def generate_ray(self, sample):
"""Generate a Ray from the camera."""
# Generate raster and camera samples
p_ras = Point(sample.image_x, sample.image_y, 0)
p_camera = self.raster_to_camera(p_ras)
ray = Ray(Point(0, 0, 0),
normalize(Vector.from_point(p_camera)),
0.0,
float('inf'))
# Modify ray for depth of field
if self.lens_radius > 0.0:
# Sample point on lens
lens_u, lens_v = concentric_sample_disk(sample.lens_u,
sample.lens_v)
lens_u *= self.lens_radius
lens_v *= self.lens_radius
# Compute point on plane of focus
ft = self.focal_distance / ray.d.z
p_focus = ray(ft)
# Update ray for effect of lens
ray.o = Point(lens_u, lens_v, 0.0)
ray.d = normalize(p_focus - ray.o)
ray.time = sample.time
ray = self.camera_to_world(ray)
return 1.0, ray
def generate_ray(self, sample):
"""Generate a Ray from the camera."""
# Generate raster and camera samples
p_ras = Point(sample.image_x, sample.image_y, 0)
p_camera = self.raster_to_camera(p_ras)
ray = Ray(Point(0, 0, 0), normalize(Vector.from_point(p_camera)), 0.0,
float('inf'))
# Modify ray for depth of field
if self.lens_radius > 0.0:
# Sample point on lens
lens_u, lens_v = concentric_sample_disk(sample.lens_u,
sample.lens_v)
lens_u *= self.lens_radius
lens_v *= self.lens_radius
# Compute point on plane of focus
ft = self.focal_distance / ray.d.z
p_focus = ray(ft)
# Update ray for effect of lens
ray.o = Point(lens_u, lens_v, 0.0)
ray.d = normalize(p_focus - ray.o)
ray.time = sample.time
ray = self.camera_to_world(ray)
return 1.0, ray
def test_intersect(self):
# test an intersection
ray = Ray(Point(0, 0, 10), Vector(0, 0, -1))
intersection = Intersection()
intersected = self.grid_accel.intersect(ray, intersection)
self.assertFalse(intersected)
ray.maxt = float('inf')
intersected = self.grid_accel.intersect_p(ray)
self.assertFalse(intersected)
# test an intersection
ray2 = Ray(Point(10, 0, 10), Vector(0, 0, -1))
intersection = Intersection()
intersected = self.grid_accel.intersect(ray2, intersection)
self.assertTrue(intersected)
self.assertEqual(intersection.primitive_id,
self.primitive_sphere1.primitive_id)
self.assertEqual(intersection.shape_id, self.sphere1.shape_id)
ray2.maxt = float('inf')
intersected = self.grid_accel.intersect_p(ray2)
self.assertTrue(intersected)
# test an intersection
ray3 = Ray(Point(-10, 0, 10), Vector(0, 0, -1))
intersection = Intersection()
intersected = self.grid_accel.intersect(ray3, intersection)
self.assertTrue(intersected)
self.assertEqual(intersection.primitive_id,
self.primitive_sphere2.primitive_id)
self.assertEqual(intersection.shape_id, self.sphere2.shape_id)
ray3.maxt = float('inf')
intersected = self.grid_accel.intersect_p(ray3)
self.assertTrue(intersected)
def pdf_wi(self, p, wi):
"""Intersect sample ray with area light geometry."""
dg_light = DifferentialGeometry()
ray = Ray(p, wi, 1e-3)
ray.depth = -1 # temp hack to ignore alpha mask
intersect, t_hit, ray_epsilon, dg_light = self.intersect(ray)
if not intersect:
return 0.0
# convert light sample weight to solid angle measure
pdf = distance_squared(p, ray(t_hit)) / \
(abs_dot(dg_light.nnm -wi) * self.area())
if pdf == float('inf'):
return 0.0
return pdf
def test_bounding_box_9(self):
bbox = BBox(Point(-1, -1, -1), Point(1, 1, 1))
ray1 = Ray(Point(10, 10, 10), Vector(-1, -1, -1))
intersect, hit0, hit1 = bbox.intersect_p(ray1)
self.assertTrue(intersect)
ray2 = Ray(Point(10, 10, 10), Vector(-1, 1, -1))
intersect, hit0, hit1 = bbox.intersect_p(ray2)
self.assertFalse(intersect)
ray3 = Ray(Point(0, 0, 10), Vector(0, 0, -1))
intersect, hit0, hit1 = bbox.intersect_p(ray3)
self.assertTrue(intersect)
self.assertEqual(hit0, 9.0)
self.assertEqual(hit1, 11.0)
def sample_p(self, p, u1, u2):
"""Sample at point p."""
# Compute coordinate system for sphere sampling
p_center = self.object_to_world(Point(0, 0, 0))
wc = normalize(p_center - p)
wc_x, wc_y = coordinate_system(wc)
# Sample uniformly on sphere if $\pt{}$ is inside it
if (distance_squared(p, p_center) - self.radius * self.radius) < 1e-4:
return self.sample(u1, u2)
# Sample sphere uniformly inside subtended cone
sin_theta_max2 = self.radius * self.radius / distance_squared(
p, p_center)
cos_theta_max = math.sqrt(max(0.0, 1.0 - sin_theta_max2))
raise Exception("next_line")
# r = Ray(p, uniform_sample_cone(u1, u2, cos_theta_max, wcX, wcY, wc), 1e-3)
r = Ray(p)
intersect, t_hit, ray_epsilon, dg_sphere = self.intersect(r)
if not intersect:
t_hit = dot(p_center - p, normalize(r.d))
ps = r(t_hit)
ns = Normal(normalize(ps - p_center))
if (self.reverse_orientation):
ns *= -1.0
return ps, ns
def test_ray(self):
r = Ray(Point(0, 0, 0), Vector(1, 2, 3))
# test copy constructor
r2 = Ray.from_ray(r)
self.assertTrue(isinstance(r2, Ray))
self.assertEqual(r2.d, r.d)
# test constructor from parent ray
r3 = Ray.from_ray_parent(r.o, r.d, r, r.mint)
self.assertTrue(isinstance(r3, Ray))
self.assertEqual(r3.depth, r.depth+1)
# test operator()
p = r(1.7)
self.assertEqual(p, Point(1.7, 3.4, 5.1))
def test_ray_differential(self):
r = Ray(Point(0, 0, 0), Vector(1, 2, 3))
rd = RayDifferential(Point(0, 0, 0), Vector(1, 2, 3))
# test copy constructor from Ray
rd.has_differentials = True
rd1 = RayDifferential.from_ray_differential(rd)
self.assertTrue(isinstance(rd1, RayDifferential))
self.assertEqual(rd1.o, rd.o)
self.assertEqual(rd1.d, rd.d)
self.assertEqual(rd1.rx_origin, rd.rx_origin)
self.assertEqual(rd1.ry_origin, rd.ry_origin)
self.assertEqual(rd1.rx_direction, rd.rx_direction)
self.assertEqual(rd1.ry_direction, rd.ry_direction)
self.assertEqual(rd1.has_differentials, rd.has_differentials)
# test copy constructor from Ray
rd2 = RayDifferential.from_ray(r)
self.assertTrue(isinstance(rd2, RayDifferential))
self.assertEqual(rd2.d, r.d)
self.assertEqual(rd2.has_differentials, False)
# test constructor from parent ray
rd3 = RayDifferential.from_ray_parent(r.o, r.d, r, r.mint)
self.assertTrue(isinstance(rd3, RayDifferential))
self.assertEqual(rd3.depth, r.depth + 1)
# test operator()
p = rd(1.7)
self.assertEqual(p, Point(1.7, 3.4, 5.1))
def test_ray(self):
r = Ray(Point(0, 0, 0), Vector(1, 2, 3))
# test copy constructor
r2 = Ray.from_ray(r)
self.assertTrue(isinstance(r2, Ray))
self.assertEqual(r2.d, r.d)
# test constructor from parent ray
r3 = Ray.from_ray_parent(r.o, r.d, r, r.mint)
self.assertTrue(isinstance(r3, Ray))
self.assertEqual(r3.depth, r.depth + 1)
# test operator()
p = r(1.7)
self.assertEqual(p, Point(1.7, 3.4, 5.1))
def test_transform_ray(self):
ray = Ray(origin=Point(1, 2, 3),
direction=Vector(10, 20, 30))
ray_transformed = translate(Point(10, 20, 30))(ray)
self.assertTrue(isinstance(ray_transformed, Ray))
self.assertEqual(ray_transformed.o, Point(11, 22, 33))
self.assertEqual(ray_transformed.d, Vector(10, 20, 30))
def test_intersect(self):
# test an intersection
ray = Ray(Point(20, 10, 10), Vector(-1, -1, -1))
intersect, t_hit, ray_epsilon, dg = self.sphere.intersect(ray)
self.assertTrue(intersect)
intersect = self.sphere.intersect_p(ray)
self.assertTrue(intersect)
# test an intersection
ray = Ray(Point(20, 10, 10), Vector(-1, 1, -1))
intersect, t_hit, ray_epsilon, dg = self.sphere.intersect(ray)
self.assertFalse(intersect)
intersect = self.sphere.intersect_p(ray)
self.assertFalse(intersect)
# test an intersection
ray = Ray(Point(10, 0, 0), Vector(3, 1, -2))
intersect, t_hit, ray_epsilon, dg = self.sphere.intersect(ray)
self.assertTrue(intersect)
intersect = self.sphere.intersect_p(ray)
self.assertTrue(intersect)
def test_intersect(self):
# test an intersection
ray = Ray(Point(0, 0, 10), Vector(0, 0, -1))
intersection = Intersection()
intersected = self.grid_accel.intersect(ray, intersection)
self.assertFalse(intersected)
ray.maxt = float('inf')
intersected = self.grid_accel.intersect_p(ray)
self.assertFalse(intersected)
# test an intersection
ray2 = Ray(Point(10, 0, 10), Vector(0, 0, -1))
intersection = Intersection()
intersected = self.grid_accel.intersect(ray2, intersection)
self.assertTrue(intersected)
self.assertEqual(intersection.primitive_id,
self.primitive_sphere1.primitive_id)
self.assertEqual(intersection.shape_id,
self.sphere1.shape_id)
ray2.maxt = float('inf')
intersected = self.grid_accel.intersect_p(ray2)
self.assertTrue(intersected)
# test an intersection
ray3 = Ray(Point(-10, 0, 10), Vector(0, 0, -1))
intersection = Intersection()
intersected = self.grid_accel.intersect(ray3, intersection)
self.assertTrue(intersected)
self.assertEqual(intersection.primitive_id,
self.primitive_sphere2.primitive_id)
self.assertEqual(intersection.shape_id,
self.sphere2.shape_id)
ray3.maxt = float('inf')
intersected = self.grid_accel.intersect_p(ray3)
self.assertTrue(intersected)
def time_sphere_intersection():
# create a transform
o2w = translate(Vector(10,0,0)) * scale(1.3, 1.8, 2.0)
w2o = o2w.inverse()
# create the sphere
sphere = Sphere(o2w, w2o, False, 1.0, -1.0, 1.0, 360)
# create a large amount of rays,
# choose so that half of them will intersect the ray
positions = [Point(random.randint(0,100),
random.randint(0,100),
random.randint(0,100)
) for i in range(size)]
ray = Ray(Point(0,0,0), Vector(1.0, 1.0, 1.0))
vectors = []
for i in xrange(size):
position = positions[i]
if i%2 == 0:
# make sure this ray hit the sphere
vector = sphere.object_to_world(Point(0, 0, 0)) - position
vector /= float(random.randint(1,10))
else:
# construct a random vector
vector = Vector((random.random()-0.5)*random.randint(1,5),
(random.random()-0.5)*random.randint(1,5),
(random.random()-0.5*random.randint(1,5)))
vectors.append(vector)
intersections = 0
t1 = time.time()
for i in xrange(nb_calls):
ray.o = positions[i%size]
ray.d = vectors[i%size]
if sphere.intersect_p(ray):
intersections += 1
t2 = time.time()
for i in xrange(nb_calls):
ray.o = positions[i%size]
ray.d = vectors[i%size]
sphere.intersect(ray)
t3 = time.time()
print "%d calls, %d intersections" % (nb_calls, intersections)
print "Sphere.intersect_p() %.2fms" % ((t2-t1)/float(nb_calls)*1000.0)
print "Sphere.intersect() %.2fms" % ((t3-t2)/float(nb_calls)*1000.0)
def __call__(self, elt):
"""Overload the operator().
Supported operations:
* Transform(Point)
* Transform(Vector)
* Transform(Normal)
* Transform(Ray)
* Transform(RayDifferential)
* Transform(BBox)
"""
if isinstance(elt, Point):
x = elt.x
y = elt.y
z = elt.z
xp = self.m.m[0][0] * x + self.m.m[0][1] * y + self.m.m[0][
2] * z + self.m.m[0][3]
yp = self.m.m[1][0] * x + self.m.m[1][1] * y + self.m.m[1][
2] * z + self.m.m[1][3]
zp = self.m.m[2][0] * x + self.m.m[2][1] * y + self.m.m[2][
2] * z + self.m.m[2][3]
wp = self.m.m[3][0] * x + self.m.m[3][1] * y + self.m.m[3][
2] * z + self.m.m[3][3]
if wp == 1.0:
return Point(xp, yp, zp)
else:
return Point(xp, yp, zp) / wp
elif isinstance(elt, Vector):
x = elt.x
y = elt.y
z = elt.z
xp = self.m.m[0][0] * x + self.m.m[0][1] * y + self.m.m[0][2] * z
yp = self.m.m[1][0] * x + self.m.m[1][1] * y + self.m.m[1][2] * z
zp = self.m.m[2][0] * x + self.m.m[2][1] * y + self.m.m[2][2] * z
return Vector(xp, yp, zp)
elif isinstance(elt, Normal):
x = elt.x
y = elt.y
z = elt.z
return Normal(
self.m_inv.m[0][0] * x + self.m_inv.m[1][0] * y +
self.m_inv.m[2][0] * z, self.m_inv.m[0][1] * x +
self.m_inv.m[1][1] * y + self.m_inv.m[2][1] * z,
self.m_inv.m[0][2] * x + self.m_inv.m[1][2] * y +
self.m_inv.m[2][2] * z)
elif isinstance(elt, RayDifferential):
ray = RayDifferential.from_ray_differential(elt)
ray.o = self(ray.o)
ray.d = self(ray.d)
ray.rx_origin = self(ray.rx_origin)
ray.ry_origin = self(ray.ry_origin)
ray.rx_direction = self(ray.rx_direction)
ray.ry_direction = self(ray.ry_direction)
return ray
elif isinstance(elt, Ray):
ray = Ray.from_ray(elt)
ray.o = self(ray.o)
ray.d = self(ray.d)
return ray
elif isinstance(elt, BBox):
ret = BBox(self(Point(elt.p_min.x, elt.p_min.y, elt.p_min.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_min.y,
elt.p_min.z)))
ret = union(ret, self(Point(elt.p_min.x, elt.p_max.y,
elt.p_min.z)))
ret = union(ret, self(Point(elt.p_min.x, elt.p_min.y,
elt.p_max.z)))
ret = union(ret, self(Point(elt.p_min.x, elt.p_max.y,
elt.p_max.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_max.y,
elt.p_min.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_min.y,
elt.p_max.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_max.y,
elt.p_max.z)))
return ret
def __call__(self, elt):
"""Overload the operator().
Supported operations:
* Transform(Point)
* Transform(Vector)
* Transform(Normal)
* Transform(Ray)
* Transform(RayDifferential)
* Transform(BBox)
"""
if isinstance(elt, Point):
x = elt.x
y = elt.y
z = elt.z
xp = self.m.m[0][0]*x + self.m.m[0][1]*y + self.m.m[0][2]*z + self.m.m[0][3]
yp = self.m.m[1][0]*x + self.m.m[1][1]*y + self.m.m[1][2]*z + self.m.m[1][3]
zp = self.m.m[2][0]*x + self.m.m[2][1]*y + self.m.m[2][2]*z + self.m.m[2][3]
wp = self.m.m[3][0]*x + self.m.m[3][1]*y + self.m.m[3][2]*z + self.m.m[3][3]
if wp == 1.0:
return Point(xp, yp, zp)
else:
return Point(xp, yp, zp)/wp
elif isinstance(elt, Vector):
x = elt.x
y = elt.y
z = elt.z
xp = self.m.m[0][0]*x + self.m.m[0][1]*y + self.m.m[0][2]*z
yp = self.m.m[1][0]*x + self.m.m[1][1]*y + self.m.m[1][2]*z
zp = self.m.m[2][0]*x + self.m.m[2][1]*y + self.m.m[2][2]*z
return Vector(xp, yp, zp)
elif isinstance(elt, Normal):
x = elt.x
y = elt.y
z = elt.z
return Normal(self.m_inv.m[0][0]*x + self.m_inv.m[1][0]*y + self.m_inv.m[2][0]*z,
self.m_inv.m[0][1]*x + self.m_inv.m[1][1]*y + self.m_inv.m[2][1]*z,
self.m_inv.m[0][2]*x + self.m_inv.m[1][2]*y + self.m_inv.m[2][2]*z)
elif isinstance(elt, RayDifferential):
ray = RayDifferential.from_ray_differential(elt)
ray.o = self(ray.o)
ray.d = self(ray.d)
ray.rx_origin = self(ray.rx_origin)
ray.ry_origin = self(ray.ry_origin)
ray.rx_direction = self(ray.rx_direction)
ray.ry_direction = self(ray.ry_direction)
return ray
elif isinstance(elt, Ray):
ray = Ray.from_ray(elt)
ray.o = self(ray.o)
ray.d = self(ray.d)
return ray
elif isinstance(elt, BBox):
ret = BBox(self(Point(elt.p_min.x, elt.p_min.y, elt.p_min.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_min.y, elt.p_min.z)))
ret = union(ret, self(Point(elt.p_min.x, elt.p_max.y, elt.p_min.z)))
ret = union(ret, self(Point(elt.p_min.x, elt.p_min.y, elt.p_max.z)))
ret = union(ret, self(Point(elt.p_min.x, elt.p_max.y, elt.p_max.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_max.y, elt.p_min.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_min.y, elt.p_max.z)))
ret = union(ret, self(Point(elt.p_max.x, elt.p_max.y, elt.p_max.z)))
return ret