# ParametricFunction¶

Qualified name: manim.mobject.graphing.functions.ParametricFunction

class ParametricFunction(function, t_range=(0, 1), scaling=<manim.mobject.graphing.scale.LinearBase object>, dt=1e-08, discontinuities=None, use_smoothing=True, use_vectorized=False, **kwargs)[source]

Bases: VMobject

A parametric curve.

Parameters:
• function (Callable[[float], Point3D]) – The function to be plotted in the form of (lambda t: (x(t), y(t), z(t)))

• t_range (Point2D | Point3D) – Determines the length that the function spans in the form of (t_min, t_max, step=0.01). By default [0, 1]

• scaling (_ScaleBase) – Scaling class applied to the points of the function. Default of LinearBase.

• use_smoothing (bool) – Whether to interpolate between the points of the function after they have been created. (Will have odd behaviour with a low number of points)

• use_vectorized (bool) – Whether to pass in the generated t value array to the function as [t_0, t_1, ...]. Only use this if your function supports it. Output should be a numpy array of shape [[x_0, x_1, ...], [y_0, y_1, ...], [z_0, z_1, ...]] but z can also be 0 if the Axes is 2D

• discontinuities (Iterable[float] | None) – Values of t at which the function experiences discontinuity.

• dt (float) – The left and right tolerance for the discontinuities.

Examples

Example: PlotParametricFunction

from manim import *

class PlotParametricFunction(Scene):
def func(self, t):
return (np.sin(2 * t), np.sin(3 * t), 0)

def construct(self):
func = ParametricFunction(self.func, t_range = (0, TAU), fill_opacity=0).set_color(RED)
class PlotParametricFunction(Scene):
def func(self, t):
return (np.sin(2 * t), np.sin(3 * t), 0)

def construct(self):
func = ParametricFunction(self.func, t_range = (0, TAU), fill_opacity=0).set_color(RED)

Example: ThreeDParametricSpring

from manim import *

class ThreeDParametricSpring(ThreeDScene):
def construct(self):
curve1 = ParametricFunction(
lambda u: (
1.2 * np.cos(u),
1.2 * np.sin(u),
u * 0.05
), color=RED, t_range = (-3*TAU, 5*TAU, 0.01)
axes = ThreeDAxes()
self.set_camera_orientation(phi=80 * DEGREES, theta=-60 * DEGREES)
self.wait()
class ThreeDParametricSpring(ThreeDScene):
def construct(self):
curve1 = ParametricFunction(
lambda u: (
1.2 * np.cos(u),
1.2 * np.sin(u),
u * 0.05
), color=RED, t_range = (-3*TAU, 5*TAU, 0.01)
axes = ThreeDAxes()
self.set_camera_orientation(phi=80 * DEGREES, theta=-60 * DEGREES)
self.wait()

Attention

If your function has discontinuities, you’ll have to specify the location of the discontinuities manually. See the following example for guidance.

Example: DiscontinuousExample

from manim import *

class DiscontinuousExample(Scene):
def construct(self):
ax1 = NumberPlane((-3, 3), (-4, 4))
ax2 = NumberPlane((-3, 3), (-4, 4))
VGroup(ax1, ax2).arrange()
discontinuous_function = lambda x: (x ** 2 - 2) / (x ** 2 - 4)
incorrect = ax1.plot(discontinuous_function, color=RED)
correct = ax2.plot(
discontinuous_function,
discontinuities=[-2, 2],  # discontinuous points
dt=0.1,  # left and right tolerance of discontinuity
color=GREEN,
)
class DiscontinuousExample(Scene):
def construct(self):
ax1 = NumberPlane((-3, 3), (-4, 4))
ax2 = NumberPlane((-3, 3), (-4, 4))
VGroup(ax1, ax2).arrange()
discontinuous_function = lambda x: (x ** 2 - 2) / (x ** 2 - 4)
incorrect = ax1.plot(discontinuous_function, color=RED)
correct = ax2.plot(
discontinuous_function,
discontinuities=[-2, 2],  # discontinuous points
dt=0.1,  # left and right tolerance of discontinuity
color=GREEN,
)

Methods

 generate_points Initializes points and therefore the shape. get_function get_point_from_function init_points Initializes points and therefore the shape.

Attributes

 animate Used to animate the application of any method of self. animation_overrides color depth The depth of the mobject. fill_color If there are multiple colors (for gradient) this returns the first one height The height of the mobject. n_points_per_curve sheen_factor stroke_color width The width of the mobject.
_original__init__(function, t_range=(0, 1), scaling=<manim.mobject.graphing.scale.LinearBase object>, dt=1e-08, discontinuities=None, use_smoothing=True, use_vectorized=False, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

Parameters:
• function (Callable[[float], Point3D])

• t_range (Point2D | Point3D)

• scaling (_ScaleBase)

• dt (float)

• discontinuities (Iterable[float] | None)

• use_smoothing (bool)

• use_vectorized (bool)

generate_points()[source]

Initializes points and therefore the shape.

Gets called upon creation. This is an empty method that can be implemented by subclasses.

init_points()

Initializes points and therefore the shape.

Gets called upon creation. This is an empty method that can be implemented by subclasses.