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A module for dealing with the polylines used throughout Matplotlib.

The primary class for polyline handling in Matplotlib is `Path`.  Almost all
vector drawing makes use of `Path`\s somewhere in the drawing pipeline.

Whilst a `Path` instance itself cannot be drawn, some `.Artist` subclasses,
such as `.PathPatch` and `.PathCollection`, can be used for convenient `Path`
visualisation.
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    A series of possibly disconnected, possibly closed, line and curve
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    These two arrays always have the same length in the first
    dimension.  For example, to represent a cubic curve, you must
    provide three vertices and three `CURVE4` codes.

    The code types are:

    - `STOP`   :  1 vertex (ignored)
        A marker for the end of the entire path (currently not required and
        ignored)

    - `MOVETO` :  1 vertex
        Pick up the pen and move to the given vertex.

    - `LINETO` :  1 vertex
        Draw a line from the current position to the given vertex.

    - `CURVE3` :  1 control point, 1 endpoint
        Draw a quadratic Bézier curve from the current position, with the given
        control point, to the given end point.

    - `CURVE4` :  2 control points, 1 endpoint
        Draw a cubic Bézier curve from the current position, with the given
        control points, to the given end point.

    - `CLOSEPOLY` : 1 vertex (ignored)
        Draw a line segment to the start point of the current polyline.

    If *codes* is None, it is interpreted as a `MOVETO` followed by a series
    of `LINETO`.

    Users of Path objects should not access the vertices and codes arrays
    directly.  Instead, they should use `iter_segments` or `cleaned` to get the
    vertex/code pairs.  This helps, in particular, to consistently handle the
    case of *codes* being None.

    Some behavior of Path objects can be controlled by rcParams. See the
    rcParams whose keys start with 'path.'.

    .. note::

        The vertices and codes arrays should be treated as
        immutable -- there are a number of optimizations and assumptions
        made up front in the constructor that will not change when the
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        Create a new path with the given vertices and codes.

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        vertices : (N, 2) array-like
            The path vertices, as an array, masked array or sequence of pairs.
            Masked values, if any, will be converted to NaNs, which are then
            handled correctly by the Agg PathIterator and other consumers of
            path data, such as :meth:`iter_segments`.
        codes : array-like or None, optional
            N-length array of integers representing the codes of the path.
            If not None, codes must be the same length as vertices.
            If None, *vertices* will be treated as a series of line segments.
        _interpolation_steps : int, optional
            Used as a hint to certain projections, such as Polar, that this
            path should be linearly interpolated immediately before drawing.
            This attribute is primarily an implementation detail and is not
            intended for public use.
        closed : bool, optional
            If *codes* is None and closed is True, vertices will be treated as
            line segments of a closed polygon.  Note that the last vertex will
            then be ignored (as the corresponding code will be set to
            `CLOSEPOLY`).
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            and codes as read-only arrays.
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        Make a compound `Path` object to draw a number of polygons with equal
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        Iterate over all curve segments in the path.

        Each iteration returns a pair ``(vertices, code)``, where ``vertices``
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        Additionally, this method can provide a number of standard cleanups and
        conversions to the path.

        Parameters
        ----------
        transform : None or :class:`~matplotlib.transforms.Transform`
            If not None, the given affine transformation will be applied to the
            path.
        remove_nans : bool, optional
            Whether to remove all NaNs from the path and skip over them using
            MOVETO commands.
        clip : None or (float, float, float, float), optional
            If not None, must be a four-tuple (x1, y1, x2, y2)
            defining a rectangle in which to clip the path.
        snap : None or bool, optional
            If True, snap all nodes to pixels; if False, don't snap them.
            If None, snap if the path contains only segments
            parallel to the x or y axes, and no more than 1024 of them.
        stroke_width : float, optional
            The width of the stroke being drawn (used for path snapping).
        simplify : None or bool, optional
            Whether to simplify the path by removing vertices
            that do not affect its appearance.  If None, use the
            :attr:`should_simplify` attribute.  See also :rc:`path.simplify`
            and :rc:`path.simplify_threshold`.
        curves : bool, optional
            If True, curve segments will be returned as curve segments.
            If False, all curves will be converted to line segments.
        sketch : None or sequence, optional
            If not None, must be a 3-tuple of the form
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        Iterate over each Bézier curve (lines included) in a `Path`.

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        **kwargs
            Forwarded to `.iter_segments`.

        Yields
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        B : `~matplotlib.bezier.BezierSegment`
            The Bézier curves that make up the current path. Note in particular
            that freestanding points are Bézier curves of order 0, and lines
            are Bézier curves of order 1 (with two control points).
        code : `~matplotlib.path.Path.code_type`
            The code describing what kind of curve is being returned.
            `MOVETO`, `LINETO`, `CURVE3`, and `CURVE4` correspond to
            Bézier curves with 1, 2, 3, and 4 control points (respectively).
            `CLOSEPOLY` is a `LINETO` with the control points correctly
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        vertex is assumed.

        Parameters
        ----------
        point : (float, float)
            The point (x, y) to check.
        transform : `~matplotlib.transforms.Transform`, optional
            If not ``None``, *point* will be compared to ``self`` transformed
            by *transform*; i.e. for a correct check, *transform* should
            transform the path into the coordinate system of *point*.
        radius : float, default: 0
            Additional margin on the path in coordinates of *point*.
            The path is extended tangentially by *radius/2*; i.e. if you would
            draw the path with a linewidth of *radius*, all points on the line
            would still be considered to be contained in the area. Conversely,
            negative values shrink the area: Points on the imaginary line
            will be considered outside the area.

        Returns
        -------
        bool

        Notes
        -----
        The current algorithm has some limitations:

        - The result is undefined for points exactly at the boundary
          (i.e. at the path shifted by *radius/2*).
        - The result is undefined if there is no enclosed area, i.e. all
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        Parameters
        ----------
        points : (N, 2) array
            The points to check. Columns contain x and y values.
        transform : `~matplotlib.transforms.Transform`, optional
            If not ``None``, *points* will be compared to ``self`` transformed
            by *transform*; i.e. for a correct check, *transform* should
            transform the path into the coordinate system of *points*.
        radius : float, default: 0
            Additional margin on the path in coordinates of *points*.
            The path is extended tangentially by *radius/2*; i.e. if you would
            draw the path with a linewidth of *radius*, all points on the line
            would still be considered to be contained in the area. Conversely,
            negative values shrink the area: Points on the imaginary line
            will be considered outside the area.

        Returns
        -------
        length-N bool array

        Notes
        -----
        The current algorithm has some limitations:

        - The result is undefined for points exactly at the boundary
          (i.e. at the path shifted by *radius/2*).
        - The result is undefined if there is no enclosed area, i.e. all
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        is useful for displaying in backends that do not support
        compound paths or Bézier curves.

        If *width* and *height* are both non-zero then the lines will
        be simplified so that vertices outside of (0, 0), (width,
        height) will be clipped.

        The resulting polygons will be simplified if the
        :attr:`Path.should_simplify` attribute of the path is `True`.

        If *closed_only* is `True` (default), only closed polygons,
        with the last point being the same as the first point, will be
        returned.  Any unclosed polylines in the path will be
        explicitly closed.  If *closed_only* is `False`, any unclosed
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            The radius of the circle.
        readonly : bool
            Whether the created path should have the "readonly" argument
            set when creating the Path instance.

        Notes
        -----
        The circle is approximated using 8 cubic Bézier curves, as described in

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        *theta2* - 360 and not a full circle plus some extra overlap.

        If *n* is provided, it is the number of spline segments to make.
        If *n* is not provided, the number of spline segments is
        determined based on the delta between *theta1* and *theta2*.

           Masionobe, L.  2003.  `Drawing an elliptical arc using
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           <https://web.archive.org/web/20190318044212/http://www.spaceroots.org/documents/ellipse/index.html>`_.
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        If *n* is provided, it is the number of spline segments to make.
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    Get bounding box of a `.PathCollection`\s internal objects.

    That is, given a sequence of `Path`\s, `.Transform`\s objects, and offsets, as found
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    Parameters
    ----------
    master_transform : `~matplotlib.transforms.Transform`
        Global transformation applied to all paths.
    paths : list of `Path`
    transforms : list of `~matplotlib.transforms.Affine2DBase`
        If non-empty, this overrides *master_transform*.
    offsets : (N, 2) array-like
    offset_transform : `~matplotlib.transforms.Affine2DBase`
        Transform applied to the offsets before offsetting the path.

    Notes
    -----
    The way that *paths*, *transforms* and *offsets* are combined follows the same
    method as for collections: each is iterated over independently, so if you have 3
    paths (A, B, C), 2 transforms (α, β) and 1 offset (O), their combinations are as
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    - (B, β, O)
    - (C, α, O)
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