def hit(self, ray: Ray, t_min: float, t_max: float,
rec: HitRecord) -> bool:
oc = ray.origin - self.cen
a = ray.direction.dot(ray.direction)
b = oc.dot(ray.direction)
c = oc.dot(oc) - self.rsquared
discriminant = b * b - a * c
if discriminant > 0:
d_sqrt = discriminant**0.5
temp = (-b - d_sqrt) / (a)
if temp < t_max and temp > t_min:
rec.t = temp
rec.p = ray.point_at_parameter(temp)
rec.normal = (rec.p - self.cen) / self.r
rec.material = self.material
return True
temp = (-b + d_sqrt) / (a)
if temp < t_max and temp > t_min:
rec.t = temp
rec.p = ray.point_at_parameter(temp)
rec.normal = (rec.p - self.cen) / self.r
rec.material = self.material
return True
return False
def hit(self, r: Ray, t_min: float, t_max: float):
oc = r.origin() - self.center
a = np.dot(r.direction(), r.direction())
b = np.dot(oc, r.direction())
c = np.dot(oc, oc) - self.radius * self.radius
discriminant = b * b - a * c
if discriminant > 0:
temp = (-b - sqrt(b * b - a * c)) / a
if (temp < t_max) and (temp > t_min):
t = temp
p = r.point_at_parameter(t)
normal = (p - self.center) / self.radius
rec = hit_record(t, p, normal, self.material)
return True, rec
temp = (-b + sqrt(b * b - a * c)) / a
if (temp < t_max) and (temp > t_min):
t = temp
p = r.point_at_parameter(t)
normal = (p - self.center) / self.radius
rec = hit_record(t, p, normal, self.material)
return True, rec
return False, None
def hit(self, ray: Ray, t_min: float, t_max: float, rec: hit_record):
oc = ray.origin() - self.center
a = Vector3.dot(ray.direction(), ray.direction())
b = Vector3.dot(oc, ray.direction())
c = Vector3.dot(oc, oc) - self.radius * self.radius
discriminant = b * b - a * c
if (discriminant > 0):
temp = (-b - math.sqrt(discriminant)) / a
if (temp < t_max and temp > t_min):
rec.t = temp
rec.p = ray.point_at_parameter(rec.t)
rec.normal = (rec.p - self.center).scalar_div(self.radius)
return True
temp = (-b + math.sqrt(discriminant)) / a
if (temp < t_max and temp > t_min):
rec.t = temp
rec.p = ray.point_at_parameter(rec.t)
rec.normal = (rec.p - self.center).scalar_div(self.radius)
return True
return False
def hit(self, r: Ray, t_min: float, t_max: float):
t: float = (self.k - r.origin()[2]) / r.direction()[2]
if (t < t_min) or (t > t_max):
return False, None
x: float = r.origin()[0] + t * r.direction()[0]
y: float = r.origin()[1] + t * r.direction()[1]
if (x < self.x0) or (x > self.x1) or (y < self.y0) or (y > self.y1):
return False, None
u = (x - self.x0) / (self.x1 - self.x0)
v = (y - self.y0) / (self.y1 - self.y0)
p = r.point_at_parameter(t)
normal = np.array((0, 0, 1))
return True, hit_record(t, p, normal, self.material, u, v)
def test_sphere_hit(self):
sphere = Sphere(np.array([0.2, -0.5, -1.4]), 0.8, None)
# ray specified by origin and direction
ray = Ray(np.array([0.3, 0.1, 0.4]), np.array([-0.1, -0.3, -1.]))
# intersect ray with sphere
rec, t = sphere.hit(ray, 0.1, 10.)
self.assertAlmostEqual(
np.linalg.norm(ray.point_at_parameter(t) - rec.point),
0,
delta=1e-14,
msg='hit record must be consistent with ray parameter')
self.assertAlmostEqual(
abs(np.linalg.norm(rec.point - sphere.center) - sphere.radius),
0,
delta=1e-14,
msg=
'distance between hit point and sphere center must be equal to sphere radius'
)
nx = 200
ny = 100
print('P3\n%d %d 255' % (nx, ny))
lower_left_corner = Vec3(-2.0, -1.0, -1.0)
horizontal = Vec3(4.0, 0.0, 0.0)
vertical = Vec3(0.0, 2.0, 0.0)
origin = Vec3(0.0, 0.0, 0.0)
hlist = [
Sphere(Vec3(0.0, 0.0, -1.0), 0.5),
Sphere(Vec3(0.0, -100.5, -1.0), 100.0)
]
world = HitableList(hlist)
for j in range(ny)[::-1]:
for i in range(nx):
u = float(i) / float(nx)
v = float(j) / float(ny)
r = Ray(origin, lower_left_corner + horizontal * u + vertical * v)
p = r.point_at_parameter(2.0)
col = color(r, world)
ir = int(255.99 * col.r)
ig = int(255.99 * col.g)
ib = int(255.99 * col.b)
print('%d %d %d' % (ir, ig, ib))
unit_direction = r.direction.unit_vector()
t = 0.5 * (unit_direction.y + 1.0)
return Vec3(1.0, 1.0, 1.0) * (1.0 - t) + Vec3(0.5, 0.7, 1.0) * t
nx = 200
ny = 100
print('P3\n%d %d 255' % (nx, ny))
lower_left_corner = Vec3(-2.0, -1.0, -1.0)
horizontal = Vec3(4.0, 0.0, 0.0)
vertical = Vec3(0.0, 2.0, 0.0)
origin = Vec3(0.0, 0.0, 0.0)
hlist = [Sphere(Vec3(0.0, 0.0, -1.0), 0.5), Sphere(Vec3(0.0, -100.5, -1.0), 100.0)]
world = HitableList(hlist)
for j in range(ny)[::-1]:
for i in range(nx):
u = float(i) / float(nx)
v = float(j) / float(ny)
r = Ray(origin, lower_left_corner + horizontal * u + vertical * v)
p = r.point_at_parameter(2.0)
col = color(r, world)
ir = int(255.99 * col.r)
ig = int(255.99 * col.g)
ib = int(255.99 * col.b)
print('%d %d %d' % (ir, ig, ib))