Update documentation and typings for ParametricFunction (#3703)

* Update documentation and typings for ParametricFunction

* Use manim tyings

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

* fix typings

* a few doc fixes

* Update manim/mobject/graphing/functions.py

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

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

for more information, see https://pre-commit.ci

* update typings

* remove extraneous line

* update example code

* add line back for comptibility

* import TYPE_CHECKING

---------

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

manim/mobject/graphing/functions.py

@@ -5,7 +5,7 @@
 __all__ = ["ParametricFunction", "FunctionGraph", "ImplicitFunction"]
 
 
-from typing import Callable, Iterable, Sequence
+from typing import TYPE_CHECKING, Callable, Iterable, Sequence
 
 import numpy as np
 from isosurfaces import plot_isoline
@@ -14,6 +14,10 @@
 from manim.mobject.graphing.scale import LinearBase, _ScaleBase
 from manim.mobject.opengl.opengl_compatibility import ConvertToOpenGL
 from manim.mobject.types.vectorized_mobject import VMobject
+
+if TYPE_CHECKING:
+    from manim.typing import Point2D, Point3D
+
 from manim.utils.color import YELLOW
 
 
@@ -23,9 +27,9 @@ class ParametricFunction(VMobject, metaclass=ConvertToOpenGL):
     Parameters
     ----------
     function
-        The function to be plotted in the form of ``(lambda x: x**2)``
+        The function to be plotted in the form of ``(lambda t: (x(t), y(t), z(t)))``
     t_range
-        Determines the length that the function spans. By default ``[0, 1]``
+        Determines the length that the function spans in the form of (t_min, t_max, step=0.01). By default ``[0, 1]``
     scaling
         Scaling class applied to the points of the function. Default of :class:`~.LinearBase`.
     use_smoothing
@@ -49,10 +53,10 @@ class ParametricFunction(VMobject, metaclass=ConvertToOpenGL):
 
         class PlotParametricFunction(Scene):
             def func(self, t):
-                return np.array((np.sin(2 * t), np.sin(3 * t), 0))
+                return (np.sin(2 * t), np.sin(3 * t), 0)
 
             def construct(self):
-                func = ParametricFunction(self.func, t_range = np.array([0, TAU]), fill_opacity=0).set_color(RED)
+                func = ParametricFunction(self.func, t_range = (0, TAU), fill_opacity=0).set_color(RED)
                 self.add(func.scale(3))
 
     .. manim:: ThreeDParametricSpring
@@ -61,11 +65,11 @@ def construct(self):
         class ThreeDParametricSpring(ThreeDScene):
             def construct(self):
                 curve1 = ParametricFunction(
-                    lambda u: np.array([
+                    lambda u: (
                         1.2 * np.cos(u),
                         1.2 * np.sin(u),
                         u * 0.05
-                    ]), color=RED, t_range = np.array([-3*TAU, 5*TAU, 0.01])
+                    ), color=RED, t_range = (-3*TAU, 5*TAU, 0.01)
                 ).set_shade_in_3d(True)
                 axes = ThreeDAxes()
                 self.add(axes, curve1)
@@ -97,8 +101,8 @@ def construct(self):
 
     def __init__(
         self,
-        function: Callable[[float, float], float],
-        t_range: Sequence[float] | None = None,
+        function: Callable[[float], Point3D],
+        t_range: Point2D | Point3D = (0, 1),
         scaling: _ScaleBase = LinearBase(),
         dt: float = 1e-8,
         discontinuities: Iterable[float] | None = None,
@@ -107,7 +111,7 @@ def __init__(
         **kwargs,
     ):
         self.function = function
-        t_range = [0, 1, 0.01] if t_range is None else t_range
+        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])