typing

added typing to `qhull.py` and `polylabel.py` for debugging. simplified test cases for `ConvexHull` and `ConvexHull3D` and rewrote control data. added tip to LabeledPolygon documentation.

manim/mobject/geometry/labeled.py

@@ -247,6 +247,10 @@ class LabeledPolygram(Polygram):
         If the input is open, LabeledPolygram will attempt to close it.
         This may cause the polygon to intersect itself leading to unexpected results.
 
+    .. tip::
+        Make sure the precision corresponds to the scale of your inputs!
+        For instance, if the bounding box of your polygon stretches from 0 to 10,000, a precision of 1.0 or 10.0 should be sufficient.
+
     Examples
     --------
     .. manim:: LabeledPolygramExample

manim/mobject/three_d/polyhedra.py

@@ -388,6 +388,7 @@ class ConvexHull3D(Polyhedron):
     --------
     .. manim:: ConvexHull3DExample
         :save_last_frame:
+        :quality: high
 
         class ConvexHull3DExample(ThreeDScene):
             def construct(self):

manim/utils/polylabel.py

@@ -2,14 +2,24 @@
 from __future__ import annotations
 
 from queue import PriorityQueue
+from typing import TYPE_CHECKING
 
 import numpy as np
 
+if TYPE_CHECKING:
+    from manim.typing import Point3D
 
-class Polygon:
-    """Polygon class to compute and store associated data."""
 
-    def __init__(self, rings):
+class Polygon:
+    def __init__(self, rings: list[np.ndarray]) -> None:
+        """
+        Initializes the Polygon with the given rings.
+
+        Parameters
+        ----------
+        rings : list[np.ndarray]
+            List of arrays, each representing a polygonal ring
+        """
         # Flatten Array
         csum = np.cumsum([ring.shape[0] for ring in rings])
         self.array = np.concatenate(rings, axis=0)
@@ -32,14 +42,14 @@ def __init__(self, rings):
             cy = np.sum((y + yr) * factor) / (6.0 * self.area)
             self.centroid = np.array([cx, cy])
 
-    def compute_distance(self, point):
+    def compute_distance(self, point: np.ndarray) -> float:
         """Compute the minimum distance from a point to the polygon."""
         scalars = np.einsum("ij,ij->i", self.norm, point - self.start)
         clips = np.clip(scalars, 0, 1).reshape(-1, 1)
         d = np.min(np.linalg.norm(self.start + self.diff * clips - point, axis=1))
         return d if self.inside(point) else -d
 
-    def inside(self, point):
+    def inside(self, point: np.ndarray) -> bool:
         """Check if a point is inside the polygon."""
         # Views
         px, py = point
@@ -53,29 +63,55 @@ def inside(self, point):
 
 
 class Cell:
-    """Cell class to represent a square in the grid covering the polygon."""
-
-    def __init__(self, c, h, polygon):
+    def __init__(self, c: np.ndarray, h: float, polygon: Polygon) -> None:
+        """
+        Initializes the Cell, a square in the mesh covering the polygon.
+
+        Parameters
+        ----------
+        c : np.ndarray
+            Center coordinates of the Cell.
+        h : float
+            Half-Size of the Cell.
+        polygon : Polygon
+            Polygon object for which the distance is computed.
+        """
         self.c = c
         self.h = h
         self.d = polygon.compute_distance(self.c)
         self.p = self.d + self.h * np.sqrt(2)
 
-    def __lt__(self, other):
+    def __lt__(self, other: Cell) -> bool:
         return self.d < other.d
 
-    def __gt__(self, other):
+    def __gt__(self, other: Cell) -> bool:
         return self.d > other.d
 
-    def __le__(self, other):
+    def __le__(self, other: Cell) -> bool:
         return self.d <= other.d
 
-    def __ge__(self, other):
+    def __ge__(self, other: Cell) -> bool:
         return self.d >= other.d
 
 
-def PolyLabel(rings, precision=1):
-    """Find the pole of inaccessibility using a grid approach."""
+def PolyLabel(rings: list[list[Point3D]], precision: float = 0.01) -> Cell:
+    """
+    Finds the pole of inaccessibility (the point that is farthest from the edges of the polygon)
+    using an iterative grid-based approach.
+
+    Parameters
+    ----------
+    rings : list[list[Point3D]]
+        A list of lists, where each list is a sequence of points representing the rings of the polygon.
+        Typically, multiple rings indicate holes in the polygon.
+    precision : float, optional
+        The precision of the result (default is 0.01).
+
+    Returns
+    -------
+    Cell
+        A Cell containing the pole of inaccessibility to a given precision.
+    """
     # Precompute Polygon Data
     array = [np.array(ring)[:, :2] for ring in rings]
     polygon = Polygon(array)

manim/utils/qhull.py

@@ -5,30 +5,30 @@
 
 
 class Point:
-    def __init__(self, coordinates):
+    def __init__(self, coordinates: np.ndarray) -> None:
         self.coordinates = coordinates
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         return hash(self.coordinates.tobytes())
 
-    def __eq__(self, other):
+    def __eq__(self, other: Point) -> bool:
         return np.array_equal(self.coordinates, other.coordinates)
 
 
 class SubFacet:
-    def __init__(self, coordinates):
+    def __init__(self, coordinates: np.ndarray) -> None:
         self.coordinates = coordinates
         self.points = frozenset(Point(c) for c in coordinates)
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         return hash(self.points)
 
-    def __eq__(self, other):
+    def __eq__(self, other: SubFacet) -> bool:
         return self.points == other.points
 
 
 class Facet:
-    def __init__(self, coordinates, normal=None, internal=None):
+    def __init__(self, coordinates: np.ndarray, internal: np.ndarray) -> None:
         self.coordinates = coordinates
         self.center = np.mean(coordinates, axis=0)
         self.normal = self.compute_normal(internal)
@@ -37,41 +37,68 @@ def __init__(self, coordinates, normal=None, internal=None):
             for i in range(self.coordinates.shape[0])
         )
 
-    def compute_normal(self, internal):
+    def compute_normal(self, internal: np.ndarray) -> np.ndarray:
         centered = self.coordinates - self.center
         _, _, vh = np.linalg.svd(centered)
         normal = vh[-1, :]
         normal /= np.linalg.norm(normal)
 
+        # If the normal points towards the internal point, flip it!
         if np.dot(normal, self.center - internal) < 0:
             normal *= -1
 
         return normal
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         return hash(self.subfacets)
 
-    def __eq__(self, other):
+    def __eq__(self, other: Facet) -> bool:
         return self.subfacets == other.subfacets
 
 
 class Horizon:
-    def __init__(self):
-        self.facets = set()
-        self.boundary = []
+    def __init__(self) -> None:
+        self.facets: set[Facet] = set()
+        self.boundary: list[SubFacet] = []
 
 
 class QuickHull:
-    def __init__(self, tolerance=1e-5):
-        self.facets = []
-        self.removed = set()
-        self.outside = {}
-        self.neighbors = {}
-        self.unclaimed = None
-        self.internal = None
+    """
+    QuickHull algorithm for constructing a convex hull from a set of points.
+
+    Parameters
+    ----------
+    tolerance: float, optional
+        A tolerance threshold for determining when points lie on the convex hull (default is 1e-5).
+
+    Attributes
+    ----------
+    facets: list[Facet]
+        List of facets considered.
+    removed: set[Facet]
+        Set of internal facets that have been removed from the hull during the construction process.
+    outside: dict[Facet, tuple[np.ndarray, np.ndarray | None]]
+        Dictionary mapping each facet to its outside points and eye point.
+    neighbors: dict[SubFacet, set[Facet]]
+        Mapping of subfacets to their neighboring facets. Each subfacet links precisely two neighbors.
+    unclaimed: np.ndarray | None
+        Points that have not yet been classified as inside or outside the current hull.
+    internal: np.ndarray | None
+        An internal point (i.e., the center of the initial simplex) used as a reference during hull construction.
+    tolerance: float
+        The tolerance used to determine if points are considered outside the current hull.
+    """
+
+    def __init__(self, tolerance: float = 1e-5) -> None:
+        self.facets: list[Facet] = []
+        self.removed: set[Facet] = set()
+        self.outside: dict[Facet, tuple[np.ndarray, np.ndarray | None]] = {}
+        self.neighbors: dict[SubFacet, set[Facet]] = {}
+        self.unclaimed: np.ndarray | None = None
+        self.internal: np.ndarray | None = None
         self.tolerance = tolerance
 
-    def initialize(self, points):
+    def initialize(self, points: np.ndarray) -> None:
         # Sample Points
         simplex = points[
             np.random.choice(points.shape[0], points.shape[1] + 1, replace=False)
@@ -90,7 +117,7 @@ def initialize(self, points):
             for sf in f.subfacets:
                 self.neighbors.setdefault(sf, set()).add(f)
 
-    def classify(self, facet):
+    def classify(self, facet: Facet) -> None:
         if not self.unclaimed.size:
             self.outside[facet] = (None, None)
             return
@@ -106,14 +133,19 @@ def classify(self, facet):
         self.outside[facet] = (outside, eye)
         self.unclaimed = self.unclaimed[~mask]
 
-    def compute_horizon(self, eye, start_facet):
+    def compute_horizon(self, eye: np.ndarray, start_facet: Facet) -> Horizon:
         horizon = Horizon()
         self._recursive_horizon(eye, start_facet, horizon)
         return horizon
 
-    def _recursive_horizon(self, eye, facet, horizon):
+    def _recursive_horizon(
+        self, eye: np.ndarray, facet: Facet, horizon: Horizon
+    ) -> int:
+        visible = np.dot(facet.normal, eye - facet.center) > 0
+        if not visible:
+            return False
         # If the eye is visible from the facet...
-        if np.dot(facet.normal, eye - facet.center) > 0:
+        else:
             # Label the facet as visible and cross each edge
             horizon.facets.add(facet)
             for subfacet in facet.subfacets:
@@ -123,11 +155,9 @@ def _recursive_horizon(self, eye, facet, horizon):
                     eye, neighbor, horizon
                 ):
                     horizon.boundary.append(subfacet)
-            return 1
-        else:
-            return 0
+            return True
 
-    def build(self, points):
+    def build(self, points: np.ndarray) -> np.ndarray | None:
         num, dim = points.shape
         if (dim == 0) or (num < dim + 1):
             raise ValueError("Not enough points supplied to build Convex Hull!")

tests/test_graphical_units/test_geometry.py

@@ -142,11 +142,11 @@ def test_RoundedRectangle(scene):
 def test_ConvexHull(scene):
     a = ConvexHull(
         *[
-            np.array([-2.753, -0.612, 0]),
-            np.array([0.226, -1.766, 0]),
-            np.array([1.950, 1.260, 0]),
-            np.array([-2.754, 0.949, 0]),
-            np.array([1.679, 2.220, 0]),
+            [-2.7, -0.6, 0],
+            [0.2, -1.7, 0],
+            [1.9, 1.2, 0],
+            [-2.7, 0.9, 0],
+            [1.6, 2.2, 0],
         ]
     )
     scene.add(a)

tests/test_graphical_units/test_polyhedra.py

@@ -24,3 +24,17 @@ def test_Icosahedron(scene):
 @frames_comparison
 def test_Dodecahedron(scene):
     scene.add(Dodecahedron())
+
+
+@frames_comparison
+def test_ConvexHull3D(scene):
+    a = ConvexHull3D(
+        *[
+            [-2.7, -0.6, 3.5],
+            [0.2, -1.7, -2.8],
+            [1.9, 1.2, 0.7],
+            [-2.7, 0.9, 1.9],
+            [1.6, 2.2, -4.2],
+        ]
+    )
+    scene.add(a)