def test_arc3_to_from_dict():
"""Test the initalization of Arc3D objects and basic properties."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
arc_dict = arc.to_dict()
new_arc = Arc3D.from_dict(arc_dict)
assert isinstance(new_arc, Arc3D)
assert new_arc.to_dict() == arc_dict
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 3)
arc_dict = arc.to_dict()
new_arc = Arc3D.from_dict(arc_dict)
assert isinstance(new_arc, Arc3D)
assert new_arc.is_circle
assert new_arc.to_dict() == arc_dict
def test_point_at_angle():
"""Test the Arc3D point_at_angle method."""
pt = Point3D(2, 0)
arc = Arc3D(Plane(o=pt), 1, 1.5 * math.pi, 0.5 * math.pi)
assert arc.point_at_angle(0.5 * math.pi).x == pytest.approx(3, rel=1e-2)
assert arc.point_at_angle(0.5 * math.pi).y == pytest.approx(0, rel=1e-2)
def test_reflect():
"""Test the Arc3D reflect method."""
pt = Point3D(2, 2, 0)
arc = Arc3D(Plane(o=pt), 2, 0, math.pi)
origin_1 = Point3D(0, 1)
origin_2 = Point3D(1, 1)
normal_1 = Vector3D(0, 1)
normal_2 = Vector3D(-1, 1).normalize()
normal_3 = Vector3D(1, 0)
assert arc.reflect(normal_1, origin_1).c.x == pytest.approx(2, rel=1e-3)
assert arc.reflect(normal_1, origin_1).c.y == pytest.approx(0, rel=1e-3)
assert arc.reflect(normal_1,
origin_1).midpoint.x == pytest.approx(2, rel=1e-3)
assert arc.reflect(normal_1,
origin_1).midpoint.y == pytest.approx(-2, rel=1e-3)
assert arc.reflect(normal_1, origin_2).c == Point3D(2, 0)
assert arc.reflect(normal_1,
origin_2).midpoint.x == pytest.approx(2, rel=1e-3)
assert arc.reflect(normal_1,
origin_2).midpoint.y == pytest.approx(-2, rel=1e-3)
test_1 = arc.reflect(normal_2, origin_2)
assert test_1.c.x == pytest.approx(2, rel=1e-3)
assert test_1.c.y == pytest.approx(2, rel=1e-3)
assert test_1.midpoint.x == pytest.approx(4, rel=1e-3)
assert test_1.midpoint.y == pytest.approx(2, rel=1e-3)
test_2 = arc.reflect(normal_3, origin_1)
assert test_2.c.x == pytest.approx(-2, rel=1e-3)
assert test_2.c.y == pytest.approx(2, rel=1e-3)
assert test_2.midpoint.x == pytest.approx(-2, rel=1e-3)
assert test_2.midpoint.y == pytest.approx(4, rel=1e-3)
def test_arc3_init():
"""Test the initalization of Arc3D objects and basic properties."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
str(arc) # test the string representation of the arc
assert isinstance(arc.arc2d, Arc2D)
assert arc.c == pt
assert arc.radius == arc.arc2d.r == 1
assert arc.a1 == arc.arc2d.a1 == 0
assert arc.a2 == arc.arc2d.a2 == math.pi
assert arc.p1 == Point3D(3, 0, 2)
assert arc.p2.x == pytest.approx(1, rel=1e-3)
assert arc.p2.y == pytest.approx(0, rel=1e-3)
assert arc.p2.z == pytest.approx(2, rel=1e-3)
assert arc.midpoint == Point3D(2, 1, 2)
assert arc.length == pytest.approx(math.pi, rel=1e-3)
assert arc.angle == pytest.approx(math.pi, rel=1e-3)
assert arc.is_circle is False
assert arc.is_inverted is False
arc2 = arc.duplicate()
assert arc2.c == pt
assert arc2.radius == 1
assert arc2.a1 == 0
assert arc2.a2 == math.pi
def test_arc3_split_with_plane():
"""Test the Arc3D split_with_plane method."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
circle = Arc3D(Plane(o=pt), 1)
plane_1 = Plane(Vector3D(0, 1, 0), Point3D(0, 0, 0))
int1 = circle.split_with_plane(plane_1)
assert len(int1) == 2
assert int1[0].p1 == Point3D(3, 0, 2)
assert int1[0].p2.x == pytest.approx(1, rel=1e-2)
assert int1[0].p2.y == pytest.approx(0, rel=1e-2)
assert int1[1].p2 == Point3D(3, 0, 2)
assert int1[1].p1.x == pytest.approx(1, rel=1e-2)
assert int1[1].p1.y == pytest.approx(0, rel=1e-2)
plane_2 = Plane(Vector3D(0, 1, 0), Point3D(0, 0.5, 0))
int2 = arc.split_with_plane(plane_2)
assert len(int2) == 3
def test_scale_world_origin():
"""Test the Arc3D scale method with None origin."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
new_arc = arc.scale(2)
assert new_arc.c == Point3D(4, 0, 4)
assert new_arc.radius == 2
assert new_arc.length == 2 * arc.length
assert new_arc.a1 == arc.a1
assert new_arc.a2 == arc.a2
def test_subdivide():
"""Test the Arc3D subdivide methods."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 1.5 * math.pi, 0.5 * math.pi)
divisions = arc.subdivide(0.5)
assert len(divisions) == 8
divisions = arc.subdivide([1, 0.5, 0.25])
assert len(divisions) == 10
divisions = arc.subdivide_evenly(4)
assert len(divisions) == 5
def test_arc3_init_circle():
"""Test the initalization of Arc3D objects as a circle."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 3)
assert arc.c == pt
assert arc.radius == 3
assert arc.a1 == 0
assert arc.a2 == 2 * math.pi
assert arc.is_circle
assert arc.length == math.pi * 6
assert arc.area == math.pi * 3**2
def test_scale():
"""Test the Arc3D scale method."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
origin_1 = Point3D(2, 0, 2)
new_arc = arc.scale(2, origin_1)
assert new_arc.c == Point3D(2, 0, 2)
assert new_arc.radius == 2
assert new_arc.length == 2 * arc.length
assert new_arc.a1 == arc.a1
assert new_arc.a2 == arc.a2
def test_intersect_arc():
"""Test the Plane intersect_arc method."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
circle = Arc3D(Plane(o=pt), 1)
plane_1 = Plane(Vector3D(0, 1, 0), Point3D(0, 0, 0))
int1 = plane_1.intersect_arc(circle)
assert len(int1) == 2
assert int1[0] == Point3D(3, 0, 2)
plane_2 = Plane(Vector3D(0, 1, 0), Point3D(0, 0.5, 0))
int2 = plane_2.intersect_arc(arc)
assert len(int2) == 2
plane_3 = Plane(Vector3D(1, 0, 0), Point3D(1.5, 0, 0))
int3 = plane_3.intersect_arc(arc)
assert len(int3) == 1
plane_4 = Plane(Vector3D(1, 0, 0), Point3D(0, 2, 0))
int4 = plane_4.intersect_arc(arc)
assert int4 is None
def test_move():
"""Test the Arc3D move method."""
pt = Point3D(2, 0, 0)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
vec_1 = Vector3D(2, 2, 2)
new_arc = arc.move(vec_1)
assert new_arc.c == Point3D(4, 2, 2)
assert new_arc.radius == arc.radius
assert new_arc.p1 == Point3D(5, 2, 2)
assert new_arc.p2 == Point3D(3, 2, 2)
assert new_arc.a1 == arc.a1
assert new_arc.a2 == arc.a2
def test_arc3_init_from_start_mid_end():
"""Test the initalization of Arc3D objects from_start_mid_end."""
p1 = Point3D(3, 0, 2)
m = Point3D(2, 1, 2)
p2 = Point3D(1, 0, 2)
arc = Arc3D.from_start_mid_end(p1, m, p2)
assert arc.c == Point3D(2, 0, 2)
assert arc.radius == 1
assert arc.a1 == 0
assert arc.a2 == math.pi
assert arc.p1 == Point3D(3, 0, 2)
assert arc.p2.x == pytest.approx(1, rel=1e-3)
assert arc.p2.y == pytest.approx(0, rel=1e-3)
assert arc.p2.z == pytest.approx(2, rel=1e-3)
assert arc.midpoint == Point3D(2, 1, 2)
assert arc.length == pytest.approx(math.pi, rel=1e-3)
assert arc.angle == pytest.approx(math.pi, rel=1e-3)
assert arc.is_circle is False
assert arc.is_inverted is False
p1 = Point3D(0, 0)
m = Point3D(0, 2)
p2 = Point3D(-1, 1)
arc = Arc3D.from_start_mid_end(p1, m, p2)
assert arc.c == Point3D(0, 1)
assert arc.radius == 1
assert arc.length == pytest.approx(1.5 * math.pi, rel=1e-3)
assert arc.is_inverted is True
p1 = Point3D(0, 0)
m = Point3D(1, 0)
p2 = Point3D(2, 0)
with pytest.raises(Exception):
arc = Arc3D.from_start_mid_end(p1, m, p2)
def test_rotate_xy():
"""Test the Arc3D rotate_xy method."""
pt = Point3D(2, 2, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
origin_1 = Point3D(0, 2, 2)
test_1 = arc.rotate_xy(math.pi, origin_1)
assert test_1.c.x == pytest.approx(-2, rel=1e-3)
assert test_1.c.y == pytest.approx(2, rel=1e-3)
assert test_1.radius == arc.radius
test_2 = arc.rotate_xy(math.pi / 2, origin_1)
assert test_2.c.x == pytest.approx(0, rel=1e-3)
assert test_2.c.y == pytest.approx(4, rel=1e-3)
assert test_2.radius == arc.radius
def test_rotate():
"""Test the Arc3D rotate method."""
pt = Point3D(2, 2, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
axis_1 = Vector3D(0, 1, 0)
origin_1 = Point3D(0, 2, 2)
test_1 = arc.rotate(axis_1, math.pi, origin_1)
assert test_1.c.x == pytest.approx(-2, rel=1e-3)
assert test_1.c.z == pytest.approx(2, rel=1e-3)
assert test_1.radius == arc.radius
test_2 = arc.rotate(axis_1, math.pi / 2, origin_1)
assert test_2.c.x == pytest.approx(0, rel=1e-3)
assert test_2.c.z == pytest.approx(0, rel=1e-3)
assert test_2.radius == arc.radius
def test_arc3_closest_point():
"""Test the Arc3D closest_point method."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 0, math.pi)
assert arc.closest_point(Point3D(2, 2)) == Point3D(2, 1, 2)
assert arc.closest_point(Point3D(3, 1)).x == pytest.approx(2.71, rel=1e-2)
assert arc.closest_point(Point3D(3, 1)).y == pytest.approx(0.71, rel=1e-2)
assert arc.closest_point(Point3D(3, -1)) == Point3D(3, 0, 2)
assert arc.closest_point(Point3D(1, -1)).x == pytest.approx(1, rel=1e-2)
assert arc.closest_point(Point3D(1, -1)).y == pytest.approx(0, rel=1e-2)
assert arc.distance_to_point(Point3D(2, 2)) == math.sqrt(5)
assert arc.distance_to_point(Point3D(3, 1)) == pytest.approx(2.0424428,
rel=1e-2)
assert arc.distance_to_point(Point3D(3, -1, 2)) == pytest.approx(1,
rel=1e-2)
assert arc.distance_to_point(Point3D(1, -1, 2)) == pytest.approx(1,
rel=1e-2)
def test_arc3_init_radius():
"""Test the initalization of Arc3D objects with a non-unit radius."""
pt = Point3D(2, 2, 2)
n = Vector3D(0, 1, 0)
arc = Arc3D(Plane(n=n, o=pt), 2, math.pi, 0)
assert arc.c == pt
assert arc.radius == arc.arc2d.r == 2
assert arc.a1 == arc.arc2d.a1 == math.pi
assert arc.a2 == arc.arc2d.a2 == 0
assert arc.p1.x == pytest.approx(0, rel=1e-3)
assert arc.p1.z == pytest.approx(2, rel=1e-3)
assert arc.p2.x == pytest.approx(4, rel=1e-3)
assert arc.p2.z == pytest.approx(2, rel=1e-3)
assert arc.midpoint.x == pytest.approx(2, rel=1e-3)
assert arc.midpoint.z == pytest.approx(4, rel=1e-3)
assert arc.length == pytest.approx(2 * math.pi, rel=1e-3)
assert arc.angle == pytest.approx(math.pi, rel=1e-3)
assert arc.is_circle is False
assert arc.is_inverted is True
def test_arc3_init_reveresed():
"""Test the initalization of Arc3D objects with reversed direction."""
pt = Point3D(2, 0, 2)
arc = Arc3D(Plane(o=pt), 1, 1.5 * math.pi, 0.5 * math.pi)
assert arc.c == pt
assert arc.radius == 1
assert arc.a1 == 1.5 * math.pi
assert arc.a2 == 0.5 * math.pi
assert arc.p1.x == pytest.approx(2, rel=1e-3)
assert arc.p1.y == pytest.approx(-1, rel=1e-3)
assert arc.p1.z == pytest.approx(2, rel=1e-3)
assert arc.p2.x == pytest.approx(2, rel=1e-3)
assert arc.p2.y == pytest.approx(1, rel=1e-3)
assert arc.p2.z == pytest.approx(2, rel=1e-3)
assert arc.midpoint.x == pytest.approx(3, rel=1e-3)
assert arc.midpoint.y == pytest.approx(0, rel=1e-3)
assert arc.length == pytest.approx(math.pi, rel=1e-3)
assert arc.angle == pytest.approx(math.pi, rel=1e-3)
assert arc.is_circle is False
assert arc.is_inverted is True