diff --git a/manim/mobject/graphing/functions.py b/manim/mobject/graphing/functions.py
index 8ed4b43c2e..1cd660b894 100644
--- a/manim/mobject/graphing/functions.py
+++ b/manim/mobject/graphing/functions.py
@@ -17,7 +17,9 @@
 from manim.mobject.types.vectorized_mobject import VMobject
 
 if TYPE_CHECKING:
-    from manim.typing import Point2D, Point3D
+    from typing_extensions import Self
+
+    from manim.typing import Point3D
 
 from manim.utils.color import YELLOW
 
@@ -103,7 +105,7 @@ def construct(self):
     def __init__(
         self,
         function: Callable[[float], Point3D],
-        t_range: Point2D | Point3D = (0, 1),
+        t_range: tuple[float, float] | tuple[float, float, float] = (0, 1),
         scaling: _ScaleBase = LinearBase(),
         dt: float = 1e-8,
         discontinuities: Iterable[float] | None = None,
@@ -112,9 +114,8 @@ def __init__(
         **kwargs,
     ):
         self.function = function
-        t_range = (0, 1, 0.01) if t_range is None else t_range
         if len(t_range) == 2:
-            t_range = np.array([*t_range, 0.01])
+            t_range = (*t_range, 0.01)
 
         self.scaling = scaling
 
@@ -126,13 +127,13 @@ def __init__(
 
         super().__init__(**kwargs)
 
-    def get_function(self):
+    def get_function(self) -> Callable[[float], Point3D]:
         return self.function
 
-    def get_point_from_function(self, t):
+    def get_point_from_function(self, t: float) -> Point3D:
         return self.function(t)
 
-    def generate_points(self):
+    def generate_points(self) -> Self:
         if self.discontinuities is not None:
             discontinuities = filter(
                 lambda t: self.t_min <= t <= self.t_max,
diff --git a/manim/mobject/mobject.py b/manim/mobject/mobject.py
index cf8a113104..2079de7923 100644
--- a/manim/mobject/mobject.py
+++ b/manim/mobject/mobject.py
@@ -406,14 +406,14 @@ def reset_points(self) -> None:
         """Sets :attr:`points` to be an empty array."""
         self.points = np.zeros((0, self.dim))
 
-    def init_colors(self) -> None:
+    def init_colors(self) -> object:
         """Initializes the colors.
 
         Gets called upon creation. This is an empty method that can be implemented by
         subclasses.
         """
 
-    def generate_points(self) -> None:
+    def generate_points(self) -> object:
         """Initializes :attr:`points` and therefore the shape.
 
         Gets called upon creation. This is an empty method that can be implemented by
diff --git a/manim/mobject/opengl/opengl_mobject.py b/manim/mobject/opengl/opengl_mobject.py
index 67404d763d..1f7d44d6a3 100644
--- a/manim/mobject/opengl/opengl_mobject.py
+++ b/manim/mobject/opengl/opengl_mobject.py
@@ -327,14 +327,14 @@ def init_data(self) -> None:
         self.bounding_box = np.zeros((3, 3))
         self.rgbas = np.zeros((1, 4))
 
-    def init_colors(self) -> None:
+    def init_colors(self) -> object:
         """Initializes the colors.
 
         Gets called upon creation
         """
         self.set_color(self.color, self.opacity)
 
-    def init_points(self):
+    def init_points(self) -> object:
         """Initializes :attr:`points` and therefore the shape.
 
         Gets called upon creation. This is an empty method that can be implemented by