Added a static method to :class:~.Circle to allow it to be defined by three points (ManimCommunity#1765)

* Added new function: perpendicular bisector

returns two points that form the perpendicular bisector of the points given

* Circle mobject may accept three points.

If the radius not specified, the three points may be given to form the circle.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update geometry.py

* Added docs

* perpendicular bisector can work in 3D

* add test file

* add test scene

* Update manim/mobject/geometry.py

Co-authored-by: Darylgolden <[email protected]>

* changed the circle points test scene to addt

* Added docs for perp bisector function space ops

* typing error

* Made a static method for a circle from three points

* Added new test

Co-authored-by: Iced-Tea3 <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Darylgolden <[email protected]>

Author: 3 people

manim/mobject/geometry.py

@@ -87,6 +87,7 @@ def construct(self):
     compass_directions,
     line_intersection,
     normalize,
+    perpendicular_bisector,
     regular_vertices,
     rotate_vector,
 )
@@ -583,6 +584,36 @@ def construct(self):
         start_angle = angle_of_vector(self.get_points()[0] - self.get_center())
         return self.point_from_proportion((angle - start_angle) / TAU)
 
+    @staticmethod
+    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)
+
 
 class Dot(Circle):
     """A circle with a very small radius.

manim/utils/space_ops.py

@@ -27,6 +27,7 @@
     "get_winding_number",
     "cross2d",
     "earclip_triangulation",
+    "perpendicular_bisector",
 ]
 
 
@@ -745,3 +746,32 @@ def earclip_triangulation(verts: np.ndarray, ring_ends: list) -> list:
 
     meta_indices = earcut(verts[indices, :2], [len(indices)])
     return [indices[mi] for mi in meta_indices]
+
+
+def perpendicular_bisector(
+    line: Sequence[np.ndarray], norm_vector=OUT
+) -> Sequence[np.ndarray]:
+    """Returns a list of two points that correspond
+    to the ends of the perpendicular bisector of the
+    two points given.
+
+    Parameters
+    ----------
+    line
+        a list of two numpy array points (corresponding
+        to the ends of a line).
+    norm_vector
+        the vector perpendicular to both the line given
+        and the perpendicular bisector.
+
+    Returns
+    -------
+    list
+        A list of two numpy array points that correspond
+        to the ends of the perpendicular bisector
+    """
+    p1 = line[0]
+    p2 = line[1]
+    direction = np.cross(p1 - p2, norm_vector)
+    m = midpoint(p1, p2)
+    return [m + direction, m - direction]

tests/control_data/graphical_units_data/geometry/CirclePointsTest.npz

@@ -49,6 +49,12 @@ def construct(self):
         self.add(circle)
 
 
+class CirclePointsTest(Scene):
+    def construct(self):
+        circle = Circle.from_three_points(LEFT, LEFT + UP, UP * 2)
+        self.add(circle)
+
+
 class DotTest(Scene):
     def construct(self):
         dot = Dot()