def from_three_points(
p1: Sequence[float], p2: Sequence[float], p3: Sequence[float], **kwargs
):
"""Returns a circle passing through the specified
three points.
Example
-------
.. manim:: CircleFromPointsExample
:save_last_frame:
class CircleFromPointsExample(Scene):
def construct(self):
circle = Circle.from_three_points(LEFT, LEFT + UP, UP * 2, color=RED)
dots = VGroup(
Dot(LEFT),
Dot(LEFT + UP),
Dot(UP * 2),
)
self.add(NumberPlane(), circle, dots)
"""
center = line_intersection(
perpendicular_bisector([p1, p2]),
perpendicular_bisector([p2, p3]),
)
radius = np.linalg.norm(p1 - center)
return Circle(radius=radius, **kwargs).shift(center)
def get_arc_center(self, warning=True):
"""Looks at the normals to the first two
anchors, and finds their intersection points
"""
# First two anchors and handles
a1, h1, h2, a2 = self.points[:4]
if np.all(a1 == a2):
# For a1 and a2 to lie at the same point arc radius
# must be zero. Thus arc_center will also lie at
# that point.
return a1
# Tangent vectors
t1 = h1 - a1
t2 = h2 - a2
# Normals
n1 = rotate_vector(t1, TAU / 4)
n2 = rotate_vector(t2, TAU / 4)
try:
return line_intersection(line1=(a1, a1 + n1), line2=(a2, a2 + n2))
except Exception:
if warning:
warnings.warn("Can't find Arc center, using ORIGIN instead")
self._failed_to_get_center = True
return np.array(ORIGIN)
def __init__(
self,
line1: Line,
line2: Line,
radius: float = None,
quadrant=(1, 1),
other_angle: bool = False,
dot=False,
dot_radius=None,
dot_distance=0.55,
dot_color=WHITE,
elbow=False,
**kwargs,
):
super().__init__(**kwargs)
self.lines = (line1, line2)
self.quadrant = quadrant
self.dot_distance = dot_distance
self.elbow = elbow
inter = line_intersection(
[line1.get_start(), line1.get_end()],
[line2.get_start(), line2.get_end()],
)
if radius is None:
if quadrant[0] == 1:
dist_1 = np.linalg.norm(line1.get_end() - inter)
else:
dist_1 = np.linalg.norm(line1.get_start() - inter)
if quadrant[1] == 1:
dist_2 = np.linalg.norm(line2.get_end() - inter)
else:
dist_2 = np.linalg.norm(line2.get_start() - inter)
if np.minimum(dist_1, dist_2) < 0.6:
radius = (2 / 3) * np.minimum(dist_1, dist_2)
else:
radius = 0.4
else:
self.radius = radius
anchor_angle_1 = inter + quadrant[0] * radius * line1.get_unit_vector()
anchor_angle_2 = inter + quadrant[1] * radius * line2.get_unit_vector()
if elbow:
anchor_middle = (inter +
quadrant[0] * radius * line1.get_unit_vector() +
quadrant[1] * radius * line2.get_unit_vector())
angle_mobject = Elbow(**kwargs)
angle_mobject.set_points_as_corners(
[anchor_angle_1, anchor_middle, anchor_angle_2], )
else:
angle_1 = angle_of_vector(anchor_angle_1 - inter)
angle_2 = angle_of_vector(anchor_angle_2 - inter)
if not other_angle:
start_angle = angle_1
if angle_2 > angle_1:
angle_fin = angle_2 - angle_1
else:
angle_fin = 2 * np.pi - (angle_1 - angle_2)
else:
start_angle = angle_1
if angle_2 < angle_1:
angle_fin = -angle_1 + angle_2
else:
angle_fin = -2 * np.pi + (angle_2 - angle_1)
self.angle_value = angle_fin
angle_mobject = Arc(
radius=radius,
angle=self.angle_value,
start_angle=start_angle,
arc_center=inter,
**kwargs,
)
if dot:
if dot_radius is None:
dot_radius = radius / 10
else:
self.dot_radius = dot_radius
right_dot = Dot(ORIGIN, radius=dot_radius, color=dot_color)
dot_anchor = (
inter + (angle_mobject.get_center() - inter) /
np.linalg.norm(angle_mobject.get_center() - inter) *
radius * dot_distance)
right_dot.move_to(dot_anchor)
self.add(right_dot)
self.set_points(angle_mobject.points)