Version 3.1.2
matplotlib
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Source code for 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 :class:`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:

.. image:: ../_static/transforms.png

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.
"""

# Note: There are a number of places in the code where we use `np.min` or
# `np.minimum` instead of the builtin `min`, and likewise for `max`.  This is
# done so that `nan`s are propagated, instead of being silently dropped.

import re
import weakref

import numpy as np
from numpy.linalg import inv

from matplotlib import cbook
from matplotlib._path import (
    affine_transform, count_bboxes_overlapping_bbox, update_path_extents)
from .path import Path

DEBUG = False


def _indent_str(obj):  # textwrap.indent(str(obj), 4) on Py3.
    return re.sub("(^|\n)", r"\1    ", str(obj))


[docs]class TransformNode(object): """ :class:`TransformNode` is 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. """ _gid = 0 # Invalidation may affect only the affine part. If the # invalidation was "affine-only", the _invalid member is set to # INVALID_AFFINE_ONLY INVALID_NON_AFFINE = 1 INVALID_AFFINE = 2 INVALID = INVALID_NON_AFFINE | INVALID_AFFINE # Some metadata about the transform, used to determine whether an # invalidation is affine-only 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. """ def __init__(self, shorthand_name=None): """ Creates a new :class:`TransformNode`. Parameters ---------- shorthand_name : str A string representing the "name" of the transform. The name carries no significance other than to improve the readability of ``str(transform)`` when DEBUG=True. """ self._parents = {} # TransformNodes start out as invalid until their values are # computed for the first time. self._invalid = 1 self._shorthand_name = shorthand_name or '' if DEBUG: def __str__(self): # either just return the name of this TransformNode, or its repr return self._shorthand_name or repr(self) def __getstate__(self): # turn the dictionary with weak values into a normal dictionary return {**self.__dict__, '_parents': {k: v() for k, v in self._parents.items()}} def __setstate__(self, data_dict): self.__dict__ = data_dict # turn the normal dictionary back into a dictionary with weak values # The extra lambda is to provide a callback to remove dead # weakrefs from the dictionary when garbage collection is done. self._parents = {k: weakref.ref(v, lambda ref, sid=k, target=self._parents: target.pop(sid)) for k, v in self._parents.items() if v is not None} def __copy__(self, *args): raise NotImplementedError( "TransformNode instances can not be copied. " "Consider using frozen() instead.") __deepcopy__ = __copy__
[docs] def invalidate(self): """ Invalidate this :class:`TransformNode` and triggers an invalidation of its ancestors. Should be called any time the transform changes. """ value = self.INVALID if self.is_affine: value = self.INVALID_AFFINE return self._invalidate_internal(value, invalidating_node=self)
def _invalidate_internal(self, value, invalidating_node): """ Called by :meth:`invalidate` and subsequently ascends the transform stack calling each TransformNode's _invalidate_internal method. """ # determine if this call will be an extension to the invalidation # status. If not, then a shortcut means that we needn't invoke an # invalidation up the transform stack as it will already have been # invalidated. # N.B This makes the invalidation sticky, once a transform has been # invalidated as NON_AFFINE, then it will always be invalidated as # NON_AFFINE even when triggered with a AFFINE_ONLY invalidation. # In most cases this is not a problem (i.e. for interactive panning and # zooming) and the only side effect will be on performance. status_changed = self._invalid < value if self.pass_through or status_changed: self._invalid = value for parent in list(self._parents.values()): # Dereference the weak reference parent = parent() if parent is not None: parent._invalidate_internal( value=value, invalidating_node=self) def set_children(self, *children): """ 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. """ # Parents are stored as weak references, so that if the # parents are destroyed, references from the children won't # keep them alive. for child in children: # Use weak references so this dictionary won't keep obsolete nodes # alive; the callback deletes the dictionary entry. This is a # performance improvement over using WeakValueDictionary. ref = weakref.ref(self, lambda ref, sid=id(self), target=child._parents: target.pop(sid)) child._parents[id(self)] = ref if DEBUG: _set_children = set_children
[docs] def set_children(self, *children): self._set_children(*children) self._children = children
set_children.__doc__ = _set_children.__doc__
[docs] def frozen(self): """ Returns a frozen copy of this transform node. The frozen copy will not update when its children change. Useful for storing a previously known state of a transform where ``copy.deepcopy()`` might normally be used. """ return self
if DEBUG: def write_graphviz(self, fobj, highlight=[]): """ For debugging purposes. Writes the transform tree rooted at 'self' to a graphviz "dot" format file. This file can be run through the "dot" utility to produce a graph of the transform tree. Affine transforms are marked in blue. Bounding boxes are marked in yellow. *fobj*: A Python file-like object Once the "dot" file has been created, it can be turned into a png easily with:: $> dot -Tpng -o $OUTPUT_FILE $DOT_FILE """ seen = set() def recurse(root): if root in seen: return seen.add(root) props = {} label = root.__class__.__name__ if root._invalid: label = '[%s]' % label if root in highlight: props['style'] = 'bold' props['shape'] = 'box' props['label'] = '"%s"' % label props = ' '.join(map('{0[0]}={0[1]}'.format, props.items())) fobj.write('%s [%s];\n' % (hash(root), props)) if hasattr(root, '_children'): for child in root._children: name = next((key for key, val in root.__dict__.items() if val is child), '?') fobj.write('"%s" -> "%s" [label="%s", fontsize=10];\n' % (hash(root), hash(child), name)) recurse(child) fobj.write("digraph G {\n") recurse(self) fobj.write("}\n")
[docs]class BboxBase(TransformNode): """ This is the base class of all bounding boxes, and provides read-only access to its data. A mutable bounding box is provided by the :class:`Bbox` class. 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. """ is_bbox = True is_affine = True if DEBUG: def _check(points): if isinstance(points, np.ma.MaskedArray): cbook._warn_external("Bbox bounds are a masked array.") points = np.asarray(points) if (points[1, 0] - points[0, 0] == 0 or points[1, 1] - points[0, 1] == 0): cbook._warn_external("Singular Bbox.") _check = staticmethod(_check)
[docs] def frozen(self): return Bbox(self.get_points().copy())
frozen.__doc__ = TransformNode.__doc__ def __array__(self, *args, **kwargs): return self.get_points()
[docs] def is_unit(self): """Return whether this is the unit box (from (0, 0) to (1, 1)).""" return self.get_points().tolist() == [[0., 0.], [1., 1.]]
@property def x0(self): """ The first of the pair of *x* coordinates that define the bounding box. This is not guaranteed to be less than :attr:`x1` (for that, use :attr:`xmin`). """ return self.get_points()[0, 0] @property def y0(self): """ The first of the pair of *y* coordinates that define the bounding box. This is not guaranteed to be less than :attr:`y1` (for that, use :attr:`ymin`). """ return self.get_points()[0, 1] @property def x1(self): """ The second of the pair of *x* coordinates that define the bounding box. This is not guaranteed to be greater than :attr:`x0` (for that, use :attr:`xmax`). """ return self.get_points()[1, 0] @property def y1(self): """ The second of the pair of *y* coordinates that define the bounding box. This is not guaranteed to be greater than :attr:`y0` (for that, use :attr:`ymax`). """ return self.get_points()[1, 1] @property def p0(self): """ 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 :attr:`min`). """ return self.get_points()[0] @property def p1(self): """ 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 :attr:`max`). """ return self.get_points()[1] @property def xmin(self): """The left edge of the bounding box.""" return np.min(self.get_points()[:, 0]) @property def ymin(self): """The bottom edge of the bounding box.""" return np.min(self.get_points()[:, 1]) @property def xmax(self): """The right edge of the bounding box.""" return np.max(self.get_points()[:, 0]) @property def ymax(self): """The top edge of the bounding box.""" return np.max(self.get_points()[:, 1]) @property def min(self): """The bottom-left corner of the bounding box.""" return np.min(self.get_points(), axis=0) @property def max(self): """The top-right corner of the bounding box.""" return np.max(self.get_points(), axis=0) @property def intervalx(self): """ The pair of *x* coordinates that define the bounding box. This is not guaranteed to be sorted from left to right. """ return self.get_points()[:, 0] @property def intervaly(self): """ The pair of *y* coordinates that define the bounding box. This is not guaranteed to be sorted from bottom to top. """ return self.get_points()[:, 1] @property def width(self): """The (signed) width of the bounding box.""" points = self.get_points() return points[1, 0] - points[0, 0] @property def height(self): """The (signed) height of the bounding box.""" points = self.get_points() return points[1, 1] - points[0, 1] @property def size(self): """The (signed) width and height of the bounding box.""" points = self.get_points() return points[1] - points[0] @property def bounds(self): """Return (:attr:`x0`, :attr:`y0`, :attr:`width`, :attr:`height`).""" (x0, y0), (x1, y1) = self.get_points() return (x0, y0, x1 - x0, y1 - y0) @property def extents(self): """Return (:attr:`x0`, :attr:`y0`, :attr:`x1`, :attr:`y1`).""" return self.get_points().flatten() # flatten returns a copy.
[docs] def get_points(self): raise NotImplementedError
[docs] def containsx(self, x): """ Return whether *x* is in the closed (:attr:`x0`, :attr:`x1`) interval. """ x0, x1 = self.intervalx return x0 <= x <= x1 or x0 >= x >= x1
[docs] def containsy(self, y): """ Return whether *y* is in the closed (:attr:`y0`, :attr:`y1`) interval. """ y0, y1 = self.intervaly return y0 <= y <= y1 or y0 >= y >= y1
[docs] def contains(self, x, y): """ Return whether ``(x, y)`` is in the bounding box or on its edge. """ return self.containsx(x) and self.containsy(y)
[docs] def overlaps(self, other): """ Return whether this bounding box overlaps with the other bounding box. Parameters ---------- other : BboxBase """ ax1, ay1, ax2, ay2 = self.extents bx1, by1, bx2, by2 = other.extents if ax2 < ax1: ax2, ax1 = ax1, ax2 if ay2 < ay1: ay2, ay1 = ay1, ay2 if bx2 < bx1: bx2, bx1 = bx1, bx2 if by2 < by1: by2, by1 = by1, by2 return ax1 <= bx2 and bx1 <= ax2 and ay1 <= by2 and by1 <= ay2
[docs] def fully_containsx(self, x): """ Return whether *x* is in the open (:attr:`x0`, :attr:`x1`) interval. """ x0, x1 = self.intervalx return x0 < x < x1 or x0 > x > x1
[docs] def fully_containsy(self, y): """ Return whether *y* is in the open (:attr:`y0`, :attr:`y1`) interval. """ y0, y1 = self.intervaly return y0 < y < y1 or y0 > y > y1
[docs] def fully_contains(self, x, y): """ Return whether ``x, y`` is in the bounding box, but not on its edge. """ return self.fully_containsx(x) and self.fully_containsy(y)
[docs] def fully_overlaps(self, other): """ Return whether this bounding box overlaps with the other bounding box, not including the edges. Parameters ---------- other : BboxBase """ ax1, ay1, ax2, ay2 = self.extents bx1, by1, bx2, by2 = other.extents if ax2 < ax1: ax2, ax1 = ax1, ax2 if ay2 < ay1: ay2, ay1 = ay1, ay2 if bx2 < bx1: bx2, bx1 = bx1, bx2 if by2 < by1: by2, by1 = by1, by2 return ax1 < bx2 and bx1 < ax2 and ay1 < by2 and by1 < ay2
[docs] def transformed(self, transform): """ Construct a `Bbox` by statically transforming this one by *transform*. """ pts = self.get_points() ll, ul, lr = transform.transform(np.array([pts[0], [pts[0, 0], pts[1, 1]], [pts[1, 0], pts[0, 1]]])) return Bbox([ll, [lr[0], ul[1]]])
[docs] def inverse_transformed(self, transform): """ Construct a `Bbox` by statically transforming this one by the inverse of *transform*. """ return self.transformed(transform.inverted())
coefs = {'C': (0.5, 0.5), 'SW': (0, 0), 'S': (0.5, 0), 'SE': (1.0, 0), 'E': (1.0, 0.5), 'NE': (1.0, 1.0), 'N': (0.5, 1.0), 'NW': (0, 1.0), 'W': (0, 0.5)}
[docs] def anchored(self, c, container=None): """ Return a copy of the :class:`Bbox`, shifted to position *c* within a container. Parameters ---------- c : (float, float) or str May 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. container : Bbox, optional The box within which the :class:`Bbox` is positioned; it defaults to the initial :class:`Bbox`. """ if container is None: container = self l, b, w, h = container.bounds if isinstance(c, str): cx, cy = self.coefs[c] else: cx, cy = c L, B, W, H = self.bounds return Bbox(self._points + [(l + cx * (w - W)) - L, (b + cy * (h - H)) - B])
[docs] def shrunk(self, mx, my): """ Return a copy of the :class:`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. """ w, h = self.size return Bbox([self._points[0], self._points[0] + [mx * w, my * h]])
[docs] def shrunk_to_aspect(self, box_aspect, container=None, fig_aspect=1.0): """ Return a copy of the :class:`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---that is, 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. """ if box_aspect <= 0 or fig_aspect <= 0: raise ValueError("'box_aspect' and 'fig_aspect' must be positive") if container is None: container = self w, h = container.size H = w * box_aspect / fig_aspect if H <= h: W = w else: W = h * fig_aspect / box_aspect H = h return Bbox([self._points[0], self._points[0] + (W, H)])
[docs] def splitx(self, *args): """ Return a list of new `Bbox` objects formed by splitting the original one with vertical lines at fractional positions given by *args*. """ xf = [0, *args, 1] x0, y0, x1, y1 = self.extents w = x1 - x0 return [Bbox([[x0 + xf0 * w, y0], [x0 + xf1 * w, y1]]) for xf0, xf1 in zip(xf[:-1], xf[1:])]
[docs] def splity(self, *args): """ Return a list of new `Bbox` objects formed by splitting the original one with horizontal lines at fractional positions given by *args*. """ yf = [0, *args, 1] x0, y0, x1, y1 = self.extents h = y1 - y0 return [Bbox([[x0, y0 + yf0 * h], [x1, y0 + yf1 * h]]) for yf0, yf1 in zip(yf[:-1], yf[1:])]
[docs] def count_contains(self, vertices): """ Count the number of vertices contained in the :class:`Bbox`. Any vertices with a non-finite x or y value are ignored. Parameters ---------- vertices : Nx2 Numpy array. """ if len(vertices) == 0: return 0 vertices = np.asarray(vertices) with np.errstate(invalid='ignore'): return (((self.min < vertices) & (vertices < self.max)).all(axis=1).sum())
[docs] def count_overlaps(self, bboxes): """ Count the number of bounding boxes that overlap this one. Parameters ---------- bboxes : sequence of :class:`BboxBase` objects """ return count_bboxes_overlapping_bbox( self, np.atleast_3d([np.array(x) for x in bboxes]))
[docs] def expanded(self, sw, sh): """ Construct a `Bbox` by expanding this one around its center by the factors *sw* and *sh*. """ width = self.width height = self.height deltaw = (sw * width - width) / 2.0 deltah = (sh * height - height) / 2.0 a = np.array([[-deltaw, -deltah], [deltaw, deltah]]) return Bbox(self._points + a)
[docs] def padded(self, p): """Construct a `Bbox` by padding this one on all four sides by *p*.""" points = self.get_points() return Bbox(points + [[-p, -p], [p, p]])
[docs] def translated(self, tx, ty): """Construct a `Bbox` by translating this one by *tx* and *ty*.""" return Bbox(self._points + (tx, ty))
[docs] def corners(self): """ Return the corners of this rectangle as an array of points. Specifically, this returns the array ``[[x0, y0], [x0, y1], [x1, y0], [x1, y1]]``. """ (x0, y0), (x1, y1) = self.get_points() return np.array([[x0, y0], [x0, y1], [x1, y0], [x1, y1]])
[docs] def rotated(self, radians): """ Return a new bounding box that bounds a rotated version of this bounding box by the given radians. The new bounding box is still aligned with the axes, of course. """ corners = self.corners() corners_rotated = Affine2D().rotate(radians).transform(corners) bbox = Bbox.unit() bbox.update_from_data_xy(corners_rotated, ignore=True) return bbox
[docs] @staticmethod def union(bboxes): """Return a `Bbox` that contains all of the given *bboxes*.""" if not len(bboxes): raise ValueError("'bboxes' cannot be empty") x0 = np.min([bbox.xmin for bbox in bboxes]) x1 = np.max([bbox.xmax for bbox in bboxes]) y0 = np.min([bbox.ymin for bbox in bboxes]) y1 = np.max([bbox.ymax for bbox in bboxes]) return Bbox([[x0, y0], [x1, y1]])
[docs] @staticmethod def intersection(bbox1, bbox2): """ Return the intersection of *bbox1* and *bbox2* if they intersect, or None if they don't. """ x0 = np.maximum(bbox1.xmin, bbox2.xmin) x1 = np.minimum(bbox1.xmax, bbox2.xmax) y0 = np.maximum(bbox1.ymin, bbox2.ymin) y1 = np.minimum(bbox1.ymax, bbox2.ymax) return Bbox([[x0, y0], [x1, y1]]) if x0 <= x1 and y0 <= y1 else None
[docs]class Bbox(BboxBase): """ A mutable bounding box. """ def __init__(self, points, **kwargs): """ Parameters ---------- points : ndarray A 2x2 numpy array of the form ``[[x0, y0], [x1, y1]]``. Notes ----- If you need to create a :class:`Bbox` object from another form of data, consider the static methods :meth:`unit`, :meth:`from_bounds` and :meth:`from_extents`. """ BboxBase.__init__(self, **kwargs) points = np.asarray(points, float) if points.shape != (2, 2): raise ValueError('Bbox points must be of the form ' '"[[x0, y0], [x1, y1]]".') self._points = points self._minpos = np.array([np.inf, np.inf]) self._ignore = True # it is helpful in some contexts to know if the bbox is a # default or has been mutated; we store the orig points to # support the mutated methods self._points_orig = self._points.copy() if DEBUG: ___init__ = __init__ def __init__(self, points, **kwargs): self._check(points) self.___init__(points, **kwargs) def invalidate(self): self._check(self._points) TransformNode.invalidate(self)
[docs] @staticmethod def unit(): """ (staticmethod) Create a new unit :class:`Bbox` from (0, 0) to (1, 1). """ return Bbox(np.array([[0.0, 0.0], [1.0, 1.0]], float))
[docs] @staticmethod def null(): """ (staticmethod) Create a new null :class:`Bbox` from (inf, inf) to (-inf, -inf). """ return Bbox(np.array([[np.inf, np.inf], [-np.inf, -np.inf]], float))
[docs] @staticmethod def from_bounds(x0, y0, width, height): """ (staticmethod) Create a new :class:`Bbox` from *x0*, *y0*, *width* and *height*. *width* and *height* may be negative. """ return Bbox.from_extents(x0, y0, x0 + width, y0 + height)
[docs] @staticmethod def from_extents(*args): """ (staticmethod) Create a new Bbox from *left*, *bottom*, *right* and *top*. The *y*-axis increases upwards. """ points = np.array(args, dtype=float).reshape(2, 2) return Bbox(points)
def __format__(self, fmt): return ( 'Bbox(x0={0.x0:{1}}, y0={0.y0:{1}}, x1={0.x1:{1}}, y1={0.y1:{1}})'. format(self, fmt)) def __str__(self): return format(self, '') def __repr__(self): return 'Bbox([[{0.x0}, {0.y0}], [{0.x1}, {0.y1}]])'.format(self)
[docs] def ignore(self, value): """ Set whether the existing bounds of the box should be ignored by subsequent calls to :meth:`update_from_data_xy`. value : bool - When ``True``, subsequent calls to :meth:`update_from_data_xy` will ignore the existing bounds of the :class:`Bbox`. - When ``False``, subsequent calls to :meth:`update_from_data_xy` will include the existing bounds of the :class:`Bbox`. """ self._ignore = value
[docs] def update_from_path(self, path, ignore=None, updatex=True, updatey=True): """ Update the bounds of the :class:`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 ---------- path : :class:`~matplotlib.path.Path` ignore : bool, optional - when ``True``, ignore the existing bounds of the :class:`Bbox`. - when ``False``, include the existing bounds of the :class:`Bbox`. - when ``None``, use the last value passed to :meth:`ignore`. updatex, updatey : bool, optional When ``True``, update the x/y values. """ if ignore is None: ignore = self._ignore if path.vertices.size == 0: return points, minpos, changed = update_path_extents( path, None, self._points, self._minpos, ignore) if changed: self.invalidate() if updatex: self._points[:, 0] = points[:, 0] self._minpos[0] = minpos[0] if updatey: self._points[:, 1] = points[:, 1] self._minpos[1] = minpos[1]
[docs] def update_from_data_xy(self, xy, ignore=None, updatex=True, updatey=True): """ Update the bounds of the :class:`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 ---------- xy : ndarray A numpy array of 2D points. ignore : bool, optional - When ``True``, ignore the existing bounds of the :class:`Bbox`. - When ``False``, include the existing bounds of the :class:`Bbox`. - When ``None``, use the last value passed to :meth:`ignore`. updatex, updatey : bool, optional When ``True``, update the x/y values. """ if len(xy) == 0: return path = Path(xy) self.update_from_path(path, ignore=ignore, updatex=updatex, updatey=updatey)
@BboxBase.x0.setter def x0(self, val): self._points[0, 0] = val self.invalidate() @BboxBase.y0.setter def y0(self, val): self._points[0, 1] = val self.invalidate() @BboxBase.x1.setter def x1(self, val): self._points[1, 0] = val self.invalidate() @BboxBase.y1.setter def y1(self, val): self._points[1, 1] = val self.invalidate() @BboxBase.p0.setter def p0(self, val): self._points[0] = val self.invalidate() @BboxBase.p1.setter def p1(self, val): self._points[1] = val self.invalidate() @BboxBase.intervalx.setter def intervalx(self, interval): self._points[:, 0] = interval self.invalidate() @BboxBase.intervaly.setter def intervaly(self, interval): self._points[:, 1] = interval self.invalidate() @BboxBase.bounds.setter def bounds(self, bounds): l, b, w, h = bounds points = np.array([[l, b], [l + w, b + h]], float) if np.any(self._points != points): self._points = points self.invalidate() @property def minpos(self): return self._minpos @property def minposx(self): return self._minpos[0] @property def minposy(self): return self._minpos[1]
[docs] def get_points(self): """ Get the points of the bounding box directly as a numpy array of the form: ``[[x0, y0], [x1, y1]]``. """ self._invalid = 0 return self._points
[docs] def set_points(self, points): """ 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. """ if np.any(self._points != points): self._points = points self.invalidate()
[docs] def set(self, other): """ Set this bounding box from the "frozen" bounds of another :class:`Bbox`. """ if np.any(self._points != other.get_points()): self._points = other.get_points() self.invalidate()
[docs] def mutated(self): 'Return whether the bbox has changed since init.' return self.mutatedx() or self.mutatedy()
[docs] def mutatedx(self): 'Return whether the x-limits have changed since init.' return (self._points[0, 0] != self._points_orig[0, 0] or self._points[1, 0] != self._points_orig[1, 0])
[docs] def mutatedy(self): 'Return whether the y-limits have changed since init.' return (self._points[0, 1] != self._points_orig[0, 1] or self._points[1, 1] != self._points_orig[1, 1])
[docs]class TransformedBbox(BboxBase): """ A :class:`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. """ def __init__(self, bbox, transform, **kwargs): """ Parameters ---------- bbox : :class:`Bbox` transform : :class:`Transform` """ if not bbox.is_bbox: raise ValueError("'bbox' is not a bbox") if not isinstance(transform, Transform): raise ValueError("'transform' must be an instance of " "'matplotlib.transform.Transform'") if transform.input_dims != 2 or transform.output_dims != 2: raise ValueError( "The input and output dimensions of 'transform' must be 2") BboxBase.__init__(self, **kwargs) self._bbox = bbox self._transform = transform self.set_children(bbox, transform) self._points = None def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._bbox), _indent_str(self._transform))) def get_points(self): # docstring inherited if self._invalid: p = self._bbox.get_points() # Transform all four points, then make a new bounding box # from the result, taking care to make the orientation the # same. points = self._transform.transform( [[p[0, 0], p[0, 1]], [p[1, 0], p[0, 1]], [p[0, 0], p[1, 1]], [p[1, 0], p[1, 1]]]) points = np.ma.filled(points, 0.0) xs = min(points[:, 0]), max(points[:, 0]) if p[0, 0] > p[1, 0]: xs = xs[::-1] ys = min(points[:, 1]), max(points[:, 1]) if p[0, 1] > p[1, 1]: ys = ys[::-1] self._points = np.array([ [xs[0], ys[0]], [xs[1], ys[1]] ]) self._invalid = 0 return self._points if DEBUG: _get_points = get_points
[docs] def get_points(self): points = self._get_points() self._check(points) return points
[docs]class LockableBbox(BboxBase): """ A :class:`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. """ def __init__(self, bbox, x0=None, y0=None, x1=None, y1=None, **kwargs): """ Parameters ---------- bbox : Bbox The child bounding box to wrap. x0 : float or None The locked value for x0, or None to leave unlocked. y0 : float or None The locked value for y0, or None to leave unlocked. x1 : float or None The locked value for x1, or None to leave unlocked. y1 : float or None The locked value for y1, or None to leave unlocked. """ if not bbox.is_bbox: raise ValueError("'bbox' is not a bbox") BboxBase.__init__(self, **kwargs) self._bbox = bbox self.set_children(bbox) self._points = None fp = [x0, y0, x1, y1] mask = [val is None for val in fp] self._locked_points = np.ma.array(fp, float, mask=mask).reshape((2, 2)) def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._bbox), _indent_str(self._locked_points))) def get_points(self): # docstring inherited if self._invalid: points = self._bbox.get_points() self._points = np.where(self._locked_points.mask, points, self._locked_points) self._invalid = 0 return self._points if DEBUG: _get_points = get_points
[docs] def get_points(self): points = self._get_points() self._check(points) return points
@property def locked_x0(self): """ float or None: The value used for the locked x0. """ if self._locked_points.mask[0, 0]: return None else: return self._locked_points[0, 0] @locked_x0.setter def locked_x0(self, x0): self._locked_points.mask[0, 0] = x0 is None self._locked_points.data[0, 0] = x0 self.invalidate() @property def locked_y0(self): """ float or None: The value used for the locked y0. """ if self._locked_points.mask[0, 1]: return None else: return self._locked_points[0, 1] @locked_y0.setter def locked_y0(self, y0): self._locked_points.mask[0, 1] = y0 is None self._locked_points.data[0, 1] = y0 self.invalidate() @property def locked_x1(self): """ float or None: The value used for the locked x1. """ if self._locked_points.mask[1, 0]: return None else: return self._locked_points[1, 0] @locked_x1.setter def locked_x1(self, x1): self._locked_points.mask[1, 0] = x1 is None self._locked_points.data[1, 0] = x1 self.invalidate() @property def locked_y1(self): """ float or None: The value used for the locked y1. """ if self._locked_points.mask[1, 1]: return None else: return self._locked_points[1, 1] @locked_y1.setter def locked_y1(self, y1): self._locked_points.mask[1, 1] = y1 is None self._locked_points.data[1, 1] = y1 self.invalidate()
[docs]class Transform(TransformNode): """ The base class of all :class:`TransformNode` instances that actually perform a transformation. All non-affine transformations should be subclasses of this class. New affine transformations should be subclasses of :class:`Affine2D`. Subclasses of this class should override the following members (at minimum): - :attr:`input_dims` - :attr:`output_dims` - :meth:`transform` - :attr:`is_separable` - :attr:`has_inverse` - :meth:`inverted` (if :attr:`has_inverse` is True) If the transform needs to do something non-standard with :class:`matplotlib.path.Path` objects, such as adding curves where there were once line segments, it should override: - :meth:`transform_path` """ input_dims = None """ The number of input dimensions of this transform. Must be overridden (with integers) in the subclass. """ output_dims = None """ The number of output dimensions of this transform. Must be overridden (with integers) in the subclass. """ has_inverse = False """True if this transform has a corresponding inverse transform.""" is_separable = False """True if this transform is separable in the x- and y- dimensions.""" def __add__(self, other): """ Composes two transforms together such that *self* is followed by *other*. """ if isinstance(other, Transform): return composite_transform_factory(self, other) raise TypeError( "Can not add Transform to object of type '%s'" % type(other)) def __radd__(self, other): """ Composes two transforms together such that *self* is followed by *other*. """ if isinstance(other, Transform): return composite_transform_factory(other, self) raise TypeError( "Can not add Transform to object of type '%s'" % type(other)) # Equality is based on object identity for `Transform`s (so we don't # override `__eq__`), but some subclasses, such as TransformWrapper & # AffineBase, override this behavior. def _iter_break_from_left_to_right(self): """ Returns an iterator breaking down this transform stack from left to right recursively. If self == ((A, N), A) then the result will be an iterator which yields I : ((A, N), A), followed by A : (N, A), followed by (A, N) : (A), but not ((A, N), A) : I. This is equivalent to flattening the stack then yielding ``flat_stack[:i], flat_stack[i:]`` where i=0..(n-1). """ yield IdentityTransform(), self @property def depth(self): """ Returns 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. """ return 1
[docs] def contains_branch(self, other): """ 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. """ if self.depth < other.depth: return False # check that a subtree is equal to other (starting from self) for _, sub_tree in self._iter_break_from_left_to_right(): if sub_tree == other: return True return False
[docs] def contains_branch_seperately(self, other_transform): """ Returns 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) """ if self.output_dims != 2: raise ValueError('contains_branch_seperately only supports ' 'transforms with 2 output dimensions') # for a non-blended transform each separate dimension is the same, so # just return the appropriate shape. return [self.contains_branch(other_transform)] * 2
def __sub__(self, other): """ Returns a transform stack which goes all the way down self's transform stack, and then ascends back up other's stack. If it can, this is optimised:: # normally A - B == a + b.inverted() # sometimes, when A contains the tree B there is no need to # descend all the way down to the base of A (via B), instead we # can just stop at B. (A + B) - (B)^-1 == A # similarly, when B contains tree A, we can avoid descending A at # all, basically: A - (A + B) == ((B + A) - A).inverted() or B^-1 For clarity, the result of ``(A + B) - B + B == (A + B)``. """ # we only know how to do this operation if other is a Transform. if not isinstance(other, Transform): return NotImplemented for remainder, sub_tree in self._iter_break_from_left_to_right(): if sub_tree == other: return remainder for remainder, sub_tree in other._iter_break_from_left_to_right(): if sub_tree == self: if not remainder.has_inverse: raise ValueError( "The shortcut cannot be computed since 'other' " "includes a non-invertible component") return remainder.inverted() # if we have got this far, then there was no shortcut possible if other.has_inverse: return self + other.inverted() else: raise ValueError('It is not possible to compute transA - transB ' 'since transB cannot be inverted and there is no ' 'shortcut possible.') def __array__(self, *args, **kwargs): """ Array interface to get at this Transform's affine matrix. """ return self.get_affine().get_matrix()
[docs] def transform(self, values): """ Performs the transformation on the given array of values. Accepts a numpy array of shape (N x :attr:`input_dims`) and returns a numpy array of shape (N x :attr:`output_dims`). Alternatively, accepts a numpy array of length :attr:`input_dims` and returns a numpy array of length :attr:`output_dims`. """ # Ensure that values is a 2d array (but remember whether # we started with a 1d or 2d array). values = np.asanyarray(values) ndim = values.ndim values = values.reshape((-1, self.input_dims)) # Transform the values res = self.transform_affine(self.transform_non_affine(values)) # Convert the result back to the shape of the input values. if ndim == 0: assert not np.ma.is_masked(res) # just to be on the safe side return res[0, 0] if ndim == 1: return res.reshape(-1) elif ndim == 2: return res raise ValueError( "Input values must have shape (N x {dims}) " "or ({dims}).".format(dims=self.input_dims))
[docs] def transform_affine(self, values): """ Performs 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)``. Accepts a numpy array of shape (N x :attr:`input_dims`) and returns a numpy array of shape (N x :attr:`output_dims`). Alternatively, accepts a numpy array of length :attr:`input_dims` and returns a numpy array of length :attr:`output_dims`. """ return self.get_affine().transform(values)
[docs] def transform_non_affine(self, values): """ Performs only the non-affine part of the 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. Accepts a numpy array of shape (N x :attr:`input_dims`) and returns a numpy array of shape (N x :attr:`output_dims`). Alternatively, accepts a numpy array of length :attr:`input_dims` and returns a numpy array of length :attr:`output_dims`. """ return values
[docs] def transform_bbox(self, bbox): """ Transform the given bounding box. Note, for smarter transforms including caching (a common requirement for matplotlib figures), see :class:`TransformedBbox`. """ return Bbox(self.transform(bbox.get_points()))
[docs] def get_affine(self): """ Get the affine part of this transform. """ return IdentityTransform()
[docs] def get_matrix(self): """ Get the Affine transformation array for the affine part of this transform. """ return self.get_affine().get_matrix()
[docs] def transform_point(self, point): """ A convenience function that returns the transformed copy of a single point. The point is given as a sequence of length :attr:`input_dims`. The transformed point is returned as a sequence of length :attr:`output_dims`. """ if len(point) != self.input_dims: raise ValueError("The length of 'point' must be 'self.input_dims'") return self.transform(np.asarray([point]))[0]
[docs] def transform_path(self, path): """ Returns a transformed path. *path*: a :class:`~matplotlib.path.Path` instance. In some cases, this transform may insert curves into the path that began as line segments. """ return self.transform_path_affine(self.transform_path_non_affine(path))
[docs] def transform_path_affine(self, path): """ Returns a path, transformed only by the affine part of this transform. *path*: a :class:`~matplotlib.path.Path` instance. ``transform_path(path)`` is equivalent to ``transform_path_affine(transform_path_non_affine(values))``. """ return self.get_affine().transform_path_affine(path)
[docs] def transform_path_non_affine(self, path): """ Returns a path, transformed only by the non-affine part of this transform. *path*: a :class:`~matplotlib.path.Path` instance. ``transform_path(path)`` is equivalent to ``transform_path_affine(transform_path_non_affine(values))``. """ x = self.transform_non_affine(path.vertices) return Path._fast_from_codes_and_verts(x, path.codes, path)
[docs] def transform_angles(self, angles, pts, radians=False, pushoff=1e-5): """ Transforms a set of angles anchored at specific locations. Parameters ---------- angles : (N,) array-like The angles to transform. pts : (N, 2) array-like The points where the angles are anchored. radians : bool, default: False Whether *angles* are radians or degrees. pushoff : float For 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. Returns ------- transformed_angles : (N,) array """ # Must be 2D if self.input_dims != 2 or self.output_dims != 2: raise NotImplementedError('Only defined in 2D') if pts.shape[1] != 2: raise ValueError("'pts' must be array with 2 columns for x,y") if angles.ndim != 1 or angles.shape[0] != pts.shape[0]: raise ValueError("'angles' must be a column vector and have same " "number of rows as 'pts'") # Convert to radians if desired if not radians: angles = angles / 180.0 * np.pi # Move a short distance away pts2 = pts + pushoff * np.c_[np.cos(angles), np.sin(angles)] # Transform both sets of points tpts = self.transform(pts) tpts2 = self.transform(pts2) # Calculate transformed angles d = tpts2 - tpts a = np.arctan2(d[:, 1], d[:, 0]) # Convert back to degrees if desired if not radians: a = np.rad2deg(a) return a
[docs] def inverted(self): """ Return the corresponding inverse transformation. 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. ``x === self.inverted().transform(self.transform(x))`` """ raise NotImplementedError()
[docs]class TransformWrapper(Transform): """ 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. Note that :class:`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. """ pass_through = True def __init__(self, child): """ *child*: A class:`Transform` instance. This child may later be replaced with :meth:`set`. """ if not isinstance(child, Transform): raise ValueError("'child' must be an instance of " "'matplotlib.transform.Transform'") self._init(child) self.set_children(child) def _init(self, child): Transform.__init__(self) self.input_dims = child.input_dims self.output_dims = child.output_dims self._set(child) self._invalid = 0 def __eq__(self, other): return self._child.__eq__(other) def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._child)))
[docs] def frozen(self): # docstring inherited return self._child.frozen()
def _set(self, child): self._child = child self.transform = child.transform self.transform_affine = child.transform_affine self.transform_non_affine = child.transform_non_affine self.transform_path = child.transform_path self.transform_path_affine = child.transform_path_affine self.transform_path_non_affine = child.transform_path_non_affine self.get_affine = child.get_affine self.inverted = child.inverted self.get_matrix = child.get_matrix # note we do not wrap other properties here since the transform's # child can be changed with WrappedTransform.set and so checking # is_affine and other such properties may be dangerous.
[docs] def set(self, child): """ 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. """ if (child.input_dims != self.input_dims or child.output_dims != self.output_dims): raise ValueError( "The new child must have the same number of input and output " "dimensions as the current child") self.set_children(child) self._set(child) self._invalid = 0 self.invalidate() self._invalid = 0
is_affine = property(lambda self: self._child.is_affine) is_separable = property(lambda self: self._child.is_separable) has_inverse = property(lambda self: self._child.has_inverse)
[docs]class AffineBase(Transform): """ The base class of all affine transformations of any number of dimensions. """ is_affine = True def __init__(self, *args, **kwargs): Transform.__init__(self, *args, **kwargs) self._inverted = None def __array__(self, *args, **kwargs): # optimises the access of the transform matrix vs the superclass return self.get_matrix() def __eq__(self, other): if getattr(other, "is_affine", False): return np.all(self.get_matrix() == other.get_matrix()) return NotImplemented
[docs] def transform(self, values): # docstring inherited return self.transform_affine(values)
[docs] def transform_affine(self, values): # docstring inherited raise NotImplementedError('Affine subclasses should override this ' 'method.')
[docs] def transform_non_affine(self, points): # docstring inherited return points
[docs] def transform_path(self, path): # docstring inherited return self.transform_path_affine(path)
[docs] def transform_path_affine(self, path): # docstring inherited return Path(self.transform_affine(path.vertices), path.codes, path._interpolation_steps)
[docs] def transform_path_non_affine(self, path): # docstring inherited return path
[docs] def get_affine(self): # docstring inherited return self
[docs]class Affine2DBase(AffineBase): """ 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 :class:`Affine2D`. Subclasses of this class will generally only need to override a constructor and :meth:`get_matrix` that generates a custom 3x3 matrix. """ has_inverse = True input_dims = 2 output_dims = 2
[docs] def frozen(self): # docstring inherited return Affine2D(self.get_matrix().copy())
@property def is_separable(self): mtx = self.get_matrix() return mtx[0, 1] == mtx[1, 0] == 0.0
[docs] def to_values(self): """ Return the values of the matrix as an ``(a, b, c, d, e, f)`` tuple. """ mtx = self.get_matrix() return tuple(mtx[:2].swapaxes(0, 1).flat)
[docs] @staticmethod def matrix_from_values(a, b, c, d, e, f): """ (staticmethod) Create a new transformation matrix as a 3x3 numpy array of the form:: a c e b d f 0 0 1 """ return np.array([[a, c, e], [b, d, f], [0.0, 0.0, 1.0]], float)
def transform_affine(self, points): mtx = self.get_matrix() if isinstance(points, np.ma.MaskedArray): tpoints = affine_transform(points.data, mtx) return np.ma.MaskedArray(tpoints, mask=np.ma.getmask(points)) return affine_transform(points, mtx)
[docs] def transform_point(self, point): # docstring inherited mtx = self.get_matrix() return affine_transform([point], mtx)[0]
if DEBUG: _transform_affine = transform_affine
[docs] def transform_affine(self, points): # docstring inherited # The major speed trap here is just converting to the # points to an array in the first place. If we can use # more arrays upstream, that should help here. if not isinstance(points, (np.ma.MaskedArray, np.ndarray)): cbook._warn_external( f'A non-numpy array of type {type(points)} was passed in ' f'for transformation, which results in poor performance.') return self._transform_affine(points)
[docs] def inverted(self): # docstring inherited if self._inverted is None or self._invalid: mtx = self.get_matrix() shorthand_name = None if self._shorthand_name: shorthand_name = '(%s)-1' % self._shorthand_name self._inverted = Affine2D(inv(mtx), shorthand_name=shorthand_name) self._invalid = 0 return self._inverted
[docs]class Affine2D(Affine2DBase): """ A mutable 2D affine transformation. """ def __init__(self, matrix=None, **kwargs): """ 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. """ Affine2DBase.__init__(self, **kwargs) if matrix is None: # A bit faster than np.identity(3). matrix = IdentityTransform._mtx.copy() self._mtx = matrix self._invalid = 0 def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._mtx)))
[docs] @staticmethod def from_values(a, b, c, d, e, f): """ (staticmethod) Create a new Affine2D instance from the given values:: a c e b d f 0 0 1 . """ return Affine2D( np.array([a, c, e, b, d, f, 0.0, 0.0, 1.0], float).reshape((3, 3)))
[docs] def get_matrix(self): """ Get the underlying transformation matrix as a 3x3 numpy array:: a c e b d f 0 0 1 . """ self._invalid = 0 return self._mtx
[docs] def set_matrix(self, mtx): """ Set the underlying transformation matrix from a 3x3 numpy array:: a c e b d f 0 0 1 . """ self._mtx = mtx self.invalidate()
[docs] def set(self, other): """ Set this transformation from the frozen copy of another :class:`Affine2DBase` object. """ if not isinstance(other, Affine2DBase): raise ValueError("'other' must be an instance of " "'matplotlib.transform.Affine2DBase'") self._mtx = other.get_matrix() self.invalidate()
[docs] @staticmethod def identity(): """ (staticmethod) Return a new :class:`Affine2D` object that is the identity transform. Unless this transform will be mutated later on, consider using the faster :class:`IdentityTransform` class instead. """ return Affine2D()
[docs] def clear(self): """ Reset the underlying matrix to the identity transform. """ # A bit faster than np.identity(3). self._mtx = IdentityTransform._mtx.copy() self.invalidate() return self
[docs] def rotate(self, theta): """ Add a rotation (in radians) to this transform in place. Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ a = np.cos(theta) b = np.sin(theta) rotate_mtx = np.array([[a, -b, 0.0], [b, a, 0.0], [0.0, 0.0, 1.0]], float) self._mtx = np.dot(rotate_mtx, self._mtx) self.invalidate() return self
[docs] def rotate_deg(self, degrees): """ Add a rotation (in degrees) to this transform in place. Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ return self.rotate(np.deg2rad(degrees))
[docs] def rotate_around(self, x, y, theta): """ 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 :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ return self.translate(-x, -y).rotate(theta).translate(x, y)
[docs] def rotate_deg_around(self, x, y, degrees): """ 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 :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ # Cast to float to avoid wraparound issues with uint8's x, y = float(x), float(y) return self.translate(-x, -y).rotate_deg(degrees).translate(x, y)
[docs] def translate(self, tx, ty): """ Adds a translation in place. Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ translate_mtx = np.array( [[1.0, 0.0, tx], [0.0, 1.0, ty], [0.0, 0.0, 1.0]], float) self._mtx = np.dot(translate_mtx, self._mtx) self.invalidate() return self
[docs] def scale(self, sx, sy=None): """ Adds a scale in place. 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 :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ if sy is None: sy = sx scale_mtx = np.array( [[sx, 0.0, 0.0], [0.0, sy, 0.0], [0.0, 0.0, 1.0]], float) self._mtx = np.dot(scale_mtx, self._mtx) self.invalidate() return self
[docs] def skew(self, xShear, yShear): """ Adds a skew in place. *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 :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ rotX = np.tan(xShear) rotY = np.tan(yShear) skew_mtx = np.array( [[1.0, rotX, 0.0], [rotY, 1.0, 0.0], [0.0, 0.0, 1.0]], float) self._mtx = np.dot(skew_mtx, self._mtx) self.invalidate() return self
[docs] def skew_deg(self, xShear, yShear): """ Adds a skew in place. *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 :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ return self.skew(np.deg2rad(xShear), np.deg2rad(yShear))
[docs]class IdentityTransform(Affine2DBase): """ A special class that does one thing, the identity transform, in a fast way. """ _mtx = np.identity(3)
[docs] def frozen(self): # docstring inherited return self
def __str__(self): return ("{}()" .format(type(self).__name__))
[docs] def get_matrix(self): # docstring inherited return self._mtx
[docs] def transform(self, points): # docstring inherited return np.asanyarray(points)
[docs] def transform_affine(self, points): # docstring inherited return np.asanyarray(points)
[docs] def transform_non_affine(self, points): # docstring inherited return np.asanyarray(points)
[docs] def transform_path(self, path): # docstring inherited return path
[docs] def transform_path_affine(self, path): # docstring inherited return path
[docs] def transform_path_non_affine(self, path): # docstring inherited return path
[docs] def get_affine(self): # docstring inherited return self
[docs] def inverted(self): # docstring inherited return self
[docs]class BlendedGenericTransform(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. """ input_dims = 2 output_dims = 2 is_separable = True pass_through = True def __init__(self, x_transform, y_transform, **kwargs): """ 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 :func:`blended_transform_factory` function instead, which can determine automatically which kind of blended transform to create. """ # Here we ask: "Does it blend?" Transform.__init__(self, **kwargs) self._x = x_transform self._y = y_transform self.set_children(x_transform, y_transform) self._affine = None def __eq__(self, other): # Note, this is an exact copy of BlendedAffine2D.__eq__ if isinstance(other, (BlendedAffine2D, BlendedGenericTransform)): return (self._x == other._x) and (self._y == other._y) elif self._x == self._y: return self._x == other else: return NotImplemented
[docs] def contains_branch_seperately(self, transform): # Note, this is an exact copy of BlendedAffine2D.contains_branch_seperately return self._x.contains_branch(transform), self._y.contains_branch(transform)
@property def depth(self): return max(self._x.depth, self._y.depth)
[docs] def contains_branch(self, other): # a blended transform cannot possibly contain a branch from two different transforms. return False
is_affine = property(lambda self: self._x.is_affine and self._y.is_affine) has_inverse = property( lambda self: self._x.has_inverse and self._y.has_inverse)
[docs] def frozen(self): # docstring inherited return blended_transform_factory(self._x.frozen(), self._y.frozen())
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._x), _indent_str(self._y)))
[docs] def transform_non_affine(self, points): # docstring inherited if self._x.is_affine and self._y.is_affine: return points x = self._x y = self._y if x == y and x.input_dims == 2: return x.transform_non_affine(points) if x.input_dims == 2: x_points = x.transform_non_affine(points)[:, 0:1] else: x_points = x.transform_non_affine(points[:, 0]) x_points = x_points.reshape((len(x_points), 1)) if y.input_dims == 2: y_points = y.transform_non_affine(points)[:, 1:] else: y_points = y.transform_non_affine(points[:, 1]) y_points = y_points.reshape((len(y_points), 1)) if (isinstance(x_points, np.ma.MaskedArray) or isinstance(y_points, np.ma.MaskedArray)): return np.ma.concatenate((x_points, y_points), 1) else: return np.concatenate((x_points, y_points), 1)
[docs] def inverted(self): # docstring inherited return BlendedGenericTransform(self._x.inverted(), self._y.inverted())
[docs] def get_affine(self): # docstring inherited if self._invalid or self._affine is None: if self._x == self._y: self._affine = self._x.get_affine() else: x_mtx = self._x.get_affine().get_matrix() y_mtx = self._y.get_affine().get_matrix() # This works because we already know the transforms are # separable, though normally one would want to set b and # c to zero. mtx = np.vstack((x_mtx[0], y_mtx[1], [0.0, 0.0, 1.0])) self._affine = Affine2D(mtx) self._invalid = 0 return self._affine
[docs]class BlendedAffine2D(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 :class:`Affine2DBase`. """ is_separable = True def __init__(self, x_transform, y_transform, **kwargs): """ 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 :func:`blended_transform_factory` function instead, which can determine automatically which kind of blended transform to create. """ is_affine = x_transform.is_affine and y_transform.is_affine is_separable = x_transform.is_separable and y_transform.is_separable is_correct = is_affine and is_separable if not is_correct: raise ValueError("Both *x_transform* and *y_transform* must be 2D " "affine transforms") Transform.__init__(self, **kwargs) self._x = x_transform self._y = y_transform self.set_children(x_transform, y_transform) Affine2DBase.__init__(self) self._mtx = None def __eq__(self, other): # Note, this is an exact copy of BlendedGenericTransform.__eq__ if isinstance(other, (BlendedAffine2D, BlendedGenericTransform)): return (self._x == other._x) and (self._y == other._y) elif self._x == self._y: return self._x == other else: return NotImplemented
[docs] def contains_branch_seperately(self, transform): # Note, this is an exact copy of BlendedTransform.contains_branch_seperately return self._x.contains_branch(transform), self._y.contains_branch(transform)
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._x), _indent_str(self._y)))
[docs] def get_matrix(self): # docstring inherited if self._invalid: if self._x == self._y: self._mtx = self._x.get_matrix() else: x_mtx = self._x.get_matrix() y_mtx = self._y.get_matrix() # This works because we already know the transforms are # separable, though normally one would want to set b and # c to zero. self._mtx = np.vstack((x_mtx[0], y_mtx[1], [0.0, 0.0, 1.0])) self._inverted = None self._invalid = 0 return self._mtx
[docs]def blended_transform_factory(x_transform, y_transform): """ 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. """ if (isinstance(x_transform, Affine2DBase) and isinstance(y_transform, Affine2DBase)): return BlendedAffine2D(x_transform, y_transform) return BlendedGenericTransform(x_transform, y_transform)
[docs]class CompositeGenericTransform(Transform): """ A composite transform formed by applying transform *a* then transform *b*. This "generic" version can handle any two arbitrary transformations. """ pass_through = True def __init__(self, a, b, **kwargs): """ 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 use the :func:`composite_transform_factory` function instead, which can automatically choose the best kind of composite transform instance to create. """ if a.output_dims != b.input_dims: raise ValueError("The output dimension of 'a' must be equal to " "the input dimensions of 'b'") self.input_dims = a.input_dims self.output_dims = b.output_dims Transform.__init__(self, **kwargs) self._a = a self._b = b self.set_children(a, b)
[docs] def frozen(self): # docstring inherited self._invalid = 0 frozen = composite_transform_factory(self._a.frozen(), self._b.frozen()) if not isinstance(frozen, CompositeGenericTransform): return frozen.frozen() return frozen
def _invalidate_internal(self, value, invalidating_node): # In some cases for a composite transform, an invalidating call to AFFINE_ONLY needs # to be extended to invalidate the NON_AFFINE part too. These cases are when the right # hand transform is non-affine and either: # (a) the left hand transform is non affine # (b) it is the left hand node which has triggered the invalidation if value == Transform.INVALID_AFFINE \ and not self._b.is_affine \ and (not self._a.is_affine or invalidating_node is self._a): value = Transform.INVALID Transform._invalidate_internal(self, value=value, invalidating_node=invalidating_node) def __eq__(self, other): if isinstance(other, (CompositeGenericTransform, CompositeAffine2D)): return self is other or (self._a == other._a and self._b == other._b) else: return False def _iter_break_from_left_to_right(self): for left, right in self._a._iter_break_from_left_to_right(): yield left, right + self._b for left, right in self._b._iter_break_from_left_to_right(): yield self._a + left, right depth = property(lambda self: self._a.depth + self._b.depth) is_affine = property(lambda self: self._a.is_affine and self._b.is_affine) is_separable = property( lambda self: self._a.is_separable and self._b.is_separable) has_inverse = property( lambda self: self._a.has_inverse and self._b.has_inverse) def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._a), _indent_str(self._b)))
[docs] def transform_affine(self, points): # docstring inherited return self.get_affine().transform(points)
[docs] def transform_non_affine(self, points): # docstring inherited if self._a.is_affine and self._b.is_affine: return points elif not self._a.is_affine and self._b.is_affine: return self._a.transform_non_affine(points) else: return self._b.transform_non_affine( self._a.transform(points))
[docs] def transform_path_non_affine(self, path): # docstring inherited if self._a.is_affine and self._b.is_affine: return path elif not self._a.is_affine and self._b.is_affine: return self._a.transform_path_non_affine(path) else: return self._b.transform_path_non_affine( self._a.transform_path(path))
[docs] def get_affine(self): # docstring inherited if not self._b.is_affine: return self._b.get_affine() else: return Affine2D(np.dot(self._b.get_affine().get_matrix(), self._a.get_affine().get_matrix()))
[docs] def inverted(self): # docstring inherited return CompositeGenericTransform(self._b.inverted(), self._a.inverted())
[docs]class CompositeAffine2D(Affine2DBase): """ 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. """ def __init__(self, a, b, **kwargs): """ Create a new composite transform that is the result of applying transform *a* then transform *b*. Both *a* and *b* must be instances of :class:`Affine2DBase`. You will generally not call this constructor directly but use the :func:`composite_transform_factory` function instead, which can automatically choose the best kind of composite transform instance to create. """ if not a.is_affine or not b.is_affine: raise ValueError("'a' and 'b' must be affine transforms") if a.output_dims != b.input_dims: raise ValueError("The output dimension of 'a' must be equal to " "the input dimensions of 'b'") self.input_dims = a.input_dims self.output_dims = b.output_dims Affine2DBase.__init__(self, **kwargs) self._a = a self._b = b self.set_children(a, b) self._mtx = None @property def depth(self): return self._a.depth + self._b.depth def _iter_break_from_left_to_right(self): for left, right in self._a._iter_break_from_left_to_right(): yield left, right + self._b for left, right in self._b._iter_break_from_left_to_right(): yield self._a + left, right def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._a), _indent_str(self._b)))
[docs] def get_matrix(self): # docstring inherited if self._invalid: self._mtx = np.dot( self._b.get_matrix(), self._a.get_matrix()) self._inverted = None self._invalid = 0 return self._mtx
[docs]def composite_transform_factory(a, b): """ 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 """ # check to see if any of a or b are IdentityTransforms. We use # isinstance here to guarantee that the transforms will *always* # be IdentityTransforms. Since TransformWrappers are mutable, # use of equality here would be wrong. if isinstance(a, IdentityTransform): return b elif isinstance(b, IdentityTransform): return a elif isinstance(a, Affine2D) and isinstance(b, Affine2D): return CompositeAffine2D(a, b) return CompositeGenericTransform(a, b)
[docs]class BboxTransform(Affine2DBase): """ :class:`BboxTransform` linearly transforms points from one :class:`Bbox` to another :class:`Bbox`. """ is_separable = True def __init__(self, boxin, boxout, **kwargs): """ Create a new :class:`BboxTransform` that linearly transforms points from *boxin* to *boxout*. """ if not boxin.is_bbox or not boxout.is_bbox: raise ValueError("'boxin' and 'boxout' must be bbox") Affine2DBase.__init__(self, **kwargs) self._boxin = boxin self._boxout = boxout self.set_children(boxin, boxout) self._mtx = None self._inverted = None def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._boxin), _indent_str(self._boxout)))
[docs] def get_matrix(self): # docstring inherited if self._invalid: inl, inb, inw, inh = self._boxin.bounds outl, outb, outw, outh = self._boxout.bounds x_scale = outw / inw y_scale = outh / inh if DEBUG and (x_scale == 0 or y_scale == 0): raise ValueError("Transforming from or to a singular bounding box.") self._mtx = np.array([[x_scale, 0.0 , (-inl*x_scale+outl)], [0.0 , y_scale, (-inb*y_scale+outb)], [0.0 , 0.0 , 1.0 ]], float) self._inverted = None self._invalid = 0 return self._mtx
[docs]class BboxTransformTo(Affine2DBase): """ :class:`BboxTransformTo` is a transformation that linearly transforms points from the unit bounding box to a given :class:`Bbox`. """ is_separable = True def __init__(self, boxout, **kwargs): """ Create a new :class:`BboxTransformTo` that linearly transforms points from the unit bounding box to *boxout*. """ if not boxout.is_bbox: raise ValueError("'boxout' must be bbox") Affine2DBase.__init__(self, **kwargs) self._boxout = boxout self.set_children(boxout) self._mtx = None self._inverted = None def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._boxout)))
[docs] def get_matrix(self): # docstring inherited if self._invalid: outl, outb, outw, outh = self._boxout.bounds if DEBUG and (outw == 0 or outh == 0): raise ValueError("Transforming to a singular bounding box.") self._mtx = np.array([[outw, 0.0, outl], [ 0.0, outh, outb], [ 0.0, 0.0, 1.0]], float) self._inverted = None self._invalid = 0 return self._mtx
[docs]class BboxTransformToMaxOnly(BboxTransformTo): """ :class:`BboxTransformTo` is a transformation that linearly transforms points from the unit bounding box to a given :class:`Bbox` with a fixed upper left of (0, 0). """
[docs] def get_matrix(self): # docstring inherited if self._invalid: xmax, ymax = self._boxout.max if DEBUG and (xmax == 0 or ymax == 0): raise ValueError("Transforming to a singular bounding box.") self._mtx = np.array([[xmax, 0.0, 0.0], [ 0.0, ymax, 0.0], [ 0.0, 0.0, 1.0]], float) self._inverted = None self._invalid = 0 return self._mtx
[docs]class BboxTransformFrom(Affine2DBase): """ :class:`BboxTransformFrom` linearly transforms points from a given :class:`Bbox` to the unit bounding box. """ is_separable = True def __init__(self, boxin, **kwargs): if not boxin.is_bbox: raise ValueError("'boxin' must be bbox") Affine2DBase.__init__(self, **kwargs) self._boxin = boxin self.set_children(boxin) self._mtx = None self._inverted = None def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._boxin)))
[docs] def get_matrix(self): # docstring inherited if self._invalid: inl, inb, inw, inh = self._boxin.bounds if DEBUG and (inw == 0 or inh == 0): raise ValueError("Transforming from a singular bounding box.") x_scale = 1.0 / inw y_scale = 1.0 / inh self._mtx = np.array([[x_scale, 0.0 , (-inl*x_scale)], [0.0 , y_scale, (-inb*y_scale)], [0.0 , 0.0 , 1.0 ]], float) self._inverted = None self._invalid = 0 return self._mtx
[docs]class ScaledTranslation(Affine2DBase): """ A transformation that translates by *xt* and *yt*, after *xt* and *yt* have been transformed by *scale_trans*. """ def __init__(self, xt, yt, scale_trans, **kwargs): Affine2DBase.__init__(self, **kwargs) self._t = (xt, yt) self._scale_trans = scale_trans self.set_children(scale_trans) self._mtx = None self._inverted = None def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._t)))
[docs] def get_matrix(self): # docstring inherited if self._invalid: xt, yt = self._scale_trans.transform_point(self._t) self._mtx = np.array([[1.0, 0.0, xt], [0.0, 1.0, yt], [0.0, 0.0, 1.0]], float) self._invalid = 0 self._inverted = None return self._mtx
[docs]class TransformedPath(TransformNode): """ A :class:`TransformedPath` caches a non-affine transformed copy of the :class:`~matplotlib.path.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. """ def __init__(self, path, transform): """ Create a new :class:`TransformedPath` from the given :class:`~matplotlib.path.Path` and :class:`Transform`. """ if not isinstance(transform, Transform): raise ValueError("'transform' must be an instance of " "'matplotlib.transform.Transform'") TransformNode.__init__(self) self._path = path self._transform = transform self.set_children(transform) self._transformed_path = None self._transformed_points = None def _revalidate(self): # only recompute if the invalidation includes the non_affine part of the transform if ((self._invalid & self.INVALID_NON_AFFINE == self.INVALID_NON_AFFINE) or self._transformed_path is None): self._transformed_path = \ self._transform.transform_path_non_affine(self._path) self._transformed_points = \ Path._fast_from_codes_and_verts( self._transform.transform_non_affine(self._path.vertices), None, self._path) self._invalid = 0
[docs] def get_transformed_points_and_affine(self): """ 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 :meth:`get_transformed_path_and_affine`, no interpolation will be performed. """ self._revalidate() return self._transformed_points, self.get_affine()
[docs] def get_transformed_path_and_affine(self): """ 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. """ self._revalidate() return self._transformed_path, self.get_affine()
[docs] def get_fully_transformed_path(self): """ Return a fully-transformed copy of the child path. """ self._revalidate() return self._transform.transform_path_affine(self._transformed_path)
[docs] def get_affine(self): return self._transform.get_affine()
[docs]class TransformedPatchPath(TransformedPath): """ A :class:`TransformedPatchPath` caches a non-affine transformed copy of the :class:`~matplotlib.path.Patch`. This cached copy is automatically updated when the non-affine part of the transform or the patch changes. """ def __init__(self, patch): """ Create a new :class:`TransformedPatchPath` from the given :class:`~matplotlib.path.Patch`. """ TransformNode.__init__(self) transform = patch.get_transform() self._patch = patch self._transform = transform self.set_children(transform) self._path = patch.get_path() self._transformed_path = None self._transformed_points = None def _revalidate(self): patch_path = self._patch.get_path() # Only recompute if the invalidation includes the non_affine part of # the transform, or the Patch's Path has changed. if (self._transformed_path is None or self._path != patch_path or (self._invalid & self.INVALID_NON_AFFINE == self.INVALID_NON_AFFINE)): self._path = patch_path self._transformed_path = \ self._transform.transform_path_non_affine(patch_path) self._transformed_points = \ Path._fast_from_codes_and_verts( self._transform.transform_non_affine(patch_path.vertices), None, patch_path) self._invalid = 0
[docs]def nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True): """ Modify the endpoints of a range as needed to avoid singularities. Parameters ---------- vmin, vmax : float The initial endpoints. expander : float, optional, default: 0.001 Fractional amount by which *vmin* and *vmax* are expanded if the original interval is too small, based on *tiny*. tiny : float, optional, default: 1e-15 Threshold 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. increasing : bool, optional, default: True If True, swap *vmin*, *vmax* if *vmin* > *vmax*. Returns ------- vmin, vmax : float Endpoints, 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*. """ if (not np.isfinite(vmin)) or (not np.isfinite(vmax)): return -expander, expander swapped = False if vmax < vmin: vmin, vmax = vmax, vmin swapped = True maxabsvalue = max(abs(vmin), abs(vmax)) if maxabsvalue < (1e6 / tiny) * np.finfo(float).tiny: vmin = -expander vmax = expander elif vmax - vmin <= maxabsvalue * tiny: if vmax == 0 and vmin == 0: vmin = -expander vmax = expander else: vmin -= expander*abs(vmin) vmax += expander*abs(vmax) if swapped and not increasing: vmin, vmax = vmax, vmin return vmin, vmax
[docs]def interval_contains(interval, val): """ Check, inclusively, whether an interval includes a given value. Parameters ---------- interval : sequence of scalar A 2-length sequence, endpoints that define the interval. val : scalar Value to check is within interval. Returns ------- bool Returns *True* if given *val* is within the *interval*. """ a, b = interval if a > b: a, b = b, a return a <= val <= b
def _interval_contains_close(interval, val, rtol=1e-10): """ Check, inclusively, whether an interval includes a given value, with the interval expanded by a small tolerance to admit floating point errors. Parameters ---------- interval : sequence of scalar A 2-length sequence, endpoints that define the interval. val : scalar Value to check is within interval. rtol : scalar Tolerance slippage allowed outside of this interval. Default 1e-10 * (b - a). Returns ------- bool Returns *True* if given *val* is within the *interval* (with tolerance) """ a, b = interval if a > b: a, b = b, a rtol = (b - a) * rtol return a - rtol <= val <= b + rtol
[docs]def interval_contains_open(interval, val): """ Check, excluding endpoints, whether an interval includes a given value. Parameters ---------- interval : sequence of scalar A 2-length sequence, endpoints that define the interval. val : scalar Value to check is within interval. Returns ------- bool Returns true if given val is within the interval. """ a, b = interval return a < val < b or a > val > b
[docs]def offset_copy(trans, fig=None, x=0.0, y=0.0, units='inches'): """ Return a new transform with an added offset. Parameters ---------- trans : :class:`Transform` instance Any transform, to which offset will be applied. fig : :class:`~matplotlib.figure.Figure`, optional, default: None Current figure. It can be None if *units* are 'dots'. x, y : float, optional, default: 0.0 Specifies the offset to apply. units : {'inches', 'points', 'dots'}, optional Units of the offset. Returns ------- trans : :class:`Transform` instance Transform with applied offset. """ if units == 'dots': return trans + Affine2D().translate(x, y) if fig is None: raise ValueError('For units of inches or points a fig kwarg is needed') if units == 'points': x /= 72.0 y /= 72.0 elif not units == 'inches': raise ValueError('units must be dots, points, or inches') return trans + ScaledTranslation(x, y, fig.dpi_scale_trans)