dy -= 2 * diry * cdp
# ----------- classes ------------------------
class Text(pygame.sprite.Sprite):
"""a pygame Sprite displaying text"""
def __init__(self, msg="The Python Game Book", color=(0,0,0)):
self.groups = allgroup
self._layer = 1
pygame.sprite.Sprite.__init__(self, self.groups)
self.newmsg(msg,color)

def update(self, time):
pass # allgroup sprites need update method that accept time

def newmsg(self, msg, color=(0,0,0)):
self.image =  write(msg,color)
self.rect = self.image.get_rect()

class Lifebar(pygame.sprite.Sprite):
"""shows a bar with the hitpoints of a Bird sprite
with a given bossnumber, the Lifebar class can
identify the boos (Bird sprite) with this codeline:
Bird.birds[bossnumber] """
def __init__(self, boss):
self.groups = allgroup
self.boss = boss
self._layer = self.boss._layer
pygame.sprite.Sprite.__init__(self, self.groups)
self.oldpercent = 0
self.paint()

def paint(self):
self.image = pygame.Surface((self.boss.rect.width,7))
self.image.set_colorkey((0,0,0)) # black transparent
pygame.draw.rect(self.image, (0,255,0), (0,0,self.boss.rect.width,7),1)
self.rect = self.image.get_rect()

def update(self, time):
self.percent = self.boss.hitpoints / self.boss.hitpointsfull * 1.0
if self.percent != self.oldpercent:
self.paint() # important ! boss.rect.width may have changed (because rotating)
pygame.draw.rect(self.image, (0,0,0), (1,1,self.boss.rect.width-2,5)) # fill black
pygame.draw.rect(self.image, (0,255,0), (1,1,
int(self.boss.rect.width * self.percent),5),0) # fill green
self.oldpercent = self.percent
self.rect.centerx = self.boss.rect.centerx
self.rect.centery = self.boss.rect.centery - self.boss.rect.height /2 - 10
if self.boss.hitpoints < 1:   #check if boss is still alive
self.kill() # kill the hitbar

class Bird(pygame.sprite.Sprite):
"""generic Bird class, to be called from SmallBird and BigBird"""
image=[]  # list of all images
birds = {} # a dictionary of all Birds, each Bird has its own number
number = 0
waittime = 1.0 # seconds
def __init__(self, layer = 4, bigbird = False ):
self.groups = birdgroup, allgroup, gravitygroup # assign groups
self._layer = layer                   # assign level
#self.layer = layer
pygame.sprite.Sprite.__init__(self,  self.groups  ) #call parent class. NEVER FORGET !
self.pos = [random.randint(50,screen.get_width()-50),
random.randint(25,screen.get_height()-25)]
self.area = screen.get_rect()
self.image = Bird.image
self.image = Bird.image
self.hitpointsfull = float(30) # maximal hitpoints
self.hitpoints = float(30) # actual hitpoints
self.rect = self.image.get_rect()
self.radius = max(self.rect.width, self.rect.height) / 2.0
self.dx = 0   # wait at the beginning
self.dy = 0
self.waittime = Bird.waittime # 1.0 # one second
self.waiting = True
self.rect.center = (-100,-100) # out of visible screen
self.crashing = False
self.frags = 25 # number of framgents if Bird is killed
self.number = Bird.number # get my personal Birdnumber
Bird.number+= 1           # increase the number for next Bird
Bird.birds[self.number] = self # store myself into the Bird dictionary
print("my number %i Bird number %i and i am a %s " % (self.number, Bird.number, getclassname(self)))
self.mass = 100.0
self.angle = 0.0
self.boostspeed = 10 # speed to fly upward
self.boostmax = 0.9 # max seconds of "fuel" for flying upward
self.boostmin = 0.4 # min seconds of "fuel" for flying upward
self.boosttime = 0.0 # time (fuel) remaining
warpsound.play()
for _ in range(8):
BlueFragment(self.pos) # blue Frags

def kill(self):
# a shower of red fragments, exploding outward
for _ in range(self.frags):
RedFragment(self.pos)
pygame.sprite.Sprite.kill(self) # kill the actual Bird

def speedcheck(self):
#if abs(self.dx) > BIRDSPEEDMAX:
#   self.dx = BIRDSPEEDMAX * (self.dx/abs(self.dx)) # dx/abs(dx) is 1 or -1
#if abs(self.dy) > BIRDSPEEDMAX:
#   self.dy = BIRDSPEEDMAX * (self.dy/abs(self.dy))
if abs(self.dx) > 0 :
self.dx *= FRICTION  # make the Sprite slower over time
if abs(self.dy) > 0 :
self.dy *= FRICTION

def areacheck(self):
if not self.area.contains(self.rect):
self.crashing = True # change colour later
# --- compare self.rect and area.rect
if self.pos + self.rect.width/2 > self.area.right:
self.pos = self.area.right - self.rect.width/2
self.dx *= -0.5 # bouncing off but loosing speed
if self.pos - self.rect.width/2 < self.area.left:
self.pos = self.area.left + self.rect.width/2
self.dx *= -0.5 # bouncing off the side but loosing speed
if self.pos + self.rect.height/2 > self.area.bottom:
self.pos = self.area.bottom - self.rect.height/2
#self.dy *= -1 # bouncing off the ground
#if reaching the bottom, the birds get a boost and fly upward to the sky
#at the bottom the bird "refuel" a random amount of "fuel" (the boostime)
self.dy = 0 # break at the bottom
self.dx *= 0.3 # x speed is reduced at the ground
self.boosttime = self.boostmin + random.random()* (self.boostmax - self.boostmin)
if self.pos - self.rect.height/2 < self.area.top:
self.pos = self.area.top + self.rect.height/2
self.dy = 0 # stop when reaching the sky
#self.dy *= -1
self.hitpoints -= 1 # reaching the sky cost 1 hitpoint
def update(self, seconds):
#---make Bird only visible after waiting time
self.waiting = False
if self.waiting:
self.rect.center = (-100,-100)
else: # the waiting time (Blue Fragments) is over
if self.boosttime > 0:   # boost flying upwards ?
self.boosttime -= seconds
self.dy -= self.boostspeed # upward is negative y !
Smoke(self.rect.center, -self.ddx , -self.ddy )
self.speedcheck()    # ------------- movement
self.pos += self.dx * seconds
self.pos += self.dy * seconds
self.areacheck() # ------- check if Bird out of screen
#--- calculate actual image: crasing, bigbird, both, nothing ?
self.image = Bird.image[self.crashing+self.big] # 0 for not crashing, 1 for crashing
self.image0 = Bird.image[self.crashing+self.big] # 0 for not crashing, 1 for crashing
#--------- rotate into direction of movement ------------
self.angle = math.atan2(-self.dx, -self.dy)/math.pi*180.0
self.image = pygame.transform.rotozoom(self.image0,self.angle,1.0)
#--- calculate new position on screen -----
self.rect.centerx = round(self.pos,0)
self.rect.centery = round(self.pos,0)
if self.hitpoints <= 0:
self.kill()

class SmallBird(Bird):
"""A bird that get pushed around by shots, red fragments and other birds."""
#gravity = True
def __init__(self):
self.big = 0
Bird.__init__(self)
Lifebar(self)

def kill(self):
crysound.play()
Bird.kill(self)

class BigBird(Bird):
"""A big bird controlled by the player"""
def __init__(self):
self.big = 2 # smallsprites have the value 0 for this attribute (.big) -> important for Bird.image
Bird.__init__(self) # create a "little" Bird but do more than that
self.hitpoints = float(100)
self.hitpointsfull = float(100)
self.image = Bird.image # big bird image
self.pos = [screen.get_width()/2, screen.get_height()/2]
self.rect = self.image.get_rect()
self.angle = 0
self.speed = 20.0 # base movement speed factor
self.rotatespeed = 1.0 # rotating speed
self.frags = 100
Lifebar(self)
self.cooldowntime = 0.08 #seconds
self.cooldown = 0.0
self.damage = 5 # how many damage one bullet inflict
self.shots = 0
self.mass = 400.0

def kill(self):
bombsound.play()
Bird.kill(self)

def update(self, time):
"""BigBird has its own update method, overwriting the
update method from the Bird class"""
self.waiting = False
if self.waiting:
self.rect.center = (-100,-100)
else:
#--- calculate actual image: crasing, bigbird, both, nothing ?
self.image = Bird.image[self.crashing+self.big] # 0 for not crashing, 2 for big
pressedkeys = pygame.key.get_pressed()
self.ddx = 0.0
self.ddy = 0.0
if pressedkeys[pygame.K_w]: # forward
Smoke(self.rect.center, -self.ddx , -self.ddy )
if pressedkeys[pygame.K_s]: # backward
Smoke(self.rect.center, -self.ddx, -self.ddy )
if pressedkeys[pygame.K_e]: # right side
Smoke(self.rect.center, -self.ddx , -self.ddy )
if pressedkeys[pygame.K_q]: # left side
Smoke(self.rect.center, -self.ddx , -self.ddy )
# ------------shoot-----------------
if self.cooldown > 0:
self.cooldown -= time
else:
if pressedkeys[pygame.K_SPACE]: # shoot forward
lasersound.play() # play sound
self.shots += 1
self.cooldown = self.cooldowntime
# ------------move------------------
if not self.waiting:
self.dx += self.ddx * self.speed
self.dy += self.ddy * self.speed
#self.speedcheck()   # friction, maxspeed
self.pos += self.dx * seconds
self.pos += self.dy * seconds
# -- check if Bird out of screen
self.areacheck()
# ------------- rotate ------------------
if pressedkeys[pygame.K_a]: # left turn , counterclockwise
self.angle += self.rotatespeed
if pressedkeys[pygame.K_d]: # right turn, clockwise
self.angle -= self.rotatespeed
self.oldcenter = self.rect.center
self.image = pygame.transform.rotate(self.image, self.angle)
self.rect = self.image.get_rect()
self.rect.center = self.oldcenter
#--- calculate new position on screen -----
self.rect.centerx = round(self.pos,0)
self.rect.centery = round(self.pos,0)
if self.hitpoints <= 0: # ----- alive----
self.kill()

class Fragment(pygame.sprite.Sprite):
"""generic Fragment class. Inherits to blue Fragment (implosion),
red Fragment (explosion), smoke (black) and shots (purple)"""
def __init__(self, pos, layer = 9):
self._layer = layer
pygame.sprite.Sprite.__init__(self, self.groups)
self.pos = [0.0,0.0]
self.fragmentmaxspeed = FRAGMENTMAXSPEED# try out other factors !

def init2(self):  # split the init method into 2 parts for better access from subclasses
self.image = pygame.Surface((10,10))
self.image.set_colorkey((0,0,0)) # black transparent
pygame.draw.circle(self.image, self.color, (5,5), random.randint(2,5))
self.image = self.image.convert_alpha()
self.rect = self.image.get_rect()
self.rect.center = self.pos #if you forget this line the sprite sit in the topleft corner
self.time = 0.0

def update(self, seconds):
self.time += seconds
self.kill()
self.pos += self.dx * seconds
self.pos += self.dy * seconds
self.rect.centerx = round(self.pos,0)
self.rect.centery = round(self.pos,0)

class RedFragment(Fragment):
"""explodes outward from (killed) Bird"""
def __init__(self,pos):
self.groups = allgroup, fragmentgroup, gravitygroup
Fragment.__init__(self,pos)
#red-only part -----------------------------
self.color = (random.randint(25,255),0,0) # red
self.pos = pos
self.pos = pos
self.dx = random.randint(-self.fragmentmaxspeed,self.fragmentmaxspeed)
self.dy = random.randint(-self.fragmentmaxspeed,self.fragmentmaxspeed)
self.lifetime = 1 + random.random()*3 # max 3 seconds
self.init2() # continue with generic Fragment class
self.mass = 48.0

class BlueFragment(Fragment):
"""implode inward toward new Bird (and a bittle outward after
reaching the target position"""
def __init__(self, pos):
self.groups = allgroup
Fragment.__init__(self, pos)
self.target = pos
self.color = (0,0,random.randint(25,255)) # blue
self.side = random.randint(1,4)
if self.side == 1:  # left side
self.pos = 0
self.pos = random.randint(0,screen.get_height())
elif self.side == 2: # top
self.pos = random.randint(0,screen.get_width())
self.pos = 0
elif self.side == 3: #right
self.pos = screen.get_width()
self.pos = random.randint(0,screen.get_height())
else: #bottom
self.pos = random.randint(0,screen.get_width())
self.pos = screen.get_height()
# calculating flytime for one second.. Bird.waittime should be 1.0
self.dx = (self.target - self.pos) * 1.0 / Bird.waittime
self.dy = (self.target - self.pos) * 1.0 / Bird.waittime
self.lifetime = Bird.waittime + random.random() * .5 # a bit more livetime after the Bird appears
self.init2()

class Smoke(Fragment):
"""black exhaust indicating that the BigBird sprite is moved by
the player. Exhaust direction is inverse of players movement direction"""
def __init__(self, pos, dx, dy):
self.color = ( random.randint(1,50), random.randint(1,50), random.randint(1,50) )
self.groups = allgroup
Fragment.__init__(self,pos, 3) # give startpos and layer
self.pos = pos
self.pos = pos
self.lifetime = 1 + random.random()*2 # max 3 seconds
Fragment.init2(self)
self.smokespeed = 120.0 # how fast the smoke leaves the Bird
self.smokearc = .3 # 0 = thin smoke stream, 1 = 180 Degrees
arc = self.smokespeed * self.smokearc
self.dx = dx * self.smokespeed + random.random()*2*arc - arc
self.dy = dy * self.smokespeed + random.random()*2*arc - arc

class Bullet(Fragment):
"""a bullet flying in the direction of the BigBird's heading. May
be subject to gravity"""
def __init__(self, boss, dx, dy):
self.color = (200,0,200)
self.boss = boss
self.groups = allgroup, bulletgroup, gravitygroup
Fragment.__init__(self, self.boss.rect.center, 3) # layer behind Bird
self.pos = self.boss.pos
self.pos = self.boss.pos
self.lifetime = 5 # 5 seconds
self.image = pygame.Surface((4,20))
self.image.set_colorkey((0,0,0)) # black transparent
pygame.draw.rect(self.image, self.color, (0,0,4,20) )
pygame.draw.rect(self.image, (10,0,0), (0,0,4,4)) # point
self.image = self.image.convert_alpha()
self.image0 = self.image.copy()
self.rect = self.image.get_rect()
self.rect.center = self.boss.rect.center
self.image = pygame.transform.rotate(self.image, self.boss.angle)
self.rect = self.image.get_rect()
self.rect.center = self.boss.rect.center
self.time = 0.0
self.bulletspeed = 250.0 # pixel per second ?
self.bulletarc = 0.05 # perfect shot has 0.0
arc = self.bulletspeed * self.bulletarc
self.dx = dx * self.bulletspeed + random.random()*2*arc -arc
self.dy = dy * self.bulletspeed + random.random()*2*arc -arc
self.mass = 25.0
self.angle = self.boss.angle

def update(self, time):
Fragment.update(self,time)
#--------- rotate into direction of movement ------------
self.angle = math.atan2(-self.dx, -self.dy)/math.pi*180.0
self.image = pygame.transform.rotozoom(self.image0,self.angle,1.0)

# ----------------- background artwork -------------
background = pygame.Surface((screen.get_width(), screen.get_height()))
background.fill((255,255,255))     # fill white
background.blit(write("navigate with w,a,s,d and q and e "),(50,40))
background.blit(write("press SPACE to fire bullets"),(50,70))
background.blit(write("press g to toggle gravity"), (50, 100))
background.blit(write("Press ESC to quit "), (50,130))
background = background.convert()  # jpg can not have transparency
screen.blit(background, (0,0))     # blit background on screen (overwriting all)
#-----------------define sprite groups------------------------
birdgroup = pygame.sprite.Group()
bulletgroup = pygame.sprite.Group()
fragmentgroup = pygame.sprite.Group()
gravitygroup = pygame.sprite.Group()
# only the allgroup draws the sprite, so i use LayeredUpdates() instead Group()
allgroup = pygame.sprite.LayeredUpdates() # more sophisticated, can draw sprites in layers

try: # load images into classes (class variable !). if not possible, draw ugly images
except:
print("no image files 'babytux.png' and 'babytux_neg.png' in subfolder %s" % folder)
image = pygame.Surface((32,36))
image.fill((255,255,255))
pygame.draw.circle(image, (0,0,0), (16,18), 15,2)
pygame.draw.polygon(image, (0,0,0), ((32,36),(0,36),(16,0)),1) # triangle
image.set_colorkey((255,255,255))
Bird.image.append(image) # alternative ugly image
image2 = image.copy()
pygame.draw.circle(image2, (0,0,255), (16,18), 13,0)
Bird.image.append(image2)
Bird.image.append(pygame.transform.scale2x(Bird.image)) # copy of first image, big bird
Bird.image.append(pygame.transform.scale2x(Bird.image)) # copy of blue image, big bird
Bird.image = Bird.image.convert_alpha()
Bird.image = Bird.image.convert_alpha()
Bird.image = Bird.image.convert_alpha()
Bird.image = Bird.image.convert_alpha()

try: # ------- load sound -------
warpsound = pygame.mixer.Sound(os.path.join(folder,'wormhole.ogg'))
bombsound = pygame.mixer.Sound(os.path.join(folder,'bomb.ogg'))
lasersound = pygame.mixer.Sound(os.path.join(folder,'shoot.ogg'))
hitsound = pygame.mixer.Sound(os.path.join(folder,'beep.ogg'))
except:
print("could not load one of the sound files from folder %s. no sound, sorry" %folder)
# ------------- before the main loop ----------------------
screentext = Text()
clock = pygame.time.Clock()        # create pygame clock object
mainloop = True
FPS = 60                           # desired max. framerate in frames per second.
amount = 7 # how many small birds should always be present on the screen
player = BigBird() # big Bird
overtime = 15 # time in seconds to admire the explosion of player before the game ends
gameOver = False
hits = 0  # how often the player was hitting a small Bird
quota = 0 # hit/miss quota
gametime = 60 # how long to play (seconds)
playtime = 0  # how long the game was played
gravity = True

while mainloop:
milliseconds = clock.tick(FPS)  # milliseconds passed since last frame
seconds = milliseconds / 1000.0 # seconds passed since last frame
playtime += seconds # keep track of playtime
for event in pygame.event.get():
if event.type == pygame.QUIT:
mainloop = False # pygame window closed by user
elif event.type == pygame.KEYDOWN:
if event.key == pygame.K_ESCAPE:
mainloop = False # user pressed ESC
elif event.key == pygame.K_x:
player.hitpoints -= 1
print(player.hitpoints)
elif event.key == pygame.K_y:
player.hitpoints += 1
print(player.hitpoints)
elif event.key == pygame.K_g:
gravity = not gravity # toggle gravity
elif event.key == pygame.K_p: # get sprites at mouse position, print info
print("=========================")
print( "-----Spritelist---------")
spritelist = allgroup.get_sprites_at(pygame.mouse.get_pos())
for sprite in spritelist:
print(sprite, "Layer:",allgroup.get_layer_of_sprite(sprite))
print("------------------------")

if player.shots > 0:
quota = (float(hits)/player.shots )* 100
pygame.display.set_caption("fps: %.2f gravity: %s hits:%i shots:%i quota:%.2f%%"  % (clock.get_fps(),
gravity, hits, player.shots, quota))
# ------ collision detection
for bird in birdgroup:  # test if a bird collides with another bird
bird.crashing = False # make bird NOT blue
# check the Bird.number to make sure the bird is not crashing with himself
if not bird.waiting: # do not check birds outside the screen
crashgroup = pygame.sprite.spritecollide(bird, birdgroup, False )
for crashbird in crashgroup:  # test bird with other bird collision
if crashbird.number > bird.number: #avoid checking twice
bird.crashing = True # make bird blue
crashbird.crashing = True # make other bird blue
if not (bird.waiting or crashbird.waiting):
elastic_collision(crashbird, bird) # change dx and dy of both birds

crashgroup = pygame.sprite.spritecollide(bird, bulletgroup, False)
for ball in crashgroup:  # test for collision with bullet
if ball.boss.number != bird.number:
hitsound.play()
hits +=1
bird.hitpoints -= ball.boss.damage
factor =  (ball.mass / bird.mass)
bird.dx += ball.dx * factor
bird.dy += ball.dy * factor
ball.kill()

crashgroup = pygame.sprite.spritecollide(bird, fragmentgroup, False)
for frag in crashgroup: # test for red fragments
bird.hitpoints -=1
factor =  frag.mass / bird.mass
bird.dx += frag.dx * factor
bird.dy += frag.dy * factor
frag.kill()

if gravity: # ---- gravity check ---
for thing in gravitygroup:
thing.dy += FORCE_OF_GRAVITY # gravity suck down all kind of things

if len(birdgroup) < amount: # create enough SmallBirds
for _ in range(random.randint(1,3)):
SmallBird()

# ------game Over ? -------------
if (player.hitpoints < 1 or playtime > gametime) and not gameOver:
gameOver = True # do those things once when the game ends
screentext.newmsg("Game Over. hits/shots: %i/%i quota: %.2f%%" % (hits, player.shots, quota), (255,0,0))
player.hitpoints = 0 # kill the player into a big explosion
if gameOver: # overtime to watch score, explosion etc
overtime -= seconds
if overtime < 0:
mainloop = False
else: # not yet gameOver
screentext.newmsg("Time left: %.2f" % (gametime - playtime))

# ----------- clear, draw , update, flip -----------------
allgroup.clear(screen, background)
allgroup.update(seconds)
allgroup.draw(screen)
pygame.display.flip()

if __name__ == "__main__":
game()

```

1)
the variable is called `boosttime`
2)
a circle with the radius 1
3)
As you already know, 2 * Pi is the circumference of the unit circle. Because of the internal representation, the constant math.pi is only an approximation of the irrational number Pi. 