def hit(self, r: Ray, t_min: float, t_max: float) -> Optional[HitRecord]:
oc: Vec3 = r.origin() - self.center
a: float = r.direction().length_squared()
half_b: float = oc @ r.direction()
c: float = oc.length_squared() - self.radius**2
discriminant: float = half_b**2 - a * c
if discriminant > 0:
root: float = np.sqrt(discriminant)
t_0: float = (-half_b - root) / a
t_1: float = (-half_b + root) / a
if t_min < t_0 < t_max:
t = t_0
elif t_min < t_1 < t_max:
t = t_1
else:
return None
point: Point3 = r.at(t)
outward_normal: Vec3 = (point - self.center) / self.radius
rec = HitRecord(point, t, self.material)
rec.set_face_normal(r, outward_normal)
return rec
return None
def hit(self, r: Ray, t_min: float, t_max: float) -> Optional[HitRecord]:
origin = r.origin().copy()
direction = r.direction().copy()
origin[0] = self.cos_theta * r.origin()[0] - self.sin_theta * r.origin(
)[2]
origin[2] = self.sin_theta * r.origin()[0] + self.cos_theta * r.origin(
)[2]
direction[0] = \
self.cos_theta*r.direction()[0] - self.sin_theta*r.direction()[2]
direction[2] = \
self.sin_theta*r.direction()[0] + self.cos_theta*r.direction()[2]
rotated_r = Ray(origin, direction, r.time())
rec = self.obj.hit(rotated_r, t_min, t_max)
if rec is None:
return None
p = rec.p.copy()
normal = rec.normal.copy()
p[0] = self.cos_theta * rec.p[0] + self.sin_theta * rec.p[2]
p[2] = -self.sin_theta * rec.p[0] + self.cos_theta * rec.p[2]
normal[0] = \
self.cos_theta*rec.normal[0] + self.sin_theta*rec.normal[2]
normal[2] = \
-self.sin_theta*rec.normal[0] + self.cos_theta*rec.normal[2]
rec.p = p
rec.set_face_normal(rotated_r, normal)
return rec
def scatter(self, r_in: Ray, rec: HitRecord) \
-> Optional[Tuple[Ray, Color]]:
reflected: Vec3 = r_in.direction().unit_vector().reflect(rec.normal) \
+ Vec3.random_in_unit_sphere() * self.fuzz
scattered = Ray(rec.p, reflected)
attenuation = self.albedo
if scattered.direction() @ rec.normal > 0:
return scattered, attenuation
return None
def hit_deprecated(self, r: Ray, tmin: float, tmax: float) -> bool:
for i in range(3):
t0: float = min((self.min()[i] - r.origin()[i]) / r.direction()[i],
(self.max()[i] - r.origin()[i]) / r.direction()[i])
t1: float = min((self.min()[i] - r.origin()[i]) / r.direction()[i],
(self.max()[i] - r.origin()[i]) / r.direction()[i])
tmin = max(t0, tmin)
tmax = min(t1, tmax)
if tmax <= tmin:
return False
return True
def hit(self, r: Ray, t_min: float, t_max: float) -> Optional[HitRecord]:
t = (self.k - r.origin().x()) / r.direction().x()
if t < t_min or t > t_max:
return None
y = r.origin().y() + t*r.direction().y()
z = r.origin().z() + t*r.direction().z()
if (y < self.y0) or (y > self.y1) or (z < self.z0) or (z > self.z1):
return None
rec = HitRecord(r.at(t), t, self.material)
rec.set_face_normal(r, Vec3(1, 0, 0))
rec.u = (y - self.y0) / (self.y1 - self.y0)
rec.v = (z - self.z0) / (self.z1 - self.z0)
return rec
def hit(self, r: Ray, t_min: float, t_max: float) -> Optional[HitRecord]:
rec1 = self.boundary.hit(r, -np.inf, np.inf)
if rec1 is None:
return None
rec2 = self.boundary.hit(r, rec1.t + 0.0001, np.inf)
if rec2 is None:
return None
if rec1.t < t_min:
rec1.t = t_min
if rec1.t < 0:
rec1.t = 0
if rec2.t > t_max:
rec2.t = t_max
if rec1.t >= rec2.t:
return None
ray_length = r.direction().length()
distance_inside_boundary = (rec2.t - rec1.t) * ray_length
hit_distance = self.neg_inv_density * np.log(random_float())
if hit_distance > distance_inside_boundary:
return None
t = rec1.t + hit_distance / ray_length
p = r.at(t)
rec = HitRecord(p, t, self.phase_function)
rec.normal = Vec3(1, 0, 0)
rec.front_face = True
return rec
def scatter(self, r_in: Ray, rec: HitRecord) \
-> Optional[Tuple[Ray, Color]]:
if rec.front_face:
etai_over_etat = 1 / self.ref_idx
else:
etai_over_etat = self.ref_idx
unit_direction: Vec3 = r_in.direction().unit_vector()
cos_theta: float = min(-unit_direction @ rec.normal, 1)
sin_theta: float = np.sqrt(1 - cos_theta**2)
reflect_prob: float = self.schlick(cos_theta, etai_over_etat)
if etai_over_etat * sin_theta > 1 or random_float() < reflect_prob:
# total internal reflection
reflected: Vec3 = unit_direction.reflect(rec.normal)
scattered = Ray(rec.p, reflected)
else:
# refraction
refracted: Vec3 = unit_direction.refract(
rec.normal, etai_over_etat
)
scattered = Ray(rec.p, refracted)
attenuation = Color(1, 1, 1)
return scattered, attenuation
def hit(self, r: Ray, t_min: float, t_max: float) -> Optional[HitRecord]:
# remove the offset to hit the real object
moved_r = Ray(r.origin() - self.offset, r.direction(), r.time())
rec = self.obj.hit(moved_r, t_min, t_max)
if rec is None:
return None
# add the offset back to simulate the move
rec.p += self.offset
rec.set_face_normal(moved_r, rec.normal)
return rec
def hit(self, r: Ray, tmin: float, tmax: float) -> bool:
for i in range(3):
invD: float = 1 / r.direction()[i]
t0: float = (self.min()[i] - r.origin()[i]) * invD
t1: float = (self.max()[i] - r.origin()[i]) * invD
if invD < 0:
t0, t1 = t1, t0
tmin = max(t0, tmin)
tmax = min(t1, tmax)
if tmax <= tmin:
return False
return True
def ray_color(r: Ray, world: HittableList, depth: int) -> Color:
if depth <= 0:
return Color(0, 0, 0)
rec: Optional[HitRecord] = world.hit(r, 0.001, np.inf)
if rec is not None:
scatter_result = rec.material.scatter(r, rec)
if scatter_result is not None:
scattered, attenuation = scatter_result
return attenuation * ray_color(scattered, world, depth - 1)
return Color(0, 0, 0)
unit_direction: Vec3 = r.direction().unit_vector()
t = (unit_direction.y() + 1) * 0.5
return Color(1, 1, 1) * (1 - t) + Color(0.5, 0.7, 1) * t
def set_face_normal(self, r: Ray, outward_normal: Vec3) -> HitRecord:
self.front_face = (r.direction() @ outward_normal) < 0
self.normal = outward_normal if self.front_face else -outward_normal
return self