def test__ray_equal__given_two_not_equal_rays__return_false():
assert (Ray(direction=Vector((1, 2, 3)), origin=Point(
(3, 5, 6))) == Ray(direction=Vector((1, 2, 3)),
origin=Point((4, 5, 7)))) is False
assert (Ray(direction=Vector((1, 2, 3)), origin=Point(
(3, 5, 6))) == Ray(direction=Vector((4, 5, 7)),
origin=Point((3, 5, 6)))) is False
def test__intersect_ray_with_sphere__two_point_intersection():
R = Ray(Point((0, 0, 2)), Vector(
(1, 0, 0))) #ray passing through the sphere
S = Sphere(Point((0, 0, 0)), 3)
val = np.sqrt(5)
assert (_intersect_ray_with_sphere(R, S) == (Point(
(val, 0, 2)), Point((-val, 0, 2)))) is True
def test__sphere_equal__given_two_not_equal_spheres__return_false():
assert (Sphere(center=Point(
(1, 2, 3)), radius=5) == Sphere(center=Point(
(1, 2, 3)), radius=6)) is False
assert (Sphere(center=Point(
(1, 2, 3)), radius=5) == Sphere(center=Point(
(3, 5, 6)), radius=5)) is False
def _intersect_ray_with_sphere(ray, sphere):
"""Function which provides the co-ordinates of intersection."""
o = ray._origin
u = ray._direction
r = sphere._radius
c = sphere._center
norm_u = np.linalg.norm(u._vector)
U = (1 / norm_u) * u._vector #finds the unit direction
b = 2 * np.dot(u._vector, (o - c)._vector)
a = 1
c = np.dot((o - c)._vector, (o - c)._vector) - r**2
discriminant = b**2 - 4 * a * c
if discriminant > 0:
"""two point intersection case."""
square_root_discriminant = np.sqrt(discriminant)
d1 = (-1 * b + square_root_discriminant) / (2 * a)
d2 = (-1 * b - square_root_discriminant) / (2 * a)
p1 = Point(o._point + (d1 * U))
p2 = Point(o._point + (d2 * U))
return p1, p2
elif discriminant == 0:
"""one point interscetion case."""
d = -1 * b / 2 * a
p = Point(o._point + (d * U))
return p
else:
return "Does not intersect"
def test_intersect_ray_with_sphere_false():
r1 = Ray((0, 0, 0), (1, 1, 1))
s1 = Sphere((10, 10, 10), 5)
d, intercepts = intersect(r1, s1)
intercepts_analytical = [Point([5.0, 0.0, 0.0]), Point([-5.0, 0.0, 0.0])]
d_analytical = 2
assert ((intercepts == intercepts_analytical) and
(d_analytical == d)) is False
def test__intersect__ray_with_sphere__return_false():
r1 = Ray((0, 0, 0), (1, 1, 1))
s1 = Sphere((10, 10, 10), 3)
d, intersections = intersect(r1, s1)
calculated_intersections = [
Point([3.0, 0.0, 0.0]),
Point([-3.0, 0.0, 0.0])
]
d_analytical = 2
assert ((intersections == calculated_intersections) and
(d_analytical == d)) is False
def test_intersect_ray_with_triangle_true():
t = Triangle((1, 0, 0), (0, 1, 0), (0, 0, 1))
r1 = Ray((0, 0, 0), (1, 1, 1))
d, intercepts = intersect(r1, t)
intercepts_analytical = Point(
[0.3333333333333333, 0.3333333333333333, 0.3333333333333333])
d_analytical = 1
assert ((intercepts == intercepts_analytical) and
(d_analytical == d)) is True
def test__point_equal__given_two_equal_points__return_true():
assert (Point((1, 2, 3)) == Point((1, 2, 3))) is True
def test__point_subtraction__given_two_points__return_correct_vector():
"""The result of a point being subtracted from another one is a vector."""
assert Point((0, 1, 2)) - Point((3, 4, 5)) == Vector((-3, -3, -3))
def test__point_right_addition__given_vector_and_point__return_correct_point():
"""The result of a vector being added to a point is a point."""
assert Vector((0, 1, 2)) + Point((3, 4, 5)) == Point((3, 5, 7))
def test__ray_equal__given_two_rays_with_different_direction_and_origin_return_false(
):
assert (Ray(Point((1, 1, 1)), Vector(
(3, -4, 5))) == Ray(Point((0, 0, 0)), Vector((3, 4, 5)))) is False
def test_intersection__sphere_center_elsewhere__given_ray_that_originates_inside_sphere__return_true(
):
assert (intersection(Ray((1, 1, 1), (0, 0, 1)), Sphere(
(1, 1, 1), 1.0)) == Point([1, 1, 2]))
def test_intersection__sphere_center_elsewhere__given_tangent_ray__return_true(
):
assert (intersection(Ray((-3, 1, 0), (1, 0, 0)), Sphere(
(1, 1, 1), 1.0)) == Point([1, 1, 0]))
def test_intersection__sphere_center_at_origin__given_ray_that_intersects_at_two_points__return_true(
):
assert array_equal(
intersection(Ray((-2, 0, 0), (1, 0, 0)), Sphere((0, 0, 0), 1.0)),
[Point([-1, 0, 0]), Point([1, 0, 0])]) is True
def test_intersection__ray_with_sphere_intersects_at_one_point_given_tangent_point__return_true(
):
assert (intersect(Ray((0, 0, 0), (1, 1, 0)), Sphere(
(0, 0, 0), 1.0)) == Point([1 / np.sqrt(2), 1 / np.sqrt(2), 0]))
# _intersect_ray_with_sphere
# inputs for non intersecting ray and sphere
x = Ray((0, 10, 0), (0, -1, 0))
y = Sphere((10, 0, 0), 5)
def test_non_intersecting_ray_sphere_return_false():
assert _intersect_ray_with_sphere(x, y) is False
# inputs for ray and sphere intersecting at 2 points
x1 = Ray((0, 10, 0), (0, -1, 0))
y1 = Sphere((0, 0, 0), 5)
# The two expected intersecting points
p1 = Point((0, -5, 0))
p2 = Point((0, 5, 0))
def test_intersecting_ray_sphere_at_two_points_return_true():
x = _intersect_ray_with_sphere(x1, y1)
diff1 = x[0] - p1
diff2 = x[1] - p2
d1 = abs(np.linalg.norm(diff1._vector))
d2 = abs(np.linalg.norm(diff2._vector))
assert (d1 < 10**(-5) and d2 < 10**(-5)) == True is True
# inputs for ray and sphere intersecting at 1 point
x2 = Ray((0, 10, 0), (0, -1, 0))
y2 = Sphere((5, 0, 0), 5)
def test__sphere_equal__given_two_not_equal_sphere__return_false():
assert (Sphere(Point((1,2,3)),5) == Sphere(Point((3,2,1)),4)) is False
def test__intersect_ray_with_sphere__one_point_intersection():
R = Ray(Point((0, 0, 3)), Vector((1, 0, 0))) #ray touching sphere surface
S = Sphere(Point((0, 0, 0)), 3)
assert (_intersect_ray_with_sphere(R, S) == Point((0, 0, 3))) is True
def test__intersect_ray_with_sphere__does_not_intersect():
R = Ray(Point((0, 0, 4)), Vector((1, 0, 0))) #ray outside sphere
S = Sphere(Point((0, 0, 0)), 3) #sphere with center at origin and radius 3
assert (_intersect_ray_with_sphere(R, S) == "Does not intersect") is True
def test__sphere_equal__given_two_spheres_with_different_centers_and_radi_return_false(
):
assert (Sphere(Point((1, 1, 1)), 5) == Sphere(Point(
(0, 0, 0)), 10)) is False
def test_sphere_equal_given_two_equal_spheres_retun_true():
assert (Sphere(Point((0, 1, 2)), 5) == Sphere(Point((0, 1, 2)), 5)) is True
def test__point_equal__given_two_not_equal_points__return_false():
assert (Point((1, 2, 3)) == Point((4, 5, 6))) is False
def test_intersection__sphere_center_at_origin__given_tangent_ray__return_true(
):
assert (intersection(Ray((-3, 1, 0), (1, 0, 0)), Sphere(
(0, 0, 0), 1.0)) == Point([0, 1, 0]))
def test_triangle_init_function_point_list():
t1 = Triangle(Point((0, 10, 0)), Point((10, 0, 0)), Point((0, 0, 10)))
t2 = Triangle((0, 10, 0), (10, 0, 0), (0, 0, 10))
assert (t1 == t2) is True
def test_intersection__sphere_center_at_origin__given_ray_that_originates_inside_sphere__return_true(
):
assert (intersection(Ray((-0.5, 0, 0), (1, 0, 0)), Sphere(
(0, 0, 0), 1.0)) == Point([1, 0, 0]))
def test_ray_init_function_point_list():
r1 = Ray(Point((0, 0, 0)), Point((1, 0, 0)))
expected = Ray((0, 0, 0), (1, 0, 0))
assert (r1 == expected) is True
def test_intersection__sphere_center_elsewhere__given_ray_that_intersects_at_two_points__return_true(
):
assert array_equal(
intersection(Ray((-2, 1, 1), (1, 0, 0)), Sphere((1, 1, 1), 1.0)),
[Point([0, 1, 1]), Point([2, 1, 1])]) is True
def test_sphere_init_function_point():
s1 = Sphere(Point((0, 0, 0)), 5)
expected = Sphere((0, 0, 0), 5)
assert (s1 == expected) is True
def test_intersection__ray_with_sphere_intersects_at_two_points_given_intersected_points__return_true(
):
assert np.array_equal(
intersect(Ray((-1, 0, 0), (1, 0, 0)), Sphere((0, 0, 0), 1.0)),
[Point([-1, 0, 0]), Point([1, 0, 0])]) is True
def test_ray_equal_given_two_equal_rays_retun_true():
assert (Ray(Point((0, 1, 2)), Vector(
(3, 4, 5))) == Ray(Point((0, 1, 2)), Vector((3, 4, 5)))) is True
