# PolarPlane¶

Qualified name: manim.mobject.coordinate\_systems.PolarPlane

Creates a polar plane with background lines.

Parameters
• azimuth_step (Optional[float]) –

The number of divisions in the azimuth (also known as the angular coordinate or polar angle). If None is specified then it will use the default specified by azimuth_units:

• "PI radians" or "TAU radians": 20

• "degrees": 36

• "gradians": 40

• None: 1

A non-integer value will result in a partial division at the end of the circle.

• size (Optional[float]) – The diameter of the plane.

• azimuth_units (Optional[str]) –

Specifies a default labelling system for the azimuth. Choices are:

• "PI radians": Fractional labels in the interval $$\left[0, 2\pi\right]$$ with $$\pi$$ as a constant.

• "TAU radians": Fractional labels in the interval $$\left[0, \tau\right]$$ (where $$\tau = 2\pi$$) with $$\tau$$ as a constant.

• "degrees": Decimal labels in the interval $$\left[0, 360\right]$$ with a degree ($$^{\circ}$$) symbol.

• "gradians": Decimal labels in the interval $$\left[0, 400\right]$$ with a superscript “g” ($$^{g}$$).

• None: Decimal labels in the interval $$\left[0, 1\right]$$.

• azimuth_compact_fraction (bool) – If the azimuth_units choice has fractional labels, choose whether to combine the constant in a compact form $$\tfrac{xu}{y}$$ as opposed to $$\tfrac{x}{y}u$$, where $$u$$ is the constant.

• azimuth_offset (float) – The angle offset of the azimuth, expressed in radians.

• azimuth_direction (str) –

The direction of the azimuth.

• "CW": Clockwise.

• "CCW": Anti-clockwise.

• azimuth_label_buff (float) – The buffer for the azimuth labels.

• azimuth_label_font_size (float) – The font size of the azimuth labels.

• background_line_style (Optional[dict]) –

• make_smooth_after_applying_functions (bool) –

Examples

Example: PolarPlaneExample

from manim import *

class PolarPlaneExample(Scene):
def construct(self):
polarplane_pi = PolarPlane(
size=6,
azimuth_label_font_size=33.6,


References: PolarPlane

Methods

 add_coordinates Adds the coordinates. get_axes Gets the axes. get_coordinate_labels Gets labels for the coordinates :param r_values: Iterable of values along the radius, by default None. get_radian_label get_vector point_to_polar Gets polar coordinates from a point. polar_to_point Gets a point from polar coordinates. pr2pt Abbreviation for polar_to_point() prepare_for_nonlinear_transform pt2pr Abbreviation for point_to_polar()

Attributes

 animate Used to animate the application of a method. animation_overrides depth The depth of the mobject. height The height of the mobject. width The width of the mobject.

Adds the coordinates. :param r_values: Iterable of values along the radius, by default None. :param a_values: Iterable of values along the azimuth, by default None.

Parameters
• r_values (Optional[Iterable[float]]) –

• a_values (Optional[Iterable[float]]) –

get_axes()[source]

Gets the axes. :returns: A pair of axes. :rtype: VGroup

Return type

manim.mobject.types.vectorized_mobject.VGroup

get_coordinate_labels(r_values=None, a_values=None, **kwargs)[source]

Gets labels for the coordinates :param r_values: Iterable of values along the radius, by default None. :param a_values: Iterable of values along the azimuth, by default None.

Returns

Labels for the radius and azimuth values.

Return type

VDict

Parameters
• r_values (Optional[Iterable[float]]) –

• a_values (Optional[Iterable[float]]) –

point_to_polar(point)[source]

Gets polar coordinates from a point.

Parameters

point (numpy.ndarray) – The point.

Returns

The coordinate radius ($$r$$) and the coordinate azimuth ($$\theta$$).

Return type

Tuple[float, float]

Gets a point from polar coordinates.

Parameters
• radius (float) – The coordinate radius ($$r$$).

• azimuth (float) – The coordinate azimuth ($$\theta$$).

Returns

The point.

Return type

numpy.ndarray

Examples

Example: PolarToPointExample

from manim import *

class PolarToPointExample(Scene):
def construct(self):
polartopoint_vector = Vector(polarplane_pi.polar_to_point(3, PI/4))


References: PolarPlane Vector

Abbreviation for polar_to_point()

Parameters

• azimuth (float) –

Return type

numpy.ndarray

pt2pr(point)[source]

Abbreviation for point_to_polar()

Parameters

point (numpy.ndarray) –

Return type

Tuple[float, float]