def __init__(self, r, name='noname', v=Vector2d(0, 0), mass=1):
self.r = r
self.v = v
self.name = name
self.mass = mass
self.force = Vector2d(0, 0)
self.color = (1, 1, 1)
def make_univer(n_particles=int(10e6)):
max_v = 1
min_v = -1
particles = [Particle(r=Vector2d(random.uniform(-box_size // 2, box_size // 2),
random.uniform(-box_size // 2, box_size // 2)),
v=Vector2d(random.uniform(min_v, max_v),
random.uniform(min_v, max_v)))]
# global box_size
i = 1
while True:
# if i % (n_particles//100) == 0:
# print('box:', i // (n_particles//100) + 1)
tmp_par = Particle(r=Vector2d(random.uniform(-box_size // 2, box_size // 2),
random.uniform(-box_size // 2, box_size // 2)),
v=Vector2d(random.uniform(min_v, max_v),
random.uniform(min_v, max_v)))
flag = 1
# for particle1 in particles:
# tmp_e = particle1.r - tmp_par.r
# if abs(tmp_e) == 0:
# continue
# tmp_f = forces.base_force(particle1, tmp_par)
# if (tmp_f.x*tmp_e.x + tmp_f.y*tmp_e.y) < 0:
# flag = 0
if flag == 1:
particles.append(tmp_par)
i += 1
if i >= n_particles:
break
# print(i)
return particles
def _add_edges(self):
for x, y in itertools.product(range(self.columns), range(self.rows)):
node = Vector2d(x, y)
right_neighbor = Vector2d((x + 1) % self.columns, y)
top_neighbor = Vector2d(x, (y + 1) % self.rows)
self._edges[node, right_neighbor] = Edges.State.unknown
self._edges[right_neighbor, node] = Edges.State.unknown
self._edges[node, top_neighbor] = Edges.State.unknown
self._edges[top_neighbor, node] = Edges.State.unknown
def calculate_force(self, particle, node=None):
if node is None:
node = self.root
force = Vector2d(0, 0)
if len(node.particles) == 0:
return force
# if (node.type == 2) and (abs(node.particles[0].r - particle.r) != 0):
if (node.type == 2) and (node.particles[0] != particle):
tmp_f = forces.base_force(particle, node.particles[0])
# print(particle.name, node.name, node.depth, len(node.particles))
# if particle.name == constants.median:
# tmp_brute_f = Vector2d()
# for particle_brute in node.particles:
# tmp_brute_f += forces.base_force(particle, particle_brute)
#
# len_error = (abs(tmp_f) - abs(tmp_brute_f)) / (abs(tmp_brute_f) + constants.epsilon)
# print(len_error, '|', tmp_f, '|', tmp_brute_f)
force += tmp_f
cm = node.get_cm()
if (node.type == 1) and (mac.mac(particle, node)):
# print(particle.name, node.name)
# print(particle.name, node.name, node.depth, len(node.particles))
tmp_f = forces.base_force(
particle,
Particle(r=cm, v=node.get_mv(), mass=node.mass, name='aprox'))
a = 0.1
b = 0.8
tmp_color = ((b - a) * np.random.random() + a,
(b - a) * np.random.random() + a,
(b - a) * np.random.random() + a)
self.save_particles += len(node.particles) - 1
for particle_color in node.particles:
particle_color.color = tmp_color
if particle.name == constants.median:
tmp_brute_f = Vector2d()
for particle_brute in node.particles:
tmp_brute_f += forces.base_force(particle, particle_brute)
len_error = (abs(tmp_f) - abs(tmp_brute_f)) / (
abs(tmp_brute_f) + constants.epsilon)
print(len_error, '|', tmp_f, '|', abs(tmp_f), '|', tmp_brute_f,
'|', abs(tmp_brute_f))
force += tmp_f
if (node.type == 1) and not (mac.mac(particle, node)):
for child in node.children:
force += self.calculate_force(particle, child)
return force
def make_net(n_particles=int(10e6)):
particles = []
n_rows = int(math.sqrt(n_particles))
h = constants.box_size // n_rows
for i in range(n_particles):
particles.append(
Particle(r=Vector2d(i % n_rows * h, i // n_rows * h),
v=Vector2d()))
# print(particles[-1].r)
return particles, h
def _handle_walls(self, walls):
"""Remove edges where there are walls."""
for w in walls:
tile1 = w.position
tile2 = None
if w.orientation == Wall.Orientation.horizontal:
tile2 = w.position - Vector2d(0, 1)
if w.orientation == Wall.Orientation.vertical:
tile2 = w.position - Vector2d(1, 0)
tile1 = self.grid.normalize(tile1)
tile2 = self.grid.normalize(tile2)
self.edges[tile1, tile2] = Edges.State.absent
def __init__(self, x, y, width, hieght, image, isPlayer=False):
self.position = Vector2d(x, y)
self.sprite = image
self.velocity = Vector2d(0, 0)
self.isPlayer = isPlayer
self.width = width
self.height = hieght
self.radius = width / 2
self.mass = self.radius * ATOM_MASS_PER_PER_PIXEL
self.isVisible = True
self.font = pygame.font.Font('freesansbold.ttf', 10)
self.colliding = False
def apply_player_direction(self, delta):
direction = Vector2d(0, 0)
if self.moveDOWN:
direction += Vector2d(0, PLAYER_ACCELERATION)
if self.moveUP:
direction += Vector2d(0, -PLAYER_ACCELERATION)
if self.moveRIGHT:
direction += Vector2d(PLAYER_ACCELERATION, 0)
if self.moveLEFT:
direction += Vector2d(-PLAYER_ACCELERATION, 0)
self.playerAtom.velocity += direction
def make_hex_2(r, center):
particles = [Particle(r=center, v=Vector2d(), name=0)]
for i in range(r):
tmp_par = []
for angle in [j * math.pi / 3 for j in range(6)]:
tmp_par.append(
Particle(r=center + Vector2d(
(i + 1) * constants.a * math.sin(angle),
(i + 1) * constants.a * math.cos(angle)),
v=Vector2d(),
name=len(particles)))
for j, particle in enumerate(tmp_par[:-1]):
particles.append(particle)
# fig, ax1 = plt.subplots(figsize=(4, 4))
# x = [particle.r.x for particle in particles]
# y = [particle.r.y for particle in particles]
# ax1.scatter(x=x, y=y, marker='o', c='r', edgecolor='b')
# ax1.set_title('Scatter: $x$ versus $y$')
# ax1.set_xlabel('$x$')
# ax1.set_ylabel('$y$')
# plt.show()
e_tmp = particle.r - tmp_par[j + 1].r
e_tmp = e_tmp * (1 / abs(e_tmp))
for k in range(i):
particles.append(
Particle(r=particle.r - e_tmp * constants.a,
v=Vector2d(),
name=len(particles)))
# fig, ax1 = plt.subplots(figsize=(4, 4))
# x = [particle.r.x for particle in particles]
# y = [particle.r.y for particle in particles]
# ax1.scatter(x=x, y=y, marker='o', c='r', edgecolor='b')
# ax1.set_title('Scatter: $x$ versus $y$')
# ax1.set_xlabel('$x$')
# ax1.set_ylabel('$y$')
# plt.show()
particles.append(tmp_par[-1])
e_tmp = tmp_par[-1].r - tmp_par[0].r
e_tmp = e_tmp * (1 / abs(e_tmp))
for k in range(i):
particles.append(
Particle(r=particle.r - e_tmp * constants.a,
v=Vector2d(),
name=len(particles)))
return particles
def _setup_walls(self):
for w in self.puzzle.walls:
self.grid.add_widget(WallWidget(w))
# Double the walls on the board's borders
if w.position.x == 0 and w.orientation == Wall.Orientation.vertical:
w2 = Wall(Vector2d(w.position.x + self.columns, w.position.y),
w.orientation)
# noinspection PyTypeChecker
self.grid.add_widget(WallWidget(w2))
if w.position.y == 0 and w.orientation == Wall.Orientation.horizontal:
w2 = Wall(Vector2d(w.position.x, w.position.y + self.rows),
w.orientation)
# noinspection PyTypeChecker
self.grid.add_widget(WallWidget(w2))
def make_univer(n_particles=int(10e6)):
particles = []
# global box_size
max_v = 1
min_v = -1
for i in range(n_particles):
if i % (n_particles // 100) == 0:
print(i // (n_particles // 100) + 1)
particles.append(
Particle(r=Vector2d(random.randint(-box_size // 2, box_size // 2),
random.randint(-box_size // 2, box_size // 2)),
v=Vector2d(random.randint(min_v, max_v),
random.randint(min_v, max_v))))
return particles
def create_sphere2(radii, lengths, num_sumples=2000, mass=1):
attempts = 100
# particles = [Particle(r=Vector3d(), mass=10)]
particles = []
num = 100
for i in range(0, len(lengths) // num):
cur_num_particles = 0
while True:
u = np.random.uniform(0, 2 * np.pi)
tmp_z = np.random.uniform(0, 1)
mul = tmp_z**(1 / 3)
# mul = (mul * lengths[i*num + num-1]) + (lengths[i*num + num-1] - lengths[i*num])
mul = lengths[i * num] + mul * (lengths[i * num + num - 1] -
lengths[i * num])
r1 = radii[0] * mul
r2 = radii[1] * mul
tmp = [r1 * np.cos(u), r2 * np.sin(u)]
if criterion(tmp, particles):
[x, y] = [tmp[0], tmp[1]]
particles.append(Particle(r=Vector2d(x, y), mass=mass))
cur_num_particles += 1
# if cur_num_particles % 1 == 0:
# print(cur_num_particles)
if cur_num_particles == num // 10:
break
return particles
def _inspect_tile(self, node, state):
"""Inspect a single tile/node and try to reduce the number of possible orientations left by trying one after
another.
"""
tile = state.tiles[node]
if len(tile.possible_orientations) <= 0:
return len(tile.possible_orientations)
tile.possible_orientations = [o for o in tile.possible_orientations if self._valid_orientation(node, o, state)]
# noinspection PyTypeChecker
for i, d in enumerate(Direction):
collected_edges = []
for o in tile.possible_orientations:
connectors = tile_connectors[tile.link][o]
collected_edges.append(connectors[i])
# Reduce: check all edges are the same, either all True or all False
if collected_edges and collected_edges.count(collected_edges[0]) == len(collected_edges):
edge_state = collected_edges[0]
else:
continue
child = node + d.vector
child = Vector2d(child.x % self.columns, child.y % self.rows)
# edge_state is either True or False
if state.edges[node, child] is not Edges.State.unknown:
assert ((edge_state is True and state.edges[node, child] is Edges.State.present) or
(edge_state is False and state.edges[node, child] is Edges.State.absent))
state.edges[node, child] = Edges.State.present if edge_state is True else Edges.State.absent
def run(self):
"""Run the solver. This might take some time."""
all_tiles = deque(n for n in self.grid)
initial_state = Solver.State(self.tiles, self.edges)
self._handle_simple_tiles(initial_state)
work_stack = [Solver.WorkItem(initial_state, all_tiles)]
while work_stack:
item = work_stack.pop()
state = item.state
work = item.work
investigate = self._forward_inference(state, work)
if not investigate:
continue # Pop next state from stack
# Choose tile with least amount of possible orientations left
minimum = None
min_pos = Vector2d(0, 0)
for node in self.grid:
orientations = len(state.tiles[node].possible_orientations)
if orientations >= 2 and (minimum is None or orientations < minimum):
minimum = orientations
min_pos = node
assert minimum is not None
for o in state.tiles[min_pos].possible_orientations:
neighbors = deque(self.grid.neighbors(min_pos))
child_state = state.clone()
child_state.tiles[min_pos].possible_orientations = [o]
self._inspect_tile(min_pos, child_state) # apply this orientation to edges
work_stack.append(Solver.WorkItem(child_state, neighbors))
print("Found {} solution(s)".format(len(self.solutions)))
def collides_with(self, entity):
retVal = False
if self.isVisible and entity.isVisible:
myPosition = Vector2d( self.position.x - self.radius,
self.position.y - self.radius)
entityPosition = Vector2d( entity.position.x - entity.radius,
entity.position.y - entity.radius)
totalRadiuses = self.radius + entity.radius
distance = myPosition - entityPosition
if distance.length() < totalRadiuses:
retVal = True
self.colliding = True
return retVal
def calculate_force(self, particle, node=None):
if node is None:
node = self.root
force = Vector2d(0, 0)
if len(node.particles) == 0:
return force
if (node.type == 2) and (node.particles[0] != particle):
tmp_f = forces.base_force(particle, node.particles[0])
# print(particle.name, node.name, node.depth, len(node.particles))
force += tmp_f
cm = node.get_cm()
if (node.type == 1) and (mac.mac(particle, node)):
# print(particle.name, node.name)
# print(particle.name, node.name, node.depth, len(node.particles))
tmp_f = forces.base_force(particle, Particle(r=cm, v=node.get_mv(), mass=node.mass))
force += tmp_f
if (node.type == 1) and not(mac.mac(particle, node)):
for child in node.children:
force += self.calculate_force(particle, child)
return force
def criterion(tmp, particles):
tmp_particle = Particle(r=Vector2d(*tmp))
for particle in particles:
# print((tmp_particle.r - particle.r).dot(forces.base_force(tmp_particle, particle)))
# if (tmp_particle.r - particle.r).dot(forces.base_force(tmp_particle, particle)) > -0.3:
if abs(tmp_particle.r - particle.r) < 1 * constants.a:
return False
return True
def main():
print("correct vector:")
correct_vector = Vector2d(-6.9, 42)
correct_vector.print_vector()
print("length:", correct_vector.vector_length())
print()
print("multiplied vector:")
multiplied_vector1 = correct_vector.multiply_vector(5)
multiplied_vector1.print_vector()
print()
print("vector multiplied by wrong factor:")
multiplied_vector2 = correct_vector.multiply_vector('f')
multiplied_vector2.print_vector()
print()
print("vector multiplied by nothing:")
multiplied_vector2 = correct_vector.multiply_vector()
multiplied_vector2.print_vector()
print()
print("wrong argument vector:")
wrong_argument_vector = Vector2d(-6.9, 'f')
wrong_argument_vector.print_vector()
print(wrong_argument_vector.vector_length())
print
print("not enough arguments vector:")
not_enough_arguments_vector = Vector2d(65)
not_enough_arguments_vector.print_vector()
print(not_enough_arguments_vector.vector_length())
print()
print("no arguments vector:")
no_arguments_vector = Vector2d()
no_arguments_vector.print_vector()
print no_arguments_vector.vector_length()
print()
print("to much arguments vector:")
to_much_arguments_vector = Vector2d(2, 3, 4)
to_much_arguments_vector.print_vector()
print(to_much_arguments_vector.vector_length())
print()
def read(read_path):
particles = []
with open(read_path, 'r') as inputfile:
s_tmp = inputfile.read()
for el in s_tmp.split('\n')[2:]:
if el != '':
rx, ry, cr, cg, cb = el.split()
particles.append(Particle(r=Vector2d(float(rx), float(ry)), name=len(particles)))
return particles
def run(self):
"""Execute the builder
:return: The created puzzle
:rtype: Puzzle
"""
self._source = Vector2d(self.columns // 2, self.rows // 2)
grid = self._create_tree()
walls = self._create_walls()
rotated_tiles = self._rotate(grid)
return Puzzle(grid, walls, self._source, rotated_tiles, self.wrap)
def make_hex(k=10, l=10):
# k количество рядов до середины
# l количество в крайнем ряду
particles = []
for i in range(k):
for j in range(i + l):
particles.append(
Particle(r=Vector2d(constants.a * i * math.sqrt(3) / 2,
constants.a * j - constants.a * 0.5 * i),
v=Vector2d(),
name=len(particles)))
for i in range(k, 2 * k - 1):
for j in range(l + k - 2 - (i - k)):
particles.append(
Particle(r=Vector2d(
constants.a * i * math.sqrt(3) / 2,
constants.a * j + constants.a * 0.5 * (i - 2 * k + 2)),
v=Vector2d(),
name=len(particles)))
return particles
def _create_walls(self, percent=0.06, rsd=0.2):
"""Randomly place some walls
The actual number of walls is drawn from a normal distribution.
:param float percent: Mean percent of walls to be created
:param float rsd: Relative standard deviation
"""
walls = set() # collect all possible walls
for x, y in itertools.product(range(self.columns), range(self.rows)):
if (self.wrap
or y != 0) and not self._nodes[x, y].edges[Direction.down]:
walls.add(Wall(Vector2d(x, y), Wall.Orientation.horizontal))
if (self.wrap
or x != 0) and not self._nodes[x, y].edges[Direction.left]:
walls.add(Wall(Vector2d(x, y), Wall.Orientation.vertical))
mean = len(walls) * percent
count = clamp(int(random.gauss(mean, rsd * mean)), 0, len(walls))
walls = random.sample(walls, count)
return walls
def get_and_plot_density(particles, radii, rotation, center, num=100):
cm = Vector2d()
particles_ = copy.deepcopy(particles)
derotation = np.linalg.inv(rotation)
for particle in particles_:
particle.r.x -= center[0]
particle.r.y -= center[1]
tmp = np.dot(np.array([particle.r.x, particle.r.y]), derotation)
particle.r = Vector2d(tmp[0], tmp[1])
cm += particle.r
cm = cm * (1 / len(particles_))
for i in range(len(particles)):
particles_[i].r.x *= 1 / radii[0]
particles_[i].r.y *= 1 / radii[1]
lengths = sorted([abs(particle.r) for particle in particles_])
density = []
l = []
# particles = sorted(particles, key=lambda particle: abs(particle.r - cm))
for i in range(len(lengths) // num):
density.append(num * particles_[0].mass /
(np.pi *
(lengths[i * num + num - 1]**2 - lengths[i * num]**2)))
# l.append(lengths[i*num] + 0.5*(lengths[i*num + num-1] - lengths[i*num]))
l.append(lengths[i * num])
ig, ax1 = plt.subplots(figsize=(4, 4))
ax1.scatter(x=l, y=density, marker='o', c='r', edgecolor='b')
ax1.set_title('Scatter: $x$ versus $y$')
ax1.set_xlabel('$x$')
ax1.set_ylabel('$y$')
plt.show()
return density, lengths
def example(cls):
"""A simple example puzzle"""
grid = GridContainer(Grid(3, 3))
grid[0, 2] = Tile(LinkType.dead_end, Direction.down)
grid[1, 2] = Tile(LinkType.t_intersection, Direction.right)
grid[2, 2] = Tile(LinkType.corner, Direction.left)
grid[0, 1] = Tile(LinkType.dead_end, Direction.down)
grid[1, 1] = Tile(LinkType.t_intersection, Direction.down)
grid[1, 1].entity = EntityType.source
grid[2, 1] = Tile(LinkType.straight, Direction.right)
grid[0, 0] = Tile(LinkType.dead_end, Direction.down)
grid[1, 0] = Tile(LinkType.corner, Direction.up)
grid[2, 0] = Tile(LinkType.dead_end, Direction.right)
walls = {
Wall(Vector2d(0, 2), Wall.Orientation.horizontal),
Wall(Vector2d(2, 1), Wall.Orientation.vertical)
}
return Puzzle(grid,
walls,
source=Vector2d(1, 1),
expected_moves=7,
wrap=False)
def _valid_orientation(self, node, orientation, state):
"""Check if for a given node/tile, the given orientation is possible, i.e. compatible with the surrounding
tiles.
"""
connectors = tile_connectors[state.tiles[node].link][orientation]
for d in Direction:
child = node + d.vector
child = Vector2d(child.x % self.columns, child.y % self.rows)
if state.edges[node, child] is Edges.State.unknown:
continue
elif ((connectors[d.index] is True and state.edges[node, child] is Edges.State.absent) or
(connectors[d.index] is False and state.edges[node, child] is Edges.State.present)):
return False
return True
def get_vertex(self, x, y=None):
"""Get a vertex from the polygon, if extant.
:param x: x coordinate of the vertex, or optionally a list of coordinates.
:keyword y: y coordinate of the vertex.
XXX: this is currently very slow!
"""
if not isinstance(x, Vector2d):
x = Vector2d(x, y)
for v in self.vertices:
if v == x:
return v
return None
def _create_tree(self):
"""Create the underlying tree.
The algorithm starts with a source in the center and chooses an already visited tile at random to extend the
tree to a random unvisited tile.
"""
self._nodes = GridContainer(Grid(self.columns, self.rows))
nodes = self._nodes # alias
for x, y in itertools.product(range(self.columns), range(self.rows)):
nodes[x, y] = Builder.Node()
visited = GridContainer(Grid(self.columns, self.rows), False)
visited[self._source] = True
boundary = {self._source}
while True:
new_boundary = set()
moves = [] # [(parent, child, direction), ...] FIXME namedtuple
for parent in boundary:
for direction in Direction:
child = parent + direction.vector
if self.wrap:
child = Vector2d(child.x % self.columns,
child.y % self.rows)
if 0 <= child.x < self.columns and 0 <= child.y < self.rows and not visited[
child]:
moves.append((parent, child, direction))
new_boundary.add(parent)
if not moves:
break
weights = []
for p, _, d in moves:
nodes[p].edges[d] = True
link = nodes[p].to_tile().link
nodes[p].edges[d] = False
weights.append(self.difficulties[self.difficulty][link])
parent, child, direction = weighted_choice(moves, weights)
new_boundary.add(child)
visited[child] = True
nodes[parent].edges[direction] = True
nodes[child].edges[-direction] = True
boundary = new_boundary
# Transform nodes/edges into tiles with link type and orientation
tiles = GridContainer(Grid(self.columns, self.rows))
for x, y in itertools.product(range(self.columns), range(self.rows)):
tiles[x, y] = nodes[x, y].to_tile()
tiles[self._source].entity = EntityType.source
return tiles
def check_power(self):
"""Check which tile is connected to the power source"""
power = GridContainer(Grid(self.columns, self.rows), False)
work = {self.puzzle.source}
while work:
parent = work.pop()
power[parent] = True
for direction in Direction:
proto_child = parent + direction.vector
if not self.puzzle.wrap and not self.board.grid.valid(
proto_child):
continue
child = Vector2d(proto_child.x % self.columns,
proto_child.y % self.rows)
# noinspection PyTypeChecker
if (not power[child]
and self._connected(parent, child, direction)
and not self._blocking_wall(parent, proto_child)):
work.add(child)
for x, y in itertools.product(range(self.columns), range(self.rows)):
self.board[x, y].powered = power[x, y]
def main():
from vector2d import Vector2d
def f(t, x):
return Vector2d(-1.9 * x[0] - 1.7 * x[1], x[0])
t = 0
dt = 0.05
x = Vector2d(20, 10)
data1 = []
data2 = []
for i in range(300):
t, x = Integrator.rk4(t, dt, x, f)
# vel
data1.append((t, x[0]))
#pos
data2.append((t, x[1]))
from pylab import plot, show, legend
p1, = plot([i for i, j in data1], [j for i, j in data1], 'k--')
p2, = plot([i for i, j in data2], [j for i, j in data2], 'k-')
legend([p1, p2], ["Velocity", "Position"])
show()
def _handle_boundary(self):
"""Initialize edges, depending on the 'wrapping' option of the game."""
for x in range(self.columns):
self.edges[Vector2d(x, 0), Vector2d(x, self.rows - 1)] = Edges.State.absent
for y in range(self.rows):
self.edges[Vector2d(0, y), Vector2d(self.columns - 1, y)] = Edges.State.absent
