def cylinderSDF(p, h, r):
inOutRadius = glm.length(p.xy) - r
inOutHeight = glm.abs(p.z) - h / 2.0
insideDistance = glm.min(glm.max(inOutRadius, inOutHeight), 0.0)
outsideDistance = glm.length(
glm.max(glm.vec2(inOutRadius, inOutHeight), 0.0))
return insideDistance + outsideDistance
def scatter(self, r_in, rec, attenuation, scattered):
outward_normal = glm.vec3
reflected = glm.vec3(reflect(r_in.direction, rec.normal))
attenuation = glm.vec3(1.0, 1.0, 1.0)
refracted = glm.vec3
if (glm.dot(r_in.direction, rec.normal) > 0):
outward_normal = -rec.normal
ni_over_nt = self.ref_idx
cosine = self.ref_idx * glm.dot(
r_in.direction, rec.normal) / glm.length(r_in.direction)
else:
outward_normal = rec.normal
ni_over_nt = 1.0 / self.ref_idx
cosine = -glm.dot(r_in.direction, rec.normal) / glm.length(
r_in.direction)
x, refracted = refract(r_in.direction, outward_normal, ni_over_nt,
refracted)
if (x == True):
reflect_prob = schlick(cosine, self.ref_idx)
else:
scattered = Ray(rec.p, reflected)
reflect_prob = 1.0
if (ran() < reflect_prob):
scattered = Ray(rec.p, reflected)
else:
scattered = Ray(rec.p, refracted)
return (True, scattered, attenuation)
def mandelbulbSDF(pos, iterations, power):
julia = False
juliaC = glm.vec3(0, 0, 0) #(-2, -2, -2) to (2, 2, 2)
orbitTrap = glm.vec4(10000)
colorIterations = 9 #0 to 100
bailout = 5 #0 to 30
alternateVersion = False
rotVector = glm.vec3(1, 1, 1) #(0, 0, 0) to (1, 1, 1)
rotAngle = 0 #0 to 180(?)
rot = rotationMatrix3(glm.normalize(rotVector), rotAngle)
z = pos
dr = 1
i = 0
r = glm.length(z)
while r < bailout and i < iterations:
if alternateVersion:
z, dr = powN2(z, r, dr, power)
else:
z, dr = powN1(z, r, dr, power)
z += juliaC if julia else pos
r = glm.length(z)
z *= rot
if i < colorIterations:
orbitTrap = min(orbitTrap, abs(glm.vec4(z.x, z.y, z.z, r * r)))
i += 1
return 0.5 * numpy.log(r) * r / dr
def processaColisao(self, corpoA, corpoB):
#impacto de corpos
if corpoA.near(corpoB, 2.0):
#calcula a forca
forcaA = corpoA.calcForce()
forcaB = corpoB.calcForce()
amplitudeForcaA = glm.length(forcaA)
amplitudeForcaB = glm.length(forcaB)
forcaResultante = glm.vec3()
if amplitudeForcaA > amplitudeForcaB:
forcaResultante = forcaA - forcaB
else:
forcaResultante = forcaB - forcaA
#remove o corpo de menor massa
if corpoA.massa >= corpoB.massa:
corpoA.massa += corpoB.massa
corpoA.impact(forcaResultante)
corpoB.enable = False
else:
corpoB.massa += corpoA.massa
corpoB.impact(forcaResultante)
corpoA.enable = False
def getTranslationRotationMatricesForCircles(mesh):
rms, tms = [], []
v_n0 = glm.vec3(0.0, 1.0, 0.0) # normal vector of first circle area!
for i in range(0, n): # 0,... n - 1 (= last position of the pose)
p_i = mesh.positions[
i] # each mesh contains the positions p_i of the pose
rm, tm = glm.mat4(), glm.mat4() # initialize unit matrices
tm = glm.translate(tm, glm.vec3(p_i[0], p_i[1],
p_i[2])) # each p_i: [x, y, z]
tms.append(tm)
# if first pose position:
if i == 0:
rms.append(rm) # append a unit matrix = no rotation
continue
# if last pose position:
if i == n - 1:
# position vector at: i-1
p_i_prev = glm.vec3(mesh.positions[i - 1][0],
mesh.positions[i - 1][1],
mesh.positions[i - 1][2])
# normalized gradient vector at p_i:
v_ni = glm.normalize(p_i - p_i_prev)
if v_ni == v_n0:
rms.append(rm) # append a unit matrix = no rotation
continue
angle = glm.acos(glm.length(v_n0 * v_ni)) # get the rotation angle
rot_axis = glm.cross(v_n0, v_ni) # get the rotation axis
rm = glm.rotate(rm, angle, rot_axis)
rms.append(rm) # append the rotation matrix
continue
# position vector at: i+1
p_i_next = glm.vec3(mesh.positions[i + 1][0], mesh.positions[i + 1][1],
mesh.positions[i + 1][2])
# position vector at: i-1
p_i_prev = glm.vec3(mesh.positions[i - 1][0], mesh.positions[i - 1][1],
mesh.positions[i - 1][2])
# normalized gradient vector at p_i:
v_ni = glm.normalize(p_i_next - p_i_prev)
if v_ni == v_n0:
rms.append(rm) # append a unit matrix = no rotation
continue
angle = glm.acos(glm.length(v_n0 * v_ni)) # get the rotation angle
rot_axis = glm.cross(v_n0, v_ni) # get the rotation axis
rm = glm.rotate(rm, angle, rot_axis)
rms.append(rm) # append the rotation matrix
return rms, tms
def seekPosition(self, worldOriginPosition,
worldDestinationPosition): # positions
vector = glm.vec2(worldDestinationPosition[0] - worldOriginPosition[0],
worldDestinationPosition[1] - worldOriginPosition[1])
if glm.length(vector) <= self.minSeekDistance:
return glm.vec2(0.0, 0.0)
direction = vector
if glm.length(vector) > 0.0:
direction = glm.normalize(vector)
acceleration = direction * self.maxLinearVelocity
return acceleration
def remove_child(self, child):
self.children.remove(child)
child_center = glm.vec3(self.M * glm.vec4(child.center, 1))
child_radius = child.radius * glm.length(self.M * glm.vec4(1, 1, 1, 0)) / glm.sqrt(3)
if len(self.children) > 1:
centers = [self.M * glm.vec4(child.center, 1) for child in self.children]
self.min_x = min([center[0] for center in centers])
self.max_x = max([center[0] for center in centers])
self.min_y = min([center[1] for center in centers])
self.max_y = max([center[1] for center in centers])
self.min_z = min([center[2] for center in centers])
self.max_z = max([center[2] for center in centers])
self.center = glm.vec3((self.min_x + self.max_x) / 2, (self.min_y + self.max_y) / 2, (self.min_z + self.max_z) / 2)
self.radius = max([glm.length(self.center - child.center) + child.radius for child in self.children])
def __init__(self, lookfrom, lookat, vup, vfov, aspect):
self.theta = vfov * M_PI / 180
self.half_height = math.tan(self.theta / 2)
self.half_width = aspect * self.half_height
self.origin = lookfrom
self.w = glm.vec3(
(lookfrom - lookat) / (glm.length(lookfrom - lookat)))
self.u = glm.vec3(
glm.cross(vup, self.w) / glm.length(glm.cross(vup, self.w)))
self.v = glm.cross(self.w, self.u)
self.lower_left_corner = glm.vec3(-self.half_width, -self.half_height,
-1.0)
self.lower_left_corner = self.origin - self.half_width * self.u - self.half_height * self.v - self.w
self.horizontal = 2 * self.half_width * self.u
self.vertical = 2 * self.half_height * self.v
def calc_distances_exact_superslow(self, max_range=None):
if max_range is None:
max_range = max(self.size())
mask = []
for z in range(-max_range, max_range+1):
#print("%s/%s" % (z, max_range*2+1))
for y in range(-max_range, max_range+1):
for x in range(-max_range, max_range+1):
mask.append((x,y,z, glm.length((x,y,z))))
mask = sorted(mask, key=lambda m: m[3])
mask = mask[1:]
max_dist = mask[-1][3]
for z in range(self.depth):
print("%s/%s" % (z, self.depth))
for y in range(self.height):
#print("%s/%s/%s" % (z, y, self.height))
for x in range(self.width):
if self.value(x, y, z):
mindist = 0
else:
mindist = max_dist
for m in mask:
if self.value(x+m[0], y+m[1], z+m[2]):
d = m[3]
#print(m[0], m[1], m[2], d)
if d > mindist:
break
mindist = d
if mindist < 1:
break
#print("------", mindist)
self.distances[self.pos_to_index(x, y, z)] = mindist
def _recalc_prediciton(self, world):
STEPS = 20
self.prediction = []
rect = self.rectangles[0].clone()
start_width = rect.width
start_height = rect.height
position = self.position * 1
velocity = glm.normalize(self.possible_velocity)
length = glm.length(self.possible_velocity)
for i in range(0, STEPS):
travel = length / STEPS
position, velocity = self._simulate_movement(
world, [rect], velocity, travel, position)
rect.position = position
prediction_rect = rect.clone()
prediction_rect.width = (start_width / float(STEPS)) * (STEPS -
float(i))
prediction_rect.height = (start_height / float(STEPS)) * (STEPS -
float(i))
self.prediction.append(prediction_rect)
def IntersectOld(self, ray):
position = self.position
radius = self.radius
ray_origin = ray.origin
ray_direction = ray.direction
sphere_center = position
t = glm.dot(sphere_center - ray_origin, ray_direction)
pos = ray.PointAtOffset(t) # ray_direction * t + ray_origin
intersection_distance = glm.length(sphere_center - pos)
if intersection_distance == radius:
intersection_result = IntersectionResult(
self, pos, t, glm.normalize(pos - sphere_center))
return intersection_result
elif intersection_distance < radius:
tHc = math.sqrt(radius * radius -
intersection_distance * intersection_distance)
ray_collision_offset = t - tHc
intersection1 = ray_origin + (ray_direction * ray_collision_offset)
intersection_result = IntersectionResult(
self, intersection1, ray_collision_offset,
glm.normalize(intersection1 - sphere_center))
return intersection_result
# ray_collision_offset = t + tHc
# intersection2 = ray_origin + (ray_direction * ray_collision_offset)
# intersection_result = IntersectionResult(intersection2, ray_collision_offset, glm.normalize(intersection2 - sphere_center))
return None
def move(self):
linearVelocity = glm.vec2(0.0, 0.0)
if self.followPath == True:
mapDestinationPosition = self.pathFollower.getWaypoint()
if mapDestinationPosition == None:
return glm.vec2(0.0, 0.0)
worldDestinationPosition = self.bot.map.getWorldPosition(
mapDestinationPosition)
vector = glm.vec2(
worldDestinationPosition[0] - self.bot.transform.position[0],
worldDestinationPosition[1] - self.bot.transform.position[1])
if glm.length(vector) <= self.minSeekDistance:
self.pathFollower.increaseWaypoint()
mapDestinationPosition = self.pathFollower.getWaypoint()
if mapDestinationPosition == None:
return glm.vec2(0.0, 0.0)
worldDestinationPosition = self.bot.map.getWorldPosition(
mapDestinationPosition)
linearVelocity = self.seekPosition(self.bot.transform.position,
worldDestinationPosition)
else:
if self.worldDestinationDirection == None:
return glm.vec2(0.0, 0.0)
linearVelocity = self.seekDirection(self.worldDestinationDirection)
return linearVelocity
def update(self, dt):
self.vel += self.force
if not self.sleeping:
if glm.length(self.vel) < .01:
self.sleeping = True
self.force *= 0
else:
self.last_y = self.pos.y
self.pos += self.vel * dt
self.force *= 0
if self.platform:
if self.vel.y > 0:
self.platform = None
elif self.platform is True:
self.pos.y = 0
self.vel.y = 0
else:
self.pos.y = self.platform.get_top(self.pos.xz)
self.vel.y = 0
self.last_y = self.pos.y
elif self.pos.y < 0:
self.pos.y = 0
self.set_platform(True)
def rotation(self, orig, dest):
identityQuat = glm.quat(1.0, 0.0, 0.0, 0.0)
epsilon = 0.00001
cosTheta = glm.dot(orig, dest)
if cosTheta >= 1.0 - epsilon:
#// orig and dest point in the same direction
return identityQuat
if cosTheta < -1.0 + epsilon:
'''
// special case when vectors in opposite directions :
// there is no "ideal" rotation axis
// So guess one; any will do as long as it's perpendicular to start
// This implementation favors a rotation around the Up axis (Y),
// since it's often what you want to do.
'''
rotationAxis = glm.cross(glm.vec3(0.0, 0.0, 1.0), orig)
if glm.length(
rotationAxis
) < epsilon: # // bad luck, they were parallel, try again!
rotationAxis = glm.cross(glm.vec3(1.0, 0.0, 0.0), orig)
rotationAxis = glm.normalize(rotationAxis)
return glm.angleAxis(glm.pi(), rotationAxis)
#// Implementation from Stan Melax's Game Programming Gems 1 article
rotationAxis = glm.cross(orig, dest)
s = math.sqrt((1.0 + cosTheta) * 2.0)
invs = 1.0 / s
return glm.quat(s * 0.5, rotationAxis.x * invs, rotationAxis.y * invs,
rotationAxis.z * invs)
def process(self):
for e_id, (ghost_col, report, velocity, animation, light,
ghost) in self.world.get_components(com.CollisionComponent,
com.CollisionReport,
com.Velocity,
com.LightAnimation,
com.Light, com.Ghost):
if self.world.player_object in report.failed:
self.world.damage_player()
report.failed.clear()
if ghost_col.is_colliding_y or ghost_col.is_colliding_x or glm.length(
velocity.value) < 1:
velocity.value = glm.normalize(
glm.vec3(rand.uniform(-1.0, 1.0), rand.uniform(-1.0, 1.0),
0.0)) * GhostSystem.SPEED
if light.enabled:
if animation.animation_delta > GhostSystem.ANIMATION_DELTA_LIMIT:
light.enabled = False
animation.enabled = False
self.free_light_count += 1
elif self.free_light_count >= 1:
if rand.randrange(0, 100) <= GhostSystem.LIGHT_CHANGE:
self.free_light_count -= 1
light.enabled = True
animation.animation_delta = 0.0
animation.delta_factor = rand.uniform(0.8, 1.4)
animation.enabled = True
def mandelboxSDF(pos, scale):
orbitTrap = glm.vec4(10000)
iterations = 17 #0 to 300
colorIterations = 3 #0 to 300
minRad2 = 0.25 #0.0 to 2.0
scale = glm.vec4(scale, scale, scale, abs(scale)) / minRad2
rotVector = glm.vec3(1, 1, 1) #(0, 0, 0) to (1, 1, 1)
rotAngle = 0 #0 to 180(?)
rot = rotationMatrix3(glm.normalize(rotVector), rotAngle)
absScalem1 = abs(scale - 1)
absScaleRaisedTo1mIters = pow(abs(scale), float(1 - iterations))
p = pos
w = 1
p0 = p
w0 = w
for i in range(iterations):
p *= rot
p = glm.clamp(p, -1, 1) * 2 - p
r2 = glm.dot(p, p)
if i < colorIterations:
orbitTrap = glm.min(orbitTrap, abs(glm.vec4(p, r2)))
p *= glm.clamp(glm.max(minRad2 / r2, minRad2), 0, 1)
w *= glm.clamp(glm.max(minRad2 / r2, minRad2), 0, 1)
p = p * glm.vec3(scale[0], scale[1], scale[2]) + p0
w = w * scale[3] + w0
if r2 > 1000:
break
return (glm.length(p) - absScalem1[3]) / w - absScaleRaisedTo1mIters[3]
def scatter(self, r_in, rec, attenuation, scattered):
reflected = glm.vec3(
reflect(r_in.direction / glm.length(r_in.direction), rec.normal))
scattered = Ray(rec.p, reflected + self.fuzz * random_in_unit_sphere())
attenuation = self.albedo
return (glm.dot(scattered.direction, rec.normal) > 0, scattered,
attenuation)
def update(self, entity, dt):
entity.ai_next_fire -= dt
if entity.ai_next_fire > 0 or not entity.alive:
return
entity.ai_next_fire = uniform(self.min_delay, self.max_delay)
player = entity.app.state.player
if player and player.alive:
# print('randomly fire')
to_player = player.position - entity.position
if BUTTERFLY_MIN_SHOOT_DIST < glm.length(to_player):
entity.play_sound("squeak.wav")
bu = entity.scene.add(
Bullet(
entity.app,
entity.scene,
entity,
entity.position,
to_player,
entity.damage,
BULLET_IMAGE_PATH,
ENEMY_BULLET_FACTOR * BULLET_SPEED,
))
def distance(self, other:"Transformation") -> float:
td = glm.distance(self.translation, other.translation)
sd = glm.distance(self.scale, other.scale)
qn : glm.Quat = glm.inverse(self.quaternion) # type: ignore
qn = qn * other.quaternion
if qn.w<0: qn = -qn
qd = glm.length(qn - glm.quat())
return td+sd+qd
def power(self, scene):
scene_size = glm.vec3(
scene.m_aabb[3], scene.m_aabb[4], scene.m_aabb[5]) - glm.vec3(
scene.m_aabb[0], scene.m_aabb[1], scene.m_aabb[2])
scene_len = glm.length(scene_size)
factor = 1.0 - math.cos(self.m_radian)
return 2.0 * math.pi * factor * scene_len * scene_len * self.d_intensity.Intensity(
)
def __init__(self,
shader,
filename=None,
material=None,
vertices=None,
vertices2=None,
colors=None,
texCoords=None,
normals=None,
indices=None,
draw_mode=GL_TRIANGLES,
line_width=1,
**kwargs):
super().__init__(**kwargs)
# Acquire shader is promised
if isinstance(shader, str):
self.shader = get_shader(shader)
else:
self.shader = shader
self.vao = glGenVertexArrays(1)
self.draw_mode = draw_mode
self.line_width = line_width
self.material = material
self.vertices = np.array(vertices, np.float32).reshape(
(-1, 3)) if vertices is not None else None
self.vertices = np.array(vertices2, np.float32).reshape(
(-1, 2)) if vertices2 is not None else self.vertices
self.colors = np.array(colors, np.float32).reshape(
(-1, 3)) if colors is not None else None
self.texCoords = np.array(texCoords, np.float32).reshape(
(-1, 2)) if texCoords is not None else None
self.normals = np.array(normals, np.float32).reshape(
(-1, 3)) if normals is not None else None
self.indices = np.array(indices, np.int32).reshape(
(-1, 1)) if indices is not None else None
if filename is not None:
self.parse(filename)
elif vertices is not None:
self.setupVec3()
elif vertices2 is not None:
self.setupVec2()
min_x = np.min(self.vertices[:, 0])
max_x = np.max(self.vertices[:, 0])
min_y = np.min(self.vertices[:, 1])
max_y = np.max(self.vertices[:, 1])
min_z = np.min(self.vertices[:, 2]) if vertices is not None else 0
max_z = np.max(self.vertices[:, 2]) if vertices is not None else 0
self.center = glm.vec3((min_x + max_x) / 2, (min_y + max_y) / 2,
(min_z + max_z) / 2)
self.radius = glm.length(glm.vec3(max_x, max_y, max_z) - self.center)
self.uniforms = dict()
def setTarget(self, target, interpolate=False):
"""Use to set a point where the camera should look. Target is expected to be a glm.vec3,
interpolate is a bool. Set interpolate to true produces an animated camera movement"""
self._desiredTransform.lookAt(target, self.worldUp)
self._desiredTargetDistance = glm.length(
target - self._desiredTransform.position)
if not interpolate:
self._currentTransform.orientation = self._desiredTransform.orientation
self._currentTargetDistance = self._desiredTargetDistance
def refract(v, n, ni_over_nt, refracted):
uv = glm.vec3(v / glm.length(v))
dt = glm.dot(uv, n)
discriminant = 1.0 - ni_over_nt * ni_over_nt * (1 - dt * dt)
if (discriminant > 0):
refracted = ni_over_nt * (uv - n * dt) - n * math.sqrt(discriminant)
return (True, refracted)
else:
refracted = glm.vec3
return (False, refracted)
def from_mat4(self, m:glm.Mat4) -> None:
self.translation = glm.vec3([m[3][0], m[3][1], m[3][2]])
rotation = glm.mat3()
for i in range(3):
v = glm.vec3([m[i][0], m[i][1], m[i][2]])
l = glm.length(v)
self.scale[i] = l
rotation[i] = v / l # type: ignore
pass
self.quaternion = quaternion_of_rotation(rotation)
pass
def set_matrix(self, M):
self.M = M
centers = [self.M * glm.vec4(child.center, 1) for child in self.children]
self.min_x = min([center[0] for center in centers])
self.max_x = max([center[0] for center in centers])
self.min_y = min([center[1] for center in centers])
self.max_y = max([center[1] for center in centers])
self.min_z = min([center[2] for center in centers])
self.max_z = max([center[2] for center in centers])
self.center = glm.vec3((self.min_x + self.max_x) / 2, (self.min_y + self.max_y) / 2, (self.min_z + self.max_z) / 2)
self.radius = max([glm.length(self.center - child.center) + child.radius for child in self.children])
def rotate(self):
if self.autoRotate == True:
if glm.length(self.linearVelocity) > 0.0:
direction = glm.normalize(self.linearVelocity)
self.lookAt((direction.x, direction.y))
if self.worldDestinationRotation == None:
return 0.0
angularVelocity = self.align(self.bot.transform.rotation,
self.worldDestinationRotation)
return angularVelocity
def update(self, entity, dt):
if not entity.alive:
return
player = entity.app.state.player # Assume state is Game
dir = player.position - entity.position
dir.z = 0
if dir != vec3(0) and length(dir.xy) < self.radius:
# Too close, go away
entity.velocity = -vec3(normalize(dir.xy), 0) * self.speed
else:
entity.velocity = vec3(0)
def update(self, bot, input):
seenBotInfo = bot.sight.getSeenBotInfo(self.seenBotEntity)
if seenBotInfo.transform == None:
return
vector = glm.vec2(
bot.transform.position[0] - seenBotInfo.transform.position[0],
bot.transform.position[1] - seenBotInfo.transform.position[1])
direction = vector
if glm.length(vector) > 0.0:
direction = glm.normalize(vector)
bot.agent.goToDirection((direction.x, direction.y))
bot.agent.lookAt((direction.x, direction.y))
def add_child(self, child: Node):
child_center = glm.vec3(self.M * glm.vec4(child.center, 1))
child_radius = child.radius * glm.length(self.M * glm.vec4(1, 1, 1, 0)) / glm.sqrt(3)
if len(self.children) == 0:
self.center = child_center
self.radius = child_radius
self.min_x = self.max_x = self.center[0]
self.min_y = self.max_y = self.center[1]
self.min_z = self.max_z = self.center[2]
else:
self.min_x = min(self.min_x, child_center[0])
self.max_x = max(self.max_x, child_center[0])
self.min_y = min(self.min_y, child_center[1])
self.max_y = max(self.max_y, child_center[1])
self.min_z = min(self.min_z, child_center[2])
self.max_z = max(self.max_z, child_center[2])
new_center = glm.vec3((self.min_x + self.max_x) / 2, (self.min_y + self.max_y) / 2, (self.min_z + self.max_z) / 2)
self.radius += glm.length(self.center - new_center)
self.center = new_center
self.radius = max(self.radius, glm.length(child_center - self.center) + child_radius)
self.children.append(child)
def decompose_matrix(
mat: glm.mat4
) -> Tuple[Optional[glm.vec3], Optional[glm.quat], Optional[glm.vec3]]:
sx = glm.length(glm.vec3(mat[0]))
sy = glm.length(glm.vec3(mat[1]))
sz = glm.length(glm.vec3(mat[2]))
if glm.determinant(mat) < 0.0:
sx = -sx
translation = glm.vec3(mat[3])
scale = glm.vec3(sx, sy, sz)
inv_sx = 1.0 / sx
inv_sy = 1.0 / sy
inv_sz = 1.0 / sz
rot_mat = copy.copy(mat)
rot_mat[0][0] *= inv_sx
rot_mat[0][1] *= inv_sx
rot_mat[0][2] *= inv_sx
rot_mat[1][0] *= inv_sy
rot_mat[1][1] *= inv_sy
rot_mat[1][2] *= inv_sy
rot_mat[2][0] *= inv_sz
rot_mat[2][1] *= inv_sz
rot_mat[2][2] *= inv_sz
rot_mat[3] = glm.vec4(0.0, 0.0, 0.0, 1.0)
rotation = glm.normalize(glm.quat_cast(rot_mat))
if translation == glm.vec3():
translation = None
if rotation == glm.quat():
rotation = None
if scale == glm.vec3():
scale = None
return (translation, rotation, scale)
