# matplotlib.transforms¶

Matplotlib includes a framework for arbitrary geometric transformations that is used determine the final position of all elements drawn on the canvas.

Transforms are composed into trees of TransformNode objects whose actual value depends on their children. When the contents of children change, their parents are automatically invalidated. The next time an invalidated transform is accessed, it is recomputed to reflect those changes. This invalidation/caching approach prevents unnecessary recomputations of transforms, and contributes to better interactive performance.

For example, here is a graph of the transform tree used to plot data to the graph:

The framework can be used for both affine and non-affine transformations. However, for speed, we want use the backend renderers to perform affine transformations whenever possible. Therefore, it is possible to perform just the affine or non-affine part of a transformation on a set of data. The affine is always assumed to occur after the non-affine. For any transform:

full transform == non-affine part + affine part


The backends are not expected to handle non-affine transformations themselves.

class matplotlib.transforms.Affine2D(matrix=None, **kwargs)[source]

A mutable 2D affine transformation.

Initialize an Affine transform from a 3x3 numpy float array:

a c e
b d f
0 0 1


If matrix is None, initialize with the identity transform.

__init__(matrix=None, **kwargs)[source]

Initialize an Affine transform from a 3x3 numpy float array:

a c e
b d f
0 0 1


If matrix is None, initialize with the identity transform.

__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

clear()[source]

Reset the underlying matrix to the identity transform.

static from_values(a, b, c, d, e, f)[source]

Create a new Affine2D instance from the given values:

a c e
b d f
0 0 1


.

get_matrix()[source]

Get the underlying transformation matrix as a 3x3 numpy array:

a c e
b d f
0 0 1


.

static identity()[source]

Return a new Affine2D object that is the identity transform.

Unless this transform will be mutated later on, consider using the faster IdentityTransform class instead.

rotate(theta)[source]

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

rotate_around(x, y, theta)[source]

Add a rotation (in radians) around the point (x, y) in place.

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

rotate_deg(degrees)[source]

Add a rotation (in degrees) to this transform in place.

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

rotate_deg_around(x, y, degrees)[source]

Add a rotation (in degrees) around the point (x, y) in place.

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

scale(sx, sy=None)[source]

If sy is None, the same scale is applied in both the x- and y-directions.

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

set(other)[source]

Set this transformation from the frozen copy of another Affine2DBase object.

set_matrix(mtx)[source]

Set the underlying transformation matrix from a 3x3 numpy array:

a c e
b d f
0 0 1


.

skew(xShear, yShear)[source]

xShear and yShear are the shear angles along the x- and y-axes, respectively, in radians.

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

skew_deg(xShear, yShear)[source]

xShear and yShear are the shear angles along the x- and y-axes, respectively, in degrees.

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

translate(tx, ty)[source]

Returns self, so this method can easily be chained with more calls to rotate(), rotate_deg(), translate() and scale().

class matplotlib.transforms.Affine2DBase(*args, **kwargs)[source]

The base class of all 2D affine transformations.

2D affine transformations are performed using a 3x3 numpy array:

a c e
b d f
0 0 1


This class provides the read-only interface. For a mutable 2D affine transformation, use Affine2D.

Subclasses of this class will generally only need to override a constructor and get_matrix() that generates a custom 3x3 matrix.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__module__ = 'matplotlib.transforms'
frozen()[source]

Return a frozen copy of this transform node. The frozen copy will not be updated when its children change. Useful for storing a previously known state of a transform where copy.deepcopy() might normally be used.

has_inverse = True
input_dims = 2
inverted()[source]

Return the corresponding inverse transformation.

It holds x == self.inverted().transform(self.transform(x)).

The return value of this method should be treated as temporary. An update to self does not cause a corresponding update to its inverted copy.

property is_separable

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

static matrix_from_values(*args, **kwargs)[source]

[Deprecated] Create a new transformation matrix as a 3x3 numpy array of the form:

a c e
b d f
0 0 1


Notes

Deprecated since version 3.2.

output_dims = 2
to_values()[source]

Return the values of the matrix as an (a, b, c, d, e, f) tuple.

transform_affine(points)[source]

Apply only the affine part of this transformation on the given array of values.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally a no-op. In affine transformations, this is equivalent to transform(values).

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
class matplotlib.transforms.AffineBase(*args, **kwargs)[source]

The base class of all affine transformations of any number of dimensions.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__array__(*args, **kwargs)[source]

Array interface to get at this Transform's affine matrix.

__eq__(other)[source]

Return self==value.

__hash__ = None
__init__(*args, **kwargs)[source]
Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__module__ = 'matplotlib.transforms'
get_affine()[source]

Get the affine part of this transform.

is_affine = True
transform(values)[source]

Apply this transformation on the given array of values.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_affine(values)[source]

Apply only the affine part of this transformation on the given array of values.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally a no-op. In affine transformations, this is equivalent to transform(values).

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_non_affine(points)[source]

Apply only the non-affine part of this transformation.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally equivalent to transform(values). In affine transformations, this is always a no-op.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_path(path)[source]

Apply the transform to Path path, returning a new Path.

In some cases, this transform may insert curves into the path that began as line segments.

transform_path_affine(path)[source]

Apply the affine part of this transform to Path path, returning a new Path.

transform_path(path) is equivalent to transform_path_affine(transform_path_non_affine(values)).

transform_path_non_affine(path)[source]

Apply the non-affine part of this transform to Path path, returning a new Path.

transform_path(path) is equivalent to transform_path_affine(transform_path_non_affine(values)).

class matplotlib.transforms.AffineDeltaTransform(transform, **kwargs)[source]

A transform wrapper for transforming displacements between pairs of points.

This class is intended to be used to transform displacements ("position deltas") between pairs of points (e.g., as the offset_transform of Collections): given a transform t such that t = AffineDeltaTransform(t) + offset, AffineDeltaTransform satisfies AffineDeltaTransform(a - b) == AffineDeltaTransform(a) - AffineDeltaTransform(b).

This is implemented by forcing the offset components of the transform matrix to zero.

This class is experimental as of 3.3, and the API may change.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__init__(transform, **kwargs)[source]
Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

get_matrix()[source]

Get the matrix for the affine part of this transform.

class matplotlib.transforms.Bbox(points, **kwargs)[source]

A mutable bounding box.

Examples

Create from known bounds

The default constructor takes the boundary "points" [[xmin, ymin], [xmax, ymax]].

>>> Bbox([[1, 1], [3, 7]])
Bbox([[1.0, 1.0], [3.0, 7.0]])


Alternatively, a Bbox can be created from the flattened points array, the so-called "extents" (xmin, ymin, xmax, ymax)

>>> Bbox.from_extents(1, 1, 3, 7)
Bbox([[1.0, 1.0], [3.0, 7.0]])


or from the "bounds" (xmin, ymin, width, height).

>>> Bbox.from_bounds(1, 1, 2, 6)
Bbox([[1.0, 1.0], [3.0, 7.0]])


Create from collections of points

The "empty" object for accumulating Bboxs is the null bbox, which is a stand-in for the empty set.

>>> Bbox.null()
Bbox([[inf, inf], [-inf, -inf]])


Adding points to the null bbox will give you the bbox of those points.

>>> box = Bbox.null()
>>> box.update_from_data_xy([[1, 1]])
>>> box
Bbox([[1.0, 1.0], [1.0, 1.0]])
>>> box.update_from_data_xy([[2, 3], [3, 2]], ignore=False)
>>> box
Bbox([[1.0, 1.0], [3.0, 3.0]])


Setting ignore=True is equivalent to starting over from a null bbox.

>>> box.update_from_data_xy([[1, 1]], ignore=True)
>>> box
Bbox([[1.0, 1.0], [1.0, 1.0]])


Warning

It is recommended to always specify ignore explicitly. If not, the default value of ignore can be changed at any time by code with access to your Bbox, for example using the method ignore.

Properties of the null bbox

Note

The current behavior of Bbox.null() may be surprising as it does not have all of the properties of the "empty set", and as such does not behave like a "zero" object in the mathematical sense. We may change that in the future (with a deprecation period).

The null bbox is the identity for intersections

>>> Bbox.intersection(Bbox([[1, 1], [3, 7]]), Bbox.null())
Bbox([[1.0, 1.0], [3.0, 7.0]])


except with itself, where it returns the full space.

>>> Bbox.intersection(Bbox.null(), Bbox.null())
Bbox([[-inf, -inf], [inf, inf]])


A union containing null will always return the full space (not the other set!)

>>> Bbox.union([Bbox([[0, 0], [0, 0]]), Bbox.null()])
Bbox([[-inf, -inf], [inf, inf]])

Parameters: pointsndarrayA 2x2 numpy array of the form [[x0, y0], [x1, y1]].
__format__(fmt)[source]

Default object formatter.

__init__(points, **kwargs)[source]
Parameters: pointsndarrayA 2x2 numpy array of the form [[x0, y0], [x1, y1]].
__module__ = 'matplotlib.transforms'
__repr__()[source]

Return repr(self).

__str__()[source]

Return str(self).

property bounds

Return (x0, y0, width, height).

static from_bounds(x0, y0, width, height)[source]

Create a new Bbox from x0, y0, width and height.

width and height may be negative.

static from_extents(*args)[source]

Create a new Bbox from left, bottom, right and top.

The y-axis increases upwards.

get_points()[source]

Get the points of the bounding box directly as a numpy array of the form: [[x0, y0], [x1, y1]].

ignore(value)[source]

Set whether the existing bounds of the box should be ignored by subsequent calls to update_from_data_xy().

valuebool
property intervalx

The pair of x coordinates that define the bounding box.

This is not guaranteed to be sorted from left to right.

property intervaly

The pair of y coordinates that define the bounding box.

This is not guaranteed to be sorted from bottom to top.

property minpos
property minposx
property minposy
mutated()[source]

Return whether the bbox has changed since init.

mutatedx()[source]

Return whether the x-limits have changed since init.

mutatedy()[source]

Return whether the y-limits have changed since init.

static null()[source]

Create a new null Bbox from (inf, inf) to (-inf, -inf).

property p0

The first pair of (x, y) coordinates that define the bounding box.

This is not guaranteed to be the bottom-left corner (for that, use min).

property p1

The second pair of (x, y) coordinates that define the bounding box.

This is not guaranteed to be the top-right corner (for that, use max).

set(other)[source]

Set this bounding box from the "frozen" bounds of another Bbox.

set_points(points)[source]

Set the points of the bounding box directly from a numpy array of the form: [[x0, y0], [x1, y1]]. No error checking is performed, as this method is mainly for internal use.

static unit()[source]

Create a new unit Bbox from (0, 0) to (1, 1).

update_from_data_xy(xy, ignore=None, updatex=True, updatey=True)[source]

Update the bounds of the Bbox based on the passed in data. After updating, the bounds will have positive width and height; x0 and y0 will be the minimal values.

Parameters: xyndarrayA numpy array of 2D points. ignorebool, optional When True, ignore the existing bounds of the Bbox. When False, include the existing bounds of the Bbox. When None, use the last value passed to ignore(). updatex, updateybool, default: TrueWhen True, update the x/y values.
update_from_path(path, ignore=None, updatex=True, updatey=True)[source]

Update the bounds of the Bbox to contain the vertices of the provided path. After updating, the bounds will have positive width and height; x0 and y0 will be the minimal values.

Parameters: pathPath ignorebool, optional when True, ignore the existing bounds of the Bbox. when False, include the existing bounds of the Bbox. when None, use the last value passed to ignore(). updatex, updateybool, default: TrueWhen True, update the x/y values.
property x0

The first of the pair of x coordinates that define the bounding box.

This is not guaranteed to be less than x1 (for that, use xmin).

property x1

The second of the pair of x coordinates that define the bounding box.

This is not guaranteed to be greater than x0 (for that, use xmax).

property y0

The first of the pair of y coordinates that define the bounding box.

This is not guaranteed to be less than y1 (for that, use ymin).

property y1

The second of the pair of y coordinates that define the bounding box.

This is not guaranteed to be greater than y0 (for that, use ymax).

class matplotlib.transforms.BboxBase(shorthand_name=None)[source]

The base class of all bounding boxes.

This class is immutable; Bbox is a mutable subclass.

The canonical representation is as two points, with no restrictions on their ordering. Convenience properties are provided to get the left, bottom, right and top edges and width and height, but these are not stored explicitly.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__array__(*args, **kwargs)[source]
__module__ = 'matplotlib.transforms'
anchored(c, container=None)[source]

Return a copy of the Bbox shifted to position c within container.

Parameters: c(float, float) or strMay be either: A sequence (cx, cy) where cx and cy range from 0 to 1, where 0 is left or bottom and 1 is right or top a string: - 'C' for centered - 'S' for bottom-center - 'SE' for bottom-left - 'E' for left - etc. containerBbox, optionalThe box within which the Bbox is positioned; it defaults to the initial Bbox.
property bounds
coefs = {'C': (0.5, 0.5), 'E': (1.0, 0.5), 'N': (0.5, 1.0), 'NE': (1.0, 1.0), 'NW': (0, 1.0), 'S': (0.5, 0), 'SE': (1.0, 0), 'SW': (0, 0), 'W': (0, 0.5)}
contains(x, y)[source]

Return whether (x, y) is in the bounding box or on its edge.

containsx(x)[source]

Return whether x is in the closed (x0, x1) interval.

containsy(y)[source]

Return whether y is in the closed (y0, y1) interval.

corners()[source]

Return the corners of this rectangle as an array of points.

Specifically, this returns the array [[x0, y0], [x0, y1], [x1, y0], [x1, y1]].

count_contains(vertices)[source]

Count the number of vertices contained in the Bbox. Any vertices with a non-finite x or y value are ignored.

Parameters: verticesNx2 Numpy array.
count_overlaps(bboxes)[source]

Count the number of bounding boxes that overlap this one.

Parameters: bboxessequence of BboxBase
expanded(sw, sh)[source]

Construct a Bbox by expanding this one around its center by the factors sw and sh.

property extents

Return (x0, y0, x1, y1).

frozen()[source]

The base class for anything that participates in the transform tree and needs to invalidate its parents or be invalidated. This includes classes that are not really transforms, such as bounding boxes, since some transforms depend on bounding boxes to compute their values.

fully_contains(x, y)[source]

Return whether x, y is in the bounding box, but not on its edge.

fully_containsx(x)[source]

Return whether x is in the open (x0, x1) interval.

fully_containsy(y)[source]

Return whether y is in the open (y0, y1) interval.

fully_overlaps(other)[source]

Return whether this bounding box overlaps with the other bounding box, not including the edges.

Parameters: otherBboxBase
get_points()[source]
property height

The (signed) height of the bounding box.

static intersection(bbox1, bbox2)[source]

Return the intersection of bbox1 and bbox2 if they intersect, or None if they don't.

property intervalx

The pair of x coordinates that define the bounding box.

This is not guaranteed to be sorted from left to right.

property intervaly

The pair of y coordinates that define the bounding box.

This is not guaranteed to be sorted from bottom to top.

inverse_transformed(transform)[source]

[Deprecated] Construct a Bbox by statically transforming this one by the inverse of transform.

Notes

Deprecated since version 3.3.

is_affine = True
is_bbox = True
is_unit()[source]

[Deprecated] Return whether this is the unit box (from (0, 0) to (1, 1)).

Notes

Deprecated since version 3.2.

property max

The top-right corner of the bounding box.

property min

The bottom-left corner of the bounding box.

overlaps(other)[source]

Return whether this bounding box overlaps with the other bounding box.

Parameters: otherBboxBase
property p0

The first pair of (x, y) coordinates that define the bounding box.

This is not guaranteed to be the bottom-left corner (for that, use min).

property p1

The second pair of (x, y) coordinates that define the bounding box.

This is not guaranteed to be the top-right corner (for that, use max).

padded(p)[source]

Construct a Bbox by padding this one on all four sides by p.

rotated(radians)[source]

Return the axes-aligned bounding box that bounds the result of rotating this Bbox by an angle of radians.

shrunk(mx, my)[source]

Return a copy of the Bbox, shrunk by the factor mx in the x direction and the factor my in the y direction. The lower left corner of the box remains unchanged. Normally mx and my will be less than 1, but this is not enforced.

shrunk_to_aspect(box_aspect, container=None, fig_aspect=1.0)[source]

Return a copy of the Bbox, shrunk so that it is as large as it can be while having the desired aspect ratio, box_aspect. If the box coordinates are relative (i.e. fractions of a larger box such as a figure) then the physical aspect ratio of that figure is specified with fig_aspect, so that box_aspect can also be given as a ratio of the absolute dimensions, not the relative dimensions.

property size

The (signed) width and height of the bounding box.

splitx(*args)[source]

Return a list of new Bbox objects formed by splitting the original one with vertical lines at fractional positions given by args.

splity(*args)[source]

Return a list of new Bbox objects formed by splitting the original one with horizontal lines at fractional positions given by args.

transformed(transform)[source]

Construct a Bbox by statically transforming this one by transform.

translated(tx, ty)[source]

Construct a Bbox by translating this one by tx and ty.

static union(bboxes)[source]

Return a Bbox that contains all of the given bboxes.

property width

The (signed) width of the bounding box.

property x0

The first of the pair of x coordinates that define the bounding box.

This is not guaranteed to be less than x1 (for that, use xmin).

property x1

The second of the pair of x coordinates that define the bounding box.

This is not guaranteed to be greater than x0 (for that, use xmax).

property xmax

The right edge of the bounding box.

property xmin

The left edge of the bounding box.

property y0

The first of the pair of y coordinates that define the bounding box.

This is not guaranteed to be less than y1 (for that, use ymin).

property y1

The second of the pair of y coordinates that define the bounding box.

This is not guaranteed to be greater than y0 (for that, use ymax).

property ymax

The top edge of the bounding box.

property ymin

The bottom edge of the bounding box.

class matplotlib.transforms.BboxTransform(boxin, boxout, **kwargs)[source]

BboxTransform linearly transforms points from one Bbox to another.

Create a new BboxTransform that linearly transforms points from boxin to boxout.

__init__(boxin, boxout, **kwargs)[source]

Create a new BboxTransform that linearly transforms points from boxin to boxout.

__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

get_matrix()[source]

Get the matrix for the affine part of this transform.

is_separable = True
class matplotlib.transforms.BboxTransformFrom(boxin, **kwargs)[source]

BboxTransformFrom linearly transforms points from a given Bbox to the unit bounding box.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__init__(boxin, **kwargs)[source]
Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

get_matrix()[source]

Get the matrix for the affine part of this transform.

is_separable = True
class matplotlib.transforms.BboxTransformTo(boxout, **kwargs)[source]

BboxTransformTo is a transformation that linearly transforms points from the unit bounding box to a given Bbox.

Create a new BboxTransformTo that linearly transforms points from the unit bounding box to boxout.

__init__(boxout, **kwargs)[source]

Create a new BboxTransformTo that linearly transforms points from the unit bounding box to boxout.

__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

get_matrix()[source]

Get the matrix for the affine part of this transform.

is_separable = True
class matplotlib.transforms.BboxTransformToMaxOnly(boxout, **kwargs)[source]

BboxTransformTo is a transformation that linearly transforms points from the unit bounding box to a given Bbox with a fixed upper left of (0, 0).

Create a new BboxTransformTo that linearly transforms points from the unit bounding box to boxout.

__module__ = 'matplotlib.transforms'
get_matrix()[source]

Get the matrix for the affine part of this transform.

class matplotlib.transforms.BlendedAffine2D(x_transform, y_transform, **kwargs)[source]

Bases: matplotlib.transforms._BlendedMixin, matplotlib.transforms.Affine2DBase

A "blended" transform uses one transform for the x-direction, and another transform for the y-direction.

This version is an optimization for the case where both child transforms are of type Affine2DBase.

Create a new "blended" transform using x_transform to transform the x-axis and y_transform to transform the y-axis.

Both x_transform and y_transform must be 2D affine transforms.

You will generally not call this constructor directly but use the blended_transform_factory function instead, which can determine automatically which kind of blended transform to create.

__init__(x_transform, y_transform, **kwargs)[source]

Create a new "blended" transform using x_transform to transform the x-axis and y_transform to transform the y-axis.

Both x_transform and y_transform must be 2D affine transforms.

You will generally not call this constructor directly but use the blended_transform_factory function instead, which can determine automatically which kind of blended transform to create.

__module__ = 'matplotlib.transforms'
get_matrix()[source]

Get the matrix for the affine part of this transform.

is_separable = True
class matplotlib.transforms.BlendedGenericTransform(x_transform, y_transform, **kwargs)[source]

Bases: matplotlib.transforms._BlendedMixin, matplotlib.transforms.Transform

A "blended" transform uses one transform for the x-direction, and another transform for the y-direction.

This "generic" version can handle any given child transform in the x- and y-directions.

Create a new "blended" transform using x_transform to transform the x-axis and y_transform to transform the y-axis.

You will generally not call this constructor directly but use the blended_transform_factory function instead, which can determine automatically which kind of blended transform to create.

__init__(x_transform, y_transform, **kwargs)[source]

Create a new "blended" transform using x_transform to transform the x-axis and y_transform to transform the y-axis.

You will generally not call this constructor directly but use the blended_transform_factory function instead, which can determine automatically which kind of blended transform to create.

__module__ = 'matplotlib.transforms'
contains_branch(other)[source]

Return whether the given transform is a sub-tree of this transform.

This routine uses transform equality to identify sub-trees, therefore in many situations it is object id which will be used.

For the case where the given transform represents the whole of this transform, returns True.

property depth

Return the number of transforms which have been chained together to form this Transform instance.

Note

For the special case of a Composite transform, the maximum depth of the two is returned.

frozen()[source]

Return a frozen copy of this transform node. The frozen copy will not be updated when its children change. Useful for storing a previously known state of a transform where copy.deepcopy() might normally be used.

get_affine()[source]

Get the affine part of this transform.

property has_inverse

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

input_dims = 2
inverted()[source]

Return the corresponding inverse transformation.

It holds x == self.inverted().transform(self.transform(x)).

The return value of this method should be treated as temporary. An update to self does not cause a corresponding update to its inverted copy.

property is_affine

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

is_separable = True
output_dims = 2
pass_through = True
transform_non_affine(points)[source]

Apply only the non-affine part of this transformation.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally equivalent to transform(values). In affine transformations, this is always a no-op.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
class matplotlib.transforms.CompositeAffine2D(a, b, **kwargs)[source]

A composite transform formed by applying transform a then transform b.

This version is an optimization that handles the case where both a and b are 2D affines.

Create a new composite transform that is the result of applying Affine2DBase a then Affine2DBase b.

You will generally not call this constructor directly but write a + b instead, which will automatically choose the best kind of composite transform instance to create.

__init__(a, b, **kwargs)[source]

Create a new composite transform that is the result of applying Affine2DBase a then Affine2DBase b.

You will generally not call this constructor directly but write a + b instead, which will automatically choose the best kind of composite transform instance to create.

__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

property depth

Return the number of transforms which have been chained together to form this Transform instance.

Note

For the special case of a Composite transform, the maximum depth of the two is returned.

get_matrix()[source]

Get the matrix for the affine part of this transform.

class matplotlib.transforms.CompositeGenericTransform(a, b, **kwargs)[source]

A composite transform formed by applying transform a then transform b.

This "generic" version can handle any two arbitrary transformations.

Create a new composite transform that is the result of applying transform a then transform b.

You will generally not call this constructor directly but write a + b instead, which will automatically choose the best kind of composite transform instance to create.

__eq__(other)[source]

Return self==value.

__hash__ = None
__init__(a, b, **kwargs)[source]

Create a new composite transform that is the result of applying transform a then transform b.

You will generally not call this constructor directly but write a + b instead, which will automatically choose the best kind of composite transform instance to create.

__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

property depth

Return the number of transforms which have been chained together to form this Transform instance.

Note

For the special case of a Composite transform, the maximum depth of the two is returned.

frozen()[source]

Return a frozen copy of this transform node. The frozen copy will not be updated when its children change. Useful for storing a previously known state of a transform where copy.deepcopy() might normally be used.

get_affine()[source]

Get the affine part of this transform.

property has_inverse

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

inverted()[source]

Return the corresponding inverse transformation.

It holds x == self.inverted().transform(self.transform(x)).

The return value of this method should be treated as temporary. An update to self does not cause a corresponding update to its inverted copy.

property is_affine

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

property is_separable

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

pass_through = True
transform_affine(points)[source]

Apply only the affine part of this transformation on the given array of values.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally a no-op. In affine transformations, this is equivalent to transform(values).

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_non_affine(points)[source]

Apply only the non-affine part of this transformation.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally equivalent to transform(values). In affine transformations, this is always a no-op.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_path_non_affine(path)[source]

Apply the non-affine part of this transform to Path path, returning a new Path.

transform_path(path) is equivalent to transform_path_affine(transform_path_non_affine(values)).

class matplotlib.transforms.IdentityTransform(*args, **kwargs)[source]

A special class that does one thing, the identity transform, in a fast way.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

frozen()[source]

Return a frozen copy of this transform node. The frozen copy will not be updated when its children change. Useful for storing a previously known state of a transform where copy.deepcopy() might normally be used.

get_affine()[source]

Get the affine part of this transform.

get_matrix()[source]

Get the matrix for the affine part of this transform.

inverted()[source]

Return the corresponding inverse transformation.

It holds x == self.inverted().transform(self.transform(x)).

The return value of this method should be treated as temporary. An update to self does not cause a corresponding update to its inverted copy.

transform(points)[source]

Apply this transformation on the given array of values.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_affine(points)[source]

Apply only the affine part of this transformation on the given array of values.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally a no-op. In affine transformations, this is equivalent to transform(values).

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_non_affine(points)[source]

Apply only the non-affine part of this transformation.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally equivalent to transform(values). In affine transformations, this is always a no-op.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_path(path)[source]

Apply the transform to Path path, returning a new Path.

In some cases, this transform may insert curves into the path that began as line segments.

transform_path_affine(path)[source]

Apply the affine part of this transform to Path path, returning a new Path.

transform_path(path) is equivalent to transform_path_affine(transform_path_non_affine(values)).

transform_path_non_affine(path)[source]

Apply the non-affine part of this transform to Path path, returning a new Path.

transform_path(path) is equivalent to transform_path_affine(transform_path_non_affine(values)).

class matplotlib.transforms.LockableBbox(bbox, x0=None, y0=None, x1=None, y1=None, **kwargs)[source]

A Bbox where some elements may be locked at certain values.

When the child bounding box changes, the bounds of this bbox will update accordingly with the exception of the locked elements.

Parameters: bboxBboxThe child bounding box to wrap. x0float or NoneThe locked value for x0, or None to leave unlocked. y0float or NoneThe locked value for y0, or None to leave unlocked. x1float or NoneThe locked value for x1, or None to leave unlocked. y1float or NoneThe locked value for y1, or None to leave unlocked.
__init__(bbox, x0=None, y0=None, x1=None, y1=None, **kwargs)[source]
Parameters: bboxBboxThe child bounding box to wrap. x0float or NoneThe locked value for x0, or None to leave unlocked. y0float or NoneThe locked value for y0, or None to leave unlocked. x1float or NoneThe locked value for x1, or None to leave unlocked. y1float or NoneThe locked value for y1, or None to leave unlocked.
__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

get_points()[source]
property locked_x0

float or None: The value used for the locked x0.

property locked_x1

float or None: The value used for the locked x1.

property locked_y0

float or None: The value used for the locked y0.

property locked_y1

float or None: The value used for the locked y1.

class matplotlib.transforms.ScaledTranslation(xt, yt, scale_trans, **kwargs)[source]

A transformation that translates by xt and yt, after xt and yt have been transformed by scale_trans.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__init__(xt, yt, scale_trans, **kwargs)[source]
Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

get_matrix()[source]

Get the matrix for the affine part of this transform.

class matplotlib.transforms.Transform(shorthand_name=None)[source]

The base class of all TransformNode instances that actually perform a transformation.

All non-affine transformations should be subclasses of this class. New affine transformations should be subclasses of Affine2D.

Subclasses of this class should override the following members (at minimum):

The following attributes may be overridden if the default is unsuitable:

If the transform needs to do something non-standard with matplotlib.path.Path objects, such as adding curves where there were once line segments, it should override:

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__add__(other)[source]

Compose two transforms together so that self is followed by other.

A + B returns a transform C so that C.transform(x) == B.transform(A.transform(x)).

__array__(*args, **kwargs)[source]

Array interface to get at this Transform's affine matrix.

classmethod __init_subclass__()[source]

This method is called when a class is subclassed.

The default implementation does nothing. It may be overridden to extend subclasses.

__module__ = 'matplotlib.transforms'
__sub__(other)[source]

Compose self with the inverse of other, cancelling identical terms if any:

# In general:
A - B == A + B.inverted()
# (but see note regarding frozen transforms below).

# If A "ends with" B (i.e. A == A' + B for some A') we can cancel
# out B:
(A' + B) - B == A'

# Likewise, if B "starts with" A (B = A + B'), we can cancel out A:
A - (A + B') == B'.inverted() == B'^-1


Cancellation (rather than naively returning A + B.inverted()) is important for multiple reasons:

• It avoids floating-point inaccuracies when computing the inverse of B: B - B is guaranteed to cancel out exactly (resulting in the identity transform), whereas B + B.inverted() may differ by a small epsilon.
• B.inverted() always returns a frozen transform: if one computes A + B + B.inverted() and later mutates B, then B.inverted() won't be updated and the last two terms won't cancel out anymore; on the other hand, A + B - B will always be equal to A even if B is mutated.
contains_branch(other)[source]

Return whether the given transform is a sub-tree of this transform.

This routine uses transform equality to identify sub-trees, therefore in many situations it is object id which will be used.

For the case where the given transform represents the whole of this transform, returns True.

contains_branch_seperately(other_transform)[source]

Return whether the given branch is a sub-tree of this transform on each separate dimension.

A common use for this method is to identify if a transform is a blended transform containing an axes' data transform. e.g.:

x_isdata, y_isdata = trans.contains_branch_seperately(ax.transData)

property depth

Return the number of transforms which have been chained together to form this Transform instance.

Note

For the special case of a Composite transform, the maximum depth of the two is returned.

get_affine()[source]

Get the affine part of this transform.

get_matrix()[source]

Get the matrix for the affine part of this transform.

has_inverse = False

True if this transform has a corresponding inverse transform.

input_dims = None

The number of input dimensions of this transform. Must be overridden (with integers) in the subclass.

inverted()[source]

Return the corresponding inverse transformation.

It holds x == self.inverted().transform(self.transform(x)).

The return value of this method should be treated as temporary. An update to self does not cause a corresponding update to its inverted copy.

is_separable = False

True if this transform is separable in the x- and y- dimensions.

output_dims = None

The number of output dimensions of this transform. Must be overridden (with integers) in the subclass.

transform(values)[source]

Apply this transformation on the given array of values.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_affine(values)[source]

Apply only the affine part of this transformation on the given array of values.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally a no-op. In affine transformations, this is equivalent to transform(values).

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_angles(angles, pts, radians=False, pushoff=1e-05)[source]

Transform a set of angles anchored at specific locations.

Parameters: angles(N,) array-likeThe angles to transform. pts(N, 2) array-likeThe points where the angles are anchored. radiansbool, default: FalseWhether angles are radians or degrees. pushofffloatFor each point in pts and angle in angles, the transformed angle is computed by transforming a segment of length pushoff starting at that point and making that angle relative to the horizontal axis, and measuring the angle between the horizontal axis and the transformed segment. (N,) array
transform_bbox(bbox)[source]

Transform the given bounding box.

For smarter transforms including caching (a common requirement in Matplotlib), see TransformedBbox.

transform_non_affine(values)[source]

Apply only the non-affine part of this transformation.

transform(values) is always equivalent to transform_affine(transform_non_affine(values)).

In non-affine transformations, this is generally equivalent to transform(values). In affine transformations, this is always a no-op.

Parameters: valuesarrayThe input values as NumPy array of length input_dims or shape (N x input_dims). arrayThe output values as NumPy array of length input_dims or shape (N x output_dims), depending on the input.
transform_path(path)[source]

Apply the transform to Path path, returning a new Path.

In some cases, this transform may insert curves into the path that began as line segments.

transform_path_affine(path)[source]

Apply the affine part of this transform to Path path, returning a new Path.

transform_path(path) is equivalent to transform_path_affine(transform_path_non_affine(values)).

transform_path_non_affine(path)[source]

Apply the non-affine part of this transform to Path path, returning a new Path.

transform_path(path) is equivalent to transform_path_affine(transform_path_non_affine(values)).

transform_point(point)[source]

Return a transformed point.

This function is only kept for backcompatibility; the more general transform method is capable of transforming both a list of points and a single point.

The point is given as a sequence of length input_dims. The transformed point is returned as a sequence of length output_dims.

class matplotlib.transforms.TransformNode(shorthand_name=None)[source]

Bases: object

The base class for anything that participates in the transform tree and needs to invalidate its parents or be invalidated. This includes classes that are not really transforms, such as bounding boxes, since some transforms depend on bounding boxes to compute their values.

Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
INVALID = 3
INVALID_AFFINE = 2
INVALID_NON_AFFINE = 1
__copy__(*args)[source]
__deepcopy__(*args)
__dict__ = mappingproxy({'__module__': 'matplotlib.transforms', '__doc__': '\n The base class for anything that participates in the transform tree\n and needs to invalidate its parents or be invalidated. This includes\n classes that are not really transforms, such as bounding boxes, since some\n transforms depend on bounding boxes to compute their values.\n ', '_gid': 0, 'INVALID_NON_AFFINE': 1, 'INVALID_AFFINE': 2, 'INVALID': 3, 'is_affine': False, 'is_bbox': False, 'pass_through': False, '__init__': <function TransformNode.__init__>, '__getstate__': <function TransformNode.__getstate__>, '__setstate__': <function TransformNode.__setstate__>, '__copy__': <function TransformNode.__copy__>, '__deepcopy__': <function TransformNode.__copy__>, 'invalidate': <function TransformNode.invalidate>, '_invalidate_internal': <function TransformNode._invalidate_internal>, 'set_children': <function TransformNode.set_children>, 'frozen': <function TransformNode.frozen>, '__dict__': <attribute '__dict__' of 'TransformNode' objects>, '__weakref__': <attribute '__weakref__' of 'TransformNode' objects>})
__getstate__()[source]
__init__(shorthand_name=None)[source]
Parameters: shorthand_namestrA string representing the "name" of the transform. The name carries no significance other than to improve the readability of str(transform) when DEBUG=True.
__module__ = 'matplotlib.transforms'
__setstate__(data_dict)[source]
__weakref__

list of weak references to the object (if defined)

frozen()[source]

Return a frozen copy of this transform node. The frozen copy will not be updated when its children change. Useful for storing a previously known state of a transform where copy.deepcopy() might normally be used.

invalidate()[source]

Invalidate this TransformNode and triggers an invalidation of its ancestors. Should be called any time the transform changes.

is_affine = False
is_bbox = False
pass_through = False

If pass_through is True, all ancestors will always be invalidated, even if 'self' is already invalid.

set_children(*children)[source]

Set the children of the transform, to let the invalidation system know which transforms can invalidate this transform. Should be called from the constructor of any transforms that depend on other transforms.

class matplotlib.transforms.TransformWrapper(child)[source]

A helper class that holds a single child transform and acts equivalently to it.

This is useful if a node of the transform tree must be replaced at run time with a transform of a different type. This class allows that replacement to correctly trigger invalidation.

TransformWrapper instances must have the same input and output dimensions during their entire lifetime, so the child transform may only be replaced with another child transform of the same dimensions.

child: A Transform instance. This child may later be replaced with set().

__eq__(other)[source]

Return self==value.

__hash__ = None
__init__(child)[source]

child: A Transform instance. This child may later be replaced with set().

__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

frozen()[source]

Return a frozen copy of this transform node. The frozen copy will not be updated when its children change. Useful for storing a previously known state of a transform where copy.deepcopy() might normally be used.

property has_inverse

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

property is_affine

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

property is_separable

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

pass_through = True
set(child)[source]

Replace the current child of this transform with another one.

The new child must have the same number of input and output dimensions as the current child.

class matplotlib.transforms.TransformedBbox(bbox, transform, **kwargs)[source]

A Bbox that is automatically transformed by a given transform. When either the child bounding box or transform changes, the bounds of this bbox will update accordingly.

Parameters: bboxBbox transformTransform
__init__(bbox, transform, **kwargs)[source]
Parameters: bboxBbox transformTransform
__module__ = 'matplotlib.transforms'
__str__()

Return str(self).

get_points()[source]
class matplotlib.transforms.TransformedPatchPath(patch)[source]

A TransformedPatchPath caches a non-affine transformed copy of the Patch. This cached copy is automatically updated when the non-affine part of the transform or the patch changes.

Parameters: patchPatch
__init__(patch)[source]
Parameters: patchPatch
__module__ = 'matplotlib.transforms'
class matplotlib.transforms.TransformedPath(path, transform)[source]

A TransformedPath caches a non-affine transformed copy of the Path. This cached copy is automatically updated when the non-affine part of the transform changes.

Note

Paths are considered immutable by this class. Any update to the path's vertices/codes will not trigger a transform recomputation.

Parameters: pathPath transformTransform
__init__(path, transform)[source]
Parameters: pathPath transformTransform
__module__ = 'matplotlib.transforms'
get_affine()[source]
get_fully_transformed_path()[source]

Return a fully-transformed copy of the child path.

get_transformed_path_and_affine()[source]

Return a copy of the child path, with the non-affine part of the transform already applied, along with the affine part of the path necessary to complete the transformation.

get_transformed_points_and_affine()[source]

Return a copy of the child path, with the non-affine part of the transform already applied, along with the affine part of the path necessary to complete the transformation. Unlike get_transformed_path_and_affine(), no interpolation will be performed.

matplotlib.transforms.blended_transform_factory(x_transform, y_transform)[source]

Create a new "blended" transform using x_transform to transform the x-axis and y_transform to transform the y-axis.

A faster version of the blended transform is returned for the case where both child transforms are affine.

matplotlib.transforms.composite_transform_factory(a, b)[source]

Create a new composite transform that is the result of applying transform a then transform b.

Shortcut versions of the blended transform are provided for the case where both child transforms are affine, or one or the other is the identity transform.

Composite transforms may also be created using the '+' operator, e.g.:

c = a + b

matplotlib.transforms.interval_contains(interval, val)[source]

Check, inclusively, whether an interval includes a given value.

Parameters: interval(float, float)The endpoints of the interval. valfloatValue to check is within interval. boolWhether val is within the interval.
matplotlib.transforms.interval_contains_open(interval, val)[source]

Check, excluding endpoints, whether an interval includes a given value.

Parameters: interval(float, float)The endpoints of the interval. valfloatValue to check is within interval. boolWhether val is within the interval.
matplotlib.transforms.nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True)[source]

Modify the endpoints of a range as needed to avoid singularities.

Parameters: vmin, vmaxfloatThe initial endpoints. expanderfloat, default: 0.001Fractional amount by which vmin and vmax are expanded if the original interval is too small, based on tiny. tinyfloat, default: 1e-15Threshold for the ratio of the interval to the maximum absolute value of its endpoints. If the interval is smaller than this, it will be expanded. This value should be around 1e-15 or larger; otherwise the interval will be approaching the double precision resolution limit. increasingbool, default: TrueIf True, swap vmin, vmax if vmin > vmax. vmin, vmaxfloatEndpoints, expanded and/or swapped if necessary. If either input is inf or NaN, or if both inputs are 0 or very close to zero, it returns -expander, expander.
matplotlib.transforms.offset_copy(trans, fig=None, x=0.0, y=0.0, units='inches')[source]

Return a new transform with an added offset.

Parameters: transTransform subclassAny transform, to which offset will be applied. figFigure, default: NoneCurrent figure. It can be None if units are 'dots'. x, yfloat, default: 0.0The offset to apply. units{'inches', 'points', 'dots'}, default: 'inches'Units of the offset. Transform subclassTransform with applied offset.