def find_target_position(origin_pos, initial_velocity, wanted_z=0):
"""
Find and return target ball position with a specified initial velocity and position.
:param pygame.Vector3 origin_pos: initial ball position in world coordinates
:param pygame.Vector3 initial_velocity: initial ball velocity in world coordinates
:param float wanted_z: specify at which z value target position will be found
:return: target ball position
:rtype pygame.Vector3:
"""
# z_t
z_t = wanted_z - origin_pos.z
# u vector : unit vector in XY plane from origin to target position
u = Vector3(initial_velocity)
u.z = 0
u = u.normalize() if u.length_squared() != 0 else Vector3()
# get final time t_t
t_t = get_time_at_z(initial_velocity.z, origin_pos.z, wanted_z)
# u_t
u_t = t_t * initial_velocity.dot(u)
return u_t * u + origin_pos + Vector3(0, 0, z_t)
def shade(self, pos):
L = Vector3(self.x * sin(t), self.y, self.z * cos(t))
L = L.normalize()
dt = 1e-6
current_val = surface_distance(pos)
x = Vector3(pos.x + dt, pos.y, pos.z)
dx = surface_distance(x) - current_val
y = Vector3(pos.x, pos.y + dt, pos.z)
dy = surface_distance(y) - current_val
z = Vector3(pos.x, pos.y, pos.z + dt)
dz = surface_distance(z) - current_val
# normal
N = Vector3(
(dx - pos.x) / dt,
(dy - pos.y) / dt,
(dz - pos.z) / dt,
)
if N.length() < 1e-9:
return PIXELS[0]
N = N.normalize()
diffuse = L.x * N.x + L.y * N.y + L.z * N.z
diffuse = (diffuse + 1) / 2 * len(PIXELS)
return PIXELS[int(diffuse) % len(PIXELS)]
def test_world_to_pixel_coords(horizontal_camera, oblique_camera,
not_centered_camera):
w, h = (100, 100)
for cam in (horizontal_camera, oblique_camera, not_centered_camera):
# center
center_pt = Vector3(cam.focus_point)
u, v = cam.world_to_pixel_coords(center_pt, (w, h))
assert u == w / 2 or u == w / 2 - 1 # -1 because of imprecision due to continuous/discrete conversion
assert v == h / 2 or v == h / 2 - 1 # same thing
# point in 4 screen areas (top-left, top-right, bottom-left and bottom-right)
tl_pt = Vector3(0, -1, 1) + cam.focus_point
tr_pt = Vector3(0, 1, 1) + cam.focus_point
bl_pt = Vector3(0, -1, -1) + cam.focus_point
br_pt = Vector3(0, 1, -1) + cam.focus_point
# test if points are in correct area
u, v = cam.world_to_pixel_coords(tl_pt, (w, h))
assert u < w / 2 and v < h / 2
u, v = cam.world_to_pixel_coords(tr_pt, (w, h))
assert u > w / 2 and v < h / 2
u, v = cam.world_to_pixel_coords(bl_pt, (w, h))
assert u < w / 2 and v > h / 2
u, v = cam.world_to_pixel_coords(br_pt, (w, h))
assert u > w / 2 and v > h / 2
def calculatePerspective(self, location: pygame.Vector3):
translation = pygame.Vector2(self.getLocation().x + self.getWidth() / 2, self.getLocation().y + self.getHeight() / 2)
#ray = Ray(self.getFocus(), location)
location = location - self.getLocation()
ray = Ray(pygame.Vector3(0, 0, -self.__focus_distance),
pygame.Vector3(location.dot(self.getHorisontal()), location.dot(self.getVertical()), location.dot(self.getFacing())))
return ray.projection(self.__focus_distance) + translation
def draw_sphere(center, radius, col=None):
"""
Draw a filled sphere on camera screen.
:param pygame.Vector3 center: center of sphere
:param float radius: radius (world scale, not in pixel) of sphere
:param tuple(int, int, int) col: drawing color. default is :var DBG_COLOR_SPHERE:
:return: rect bounding the changed pixels
:rtype pygame.Rect:
"""
display_manager = DisplayManager.get_instance()
if col is None:
col = DBG_COLOR_SPHERE
# process r_px : radius in pixel
camera = display_manager.camera
surface = display_manager.debug_3d.image
surface_size = surface.get_size()
c_pos = Vector3(center)
if SIZE_INDEPENDENT_FROM_Y_POS:
c_pos.y = camera.position.y
if SIZE_INDEPENDENT_FROM_Z_POS:
c_pos.z = camera.position.z
r_px = int((Vector2(
camera.world_to_pixel_coords(c_pos, surface_size) - Vector2(
camera.world_to_pixel_coords(c_pos + radius * Vector3(0, 1, 0),
surface_size))).magnitude()))
return draw.circle(surface, col,
camera.world_to_pixel_coords(center, surface_size),
r_px)
def update_physics(self, dt):
self.previous_position = Vector3(self.position)
if not self.will_be_served:
self.add_velocity(Vector3(0, 0, -0.001 * dt * G))
self.move_rel(0.001 * dt * self.velocity)
else:
self.velocity = Vector3()
def _set_n_debug_3d_points(self, n):
"""
Process n 3D-points in ball trajectory.
:param int n: points count
:return: n points in list
:rtype list(Vector3):
"""
if self.origin_pos is None or self.target_pos is None or self.initial_velocity is None:
self.debug_pts = []
else:
assert n > 1
# u vector : unit vector in XY plane from origin to target position
u = Vector3(self.initial_velocity)
u.z = 0
u = u.normalize() if u.length_squared() != 0 else Vector3(0, 0, 0)
# get t_t : final time
t_t = self.get_final_time()
dt = t_t / (n - 1)
self.debug_pts = []
for i in range(n):
t_i = i * dt
u_i = t_i * self.initial_velocity.dot(u)
z_i = -t_i**2 / 2 * G + t_i * self.initial_velocity.z
self.debug_pts.append(
Vector3(u_i * u + self.origin_pos + Vector3(0, 0, z_i)))
def explode(self):
explode_force = randint(10, 30)
for i in range(300):
r = (random() * 360) * math.pi / 180
f = random() * explode_force + 1
self.particles.append(
Particle(self.screen, False, Vector3(self.firework.pos),
Vector3(math.sin(r) * f,
math.cos(r) * f, 0)))
def __init__(self,
location: pygame.Vector3 = pygame.Vector3(0, 0, 0),
facing: pygame.Vector3 = pygame.Vector3(1, 0, 0),
vertical: pygame.Vector3 = pygame.Vector3(0, 1, 0),
**kwargs):
super().__init__(**kwargs)
self.__centre: pygame.Vector3 = location
self.__facing: pygame.Vector3 = facing.normalize()
self.__vertical: pygame.Vector3 = vertical.normalize()
def test_world_to_cam_3d_coords(horizontal_camera, oblique_camera,
not_centered_camera):
center_pt = Vector3(0, 0, 0)
assert horizontal_camera.world_to_cam_3d_coords(center_pt) == Vector3(
0, 0, -5)
assert oblique_camera.world_to_cam_3d_coords(center_pt) == Vector3(
0, 0, -5)
assert not_centered_camera.world_to_cam_3d_coords(
not_centered_camera.focus_point) == Vector3(0, 0, -5)
def __init__(self, screen, width, height, gravity):
self.screen = screen
self.width = width
self.height = height
self.gravity = gravity
self.firework = Particle(screen, True,
Vector3(randint(0, width), height, 0),
Vector3(0, randint(-16, -10), 0))
self.exploded = False
self.particles = []
def _rotate(vec, angle, axis):
"""Rotate vec around axis by the given angle in radians."""
# We are using the Pygame's vectors here
# because pyglm documentation is SHIT and
# I can't find a way do do the same SIMPLE thing.
vec = Vector3(vec)
axis = Vector3(axis)
vec.rotate_ip(angle * 180 / pi, axis)
return vec3(vec)
def __init__(self, pos, WW, WH):
gluPerspective(50, (WW / WH), 0.1, 50)
glTranslatef(pos[0], pos[1], pos[2])
glRotatef(0, 0, 0, 0)
self.pos = Vector3(pos)
self.rot = Vector3(0, 0, 0)
self.rot_angle = 0
self.velocity = Vector3(0, 0, 0)
self.rot_velocity = Vector3(0, 0, 0)
def _create_gradient_steps(self, *colors):
current = Vector3(colors[0][:3])
self.gradient_steps = []
distance = 0
for color in colors[1:]:
vector = Vector3(color)
gradient_step = GradientStep(current, vector, distance)
self.gradient_steps.append(gradient_step)
distance += gradient_step.distance
current = Vector3(vector)
return distance
def __init__(self,
screen,
fire,
pos=Vector3(0, 0, 0),
vel=Vector3(0, 0, 0),
col=white):
self.screen = screen
self.firework = fire
self.pos = pos
self.vel = vel
self.acc = Vector3(0, 0, 0)
self.col = col
self.transparency = 255
def find_initial_velocity(origin_pos, target_pos, wanted_height):
"""
Return initial velocity to apply to a ball to reach a target from an origin position and a specified height.
Process initial velocity in world coordinates to apply on a ball. The specified height is taken in account for the
ball trajectory. If target and origin y sign values are different, the wanted height will be on y = 0 (net
position). Else, the wanted height will be on the middle of trajectory, or at apogee trajectory during a
vertical throw.
:param pygame.Vector3 origin_pos: origin position, the point where the ball will be thrown from
:param pygame.Vector3 target_pos: the desired target position the ball will reach
:param float wanted_height: height desired on net place, middle of trajectory or at apogee
:return: velocity to apply to the ball
:rtype pygame.Vector3:
"""
assert wanted_height > origin_pos.z
assert wanted_height > target_pos.z
if target_pos.x == origin_pos.x and target_pos.y == origin_pos.y: # vertical throw
zh = wanted_height - origin_pos.z
vo_z = sqrt(2 * G * zh)
return Vector3(0, 0, vo_z)
else:
# u vector : unit vector in XY plane from origin to target position
u = Vector3(target_pos - origin_pos)
u.z = 0
u = u.normalize()
# ut, zt : coordinates of target point in (u, z) ref
to_vect = (target_pos - origin_pos)
to_vect.z = 0
ut = to_vect.length()
zt = target_pos.z - origin_pos.z
# uh, zh : coordinates of point above the net in (u, z) ref
alpha = 0.5
if origin_pos.y * target_pos.y < 0: # if target and origin points are not in the same court side
alpha = abs(origin_pos.y / (target_pos.y - origin_pos.y))
uh = alpha * ut
zh = wanted_height - origin_pos.z
# process initial velocity to apply in (u, z) ref : vo_u, vo_z
# not trivial equations, from math and physics resolutions
a = (ut / uh * zh - zt)
c = G * ut / 2 * (uh - ut)
delta = -4 * a * c
vo_u = sqrt(delta) / (2 * a)
vo_z = zh * (vo_u / uh) + uh / vo_u * G / 2
return Vector3(vo_u * u + Vector3(0, 0, vo_z))
def __init__(self,
origin_pos=None,
target_pos=None,
initial_velocity=None):
self.origin_pos = Vector3(
origin_pos) if origin_pos is not None else None
self.target_pos = Vector3(
target_pos) if target_pos is not None else None
self.initial_velocity = Vector3(
initial_velocity) if initial_velocity is not None else None
self.t0 = None
self.debug_pts = None
self._create()
def __init__(self):
#self.modelcanon = pygame.image.load('Model/canon.png')
self.vitesse = 0
self.position = Vector2(400, 450)
self.direction = Vector2()
self.couleur = Vector3()
self.pointdevie = 3
def __init__(self, w, h, net_z1, net_z2):
self.w = w
self.h = h
self.net_z1 = net_z1
self.net_z2 = net_z2
self.collider = AABBCollider(Vector3(0, 0, (net_z1 + net_z2) / 2),
(h, 0, net_z2 - net_z1))
# sprite
self.rects = [pg.Rect(0, 0, 0, 0) for _ in range(10)]
def test_move_time(character):
dt = 10
origin_pos = Vector3()
character.position = Vector3(origin_pos)
n = 100
# move along +y axis for n frames
for _ in range(n):
character.move(Vector3(0, 1, 0), dt, free_displacement=True)
assert n * dt / 1000 == pytest.approx(
character.get_time_to_run_to(origin_pos), 0.01)
# move along +x +y axis for n frames
for _ in range(n):
character.move(Vector3(0.7071, 0.7071, 0), dt, free_displacement=True)
assert 2 * n * dt / 1000 == pytest.approx(
character.get_time_to_run_to(origin_pos), 0.01)
def draw(self, surface, vertical):
vector = Vector3(self.color)
step = self.start_distance
for i in range(self.distance):
if vertical:
surface.set_at((0, i + step), Color(*map(int, vector)))
else:
surface.set_at((i + step, 0), Color(*map(int, vector)))
vector += self.step
self.minmax_color_vector(vector)
def perspective_projection(pt):
# Assuming camera has orientation along -z axis to easy calculations.
# Thus the display surface is perpendicular to z-axis
# display_surface_distance is the distance between camera and the display surface
# https://en.wikipedia.org/wiki/3D_projection#Perspective_projection
camera = Vector3(0, 0, 6)
display_surface_distance = 0.2
projected_point = (pt - camera) * \
display_surface_distance / (camera.z - pt.z)
# Return the point after normalizing
return projected_point * camera.z / display_surface_distance
def draw_debug(self):
prev_rect = self.rect
prev_rect_shadow = self.rect_shadow
self.rect = debug3D_utils.draw_horizontal_ellipse(
Vector3(self.position[0], self.position[1], 0), self.radius)
self.rect_shadow = self.collider.draw_debug()
return [
prev_rect.union(self.rect),
prev_rect_shadow.union(self.rect_shadow)
]
def __init__(self, position=None, radius=0.5, sprite_groups=[]):
pg.sprite.DirtySprite.__init__(self, *sprite_groups)
self.radius = radius
self.acceleration = Vector3()
self.velocity = Vector3()
self._position = Vector3(
position) if position is not None else Vector3()
self.previous_position = Vector3(self._position)
self.collider = SphereCollider(position, radius)
self.is_colliding_ground = False
self.is_colliding_net = False
self.is_colliding_character = False
self.will_be_served = False
# sprite
self.rect_shadow = pg.Rect(0, 0, 0, 0)
self.rect = pg.Rect(0, 0, 0, 0)
# game rules
self._current_team_touches = []
def draw_horizontal_ellipse(center, radius):
"""
Draw a filled ellipse and a unfilled bound trapeze in XY 3D plane on camera screen.
:param pygame.Vector3 center: center of ellipse
:param float radius: radius (world scale, not in pixel) of ellipse
:return: rect bounding the changed pixels
:rtype pygame.Rect:
"""
display_manager = DisplayManager.get_instance()
camera = display_manager.camera
surface = display_manager.debug_3d.image
surface_size = surface.get_size()
# corners of shadow (trapeze)
t_l = camera.world_to_pixel_coords(
Vector3(center) + (-radius, -radius, 0), surface_size)
t_r = camera.world_to_pixel_coords(
Vector3(center) + (-radius, radius, 0), surface_size)
b_l = camera.world_to_pixel_coords(
Vector3(center) + (radius, -radius, 0), surface_size)
b_r = camera.world_to_pixel_coords(
Vector3(center) + (radius, radius, 0), surface_size)
# approximate rect
r_pos = [int(0.5 * (t_l[0] + b_l[0])), t_l[1]]
r_w = int(0.5 * (t_r[0] + b_r[0]) - r_pos[0])
r_h = b_r[1] - r_pos[1]
if r_h < 0:
r_pos[1] += r_h
r_h = -r_h
rect = Rect(r_pos, (r_w, r_h))
if r_w >= r_h:
draw.ellipse(surface, DBG_COLOR_HOR_ELLIPSE, rect)
# ellipse is in polygon rect, not need to return both rects
return draw.polygon(surface, DBG_COLOR_SHADOW_HOR_ELLIPSE_TRAPEZE,
[t_l, t_r, b_r, b_l], 1)
def test_move_rel(character):
assert character.position == Vector3()
assert character.collider.center == Vector3(
) + character.collider_relative_position
# move
character.move_rel(Vector3(0, 1, 0.1), free_displacement=True)
assert character.position == Vector3(0, 1, 0.1)
assert character.collider.center == Vector3(
0, 1, 0.1) + character.collider_relative_position
# move
character.move_rel(Vector3(-0.2, 0, 0), free_displacement=True)
assert character.position == Vector3(-0.2, 1, 0.1)
assert character.collider.center == Vector3(
-0.2, 1, 0.1) + character.collider_relative_position
def blend(self, *colors):
if len(colors) < 2:
return False
vectors = []
for color in colors:
vectors.append(Vector3(color[:3]))
distance = self._create_gradient_steps(*vectors)
self.surface = self._create_surface(distance)
for gstep in self.gradient_steps:
gstep.draw(self.surface, self.vertical)
return True
def run():
global SPHERE_RADIUS
global t
pygame.font.init()
clock = pygame.time.Clock()
font = pygame.font.Font(None, 30)
screen = pygame.display.set_mode((800, 800))
buffer = pygame.Surface((80, 40))
rect = buffer.get_rect()
position = Vector3(0, 0, -2)
step = .005
shader = Shader()
running = True
while running:
elapsed = clock.tick(60)
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False
elif event.type == pygame.KEYDOWN:
if event.key in (pygame.K_ESCAPE, pygame.K_q):
pygame.event.post(pygame.event.Event(pygame.QUIT))
elif event.key == pygame.K_LEFT:
SPHERE_RADIUS += step
print(SPHERE_RADIUS)
elif event.key == pygame.K_RIGHT:
SPHERE_RADIUS -= step
print(SPHERE_RADIUS)
#
pressed = pygame.key.get_pressed()
if pressed[pygame.K_UP]:
position.z += step
print(position)
elif pressed[pygame.K_DOWN]:
position.z -= step
print(position)
elif pressed[pygame.K_a]:
shader.x += 1
print(shader.x)
elif pressed[pygame.K_z]:
shader.x -= 1
print(shader.x)
#
buffer.fill((0, 0, 0))
draw(rect, buffer, position, shader)
pygame.transform.scale(buffer, screen.get_rect().size, screen)
img = font.render(f'{t:.04f}', True, (200, 200, 200))
screen.blit(img, (0, 0))
pygame.display.flip()
#
t = (t + elapsed / 1000 * 1) % tau
def test_change_collider(character):
char_original_pos = Vector3(character.position)
char_original_collider_rel_pos = Vector3(
character.collider_relative_position)
coll_original_size = Vector3(character.collider.size3)
coll_original_center = Vector3(character.collider.center)
# set default collider
character.set_default_collider()
assert character.collider.size3 == coll_original_size
assert character.collider.center == coll_original_center
assert character.position == char_original_pos
assert character.collider_relative_position == char_original_collider_rel_pos
# change and reset collider
direction = Vector3(0, 1, 0)
character.set_diving_collider(direction)
character.set_default_collider()
assert character.collider.size3 == coll_original_size
assert character.collider.center == coll_original_center
assert character.position == char_original_pos
assert character.collider_relative_position == char_original_collider_rel_pos
# move, change collider, move again and reset collider
direction = Vector3(0, 1, 0)
character.move(Vector3(1, 0, 0), 1000, free_displacement=True)
character.set_diving_collider(direction)
character.move(Vector3(0, 1, 0), 500, free_displacement=True)
character.set_default_collider()
assert character.collider.size3 == coll_original_size
assert character.collider.center == coll_original_center + character.max_velocity * Vector3(
1, 0.5, 0)
assert character.position == char_original_pos + character.max_velocity * Vector3(
1, 0.5, 0)
assert character.collider_relative_position == char_original_collider_rel_pos
def draw(rect, surface, position, shader):
for y in range(rect.height):
for x in range(rect.width):
pos = position
target = Vector3(x / rect.width - .5, (y / rect.height - .5) *
(rect.height / rect.width) * 1.5, -1.5)
ray = target - pos
ray.normalize()
pixel = PIXELS[0]
max_ = 9_999
for _ in range(15_000):
if (fabs(pos.x) > max_ or fabs(pos.y) > max_
or fabs(pos.z) > max_):
break
dist = surface_distance(pos)
if dist < 1e-1:
pixel = shader.shade(pos)
break
pos = pos + ray * dist
surface.set_at((x, y), pixel)
