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msgstr ""
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#: ../../source/reference/manim.utils.bezier.rst:2
msgid "bezier"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier:1
msgid "Utility functions related to Bézier curves."
msgstr ""

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

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.bezier:1
msgid "Classic implementation of a bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.diag_to_matrix:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.get_smooth_handle_points:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.integer_interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.inverse_interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.is_closed:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.match_interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.mid:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.quadratic_bezier_remap:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.subdivide_quadratic_bezier:0
msgid "Parameters"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.bezier:3
msgid "points defining the desired bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.get_smooth_handle_points:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:0
msgid "Returns"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.bezier:6
msgid "function describing the bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.diag_to_matrix:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.get_smooth_handle_points:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.integer_interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.inverse_interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.is_closed:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.match_interpolate:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.mid:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.quadratic_bezier_remap:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:0
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.subdivide_quadratic_bezier:0
msgid "Return type"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.diag_to_matrix:1
msgid "Converts array whose rows represent diagonal entries of a matrix into the matrix itself. See scipy.linalg.solve_banded"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.get_smooth_handle_points:1
msgid "Given some anchors (points), compute handles so the resulting bezier curve is smooth."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.get_smooth_handle_points:3
msgid "Anchors."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.get_smooth_handle_points:6
msgid "Computed handles."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.integer_interpolate:1
msgid "Alpha is a float between 0 and 1.  This returns an integer between start and end (inclusive) representing appropriate interpolation between them, along with a \"residue\" representing a new proportion between the returned integer and the next one of the list."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.integer_interpolate:8
msgid "For example, if start=0, end=10, alpha=0.46, This would return (4, 0.6)."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:1
msgid "Given an array of points which define bezier curve, and two numbers 0<=a<b<=1, return an array of the same size, which describes the portion of the original bezier curve on the interval [a, b]."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:4
msgid "This algorithm is pretty nifty, and pretty dense."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:6
msgid "set of points defining the bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:8
msgid "lower bound of the desired partial bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:10
msgid "upper bound of the desired partial bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.partial_bezier_points:13
msgid "Set of points defining the partial bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:1
msgid "Checks if a given point lies on the bezier curves with the given control points."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:3
msgid "This is done by solving the bezier polynomial with the point as the constant term; if any real roots exist, the point lies on the bezier curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:6
msgid "The Cartesian Coordinates of the point to check."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:7
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:11
msgid "The Cartesian Coordinates of the ordered control points of the bezier curve on which the point may or may not lie."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:10
#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:14
msgid "A float whose number of decimal places all values such as coordinates of points will be rounded."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.point_lies_on_bezier:13
msgid "Whether the point lies on the curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:1
msgid "Obtains the proportion along the bezier curve corresponding to a given point given the bezier curve's control points."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:4
msgid "The bezier polynomial is constructed using the coordinates of the given point as well as the bezier curve's control points. On solving the polynomial for each dimension, if there are roots common to every dimension, those roots give the proportion along the curve the point is at. If there are no real roots, the point does not lie on the curve."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:9
msgid "The Cartesian Coordinates of the point whose parameter should be obtained."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:17
msgid "List containing possible parameters (the proportions along the bezier curve) for the given point on the given bezier curve. This usually only contains one or zero elements, but if the point is, say, at the beginning/end of a closed loop, may return a list with more than 1 value, corresponding to the beginning and end etc. of the loop."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:0
msgid "Raises"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.proportions_along_bezier_curve_for_point:25
msgid "When ``point`` and the control points have different shapes."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.quadratic_bezier_remap:1
msgid "Remaps the number of curves to a higher amount by splitting bezier curves"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.quadratic_bezier_remap:3
msgid "The triplets of the quadratic bezier curves to be remapped"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.quadratic_bezier_remap:4
msgid "The number of curves that the output will contain. This needs to be higher than the current number."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:1
msgid "Split a quadratic Bézier curve at argument ``t`` into two quadratic curves."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:3
msgid "The control points of the bezier curve has shape ``[a1, h1, b1]``"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:5
msgid "The ``t``-value at which to split the Bézier curve"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:7
msgid "* *The two Bézier curves as a list of tuples,* * has the shape ``[a1, h1, b1], [a2, h2, b2]``"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:7
msgid "*The two Bézier curves as a list of tuples,*"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.split_quadratic_bezier:8
msgid "has the shape ``[a1, h1, b1], [a2, h2, b2]``"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.subdivide_quadratic_bezier:1
msgid "Subdivide a quadratic Bézier curve into ``n`` subcurves which have the same shape."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.subdivide_quadratic_bezier:3
msgid "The points at which the curve is split are located at the arguments :math:`t = i/n` for :math:`i = 1, ..., n-1`."
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.subdivide_quadratic_bezier:6
msgid "The control points of the Bézier curve in form ``[a1, h1, b1]``"
msgstr ""

#: ../../../manim/utils/bezier.py:docstring of manim.utils.bezier.subdivide_quadratic_bezier:7
msgid "The number of curves to subdivide the Bézier curve into"
msgstr ""


