
msgid ""
msgstr ""
"Project-Id-Version: Manim \n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"

#: ../../source/reference/manim.utils.space_ops.rst:2
msgid "space\\_ops"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops:1
msgid "Utility functions for two- and three-dimensional vectors."
msgstr ""

#: ../../source/reference/manim.utils.space_ops.rst:20
msgid "Functions"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.R3_to_complex:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_axis_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_between_vectors:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_of_vector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.cartesian_to_spherical:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.center_of_mass:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.compass_directions:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.complex_to_R3:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.earclip_triangulation:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.find_intersection:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_winding_number:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.midpoint:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.norm_squared:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize_along_axis:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.perpendicular_bisector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_conjugate:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_mult:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_about_z:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace_direction:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.thick_diagonal:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.z_to_vector:0
msgid "Parameters"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.R3_to_complex:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_axis_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_between_vectors:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_of_vector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.cartesian_to_spherical:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.center_of_mass:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.compass_directions:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.complex_to_R3:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.earclip_triangulation:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.find_intersection:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_winding_number:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.midpoint:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.norm_squared:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize_along_axis:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.perpendicular_bisector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_conjugate:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_mult:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_about_z:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace_direction:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.thick_diagonal:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.z_to_vector:0
msgid "Return type"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_axis_from_quaternion:1
msgid "Gets angle and axis from a quaternion."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_axis_from_quaternion:3
msgid "The quaternion from which we get the angle and axis."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_axis_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_between_vectors:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_of_vector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.center_of_mass:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.compass_directions:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.earclip_triangulation:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.midpoint:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize_along_axis:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.perpendicular_bisector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_conjugate:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_mult:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_about_z:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose_from_quaternion:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace_direction:0
msgid "Returns"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_axis_from_quaternion:5
msgid "Gives the angle and axis"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_between_vectors:1
msgid "Returns the angle between two vectors. This angle will always be between 0 and pi"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_between_vectors:4
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:3
msgid "The first vector."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_between_vectors:5
msgid "The second vector."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_between_vectors:7
msgid "The angle between the vectors."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_of_vector:1
msgid "Returns polar coordinate theta when vector is projected on xy plane."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_of_vector:3
msgid "The vector to find the angle for."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.angle_of_vector:5
msgid "The angle of the vector projected."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.cartesian_to_spherical:1
msgid "Returns an array of numbers corresponding to each polar coordinate value (distance, phi, theta)."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.cartesian_to_spherical:4
msgid "A numpy array ``[x, y, z]``."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.center_of_mass:1
msgid "Gets the center of mass of the points in space."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.center_of_mass:3
msgid "The points to find the center of mass from."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.center_of_mass:5
msgid "The center of mass of the points."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.compass_directions:1
msgid "Finds the cardinal directions using tau."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.compass_directions:3
msgid "The amount to be rotated, by default 4"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.compass_directions:4
msgid "The direction for the angle to start with, by default RIGHT"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.compass_directions:6
msgid "The angle which has been rotated."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.earclip_triangulation:1
msgid "Returns a list of indices giving a triangulation of a polygon, potentially with holes."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.earclip_triangulation:4
msgid "verts is a numpy array of points."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.earclip_triangulation:5
msgid "ring_ends is a list of indices indicating where"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.earclip_triangulation:8
msgid "A list of indices giving a triangulation of a polygon."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.find_intersection:1
msgid "Return the intersection of a line passing through p0 in direction v0 with one passing through p1 in direction v1 (or array of intersections from arrays of such points/directions). For 3d values, it returns the point on the ray p0 + v0 * t closest to the ray p1 + v1 * t"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:1
msgid "Gets the unit normal of the vectors."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:4
msgid "The second vector"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:5
msgid "[description], by default 1e-6"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.get_unit_normal:7
msgid "The normal of the two vectors."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:1
msgid "Returns the intersection point of two lines, each defined by a pair of distinct points lying on the line."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:4
msgid "A list of two points that determine the first line."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:5
msgid "A list of two points that determine the second line."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:7
msgid "The intersection points of the two lines which are intersecting."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:0
#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:0
msgid "Raises"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.line_intersection:10
msgid "Error is produced if the two lines don't intersect with each other     or if the coordinates don't lie on the xy-plane."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.midpoint:1
msgid "Gets the midpoint of two points."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.midpoint:3
msgid "The first point."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.midpoint:4
msgid "The second point."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.midpoint:6
msgid "The midpoint of the points"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize_along_axis:1
msgid "Normalizes an array with the provided axis."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize_along_axis:3
msgid "The array which has to be normalized."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize_along_axis:4
msgid "The axis to be normalized to."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.normalize_along_axis:6
msgid "Array which has been normalized according to the axis."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.perpendicular_bisector:1
msgid "Returns a list of two points that correspond to the ends of the perpendicular bisector of the two points given."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.perpendicular_bisector:5
msgid "a list of two numpy array points (corresponding to the ends of a line)."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.perpendicular_bisector:7
msgid "the vector perpendicular to both the line given and the perpendicular bisector."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.perpendicular_bisector:10
msgid "A list of two numpy array points that correspond to the ends of the perpendicular bisector"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_conjugate:1
msgid "Used for finding the conjugate of the quaternion"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_conjugate:3
msgid "The quaternion for which you want to find the conjugate for."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_conjugate:5
msgid "The conjugate of the quaternion."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:1
msgid "Gets a quaternion from an angle and an axis. For more information, check `this Wikipedia page <https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles>`__."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:5
msgid "The angle for the quaternion."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:6
msgid "The axis for the quaternion"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:7
msgid "Checks whether the axis is normalized, by default False"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_from_angle_axis:10
msgid "Gives back a quaternion from the angle and axis"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_mult:1
msgid "Gets the Hamilton product of the quaternions provided. For more information, check `this Wikipedia page <https://en.wikipedia.org/wiki/Quaternion>`__."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.quaternion_mult:5
msgid "Returns a list of product of two quaternions."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:1
msgid "Generates regularly spaced vertices around a circle centered at the origin."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:3
msgid "The number of vertices"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:4
msgid "The radius of the circle that the vertices are placed on."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:5
msgid "The angle the vertices start at.  If unspecified, for even ``n`` values, ``0`` will be used. For odd ``n`` values, 90 degrees is used."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:5
msgid "The angle the vertices start at."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:7
msgid "If unspecified, for even ``n`` values, ``0`` will be used. For odd ``n`` values, 90 degrees is used."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:10
msgid "* **vertices** (:class:`numpy.ndarray`) -- The regularly spaced vertices. * **start_angle** (:class:`float`) -- The angle the vertices start at."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:10
msgid "**vertices** (:class:`numpy.ndarray`) -- The regularly spaced vertices."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.regular_vertices:11
msgid "**start_angle** (:class:`float`) -- The angle the vertices start at."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:1
msgid "Function for rotating a vector."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:3
msgid "The vector to be rotated."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:4
msgid "The angle to be rotated by."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:5
msgid "The axis to be rotated, by default OUT"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:7
msgid "The rotated vector with provided angle and axis."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotate_vector:10
msgid "If vector is not of dimension 2 or 3."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_about_z:1
msgid "Returns a rotation matrix for a given angle."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_about_z:3
msgid "Angle for the rotation matrix."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_about_z:6
msgid "Gives back the rotated matrix."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix:1
msgid "Rotation in R^3 about a specified axis of rotation."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose_from_quaternion:1
msgid "Converts the quaternion, quat, to an equivalent rotation matrix representation. For more information, check `this page <https://in.mathworks.com/help/driving/ref/quaternion.rotmat.html>`_."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose_from_quaternion:5
msgid "The quaternion which is to be converted."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.rotation_matrix_transpose_from_quaternion:7
msgid "Gives back the Rotation matrix representation, returned as a 3-by-3 matrix or 3-by-3-by-N multidimensional array."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace:1
msgid "2D implementation of the shoelace formula."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace:3
msgid "Returns signed area."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace_direction:1
msgid "Uses the area determined by the shoelace method to determine whether the input set of points is directed clockwise or counterclockwise."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.shoelace_direction:4
msgid "Either ``\"CW\"`` or ``\"CCW\"``."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:1
msgid "Returns a numpy array ``[x, y, z]`` based on the spherical coordinates given."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:4
msgid "A list of three floats that correspond to the following:  r - The distance between the point and the origin.  theta - The azimuthal angle of the point to the positive x-axis.  phi - The vertical angle of the point to the positive z-axis."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:4
msgid "A list of three floats that correspond to the following:"
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:6
msgid "r - The distance between the point and the origin."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:8
msgid "theta - The azimuthal angle of the point to the positive x-axis."
msgstr ""

#: ../../../manim/utils/space_ops.py:docstring of manim.utils.space_ops.spherical_to_cartesian:10
msgid "phi - The vertical angle of the point to the positive z-axis."
msgstr ""


