# DEVELOPING A RAYCASTING ‘3D’ ENGINE GAME IN PYTHON AND PYGAME – PART 4

In this post, we will cover the following:

1. Fixing a KeyError bug related to the door sprites.
2. Refactoring the player collision detection algorithm so that enemies and other non-playable characters can also use it.
3. Adding very basic enemy artificial intelligence and adding movement animation to the enemy, so the effect of a walking character is created.

Door Sprite KeyError Bug

Because doors had 16 angles, and angle to change the sprite image was calculated with:

``sprite_angle_delta = int(360 / len(self.sprite_object)) ``

So for 16 images, this would result in 22.5 degrees. The decimal 0.5 would be dropped because we use int(), and all operations dependent on the sprite_angle_delta uses an integer number.

This decimal loss results in a dead zone between 352 and 360 degrees that caused the KeyError.

To fix this, the number of sprite images was reduced to 8, as 16 was unnecessary for the purposes we require in this scenario.

Alternatively, the sprite_angle_delta could have been changed to a float variable, and all the dependent operations could have been modified accordingly to facilitate this. However, this would have added unnecessary complexity for the functionality required in the game.

Refactoring of Collision Detection Algorithm to be More Generic and Reusable

Firstly, the check_collision function was moved out of the Player class and into the common.py file. Next, the function was refactored as per the code below so that it returns either the existing x and y values (before the move) if a collision occurred or the new x and y values (after the move) if no collision was detected:

``````def check_collision(x, y, new_x, new_y, map_to_check, margin):
location = align_grid(new_x, new_y)
if location in map_to_check:
#  collision
return x, y

location = align_grid(new_x - margin, new_y - margin)
if location in map_to_check:
#  collision
return x, y

location = align_grid(new_x + margin, new_y - margin)
if location in map_to_check:
#  collision
return x, y

location = align_grid(new_x - margin, new_y + margin)
if location in map_to_check:
#  collision
return x, y

location = align_grid(new_x + margin, new_y + margin)
if location in map_to_check:
#  collision
return x, y

return new_x, new_y``````

The Player keys_control method was modified as per below to facilitate the new check_collision function:

``````def keys_control(self, object_map):
sin_a = math.sin(self.angle)
cos_a = math.cos(self.angle)
keys = pygame.key.get_pressed()
if keys[pygame.K_ESCAPE]:
exit()
if keys[pygame.K_w]:
nx = self.x + player_speed * cos_a
ny = self.y + player_speed * sin_a
self.x, self.y = check_collision(self.x, self.y, nx, ny, object_map, HALF_PLAYER_MARGIN)
if nx != self.x and ny != self.y:
self.play_sound(self.step_sound)
if keys[pygame.K_s]:
nx = self.x + -player_speed * cos_a
ny = self.y + -player_speed * sin_a
self.x, self.y = check_collision(self.x, self.y, nx, ny, object_map, HALF_PLAYER_MARGIN)
if nx != self.x and ny != self.y:
self.play_sound(self.step_sound)
if keys[pygame.K_a]:
nx = self.x + player_speed * sin_a
ny = self.y + -player_speed * cos_a
self.x, self.y = check_collision(self.x, self.y, nx, ny, object_map, HALF_PLAYER_MARGIN)
if nx != self.x and ny != self.y:
self.play_sound(self.step_sound)
if keys[pygame.K_d]:
nx = self.x + -player_speed * sin_a
ny = self.y + player_speed * cos_a
self.x, self.y = check_collision(self.x, self.y, nx, ny, object_map, HALF_PLAYER_MARGIN)
if nx != self.x and ny != self.y:
self.play_sound(self.step_sound)
if keys[pygame.K_e]:
self.interact = True
if keys[pygame.K_LEFT]:
self.angle -= 0.02
if keys[pygame.K_RIGHT]:
self.angle += 0.02``````

Where object_map is passed in from the main.py file and is created as follows:

``object_map = {**sprites.sprite_map, **world_map}``

object_map is thus a new dictionary that contains the values of the sprite_map and world_map dictionaries combined.

The check_collision function can now be easily used by enemies as well.

Basic Enemy Artificial Intelligence and Enemy Walking Animation

The enemy will, for now, only have very basic behavior and will try to move towards the player except if an obstacle is in the way.

A new Enemy class was created to accommodate this and is located in a new file called enemy.py.
The contents of the enemy.py file:

`````` from common import *

class Enemy:
def __init__(self, x, y, subtype):
self.x = x
self.y = y
self.subtype = subtype
self.activated = False
self.moving = False

def move(self, player, object_map):
new_x, new_y = player.x, player.y
if self.activated:
if player.x > self.x:
new_x = self.x + ENEMY_SPEED
elif player.x < self.x:
new_x = self.x - ENEMY_SPEED

if player.y > self.y:
new_y = self.y + ENEMY_SPEED
elif player.y < self.y:
new_y = self.y - ENEMY_SPEED

self.x, self.y = check_collision(self.x, self.y, new_x, new_y, object_map, ENEMY_MARGIN)
if (self.x == new_x) or (self.y == new_y):
self.moving = True
else:
self.moving = False``````

Sprites have also now been given types and subtypes to help assign appropriate behavior. Sprites are now configured as per this code:

``````self.list_of_sprites = {
'barrel': {
'viewing_angles': None,
'shift': 0.8,
'scale': (0.8, 0.8),
'animation': deque(
range(6)]),
'animation_distance': 2000,
'animation_speed': 10,
'type': 'object',
'subtype': 'barrel',
'interactive': False,
'interaction_sound': None,
},
'car': {
'viewing_angles': False,
'shift': 0.3,
'scale': (2.0, 2.0),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'object',
'subtype': 'car',
'interactive': False,
'interaction_sound': None,
},
'blank': {
in
range(8)],
'viewing_angles': True,
'shift': 0.1,
'scale': (1.0, 1.0),
'animation': deque(
range(8)]),
'animation_distance': 3000,
'animation_speed': 6,
'type': 'enemy',
'subtype': 'blank',
'interactive': False,
'interaction_sound': None,
},
'sprite_door_y_axis': {
range(8)],
'viewing_angles': True,
'shift': 0.01,
'scale': (2.4, 1.4),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'door',
'subtype': 'door_y_axis',
'interactive': True,
'interaction_sound': pygame.mixer.Sound('assets/audio/door.wav'),
},
'sprite_door_x_axis': {
range(8)],
'viewing_angles': True,
'shift': 0.01,
'scale': (2.4, 1.4),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'door',
'subtype': 'door_x_axis',
'interactive': True,
'interaction_sound': pygame.mixer.Sound('assets/audio/door.wav'),
},
}``````

The update_sprite_map method has been modified to include enemy flags for where enemies are located. This will be used in the future when enemies can damage the player:

``````def update_sprite_map(self):
self.sprite_map = {} # used for collision detection with sprites - this will need to move when sprites can move
self.enemy_map = {}
for sprite in self.list_of_sprites:
if not sprite.delete and sprite.type != 'enemy':
sprite_location = common.align_grid(sprite.x, sprite.y)
self.sprite_map[sprite_location] = 'sprite'
elif not sprite.delete and sprite.type == 'enemy':
enemy_location = common.align_grid(sprite.x, sprite.y)
self.enemy_map[enemy_location] = 'enemy'``````

The SpriteBase __init__, and locate_sprite methods had to be modified to implement the new enemy class and also implement logic to determine if the enemy is moving so that the images loaded under the animation variable could be used to create a walking animation.

Here is the code of the __init__, and locate_sprite methods:

``````def __init__(self, parameters, pos):
self.sprite_object = parameters['sprite']
self.shift = parameters['shift']
self.scale = parameters['scale']
self.animation = parameters['animation'].copy()
self.animation_distance = parameters['animation_distance']
self.animation_speed = parameters['animation_speed']
self.type = parameters['type']
self.subtype = parameters['subtype']
self.viewing_angles = parameters['viewing_angles']
self.animation_count = 0
self.pos = self.x, self.y = pos * GRID_BLOCK, pos * GRID_BLOCK
self.interact_trigger = False
self.previous_position_y = self.y
self.previous_position_x = self.x
self.delete = False
self.interactive = parameters['interactive']
self.interaction_sound = parameters['interaction_sound']
if self.type == 'enemy':
self.object = Enemy(self.x, self.y, self.subtype)
else:
self.object = None

if self.viewing_angles:
sprite_angle_delta = int(360 / len(self.sprite_object)) # Used to determine at what degree angle to
# change the sprite image- this is based on the number of images loaded for the item.
self.sprite_angles = [frozenset(range(i, i + sprite_angle_delta)) for i in
range(0, 360, sprite_angle_delta)]
self.sprite_positions = {angle: pos for angle, pos in zip(self.sprite_angles, self.sprite_object)}
self.sprite_object = self.sprite_object # set a default image until correct one is selected

def locate_sprite(self, player, object_map):
if self.object:
self.object.move(player, object_map)
dx, dy = self.x - player.x, self.y - player.y
self.distance_to_sprite = math.sqrt(dx ** 2 + dy ** 2)

theta = math.atan2(dy, dx)
gamma = theta - player.angle

if dx > 0 and 180 <= math.degrees(player.angle) <= 360 or dx < 0 and dy < 0:
gamma += DOUBLE_PI

delta_rays = int(gamma / DELTA_ANGLE)
current_ray = CENTER_RAY + delta_rays
self.distance_to_sprite *= math.cos(HALF_FOV - current_ray * DELTA_ANGLE)

sprite_ray = current_ray + SPRITE_RAYS
if 0 <= sprite_ray <= SPRITE_RAYS_RANGE and self.distance_to_sprite > 30:
projected_height = min(int(WALL_HEIGHT / self.distance_to_sprite), resY * 2)
sprite_width = int(projected_height * self.scale)
sprite_height = int(projected_height * self.scale)
half_sprite_width = sprite_width // 2
half_sprite_height = sprite_height // 2
shift = half_sprite_height * self.shift

if self.interact_trigger:
self.interact()
if self.interaction_sound and not self.delete:
if not pygame.mixer.Channel(3).get_busy():
pygame.mixer.Channel(3).play(pygame.mixer.Sound(self.interaction_sound))

if self.viewing_angles:
if theta < 0:
theta += DOUBLE_PI
theta = 360 - int(math.degrees(theta))

if self.type == "enemy":
if self.object.activated:
theta = 0

for angles in self.sprite_angles:
if theta in angles:
self.sprite_object = self.sprite_positions[angles]
break

if self.animation and self.distance_to_sprite < self.animation_distance:
if self.type == 'enemy':
if self.object.moving:
self.sprite_object = self.animation
else:
self.sprite_object = self.animation
if self.animation_count < self.animation_speed:
self.animation_count += 1
else:
self.animation.rotate()
self.animation_count = 0

sprite = pygame.transform.scale(self.sprite_object, (sprite_width, sprite_height))
if not self.delete:
if (self.type == 'enemy') and self.object:
self.object.activated = True
self.pos = self.x, self.y = self.object.x, self.object.y

return {'image': sprite, 'x': (current_ray * SCALE - half_sprite_width),
'y': (HALF_HEIGHT - half_sprite_height + shift), 'distance': self.distance_to_sprite}
else:
if (self.type == 'enemy') and self.object:
self.object.activated = False
self.pos = self.x, self.y = self.object.x, self.object.y
None
else:
return None``````

The source code for everything discussed in the post can be downloaded here and the executable here.

# DEVELOPING A RAYCASTING ‘3D’ ENGINE GAME IN PYTHON AND PYGAME – PART 3

In this post, the following features added to the game engine will be covered:

1. Adding music to the game.
3. Fixed the distortion of wall textures if the player stands too close to them.
4. Changed sprite scaling to handle height and width independently.

Music

To add music the following lines of code was added to the main.py file:

``````pygame.mixer.music.set_volume(0.05)
pygame.mixer.music.play(-1)``````

The ‘-1’ parameter in the play function sets the music to loop, so when the track has completed playing, it will start playing from the beginning again.

Animated Sprites and Scaling of Sprites

To facilitate the additional values required to implement animated sprites as well as separate width and height scaling, the definition of the parameters of each sprite is now handled in a dictionary as below:

``````self.list_of_sprites = {
'barrel': {
'viewing_angles': None,
'shift': 0.8,
'scale': (0.8, 0.8),
'animation': deque(
range(6)]),
'animation_distance': 2000,
'animation_speed': 10,
'type': 'barrel',
'interactive': False,
'interaction_sound': None,
},
'zombie360': {
range(4)],
'viewing_angles': True,
'shift': 0.6,
'scale': (1.1, 1.1),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'zombie',
'interactive': False,
'interaction_sound': None,
},
'car': {
'viewing_angles': False,
'shift': 0.3,
'scale': (2.0, 2.0),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'car',
'interactive': False,
'interaction_sound': None,
},
'blank': {
range(8)],
'viewing_angles': True,
'shift': 0.6,
'scale': (1.0, 1.4),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'blank',
'interactive': False,
'interaction_sound': None,
},
'sprite_door_y_axis': {
'sprite': [pygame.image.load(f'assets/images/sprites/objects/door_v/{i}.png').convert_alpha() for i in range(16)],
'viewing_angles': True,
'shift': 0.01,
'scale': (2.4, 1.4),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'door_y_axis',
'interactive': True,
'interaction_sound': pygame.mixer.Sound('assets/audio/door.wav'),
},
'sprite_door_x_axis': {
'sprite': [pygame.image.load(f'assets/images/sprites/objects/door_h/{i}.png').convert_alpha() for i in range(16)],
'viewing_angles': True,
'shift': 0.01,
'scale': (2.4, 1.4),
'animation': [],
'animation_distance': 0,
'animation_speed': 0,
'type': 'door_x_axis',
'interactive': True,
'interaction_sound': pygame.mixer.Sound('assets/audio/door.wav'),
},
}``````

scale is now a tuple containing a value for width and height scaling values separately.

Additionally, the following values were added, which are related to animating of sprites:

animation – if the sprite is an animated sprite, this will contain a list of images used in rendering the animation. The images used for the animation are loaded into a double-ended queue. This is a queue structure where data can be added and removed from the queue at both ends.

animation_distance – at which distance from the player the animation will start being rendered.

animation_speed – the speed at which the animation will be played.

type – used to determine the type of the sprite.

The next two variables will be used later in this post when we discuss interactive sprites (doors), they are:

interactive – which is set for whether a sprite can be interacted with or not.

interaction_sound – This stores an audio file that will be triggered if interaction with the sprite is triggered.

The implementation of how sprites are scaled has been changed to scale the width and height of the sprite separately, this will allow for more accurate scaling as well as fixing distortion of sprites that have a non-symmetrical aspect ratio.

``````    sprite_width = int(projected_height * self.scale)
sprite_height = int(projected_height * self.scale)
half_sprite_width = sprite_width // 2
half_sprite_height = sprite_height // 2
shift = half_sprite_height * self.shift``````

And when the sprite is returned by the locate_sprite function, the x and y values are now determined as follows:

``````return {'image': sprite, 'x': (current_ray * SCALE - half_sprite_width),
'y': (HALF_HEIGHT - half_sprite_height + shift), 'distance': self.distance_to_sprite}``````

The following logic has been added to the locate_sprite function in the sprite.py file to play the animation:

``````  if self.animation and self.distance_to_sprite < self.animation_dist:
self.sprite_object = self.animation
if self.animation_count < self.animation_speed:
self.animation_count += 1
else:
self.animation.rotate()
self.animation_count = 0``````

In the function above, the current sprite object that will be rendered to the screen is set to the first object in the double-ended queue, and if the sprite animation speed has been exceeded, the double-ended queue will then be rotated, i.e., the first item in the double-ended queue will be moved to the back of the queue.

Fix for the Distortion of Wall Textures

There was a distortion of wall textures that occurred if the player moved too close to the walls. The issue resulted because the wall height was larger than the screen height at that point, and this was rectified by modifying the raycasting function as per below:

``````            projected_height = int(WALL_HEIGHT / depth)

if projected_height > resY:
texture_height = TEXTURE_HEIGHT / (projected_height / resY)
wall_column = textures[texture].subsurface(offset * TEXTURE_SCALE,
(TEXTURE_HEIGHT // 2) - texture_height // 2,
TEXTURE_SCALE, texture_height)
wall_column = pygame.transform.scale(wall_column, (SCALE, resY))
wall_position = (ray * SCALE, 0)

else:
wall_column = textures[texture].subsurface(offset * TEXTURE_SCALE, 0, TEXTURE_SCALE, TEXTURE_HEIGHT)
wall_column = pygame.transform.scale(wall_column, (SCALE, projected_height))
wall_position = (ray * SCALE, HALF_HEIGHT - projected_height // 2)

x, y = wall_position
walls.append(
{'image': wall_column, 'x': x, 'y': y, 'distance': depth})``````

Interactive Doors (with Sound)

To implement interactivity in the game world, a few changes have to be implemented.

Firstly a new variable needed to be added to the Player class called interact. This is a Boolean value that will be set to true if the player presses the ‘e’ key. here is the updated player.py file:

``````from common import *
from map import *

class Player:
def __init__(self):
player_pos = ((map_width / 2), (map_height / 2))
self.x, self.y = player_pos
self.angle = player_angle
self.sensitivity = 0.001
self.step_sound = pygame.mixer.Sound('assets/audio/footstep.wav')
self.interact = False
pygame.mixer.Channel(2).set_volume(0.2)

@property
def pos(self):
return (self.x, self.y)

def movement(self, sprite_map):
self.keys_control(sprite_map)
self.mouse_control()
self.angle %= DOUBLE_PI  # Convert player angle to 0-360 degree values

def check_collision(self, new_x, new_y, sprite_map):
player_location = align_grid(new_x, new_y)
if player_location in world_map or player_location in sprite_map:
#  collision
print("Center Collision" + str(new_x) + " " + str(new_y))
return

player_location = align_grid(new_x - HALF_PLAYER_MARGIN, new_y - HALF_PLAYER_MARGIN)
if player_location in world_map or player_location in sprite_map:
#  collision
print("Top Left Corner Collision" + str(new_x) + " " + str(new_y))
return

player_location = align_grid(new_x + HALF_PLAYER_MARGIN, new_y - HALF_PLAYER_MARGIN)
if player_location in world_map or player_location in sprite_map:
#  collision
print("Top Right Corner Collision" + str(new_x) + " " + str(new_y))
return

player_location = align_grid(new_x - HALF_PLAYER_MARGIN, new_y + HALF_PLAYER_MARGIN)
if player_location in world_map or player_location in sprite_map:
#  collision
print("Bottom Left Corner Collision" + str(new_x) + " " + str(new_y))
return

player_location = align_grid(new_x + HALF_PLAYER_MARGIN, new_y + HALF_PLAYER_MARGIN)
if player_location in world_map or player_location in sprite_map:
#  collision
print("Bottom Right Corner Collision" + str(new_x) + " " + str(new_y))
return

if not pygame.mixer.Channel(2).get_busy():
pygame.mixer.Channel(2).play(pygame.mixer.Sound(self.step_sound))
self.x = new_x
self.y = new_y

def keys_control(self,sprite_map):
sin_a = math.sin(self.angle)
cos_a = math.cos(self.angle)
keys = pygame.key.get_pressed()
if keys[pygame.K_ESCAPE]:
exit()
if keys[pygame.K_w]:
nx = self.x + player_speed * cos_a
ny = self.y + player_speed * sin_a
self.check_collision(nx, ny, sprite_map)
if keys[pygame.K_s]:
nx = self.x + -player_speed * cos_a
ny = self.y + -player_speed * sin_a
self.check_collision(nx, ny, sprite_map)
if keys[pygame.K_a]:
nx = self.x + player_speed * sin_a
ny = self.y + -player_speed * cos_a
self.check_collision(nx, ny, sprite_map)
if keys[pygame.K_d]:
nx = self.x + -player_speed * sin_a
ny = self.y + player_speed * cos_a
self.check_collision(nx, ny, sprite_map)
if keys[pygame.K_e]:
self.interact = True
if keys[pygame.K_LEFT]:
self.angle -= 0.02
if keys[pygame.K_RIGHT]:
self.angle += 0.02

def mouse_control(self):
if pygame.mouse.get_focused():
difference = pygame.mouse.get_pos() - HALF_WIDTH
pygame.mouse.set_pos((HALF_WIDTH, HALF_HEIGHT))
self.angle += difference * self.sensitivity``````

Next, we need to implement a new class called Interaction. This class is implemented in the interactions.py file.

In this class, a function called interaction_world_objects is defined. This function first checks if the player has pressed the interact button (‘e’) and, if so, iterates through each sprite in the game world, checking that the sprite’s distance from the player is within range. If the sprite is in range and it is an interactive sprite, the sprites interact_trigger variable will be set to true.

Here is the code contained in the interactions.py file:

``````from settings import *
from common import *

class Interactions:
def __init__(self, player, sprites, drawing):
self.player = player
self.sprites = sprites
self.drawing = drawing

def interaction_world_objects(self):
if self.player.interact:
for obj in sorted(self.sprites.list_of_sprites, key=lambda obj: obj.distance_to_sprite):
px, py = align_grid(self.player.x, self.player.y)
sx, sy = align_grid(obj.x, obj.y)
x_dist = px - sx
y_dist = py - sy
print('x distance : ' + str(x_dist))
print('y distance : ' + str(y_dist))
if obj.interactive:
if ((-INTERACTION_RANGE <= x_dist <= INTERACTION_RANGE) and (
-INTERACTION_RANGE <= y_dist <= INTERACTION_RANGE)) and not obj.interact_trigger:
obj.interact_trigger = True``````

Lastly, the sprite.py file needs to be updated. First, a check must be done in the locate_sprite function to see if the sprite’s interact_trigger value has been set to true:

`````` if self.interact_trigger:
self.interact()
if self.interaction_sound and not self.delete:
if not pygame.mixer.Channel(3).get_busy():
pygame.mixer.Channel(3).play(pygame.mixer.Sound(self.interaction_sound))``````

This calls the sprite’s interact function and plays the audio file associated with the sprites interaction.

The interact function as shown below determines the type of the sprite and performs some action based thereon:

``````    def interact(self):
if self.type == 'door_y_axis':
self.y -= 1
if abs(self.y - self.previous_position_y) > GRID_BLOCK:
self.delete = True
elif self.type == 'door_x_axis':
self.x -= 1
if abs(self.x - self.previous_position_x) > GRID_BLOCK:
self.delete = True``````

In the event of the x-axis and y-axis doors, the function moves the sprite to the side, creating the effect of a door opening.

The source code for everything discussed in the post can be downloaded here and the executable here.

The next thing to be implemented is NPC characters that move around the game world. Check for future posts on this topic.

# Developing a Raycasting ‘3D’ Engine Game in Python and PyGame – PART 1

I have started developing a raycasting game in Python (using PyGame) as a learning exercise and to get a better understanding of the math and techniques involved.

Raycasting is a graphic technique used to render pseudo-3D graphics based on a 2D game world. The best-known example of a raycasting engine used in a computer game is probably Wolfenstein 3D, developed by id Software in 1992.

So firstly, here are some resources I used to upskill and get my head around the topic:

YouTube tutorial series by Standalone Coder. These videos are in Russian, but the YouTube subtitles do a good enough job to follow along.

YouTube tutorial series by Code Monkey King.

Lastly, I recommend the book Game Engine Black Book: Wolfenstein 3D by Fabien Sanglard, it is not an easy read, but it gives excellent insight into the development of Wolfenstein 3D and a great deal of information into the intricate details of Raycasting and texture mapping.

The Basics of Raycasting

The first thing to understand is that Raycasting is not true 3D, but rather rendering a 2D world in pseudo 3D. Therefore, all movement and game positions consist of only x and y positions, with no height or z positions.

The entire game world consists of a grid, with some blocks in the grid being populated with walls and others being empty. An example of this is shown in the picture below:

In the current version of the game, the world map is implemented as a list of strings, where each character in the string represents a block in the grid. The ‘0’ character represents an empty block, and all other numbers represent a wall. The numbers ‘1’, ‘2’, and ‘3’ are used to show different wall textures according to the different numbers, something covered later in this post.

``````game_map = [
'11111111111111111111',
'10000000000003330001',
'10011100000000000001',
'10030000000000000001',
'10020000000000300001',
'10020001110000000001',
'10000330000000000001',
'10000330000000000001',
'10000330000000000001',
'10000330000000000001',
'10000330000000000001',
'10000330000000000001',
'10020000000000300001',
'10020001110000000001',
'10000330000000000001',
'10000330000000000001',
'10020000000000300001',
'10020001110000000001',
'10000330000000000001',
'11111111111111111111'
]``````

This is then converted into a dictionary as follows:

``````world_map = {}
for j, row in enumerate(game_map):
for i, char in enumerate(row):
if char != '0':
if char == '1':
world_map[(i * GRID_BLOCK, j * GRID_BLOCK)] = '1'
elif char == '2':
world_map[(i * GRID_BLOCK, j * GRID_BLOCK)] = '2'
elif char == '3':
world_map[(i * GRID_BLOCK, j * GRID_BLOCK)] = '3'``````

The player is placed on this grid with a x and y coordinates determining the player’s position on the grid. Along with the x and y coordinates, the player also has a viewing angle, i.e., a direction the player is facing.

Now that we have the foundation in place, we can get to the raycasting.

To understand this concept, imagine a line originating from the player and heading off in the direction the player is facing.

Now, this is not an endless line, but rather a line that keeps expanding from one world grid line to the next. (this is done with a for loop).

At every point where this ‘ray’ intersects a grid line on the game world, a check is done to determine if the grid line in question is a wall or not.

If it is a wall, the loop expanding the line is stopped, and the x and y coordinates where the wall was intersected will be noted. We will use this a bit later when drawing the pseudo-3D rendering of the world.

The above is the simplest form of raycasting. However, a single ray will not give us a usable amount of information to do the pseudo-3D render with. This is where a player’s FOV (field of view) and more rays come in.

The Player FOV is an angle on the game world originating at the player and extending out in a triangular form. This determines where the player’s visible range at present begins and ends. For this game, I will use a FOV of 60% (i.e., pi/3).

To change the FOV, the following can be used as a guide:

Within this FOV, several rays will be generated, exactly as per the single one in the example discussed earlier.

In this game, a value of 480 rays has been defined, which will be generated within the FOV, so the process above for a single ray will be repeated 480 times, with each ray cast having its angle increased by a marginal amount from the previous ray.

The angle of the first ray will be determined as follows:

Starting angle = Player Angle – Half the FOV

Where Player Angle is defined as the center point of direction player is facing.

For each subsequent ray, the angle of the ray will be increased by a delta angle calculated as followed:

Delta Angle = FOV/Number of Rays

This will allow for a sufficient set of information to draw a pseudo-3D rendering from.

To see how this is implemented, please look at lines 6 to 39 in the raycasting.py file.

Sine and Cosine functions are used to determine the intersecting coordinates, and if you require a refresher on these functions, I recommend this web article from mathisfun.com.

For calculating the y coordinate where the ray intersects with a wall, the following formula is used:

y = (player y) + depth * sin(ray angle)

And to calculate the x coordinate where the ray intersects with a wall, the following formula is used:

x = (player x) + depth * cos(ray angle)

For depth value in the above formulas, a sequence of numbers would usually be looped through, starting at 0 and ending at some defined maximum depth.

The above formulas would then be executed at each new depth level to get the corresponding x and y coordinates.

This does provide the desired results, but it is not very optimized.

To improve the performance of this operation, the Digital Differential Analyzer (DDA) algorithm will be used. At a high level, the DDA algorithm functions by not checking every pixel of the 2D game world for an intersection of a ray and a wall but only checking on the grid lines of the 2D world (the only place where walls can occur).

To implement the DDA algorithm, we are going to need four extra variables in conjunction with the Player x and y coordinates, namely:

dx and dy – these two variables will determine the step size to the next grid line. Based on the direction of the angle, these either have the value of 1 or -1.

gx and gy – This will be the x and y coordinates of the grid lines that will be iterated through, starting with the grid line the closest to the player x and y position. The initial value is determined using the following function, located in the common.py file:

``````def align_grid(x, y):
return (x // GRID_BLOCK) * GRID_BLOCK, (y // GRID_BLOCK) * GRID_BLOCK
``````

This will ensure that the returned x and y coordinates are located on the closet grid line (based on game world tile size). For reference, the // operator in Python is floor division and rounds the resulting number to the nearest whole number down.

To determine the depth to the next y-axis grid line, the following equation will be used:

Depth Y = (gx – player x) / cos (ray angle)

And to determine the depth of the next x-axis grid line, this equation is used:

Depth X = (gy – player y) / sin (ray angle)

The below two code blocks implement what was just described, the first block of code is to determine intersections with walls on the y axis of the world map:

``````        # checks for walls on y axis
gx, dx = (xm + GRID_BLOCK, 1) if cos_a >= 0 else (xm, -1)
for count in range(0, MAX_DEPTH, GRID_BLOCK):
depth_y = (gx - px) / cos_a
y = py + depth_y * sin_a
tile_y = align_grid(gx + dx, y)
if tile_y in world_map:
# Ray has intersection with wall
texture_y = world_map[tile_y]
ray_col_y = True
break
gx += dx * GRID_BLOCK``````

And the next block of code is to determine intersections with walls on the x axis of the world map:

``````        # checks for walls on x axis
gy, dy = (ym + GRID_BLOCK, 1) if sin_a >= 0 else (ym, -1)
for count in range(0, MAX_DEPTH, GRID_BLOCK):
depth_x = (gy - py) / sin_a
x = px + depth_x * cos_a
tile_x = align_grid(x, gy + dy)
if tile_x in world_map:
# Ray has intersection with wall
texture_x = world_map[tile_x]
ray_col_x = True
break
gy += dy * GRID_BLOCK``````

texture_x and texture_y are used to store the index of the texture to display on the wall. We will cover this later in this post.

Now that we have the raycasting portion covered, which is the most complex, we can focus on simply rendering the pseudo-3D graphics to the screen.

At a very high level, the basic concept of how the pseudo-3D graphics will be created, is to draw a rectangle for every ray that has intersected a wall. The x position of the rectangle will be based on the angle of the ray. The y position will be determined based on the distance of the wall from the player, with a width of the rectangle equal to the distance between the rays (calculated with Window resolution width / Number of Rays) and a user-defined height.

This will create a very basic pseudo-3D effect, and it would be much nicer using textured walls.

To implement textured walls the concept remains the same, but instead of just drawing rectangles, we will copy a small strip from a texture image and draw that to the screen instead.

In the code blocks above, there were two variables texture_x and texture_y. Where a wall intersection did occur these variables will contain a value of ‘1’, ‘2’ or ‘3’ based on the value in the world map, and these correspond to different textures that are loaded in a dictionary as follows:

``````textures = {
}``````

Firstly the correct section of the texture needs to be loaded based on the ray’s position on the wall. This is done as follows:

``wall_column = textures[texture].subsurface(offset * TEXTURE_SCALE, 0, TEXTURE_SCALE, TEXTURE_HEIGHT)``

Depending if it is for a x-axis or y-axis wall, the follwoing values will be as follows:

For a x-axis wall:

texture = texture_x

offset = int(x) % GRID_BLOCK

Where x is the x coordinate of the wall intersection.

And for a y-axis wall:

texture = texture_y

offset = int(y) % GRID_BLOCK

Where y is the y coordinate of the wall intersection.

Next, the section of the texture needs to be resized correctly based on its distance from the player as follows:

``wall_column = pygame.transform.scale(wall_column, (SCALE, projected_height))``

Where the values are determined as below:

projected_height = min(int(WALL_HEIGHT / depth), 2 * resY)

resY = Window Resolution Height

For a x-axis wall:

depth = max((depth_x * math.cos(player_angle – cur_angle)),0.00001)

For a y-axis wall:

depth = max((depth_y * math.cos(player_angle – cur_angle)),0.00001)

The last thing to do then is to draw the resized texture portion to the screen:

``sc.blit(wall_column, (ray * SCALE, HALF_HEIGHT - projected_height // 2))``

The above operations of copying a section of a texture, resizing it, and drawing it to the screen is done for every ray that intersects a wall.

The last thing to do and by far the least complex is to draw in the sky box and the floor. The sky box is simply an image, loaded in the texture dictionary under the ‘S’ key, which is drawn to the screen. The sky box is drawn in three blocks:

``````        sky_offset = -5 * math.degrees(angle) % resX
self.screen.blit(self.textures['S'], (sky_offset, 0))
self.screen.blit(self.textures['S'], (sky_offset - resX, 0))
self.screen.blit(self.textures['S'], (sky_offset + resX, 0))``````

This ensures that no gap appears as the player turns and creates the impression of an endless sky.

Lastly, for the floor, a solid color rectangle is drawn as below:

``pygame.draw.rect(self.screen, GREY, (0, HALF_HEIGHT, resX, HALF_HEIGHT)) ``

For reference, the following PyGame functions are used in the game up to this point:

pygame.init
Used to initialize pygame modules and get them ready to use.

pygame.display.set_mode
Used to initialize a window to display the game.

Used to load an image file from the supplied path into a variable to be used when needed.

pygame.Surface.subsurface
Used to get a copy of a section of an image (surface) based on the supplied x position,y position, width, and height values.

pygame.transform.scale
Used to resize an image (surface) to the supplied width and height.

pygame.Surface.blit
Used to draw images to the screen.

pygame.display.flip
Used to update the full display Surface to the screen.

pygame.Surface.fill
Used to fill the display surface with a background color.

pygame.draw.rect
Used to draw a rectangle to the screen (used for the floor).

Also used pygame.key.get_pressed, pygame.event.get and pygame.mouse methods for user input.

Collision Detection

Because the game plays out in a 2D world, collision detection is rather straightforward.

The player has a square hitbox, and every time the player inputs a movement, the check_collision function is called with the new x and y positions the player wants to move to. The function then uses the new x and y positions to determine the player hitbox and check if it is in contact with any walls; if so, the move is not allowed. Otherwise, the player x and y positions are updated to the new positions.

Here is the check_collision function that forms part of the Player class:

`````` def check_collision(self, new_x, new_y):
player_location = mapping(new_x , new_y)
if player_location in world_map:
#  collision
print("Center Collision" + str(new_x) + " " + str(new_y))
return

player_location = mapping(new_x - HALF_PLAYER_MARGIN, new_y - HALF_PLAYER_MARGIN)
if player_location in world_map:
#  collision
print("Top Left Corner Collision" + str(new_x) + " " + str(new_y))
return

player_location = mapping(new_x + HALF_PLAYER_MARGIN, new_y - HALF_PLAYER_MARGIN)
if player_location in world_map:
#  collision
print("Top Right Corner Collision" + str(new_x) + " " + str(new_y))
return

player_location = mapping(new_x - HALF_PLAYER_MARGIN, new_y + HALF_PLAYER_MARGIN)
if player_location in world_map:
#  collision
print("Bottom Left Corner Collision" + str(new_x) + " " + str(new_y))
return

player_location = mapping(new_x + HALF_PLAYER_MARGIN, new_y + HALF_PLAYER_MARGIN)
if player_location in world_map:
#  collision
print("Bottom Right Corner Collision" + str(new_x) + " " + str(new_y))
return

self.x = new_x
self.y = new_y``````

Here is a video of the current version of the game in action:

The current version of this game is still a work in progress, but if you are interested, the source code can be downloaded here and the executable here.

Some of the next things on the to-do list are loading levels from the file, adding sprites to the game world, and adding some interactive world items, such as doors that open and close.

I will keep creating posts on this topic as I progress with this project.

# LEARNING PYTHON AND DEVELOPING A GAME As I mentioned in my Surviving Lockdown post, I started upskilling on Python, and when upskilling on a new programming language, I usually do a project to build on and enforce the things I am learning.

For my Python-based project, I decided to use PyGame to develop a small game. One piece of advice I can offer when developing a game is that it is better to develop a small and basic game that you finish than a large and ambitious game you never complete. I believe everyone who has tried some form of game development has at least one over-ambitious project they never completed, so it is better to start small.

The game I developed is called “Space Octopus Invasion” and here is a video of the game in action:

The tools and resources I used in the development process are as follows:

• Trello
I used Trello for task tracking and planning. • PyCharm
PyCharm is my favorite Python IDE developed by JetBrains, and it offers a free community edition. • PyInstaller
A great utility to package a python application into an executable file.
• InstallForge
A free installer maker that allows you to create a professional-looking setup wizard to install your game.
• GameDevMarket.net
I am not an artistically inclined person, and typically I use art, sound, and music assets when developing a game, I recommend GameDevMarket.net as they have a great selection of assets available.