def all_boundary_circles(self):
"""Get an array of 3 Arc2Ds for the circles of the compass."""
arc2 = Arc2D(self.center,
self.radius * (1 + self.spacing_factor * 0.1))
arc3 = Arc2D(self.center,
self.radius * (1 + self.spacing_factor * 0.3))
return [self.inner_boundary_circle, arc2, arc3]
def test_arc2_init_from_start_mid_end():
"""Test the initalization of Arc2D objects from_start_mid_end."""
p1 = Point2D(3, 0)
m = Point2D(2, 1)
p2 = Point2D(1, 0)
arc = Arc2D.from_start_mid_end(p1, m, p2)
assert arc.c == Point2D(2, 0)
assert arc.r == 1
assert arc.a1 == 0
assert arc.a2 == math.pi
assert arc.p1 == Point2D(3, 0)
assert arc.p2.x == pytest.approx(1, rel=1e-3)
assert arc.p2.y == pytest.approx(0, rel=1e-3)
assert arc.midpoint == Point2D(2, 1)
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 = Point2D(0, 0)
m = Point2D(0, 2)
p2 = Point2D(-1, 1)
arc = Arc2D.from_start_mid_end(p1, m, p2)
assert arc.c == Point2D(0, 1)
assert arc.r == 1
assert arc.length == pytest.approx(1.5 * math.pi, rel=1e-3)
assert arc.is_inverted is True
p1 = Point2D(0, 0)
m = Point2D(1, 0)
p2 = Point2D(2, 0)
with pytest.raises(Exception):
arc = Arc2D.from_start_mid_end(p1, m, p2)
def test_arc2_intersect_line_ray():
"""Test the Arc2D intersect_line_ray method."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
circle = Arc2D(pt, 1)
seg1 = LineSegment2D(pt, Vector2D(2, 2))
seg2 = LineSegment2D(Point2D(0, -2), Vector2D(6, 6))
seg3 = LineSegment2D(pt, Vector2D(0.5, 0.5))
int1 = arc.intersect_line_ray(seg1)
assert len(int1) == 1
assert int1[0].x == pytest.approx(2.71, rel=1e-2)
assert int1[0].y == pytest.approx(0.71, rel=1e-2)
int2 = circle.intersect_line_ray(seg1)
assert len(int2) == 1
assert int2[0].x == pytest.approx(2.71, rel=1e-2)
assert int2[0].y == pytest.approx(0.71, rel=1e-2)
int3 = arc.intersect_line_ray(seg2)
assert len(int3) == 1
assert int3[0].x == pytest.approx(2.71, rel=1e-2)
assert int3[0].y == pytest.approx(0.71, rel=1e-2)
int4 = circle.intersect_line_ray(seg2)
assert len(int4) == 2
assert int4[0].x == pytest.approx(2.71, rel=1e-2)
assert int4[0].y == pytest.approx(0.71, rel=1e-2)
assert int4[1].x == pytest.approx(1.29, rel=1e-2)
assert int4[1].y == pytest.approx(-0.71, rel=1e-2)
assert arc.intersect_line_ray(seg3) is None
def test_equality():
"""Test the equality of Arc2D objects."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
arc_dup = arc.duplicate()
arc_alt = Arc2D(pt, 1, 0.1, math.pi)
assert arc is arc
assert arc is not arc_dup
assert arc == arc_dup
assert hash(arc) == hash(arc_dup)
assert arc != arc_alt
assert hash(arc) != hash(arc_alt)
def test_reflect():
"""Test the Arc2D reflect method."""
pt = Point2D(2, 2)
arc = Arc2D(pt, 2, 0, math.pi)
origin_1 = Point2D(0, 1)
origin_2 = Point2D(1, 1)
normal_1 = Vector2D(0, 1)
normal_2 = Vector2D(-1, 1).normalize()
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 == Point2D(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)
def test_arc2_to_from_dict():
"""Test the initalization of Arc2D objects and basic properties."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
arc_dict = arc.to_dict()
new_arc = Arc2D.from_dict(arc_dict)
assert isinstance(new_arc, Arc2D)
assert new_arc.to_dict() == arc_dict
pt = Point2D(2, 0)
arc = Arc2D(pt, 3)
arc_dict = arc.to_dict()
new_arc = Arc2D.from_dict(arc_dict)
assert isinstance(new_arc, Arc2D)
assert new_arc.is_circle
assert new_arc.to_dict() == arc_dict
def test_point_at_angle():
"""Test the Arc2D point_at_angle method."""
pt = Point2D(2, 0)
arc = Arc2D(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_arc2_split_line_infinite():
"""Test the Arc2D split_line_ray_infinite method."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
circle = Arc2D(pt, 1)
int1 = circle.split_line_infinite(Ray2D(Point2D(), Vector2D(1, 0)))
assert len(int1) == 2
assert int1[0].p1 == Point2D(3, 0)
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 == Point2D(3, 0)
assert int1[1].p1.x == pytest.approx(1, rel=1e-2)
assert int1[1].p1.y == pytest.approx(0, rel=1e-2)
int2 = arc.split_line_infinite(Ray2D(Point2D(0, 0.5), Vector2D(1, 0)))
assert len(int2) == 3
def orthographic_altitude_circles(self):
"""Get a list of circles for the orthographic altitude labels."""
circles = []
for angle in self.ALTITUDES:
circles.append(
Arc2D(self.center,
self.radius * math.cos(math.radians(angle))))
return circles
def stereographic_altitude_circles(self):
"""Get a list of circles for the stereographic altitude labels."""
circles = []
for angle in self.ALTITUDES:
ang = math.radians(angle)
pt3d = Point3D(math.cos(ang), 0, math.sin(ang))
radius = self.point3d_to_stereographic(pt3d, 1).x * self.radius
circles.append(Arc2D(self.center, radius))
return circles
def test_subdivide():
"""Test the Arc2D subdivide methods."""
pt = Point2D(2, 0)
arc = Arc2D(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_scale_world_origin():
"""Test the Arc2D scale method with None origin."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
new_arc = arc.scale(2)
assert new_arc.c == Point2D(4, 0)
assert new_arc.r == 2
assert new_arc.length == 2 * arc.length
assert new_arc.a1 == arc.a1
assert new_arc.a2 == arc.a2
def test_to_polyline():
"""Test the Arc3D to_polyline methods."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 1.5 * math.pi, 0.5 * math.pi)
pline = arc.to_polyline(4, True)
assert isinstance(pline, Polyline2D)
assert pline.vertices[0] == arc.p1
assert pline.vertices[-1] == arc.p2
assert len(pline.vertices) == 5
assert pline.interpolated
def test_scale():
"""Test the Arc2D scale method."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
origin_1 = Point2D(2, 0)
new_arc = arc.scale(2, origin_1)
assert new_arc.c == Point2D(2, 0)
assert new_arc.r == 2
assert new_arc.length == 2 * arc.length
assert new_arc.a1 == arc.a1
assert new_arc.a2 == arc.a2
def test_arc2_init_circle():
"""Test the initalization of Arc2D objects as a circle."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 3)
assert arc.c == pt
assert arc.r == 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_move():
"""Test the Arc2D move method."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
vec_1 = Vector2D(2, 2)
new_arc = arc.move(vec_1)
assert new_arc.c == Point2D(4, 2)
assert new_arc.r == arc.r
assert new_arc.p1 == Point2D(5, 2)
assert new_arc.p2 == Point2D(3, 2)
assert new_arc.a1 == arc.a1
assert new_arc.a2 == arc.a2
def label_points_from_angles(self, angles, factor=0.8):
"""Get a list of label points from a list of angles between 0 and 360.
Args:
angles: An array of numbers between 0 and 360 for the angles of
custom angle labels to be generated for the compass.
factor: A number between 0 and 1 for the fraction of the
"""
circle = Arc2D(self.center,
self.radius * (1 + self.spacing_factor * factor))
return [
circle.point_at_angle(self._north_angle - math.radians(angle - 90))
for angle in angles
]
def test_rotate():
"""Test the Arc2D rotate method."""
pt = Point2D(2, 2)
arc = Arc2D(pt, 1, 0, math.pi)
origin_1 = Point2D(0, 2)
test_1 = arc.rotate(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.r == arc.r
test_2 = arc.rotate(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.r == arc.r
def test_arc2_closest_point():
"""Test the Arc2D closest_point method."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
assert arc.closest_point(Point2D(2, 2)) == Point2D(2, 1)
assert arc.closest_point(Point2D(3, 1)).x == pytest.approx(2.71, rel=1e-2)
assert arc.closest_point(Point2D(3, 1)).y == pytest.approx(0.71, rel=1e-2)
assert arc.closest_point(Point2D(3, -1)) == Point2D(3, 0)
assert arc.closest_point(Point2D(1, -1)).x == pytest.approx(1, rel=1e-2)
assert arc.closest_point(Point2D(1, -1)).y == pytest.approx(0, rel=1e-2)
assert arc.distance_to_point(Point2D(2, 2)) == 1
assert arc.distance_to_point(Point2D(3, 1)) == pytest.approx(0.4142,
rel=1e-2)
assert arc.distance_to_point(Point2D(3, -1)) == pytest.approx(1, rel=1e-2)
assert arc.distance_to_point(Point2D(1, -1)) == pytest.approx(1, rel=1e-2)
def test_arc2_init_reveresed():
"""Test the initalization of Arc2D objects with reversed direction."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 1.5 * math.pi, 0.5 * math.pi)
assert arc.c == pt
assert arc.r == 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.p2.x == pytest.approx(2, rel=1e-3)
assert arc.p2.y == pytest.approx(1, 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
def test_arc2_init_radius():
"""Test the initalization of Arc2D objects with a non-unit radius."""
pt = Point2D(2, 2)
arc = Arc2D(pt, 2, math.pi, 0)
assert arc.c == pt
assert arc.r == 2
assert arc.a1 == math.pi
assert arc.a2 == 0
assert arc.p1.x == pytest.approx(0, rel=1e-3)
assert arc.p1.y == pytest.approx(2, rel=1e-3)
assert arc.p2.x == pytest.approx(4, rel=1e-3)
assert arc.p2.y == pytest.approx(2, rel=1e-3)
assert arc.midpoint.x == pytest.approx(2, rel=1e-3)
assert arc.midpoint.y == pytest.approx(0, 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_arc2_init():
"""Test the initalization of Arc2D objects and basic properties."""
pt = Point2D(2, 0)
arc = Arc2D(pt, 1, 0, math.pi)
str(arc) # test the string representation of the arc
assert arc.c == pt
assert arc.r == 1
assert arc.a1 == 0
assert arc.a2 == math.pi
assert arc.p1 == Point2D(3, 0)
assert arc.p2.x == pytest.approx(1, rel=1e-3)
assert arc.p2.y == pytest.approx(0, rel=1e-3)
assert arc.midpoint == Point2D(2, 1)
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.r == 1
assert arc2.a1 == 0
assert arc2.a2 == math.pi
def inner_boundary_circle(self):
"""Get a Arc2D for the inner circle of the compass.
This is essentially a circle with the compass radius.
"""
return Arc2D(self.center, self.radius)