def testTransformation(self):
sphere = Sphere(transformation=translation(Vec(10.0, 0.0, 0.0)))
ray1 = Ray(origin=Point(10, 0, 2), dir=-VEC_Z)
intersection1 = sphere.ray_intersection(ray1)
assert intersection1
assert HitRecord(
world_point=Point(10.0, 0.0, 1.0),
normal=Normal(0.0, 0.0, 1.0),
surface_point=Vec2d(0.0, 0.0),
t=1.0,
ray=ray1,
material=sphere.material,
).is_close(intersection1)
ray2 = Ray(origin=Point(13, 0, 0), dir=-VEC_X)
intersection2 = sphere.ray_intersection(ray2)
assert intersection2
assert HitRecord(
world_point=Point(11.0, 0.0, 0.0),
normal=Normal(1.0, 0.0, 0.0),
surface_point=Vec2d(0.0, 0.5),
t=2.0,
ray=ray2,
material=sphere.material,
).is_close(intersection2)
# Check if the sphere failed to move by trying to hit the untransformed shape
assert not sphere.ray_intersection(
Ray(origin=Point(0, 0, 2), dir=-VEC_Z))
# Check if the *inverse* transformation was wrongly applied
assert not sphere.ray_intersection(
Ray(origin=Point(-10, 0, 0), dir=-VEC_Z))
def testHit(self):
sphere = Sphere()
ray1 = Ray(origin=Point(0, 0, 2), dir=-VEC_Z)
intersection1 = sphere.ray_intersection(ray1)
assert intersection1
assert HitRecord(
world_point=Point(0.0, 0.0, 1.0),
normal=Normal(0.0, 0.0, 1.0),
surface_point=Vec2d(0.0, 0.0),
t=1.0,
ray=ray1,
material=sphere.material,
).is_close(intersection1)
ray2 = Ray(origin=Point(3, 0, 0), dir=-VEC_X)
intersection2 = sphere.ray_intersection(ray2)
assert intersection2
assert HitRecord(
world_point=Point(1.0, 0.0, 0.0),
normal=Normal(1.0, 0.0, 0.0),
surface_point=Vec2d(0.0, 0.5),
t=2.0,
ray=ray2,
material=sphere.material,
).is_close(intersection2)
assert not sphere.ray_intersection(
Ray(origin=Point(0, 10, 2), dir=-VEC_Z))
def testTransformation(self):
plane = Plane(transformation=rotation_y(angle_deg=90.0))
ray1 = Ray(origin=Point(1, 0, 0), dir=-VEC_X)
intersection1 = plane.ray_intersection(ray1)
assert intersection1
assert HitRecord(
world_point=Point(0.0, 0.0, 0.0),
normal=Normal(1.0, 0.0, 0.0),
surface_point=Vec2d(0.0, 0.0),
t=1.0,
ray=ray1,
material=plane.material,
).is_close(intersection1)
ray2 = Ray(origin=Point(0, 0, 1), dir=VEC_Z)
intersection2 = plane.ray_intersection(ray2)
assert not intersection2
ray3 = Ray(origin=Point(0, 0, 1), dir=VEC_X)
intersection3 = plane.ray_intersection(ray3)
assert not intersection3
ray4 = Ray(origin=Point(0, 0, 1), dir=VEC_Y)
intersection4 = plane.ray_intersection(ray4)
assert not intersection4
def ray_intersection(self, ray: Ray) -> Union[HitRecord, None]:
"""Checks if a ray intersects the sphere
Return a `HitRecord`, or `None` if no intersection was found.
"""
inv_ray = ray.transform(self.transformation.inverse())
origin_vec = inv_ray.origin.to_vec()
a = inv_ray.dir.squared_norm()
b = 2.0 * origin_vec.dot(inv_ray.dir)
c = origin_vec.squared_norm() - 1.0
delta = b * b - 4.0 * a * c
if delta <= 0.0:
return None
sqrt_delta = sqrt(delta)
tmin = (-b - sqrt_delta) / (2.0 * a)
tmax = (-b + sqrt_delta) / (2.0 * a)
if (tmin > inv_ray.tmin) and (tmin < inv_ray.tmax):
first_hit_t = tmin
elif (tmax > inv_ray.tmin) and (tmax < inv_ray.tmax):
first_hit_t = tmax
else:
return None
hit_point = inv_ray.at(first_hit_t)
return HitRecord(
world_point=self.transformation * hit_point,
normal=self.transformation *
_sphere_normal(hit_point, inv_ray.dir),
surface_point=_sphere_point_to_uv(hit_point),
t=first_hit_t,
ray=ray,
)
def ray_intersection(self, ray: Ray) -> Union[HitRecord, None]:
"""Checks if a ray intersects the plane
Return a `HitRecord`, or `None` if no intersection was found.
"""
inv_ray = ray.transform(self.transformation.inverse())
if abs(inv_ray.dir.z) < 1e-5:
return None
t = -inv_ray.origin.z / inv_ray.dir.z
if (t <= inv_ray.tmin) or (t >= inv_ray.tmax):
return None
hit_point = inv_ray.at(t)
return HitRecord(
world_point=self.transformation * hit_point,
normal=self.transformation *
Normal(0.0, 0.0, 1.0 if inv_ray.dir.z < 0.0 else -1.0),
surface_point=Vec2d(hit_point.x - floor(hit_point.x),
hit_point.y - floor(hit_point.y)),
t=t,
ray=ray,
material=self.material,
)
def testInnerHit(self):
sphere = Sphere()
ray = Ray(origin=Point(0, 0, 0), dir=VEC_X)
intersection = sphere.ray_intersection(ray)
assert intersection
assert HitRecord(
world_point=Point(1.0, 0.0, 0.0),
normal=Normal(-1.0, 0.0, 0.0),
surface_point=Vec2d(0.0, 0.5),
t=1.0,
ray=ray,
).is_close(intersection)