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 testCheckeredPigment(self):
color1 = Color(1.0, 2.0, 3.0)
color2 = Color(10.0, 20.0, 30.0)
pigment = CheckeredPigment(color1=color1,
color2=color2,
num_of_steps=2)
# With num_of_steps == 2, the pattern should be the following:
#
# (0.5, 0)
# (0, 0) +------+------+ (1, 0)
# | | |
# | col1 | col2 |
# | | |
# (0, 0.5) +------+------+ (1, 0.5)
# | | |
# | col2 | col1 |
# | | |
# (0, 1) +------+------+ (1, 1)
# (0.5, 1)
assert pigment.get_color(Vec2d(0.25, 0.25)).is_close(color1)
assert pigment.get_color(Vec2d(0.75, 0.25)).is_close(color2)
assert pigment.get_color(Vec2d(0.25, 0.75)).is_close(color2)
assert pigment.get_color(Vec2d(0.75, 0.75)).is_close(color1)
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 testUniformPigment(self):
color = Color(1.0, 2.0, 3.0)
pigment = UniformPigment(color=color)
assert pigment.get_color(Vec2d(0.0, 0.0)).is_close(color)
assert pigment.get_color(Vec2d(1.0, 0.0)).is_close(color)
assert pigment.get_color(Vec2d(0.0, 1.0)).is_close(color)
assert pigment.get_color(Vec2d(1.0, 1.0)).is_close(color)
def testUVCoordinates(self):
plane = Plane()
ray1 = Ray(origin=Point(0, 0, 1), dir=-VEC_Z)
intersection1 = plane.ray_intersection(ray1)
assert intersection1.surface_point.is_close(Vec2d(0.0, 0.0))
ray2 = Ray(origin=Point(0.25, 0.75, 1), dir=-VEC_Z)
intersection2 = plane.ray_intersection(ray2)
assert intersection2.surface_point.is_close(Vec2d(0.25, 0.75))
ray3 = Ray(origin=Point(4.25, 7.75, 1), dir=-VEC_Z)
intersection3 = plane.ray_intersection(ray3)
assert intersection3.surface_point.is_close(Vec2d(0.25, 0.75))
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 testImagePigment(self):
image = HdrImage(width=2, height=2)
image.set_pixel(0, 0, Color(1.0, 2.0, 3.0))
image.set_pixel(1, 0, Color(2.0, 3.0, 1.0))
image.set_pixel(0, 1, Color(2.0, 1.0, 3.0))
image.set_pixel(1, 1, Color(3.0, 2.0, 1.0))
pigment = ImagePigment(image)
assert pigment.get_color(Vec2d(0.0,
0.0)).is_close(Color(1.0, 2.0, 3.0))
assert pigment.get_color(Vec2d(1.0,
0.0)).is_close(Color(2.0, 3.0, 1.0))
assert pigment.get_color(Vec2d(0.0,
1.0)).is_close(Color(2.0, 1.0, 3.0))
assert pigment.get_color(Vec2d(1.0,
1.0)).is_close(Color(3.0, 2.0, 1.0))
def _sphere_point_to_uv(point: Point) -> Vec2d:
"""Convert a 3D point on the surface of the unit sphere into a (u, v) 2D point"""
u = atan2(point.y, point.x) / (2.0 * pi)
return Vec2d(
u=u if u >= 0.0 else u + 1.0,
v=acos(point.z) / pi,
)
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)
def testUVCoordinates(self):
sphere = Sphere()
# The first four rays hit the unit sphere at the
# points P1, P2, P3, and P4.
#
# ^ y
# | P2
# , - ~ * ~ - ,
# , ' | ' ,
# , | ,
# , | ,
# , | , P1
# -----*-------------+-------------*---------> x
# P3 , | ,
# , | ,
# , | ,
# , | , '
# ' - , _ * _ , '
# | P4
#
# P5 and P6 are aligned along the x axis and are displaced
# along z (ray5 in the positive direction, ray6 in the negative
# direction).
ray1 = Ray(origin=Point(2.0, 0.0, 0.0), dir=-VEC_X)
assert sphere.ray_intersection(ray1).surface_point.is_close(
Vec2d(0.0, 0.5))
ray2 = Ray(origin=Point(0.0, 2.0, 0.0), dir=-VEC_Y)
assert sphere.ray_intersection(ray2).surface_point.is_close(
Vec2d(0.25, 0.5))
ray3 = Ray(origin=Point(-2.0, 0.0, 0.0), dir=VEC_X)
assert sphere.ray_intersection(ray3).surface_point.is_close(
Vec2d(0.5, 0.5))
ray4 = Ray(origin=Point(0.0, -2.0, 0.0), dir=VEC_Y)
assert sphere.ray_intersection(ray4).surface_point.is_close(
Vec2d(0.75, 0.5))
ray5 = Ray(origin=Point(2.0, 0.0, 0.5), dir=-VEC_X)
assert sphere.ray_intersection(ray5).surface_point.is_close(
Vec2d(0.0, 1 / 3))
ray6 = Ray(origin=Point(2.0, 0.0, -0.5), dir=-VEC_X)
assert sphere.ray_intersection(ray6).surface_point.is_close(
Vec2d(0.0, 2 / 3))