def __init__(self, object_to_world, world_to_object, reverse_orientation, radius, z0, z1, phi_max):
"""Default constructor for Sphere."""
super(Sphere, self).__init__(object_to_world, world_to_object, reverse_orientation)
self.radius = float(radius)
self.z_min = clamp(min(z0, z1), -radius, radius)
self.z_max = clamp(max(z0, z1), -radius, radius)
self.theta_min = math.acos(clamp(self.z_min / radius, -1.0, 1.0))
self.theta_max = math.acos(clamp(self.z_max / radius, -1.0, 1.0))
self.phi_max = math.radians(clamp(phi_max, 0.0, 360.0))
def __init__(self, object_to_world, world_to_object, reverse_orientation,
radius, z0, z1, phi_max):
"""Default constructor for Sphere."""
super(Sphere, self).__init__(object_to_world, world_to_object,
reverse_orientation)
self.radius = float(radius)
self.z_min = clamp(min(z0, z1), -radius, radius)
self.z_max = clamp(max(z0, z1), -radius, radius)
self.theta_min = math.acos(clamp(self.z_min / radius, -1.0, 1.0))
self.theta_max = math.acos(clamp(self.z_max / radius, -1.0, 1.0))
self.phi_max = math.radians(clamp(phi_max, 0.0, 360.0))
def slerp(t, q1, q2):
"""Spherical Linear Interpolation between two quaternions."""
cos_theta = dot_quaternions(q1, q2)
if cos_theta > 0.9995:
return normalize((1.0 - t) * q1 + t * q2)
else:
theta = math.acos(clamp(cos_theta, -1.0, 1.0))
theta_p = theta * t
q_perp = normalize(q2 - q1 * cos_theta)
return q1 * math.cos(theta_p) + q_perp * math.sin(theta_p)
def slerp(t, q1, q2):
"""Spherical Linear Interpolation between two quaternions."""
cos_theta = dot_quaternions(q1, q2)
if cos_theta > 0.9995:
return normalize((1.0 - t)*q1 + t*q2)
else:
theta = math.acos(clamp(cos_theta, -1.0, 1.0))
theta_p = theta * t
q_perp = normalize(q2 - q1*cos_theta)
return q1*math.cos(theta_p) + q_perp*math.sin(theta_p)
def intersect(self, r):
"""Intersect the ray with the shape."""
# Transform _Ray_ to object space
ray = self.world_to_object(r)
# Compute quadratic sphere coefficients
A = ray.d.x * ray.d.x + ray.d.y * ray.d.y + ray.d.z * ray.d.z
B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y + ray.d.z * ray.o.z)
C = ray.o.x*ray.o.x + ray.o.y*ray.o.y + \
ray.o.z*ray.o.z - self.radius*self.radius
# Solve quadratic equation for _t_ values
found, t0, t1 = quadratic(A, B, C)
if not found:
return False, float('inf'), 0.0, None
# Compute intersection distance along ray
if (t0 > ray.maxt or t1 < ray.mint):
return False, float('inf'), 0.0, None
t_hit = t0
if (t0 < ray.mint):
t_hit = t1
if (t_hit > ray.maxt):
return False, float('inf'), 0.0, None
# Compute sphere hit position and $\phi$
phi_t = ray(t_hit)
if (phi_t.x == 0.0 and phi_t.y == 0.0):
phi_t.x = 1e-5 * self.radius
phi = math.atan2(phi_t.y, phi_t.x)
if (phi < 0.0):
phi += 2.0 * math.pi
# Test sphere intersection against clipping parameters
if ((self.z_min > -self.radius and phi_t.z < self.z_min) or \
(self.z_max < self.radius and phi_t.z > self.z_max) or \
phi > self.phi_max):
if (t_hit == t1):
return False, float('inf'), 0.0, None
if (t1 > ray.maxt):
return False, float('inf'), 0.0, None
t_hit = t1
# Compute sphere hit position and $\phi$
phi_t = ray(t_hit)
if (phi_t.x == 0.0 and phi_t.y == 0.0):
phi_t.x = 1e-5 * self.radius
phi = math.atan2(phi_t.y, phi_t.x)
if (phi < 0.0):
phi += 2.0 * math.pi
if ((self.z_min > -self.radius and phi_t.z < self.z_min) or \
(self.z_max < self.radius and phi_t.z > self.z_max) or \
phi > self.phi_max):
return False, float('inf'), 0.0, None
# Find parametric representation of sphere hit
u = phi / self.phi_max
theta = math.acos(clamp(phi_t.z / self.radius, -1.0, 1.0))
v = (theta - self.theta_min) / (self.theta_max - self.theta_min)
# Compute sphere $\dpdu$ and $\dpdv$
zradius = math.sqrt(phi_t.x * phi_t.x + phi_t.y * phi_t.y)
inv_z_radius = 1.0 / zradius
cos_phi = phi_t.x * inv_z_radius
sin_phi = phi_t.y * inv_z_radius
dpdu = Vector(-self.phi_max * phi_t.y, self.phi_max * phi_t.x, 0)
dpdv = (self.theta_max-self.theta_min) * \
Vector(phi_t.z * cos_phi,
phi_t.z * sin_phi,
-self.radius * math.sin(theta))
# Compute sphere $\dndu$ and $\dndv$
d2Pduu = -self.phi_max * self.phi_max * Vector(phi_t.x, phi_t.y, 0)
d2Pduv = (self.theta_max - self.theta_min) * phi_t.z * self.phi_max * \
Vector(-sin_phi, cos_phi, 0.0)
d2Pdvv = -(self.theta_max - self.theta_min) * \
(self.theta_max - self.theta_min) * \
Vector(phi_t.x, phi_t.y, phi_t.z)
# Compute coefficients for fundamental forms
E = dot(dpdu, dpdu)
F = dot(dpdu, dpdv)
G = dot(dpdv, dpdv)
N = normalize(cross(dpdu, dpdv))
e = dot(N, d2Pduu)
f = dot(N, d2Pduv)
g = dot(N, d2Pdvv)
# Compute $\dndu$ and $\dndv$ from fundamental form coefficients
invEGF2 = 1.0 / (E * G - F * F)
dndu = Normal.from_vector((f*F - e*G) * invEGF2 * dpdu + \
(e*F - f*E) * invEGF2 * dpdv)
dndv = Normal.from_vector((g*F - f*G) * invEGF2 * dpdu + \
(f*F - g*E) * invEGF2 * dpdv)
# Initialize _DifferentialGeometry_ from parametric information
o2w = self.object_to_world
dg = DifferentialGeometry.from_intersection(o2w(phi_t), o2w(dpdu),
o2w(dpdv), o2w(dndu),
o2w(dndv), u, v, self)
# Compute _rayEpsilon_ for quadric intersection
ray_epsilon = 5e-4 * t_hit
return True, t_hit, ray_epsilon, dg
def __init__(self, primitives, refine_immediately):
"""Default constructor for GridAccel."""
# initialize self.primitives with primitives for grid
if refine_immediately:
self.primitives = []
for primitive in primitives:
primitive.fully_refine(self.primitives)
else:
self.primitives = list(primitives)
# compute bounds and choose grid resolution
self.bounds = BBox()
for primitive in self.primitives:
self.bounds = union(self.bounds, primitive.world_bound())
delta = self.bounds.p_max - self.bounds.p_min
# find voxels_per_unit_dist for grid
max_axis = self.bounds.maximum_extent()
inv_max_width = 1.0 / delta[max_axis]
cube_root = 3.0 * pow(len(self.primitives), 1.0 / 3.0)
voxels_per_unit_dist = cube_root * inv_max_width
self.n_voxels = []
for axis in range(3):
self.n_voxels.append(
clamp(round_to_int(delta[axis] * voxels_per_unit_dist), 1, 64))
# compute voxel widths and allocate voxels
self.width = Vector()
self.inv_width = Vector()
for axis in range(3):
self.width[axis] = delta[axis] / self.n_voxels[axis]
if self.width[axis] == 0.0:
self.inv_width[axis] = 0.0
else:
self.inv_width[axis] = 1.0 / self.width[axis]
nv = self.n_voxels[0] * self.n_voxels[1] * self.n_voxels[2]
# array of voxels, initialized at None
self.voxels = [None] * nv
# add primitives to grid voxels
for primitive in self.primitives:
# find voxel extent of primitive
primitive_bound = primitive.world_bound()
v_min = []
v_max = []
for axis in range(3):
v_min.append(self._pos_to_voxel(primitive_bound.p_min, axis))
v_max.append(self._pos_to_voxel(primitive_bound.p_max, axis))
# add primitive to overlapping voxels
for z in range(v_min[2], v_max[2] + 1):
for y in range(v_min[1], v_max[1] + 1):
for x in range(v_min[0], v_max[0] + 1):
index = self._offset(x, y, z)
if self.voxels[index] is None:
self.voxels[index] = Voxel(primitive)
else:
self.voxels[index].add_primitive(primitive)
# create reader-writer mutex for grid
self.rw_lock = DummyRWLock()
def _pos_to_voxel(self, point, axis):
"""Convert a 1D position into a voxel index."""
v = int((point[axis] - self.bounds.p_min[axis]) * self.inv_width[axis])
return clamp(v, 0, self.n_voxels[axis] - 1)
def test_clamp(self):
low = -10.0
high = 10.0
self.assertEqual(clamp(3.4, low, high), 3.4)
self.assertEqual(clamp(-100.0, low, high), low)
self.assertEqual(clamp(100.0, low, high), high)
def __init__(self, primitives, refine_immediately):
"""Default constructor for GridAccel."""
# initialize self.primitives with primitives for grid
if refine_immediately:
self.primitives = []
for primitive in primitives:
primitive.fully_refine(self.primitives)
else:
self.primitives = list(primitives)
# compute bounds and choose grid resolution
self.bounds = BBox()
for primitive in self.primitives:
self.bounds = union(self.bounds, primitive.world_bound())
delta = self.bounds.p_max - self.bounds.p_min
# find voxels_per_unit_dist for grid
max_axis = self.bounds.maximum_extent()
inv_max_width = 1.0 / delta[max_axis]
cube_root = 3.0 * pow(len(self.primitives), 1.0/3.0)
voxels_per_unit_dist = cube_root * inv_max_width
self.n_voxels = []
for axis in range(3):
self.n_voxels.append(clamp(
round_to_int(delta[axis] * voxels_per_unit_dist), 1, 64))
# compute voxel widths and allocate voxels
self.width = Vector()
self.inv_width = Vector()
for axis in range(3):
self.width[axis] = delta[axis] / self.n_voxels[axis]
if self.width[axis] == 0.0:
self.inv_width[axis] = 0.0
else:
self.inv_width[axis] = 1.0 / self.width[axis]
nv = self.n_voxels[0] * self.n_voxels[1] * self.n_voxels[2]
# array of voxels, initialized at None
self.voxels = [None] * nv
# add primitives to grid voxels
for primitive in self.primitives:
# find voxel extent of primitive
primitive_bound = primitive.world_bound()
v_min = []
v_max = []
for axis in range(3):
v_min.append(self._pos_to_voxel(primitive_bound.p_min, axis))
v_max.append(self._pos_to_voxel(primitive_bound.p_max, axis))
# add primitive to overlapping voxels
for z in range(v_min[2], v_max[2]+1):
for y in range(v_min[1], v_max[1]+1):
for x in range(v_min[0], v_max[0]+1):
index = self._offset(x, y, z)
if self.voxels[index] is None:
self.voxels[index] = Voxel(primitive)
else:
self.voxels[index].add_primitive(primitive)
# create reader-writer mutex for grid
self.rw_lock = DummyRWLock()
def _pos_to_voxel(self, point, axis):
"""Convert a 1D position into a voxel index."""
v = int((point[axis] - self.bounds.p_min[axis]) *
self.inv_width[axis])
return clamp(v, 0, self.n_voxels[axis]-1)
def intersect(self, r):
"""Intersect the ray with the shape."""
# Transform _Ray_ to object space
ray = self.world_to_object(r)
# Compute quadratic sphere coefficients
A = ray.d.x * ray.d.x + ray.d.y * ray.d.y + ray.d.z * ray.d.z
B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y + ray.d.z * ray.o.z)
C = ray.o.x * ray.o.x + ray.o.y * ray.o.y + ray.o.z * ray.o.z - self.radius * self.radius
# Solve quadratic equation for _t_ values
found, t0, t1 = quadratic(A, B, C)
if not found:
return False, float("inf"), 0.0, None
# Compute intersection distance along ray
if t0 > ray.maxt or t1 < ray.mint:
return False, float("inf"), 0.0, None
t_hit = t0
if t0 < ray.mint:
t_hit = t1
if t_hit > ray.maxt:
return False, float("inf"), 0.0, None
# Compute sphere hit position and $\phi$
phi_t = ray(t_hit)
if phi_t.x == 0.0 and phi_t.y == 0.0:
phi_t.x = 1e-5 * self.radius
phi = math.atan2(phi_t.y, phi_t.x)
if phi < 0.0:
phi += 2.0 * math.pi
# Test sphere intersection against clipping parameters
if (
(self.z_min > -self.radius and phi_t.z < self.z_min)
or (self.z_max < self.radius and phi_t.z > self.z_max)
or phi > self.phi_max
):
if t_hit == t1:
return False, float("inf"), 0.0, None
if t1 > ray.maxt:
return False, float("inf"), 0.0, None
t_hit = t1
# Compute sphere hit position and $\phi$
phi_t = ray(t_hit)
if phi_t.x == 0.0 and phi_t.y == 0.0:
phi_t.x = 1e-5 * self.radius
phi = math.atan2(phi_t.y, phi_t.x)
if phi < 0.0:
phi += 2.0 * math.pi
if (
(self.z_min > -self.radius and phi_t.z < self.z_min)
or (self.z_max < self.radius and phi_t.z > self.z_max)
or phi > self.phi_max
):
return False, float("inf"), 0.0, None
# Find parametric representation of sphere hit
u = phi / self.phi_max
theta = math.acos(clamp(phi_t.z / self.radius, -1.0, 1.0))
v = (theta - self.theta_min) / (self.theta_max - self.theta_min)
# Compute sphere $\dpdu$ and $\dpdv$
zradius = math.sqrt(phi_t.x * phi_t.x + phi_t.y * phi_t.y)
inv_z_radius = 1.0 / zradius
cos_phi = phi_t.x * inv_z_radius
sin_phi = phi_t.y * inv_z_radius
dpdu = Vector(-self.phi_max * phi_t.y, self.phi_max * phi_t.x, 0)
dpdv = (self.theta_max - self.theta_min) * Vector(
phi_t.z * cos_phi, phi_t.z * sin_phi, -self.radius * math.sin(theta)
)
# Compute sphere $\dndu$ and $\dndv$
d2Pduu = -self.phi_max * self.phi_max * Vector(phi_t.x, phi_t.y, 0)
d2Pduv = (self.theta_max - self.theta_min) * phi_t.z * self.phi_max * Vector(-sin_phi, cos_phi, 0.0)
d2Pdvv = (
-(self.theta_max - self.theta_min) * (self.theta_max - self.theta_min) * Vector(phi_t.x, phi_t.y, phi_t.z)
)
# Compute coefficients for fundamental forms
E = dot(dpdu, dpdu)
F = dot(dpdu, dpdv)
G = dot(dpdv, dpdv)
N = normalize(cross(dpdu, dpdv))
e = dot(N, d2Pduu)
f = dot(N, d2Pduv)
g = dot(N, d2Pdvv)
# Compute $\dndu$ and $\dndv$ from fundamental form coefficients
invEGF2 = 1.0 / (E * G - F * F)
dndu = Normal.from_vector((f * F - e * G) * invEGF2 * dpdu + (e * F - f * E) * invEGF2 * dpdv)
dndv = Normal.from_vector((g * F - f * G) * invEGF2 * dpdu + (f * F - g * E) * invEGF2 * dpdv)
# Initialize _DifferentialGeometry_ from parametric information
o2w = self.object_to_world
dg = DifferentialGeometry.from_intersection(o2w(phi_t), o2w(dpdu), o2w(dpdv), o2w(dndu), o2w(dndv), u, v, self)
# Compute _rayEpsilon_ for quadric intersection
ray_epsilon = 5e-4 * t_hit
return True, t_hit, ray_epsilon, dg