def __init__(self):
"""Default constructor for Intersection."""
self.dg = DifferentialGeometry()
self.primitive = None
self.world_to_object = Transform()
self.object_to_world = Transform()
self.shape_id = 0
self.primitive_id = 0
self.ray_epsilon = 0.0
class Intersection(object):
"""Class describing an intersection of a Primitive."""
def __init__(self):
"""Default constructor for Intersection."""
self.dg = DifferentialGeometry()
self.primitive = None
self.world_to_object = Transform()
self.object_to_world = Transform()
self.shape_id = 0
self.primitive_id = 0
self.ray_epsilon = 0.0
def get_bsdf(self, ray):
"""Compute the BSDF."""
if self.primitive is None:
logger.error("Intersect.get_bsdf() called with no primitive.")
return 0.0
self.dg.compute_differentials(ray)
bsdf = self.primitive.get_bsdf(self.dg, self.object_to_world)
return bsdf
def get_bssrdf(self, ray):
"""Compute the BSSRDF."""
if self.primitive is None:
logger.error("Intersect.get_bssrddf() called with no primitive.")
return 0.0
self.dg.compute_differentials(ray)
bssrdf = self.primitive.get_bssrdf(self.dg, self.object_to_world)
return bssrdf
def Le(self, w):
"""Return the light emitted by the object."""
if self.primitive is None:
logger.error("Intersect.Le() called with no primitive.")
return Spectrum(0.0)
area = self.primitive.get_area_light()
if area:
return area.L(self.dg.p, self.dg.nn, w)
else:
return Spectrum(0.0)
def __str__(self):
"""Return a string describing the intersection."""
return "Intersection (ids=%d/%d, prim='%s', dg='%s')" % \
(self.shape_id, self.primitive_id, self.primitive, self.dg)
class Intersection(object):
"""Class describing an intersection of a Primitive."""
def __init__(self):
"""Default constructor for Intersection."""
self.dg = DifferentialGeometry()
self.primitive = None
self.world_to_object = Transform()
self.object_to_world = Transform()
self.shape_id = 0
self.primitive_id = 0
self.ray_epsilon = 0.0
def get_bsdf(self, ray):
"""Compute the BSDF."""
if self.primitive is None:
logger.error("Intersect.get_bsdf() called with no primitive.")
return 0.0
self.dg.compute_differentials(ray)
bsdf = self.primitive.get_bsdf(self.dg, self.object_to_world)
return bsdf
def get_bssrdf(self, ray):
"""Compute the BSSRDF."""
if self.primitive is None:
logger.error("Intersect.get_bssrddf() called with no primitive.")
return 0.0
self.dg.compute_differentials(ray)
bssrdf = self.primitive.get_bssrdf(self.dg, self.object_to_world)
return bssrdf
def Le(self, w):
"""Return the light emitted by the object."""
if self.primitive is None:
logger.error("Intersect.Le() called with no primitive.")
return Spectrum(0.0)
area = self.primitive.get_area_light()
if area:
return area.L(self.dg.p, self.dg.nn, w)
else:
return Spectrum(0.0)
def __str__(self):
"""Return a string describing the intersection."""
return "Intersection (ids=%d/%d, prim='%s', dg='%s')" % \
(self.shape_id, self.primitive_id, self.primitive, self.dg)
def __init__(self):
"""Default constructor for Intersection."""
self.dg = DifferentialGeometry()
self.primitive = None
self.world_to_object = Transform()
self.object_to_world = Transform()
self.shape_id = 0
self.primitive_id = 0
self.ray_epsilon = 0.0
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 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
