def circle_aabb(A, B, collision_class=Collision):
cx, cx_, cy, cy_ = A.rect_coords
ax, ax_, ay, ay_ = B.rect_coords
dx = min(cx_, ax_) - max(cx, ax)
dy = min(cy_, ay_) - max(cy, ay)
if dy < 0 or dx < 0:
return None
x, y = pos = A.pos
if dx < dy:
# Circle is right at the bottom/top of AABB
if ay <= y <= ay_:
left = x < ax
pos = Vec2(ax if left else ax_, y)
normal = Vec2(1 if left else -1, 0)
delta = dx / 2
return collision_class(A, B, pos=pos, normal=normal, delta=delta)
else:
# Circle is right at the bottom/top of AABB
if ax <= x <= ax_:
bottom = y < ay
pos = Vec2(x, ay if bottom else ay_)
normal = Vec2(0, 1 if bottom else -1)
delta = dy / 2
return collision_class(A, B, pos=pos, normal=normal, delta=delta)
# If we reached this point, the circle encountered the AABB at a vertex.
# We must find the vertex that is closest to the center and define the
# normal vector using it.
vertex = min(B.vertices, key=lambda v: abs(v - pos))
normal = (vertex - pos).normalize()
delta = A.radius - (pos - vertex).norm()
return collision_class(A, B, pos=vertex, normal=normal, delta=delta)
def _vertices(self, N, pos):
length = self.length
alpha = pi / N
theta = 2 * alpha
b = length / (2 * sin(alpha))
P0 = Vec2(b, 0)
pos = Vec2(*pos)
return [(P0.rotate(n * theta)) + pos for n in range(N)]
def gravity(self, value):
owns_prop = flags.owns_gravity
old = self._gravity
try:
gravity = self._gravity = Vec2(*value)
except TypeError:
gravity = self._gravity = Vec2(0, -value)
for obj in self._objects:
if not obj.flags & owns_prop:
obj._gravity = gravity
gravity_changed_signal.trigger(self, old, self._gravity)
def __init__(self, shape=(800, 600), pos=(0, 0), zoom=1, background=None):
self.width, self.height = shape
self.pos = Vec2(*pos)
self.zoom = zoom
self.background = background
self.camera = Camera(self)
self.visible = False
def __init__(self, obj, k, pos=(0, 0), register=False):
self._k = k
kxy = 0
x0, y0 = self._pos = Vec2(*pos)
try: # Caso isotrópico
kx = ky = k = self._k = float(k)
except TypeError: # Caso anisotrópico
k = self._k = tuple(map(float, k))
if len(k) == 2:
kx, ky = k
else:
kx, ky, kxy = k
# Define forças e potenciais
def F(R):
Dx = x0 - R.x
Dy = y0 - R.y
return Vec2(kx * Dx + kxy * Dy, ky * Dy + kxy * Dx)
def U(R):
Dx = x0 - R.x
Dy = y0 - R.y
return (kx * Dx**2 + ky * Dy**2 + 2 * kxy * Dx * Dy) / 2.0
super(SpringTensor, self).__init__(obj, F, U, register=register)
def __init__(self,
vertices,
pos=None,
vel=(0, 0),
theta=0.0,
omega=0.0,
mass=None,
density=None,
inertia=None,
**kwargs):
if isinstance(vertices, int):
raise ValueError('must pass a list of vertices. '
'Use RegularPoly to define a polygon by the '
'number of vertices')
vertices = [Vec2(*pt) for pt in vertices]
pos_cm = center_of_mass(vertices)
vertices = [v - pos_cm for v in vertices]
self._vertices = vertices
# Cache vertices
self._cache_theta = None
self._cache_rvertices_last = None
self._cache_rbbox_last = None
super(Poly, self).__init__(pos_cm,
vel,
theta,
omega,
mass=mass,
density=density,
inertia=inertia,
cbb_radius=max(v.norm() for v in vertices),
**kwargs)
self.num_sides = len(vertices)
self._normals_idxs = self.get_li_indexes()
self.num_normals = len(self._normals_idxs or self.vertices)
# Slightly faster when all normals are linear dependent: if
# self._normals_idx = None, all normals are recomputed at each frame.
if self.num_normals == self.num_sides:
self._normals_idxs = None
# Move to specified position, if pos is given.
if pos is not None:
self._pos = Vec2(*pos)
def runner(self, dt, target, **kwds):
time = 0
interval = self.interval
position = self.trajectory
pos_shift = Vec2(0, 0) if not self.relative else target.pos
while time < interval:
time += dt
target.pos = pos_shift + position(time)
def momentumP(self):
"""
Linear momentum.
"""
try:
return self._vel / self._invmass
except ZeroDivisionError:
return Vec2(float('inf'), float('inf'))
def fast_func(t):
F = null2D
for k, func in nmuls:
Fi = asvector(func(t))
try:
F += Fi * k
except TypeError:
x, y = Fi
F += Vec2(k * x, k * y)
return F
def get_normal(self, i):
"""
Normal unity vector to the ith side.
Each segment goes from point i to i + 1.
"""
points = self.vertices
x, y = points[(i + 1) % self.num_sides] - points[i]
return Vec2(y, -x).normalize()
def orientation(self, theta=0.0):
"""
Return an unitary vector in the direction the object is oriented.
If the rotation is zero, the orientation vector is Vec2(1, 0). Rotation
is applied accordingly.
"""
theta += self._theta
return Vec2(self._cos(theta), self._sin(theta))
def fast_func(t):
F = null2D
for scalar_func, func in fmuls:
Fi = func(t)
k = scalar_func(t)
try:
F += Fi * k
except TypeError:
x, y = Fi
F += Vec2(k * x, k * y)
return F
def collision_aabb(A, B):
# Detects collision using bounding box shadows.
x0, x1 = max(A.xmin, B.xmin), min(A.xmax, B.xmax)
y0, y1 = max(A.ymin, B.ymin), min(A.ymax, B.ymax)
dx = x1 - x0
dy = y1 - y0
if x1 < x0 or y1 < y0:
return None
# Chose collision center as the center point in the intersection
pos = Vec2((x1 + x0) / 2, (y1 + y0) / 2)
# Normal is the direction with smallest penetration
if dy < dx:
delta = dy
normal = Vec2(0, (1 if A.pos.y < B.pos.y else -1))
else:
delta = dx
normal = Vec2((1 if A.pos.x < B.pos.x else -1), 0)
return Collision(A, B, pos=pos, normal=normal, delta=delta)
def get_normals(self):
"""
List of linearly independent normals.
"""
if self._normals_idxs is None:
N = self.num_sides
points = self.vertices
segmentos = (points[(i + 1) % N] - points[i] for i in range(N))
return [Vec2(y, -x).normalize() for (x, y) in segmentos]
else:
return [self.get_normal(i) for i in self._normals_idxs]
def momentumL(self, *args):
"""
Angular momentum.
Angular momentum depends on a reference point. By default, we use the
object's center of mass. One can pass any coordinate to specify the
reference.
Example:
Consider the object
>>> b1 = Body(pos=(0, 1), vel=(1, 0), mass=2)
Its center of mass angualar momentum is zero since it has no angular
velocity
>>> b1.momentumL()
0.0
However, linear movement creates an angular moment around origin or
other reference points
>>> b1.momentumL(0, 0)
-2.0
>>> b1.momentumL(0, 2)
2.0
"""
if not args:
momentumL = None
else:
if len(args) == 1:
vec = args[0]
else:
vec = Vec2(*args)
delta_pos = self.pos - vec
momentumL = delta_pos.cross(self.momentumP())
if self._invinertia:
return momentumL + self.omega * self.inertia
else:
return momentumL
def __init__(self, obj, G, M=None, epsilon=0, pos=(0, 0), register=False):
if M is None:
M = obj.mass
self._M = M = float(M)
self._epsilon = epsilon = float(epsilon)
self._G = G = float(G)
self._pos = pos = Vec2(*pos)
def F(R):
R = pos - R
r = R.norm()
r3 = (r + epsilon)**2 * r
R *= G * obj.mass * M / r3
return R
def U(R):
R = (R - pos).norm()
return -self._G * obj.mass * M / (R + epsilon)
super(Gravity, self).__init__(obj, F, U, register=register)
def random(self, *args):
"""
Return random position in the visible screen.
Signature:
``pos.random(size)``: create objects within screen and inside a
margin with the given number of pixels.
``pos.random(margin_x, margin_y)``: specify margin in x and y
directions.
``pos.random(margin_left, margin_bottom, margin_right, margin_top)``:
specify each margin separately
"""
x0 = y0 = 0
x1, y1 = self._shape
if len(args) == 1:
margin = args[0]
x0 += margin
x1 -= margin
y0 += margin
y1 -= margin
elif len(args) == 2:
dx, dy = args
x0 += dx
x1 -= dx
y0 += dy
y1 -= dy
elif len(args) == 4:
x0 += args[0]
y0 += args[1]
x1 -= args[2]
y1 -= args[3]
elif len(args) != 0:
raise TypeError('must be called with 0, 1, 2, or 4 arguments')
return Vec2(random.uniform(x0, x1), random.uniform(y0,
y1)) + self._origin
def vy(self, value):
self._vel = Vec2(self._vel.x, value)
def runner(self, dt, target, **kwds):
n_steps = dt / self.duration
delta = self.step / n_steps
for _ in range(n_steps):
target.pos += Vec2.frompolar(delta, target.theta)
def __init__(self, pos, interval):
super(move_to, self).__init__(interval)
self.pos = Vec2(*pos)
def test_move_functions_signature(self, obj):
for args in [[Vec2(1, 2)], [(1, 2)], (1, 2)]:
obj.move(*args)
obj.imove(*args)
obj.boost(*args)
obj.move_to(*args)
def move_tip(self, pos):
'''Move a ponta para a nova posição pos'''
self._pos = self._current[-1] = Vec2(*pos)
def vx(self, value):
self._vel = Vec2(value, self._vel.y)
def _origin(self):
return Vec2(0, 0)
def F(R):
Dx = x0 - R.x
Dy = y0 - R.y
return Vec2(kx * Dx + kxy * Dy, ky * Dy + kxy * Dx)
def vel(self):
return Vec2(1, 0)
def gravity(self, value):
try:
self._gravity = Vec2(*value)
except TypeError:
self._gravity = Vec2(0, -value)
self.owns_gravity = True
def __init__(self, x, y=None):
if y is None:
self.pos = Vec2(*x)
else:
self.pos = Vec2(x, y)
def F(rA, rB):
dx, dy = rB - rA
return Vec2(kx * dx + kxy * dy, +ky * dy + kxy * dx)
def from_pos(self, x, y):
w, h = self._shape
x0, y0 = self._origin
return Vec2(x0 + a * w + x, y0 + b * h + y)