00001 """
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.
"""
import numpy as np
from numpy import ma
from matplotlib._path import affine_transform
from numpy.linalg import inv
from weakref import WeakKeyDictionary
import warnings
import sets
import cbook
from path import Path
from _path import count_bboxes_overlapping_bbox, update_path_extents
DEBUG = False
if DEBUG:
import warnings
MaskedArray = ma.MaskedArray
00051 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
INVALID_NON_AFFINE = 1
INVALID_AFFINE = 2
INVALID = INVALID_NON_AFFINE | INVALID_AFFINE
is_affine = False
is_bbox = False
pass_through = False
00077 def __init__(self):
"""
Creates a new TransformNode.
"""
self._parents = WeakKeyDictionary()
self._invalid = 1
def __copy__(self, *args):
raise NotImplementedError(
"TransformNode instances can not be copied. " +
"Consider using frozen() instead.")
__deepcopy__ = __copy__
00096 def invalidate(self):
"""
Invalidate this transform node and all of its ancestors.
Should be called any time the transform changes.
"""
value = (self.is_affine) and self.INVALID_AFFINE or self.INVALID
if self._invalid == value:
return
if not len(self._parents):
self._invalid = value
return
parent = None
stack = [self]
while len(stack):
root = stack.pop()
if root._invalid != value or root.pass_through:
root._invalid = value
stack.extend(root._parents.keys())
00124 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.
"""
for child in children:
child._parents[self] = None
if DEBUG:
_set_children = set_children
def set_children(self, *children):
self._set_children(*children)
self._children = children
set_children.__doc__ = _set_children.__doc__
00141 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:
00151 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
"""
seen = sets.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(['%s=%s' % (key, val) for key, val in props.items()])
fobj.write('%s [%s];\n' %
(hash(root), props))
if hasattr(root, '_children'):
for child in root._children:
name = '?'
for key, val in root.__dict__.items():
if val is child:
name = key
break
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")
else:
def write_graphviz(self, fobj, highlight=[]):
return
00204 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 explicity.
"""
is_bbox = True
is_affine = True
if DEBUG:
def _check(points):
if ma.isMaskedArray(points):
warnings.warn("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):
warnings.warn("Singular Bbox.")
_check = staticmethod(_check)
00233 def frozen(self):
return Bbox(self.get_points().copy())
frozen.__doc__ = TransformNode.__doc__
def __array__(self, *args, **kwargs):
return self.get_points()
00240 def is_unit(self):
"""
Returns True if the Bbox is the unit bounding box from (0, 0)
to (1, 1).
"""
return list(self.get_points().flatten()) == [0., 0., 1., 1.]
def _get_x0(self):
return self.get_points()[0, 0]
x0 = property(_get_x0, None, None, """
(property) :attr:`x0` is the first of the pair of *x* coordinates that
define the bounding box. :attr:`x0` is not guaranteed to be
less than :attr:`x1`. If you require that, use :attr:`xmin`.""")
def _get_y0(self):
return self.get_points()[0, 1]
y0 = property(_get_y0, None, None, """
(property) :attr:`y0` is the first of the pair of *y* coordinates that
define the bounding box. :attr:`y0` is not guaranteed to be
less than :attr:`y1`. If you require that, use :attr:`ymin`.""")
def _get_x1(self):
return self.get_points()[1, 0]
x1 = property(_get_x1, None, None, """
(property) :attr:`x1` is the second of the pair of *x* coordinates that
define the bounding box. :attr:`x1` is not guaranteed to be
greater than :attr:`x0`. If you require that, use :attr:`xmax`.""")
def _get_y1(self):
return self.get_points()[1, 1]
y1 = property(_get_y1, None, None, """
(property) :attr:`y1` is the second of the pair of *y* coordinates that
define the bounding box. :attr:`y1` is not guaranteed to be
greater than :attr:`y0`. If you require that, use :attr:`ymax`.""")
def _get_p0(self):
return self.get_points()[0]
p0 = property(_get_p0, None, None, """
(property) :attr:`p0` is the first pair of (*x*, *y*) coordinates that
define the bounding box. It is not guaranteed to be the bottom-left
corner. For that, use :attr:`min`.""")
def _get_p1(self):
return self.get_points()[1]
p1 = property(_get_p1, None, None, """
(property) :attr:`p1` is the second pair of (*x*, *y*) coordinates that
define the bounding box. It is not guaranteed to be the top-right
corner. For that, use :attr:`max`.""")
def _get_xmin(self):
return min(self.get_points()[:, 0])
xmin = property(_get_xmin, None, None, """
(property) :attr:`xmin` is the left edge of the bounding box.""")
def _get_ymin(self):
return min(self.get_points()[:, 1])
ymin = property(_get_ymin, None, None, """
(property) :attr:`ymin` is the bottom edge of the bounding box.""")
def _get_xmax(self):
return max(self.get_points()[:, 0])
xmax = property(_get_xmax, None, None, """
(property) :attr:`xmax` is the right edge of the bounding box.""")
def _get_ymax(self):
return max(self.get_points()[:, 1])
ymax = property(_get_ymax, None, None, """
(property) :attr:`ymax` is the top edge of the bounding box.""")
def _get_min(self):
return [min(self.get_points()[:, 0]),
min(self.get_points()[:, 1])]
min = property(_get_min, None, None, """
(property) :attr:`min` is the bottom-left corner of the bounding box.""")
def _get_max(self):
return [max(self.get_points()[:, 0]),
max(self.get_points()[:, 1])]
max = property(_get_max, None, None, """
(property) :attr:`max` is the top-right corner of the bounding box.""")
def _get_intervalx(self):
return self.get_points()[:, 0]
intervalx = property(_get_intervalx, None, None, """
(property) :attr:`intervalx` is the pair of *x* coordinates that define the
bounding box. It is not guaranteed to be sorted from left to right.""")
def _get_intervaly(self):
return self.get_points()[:, 1]
intervaly = property(_get_intervaly, None, None, """
(property) :attr:`intervaly` is the pair of *y* coordinates that define the
bounding box. It is not guaranteed to be sorted from bottom to top.""")
def _get_width(self):
points = self.get_points()
return points[1, 0] - points[0, 0]
width = property(_get_width, None, None, """
(property) The width of the bounding box. It may be negative if :attr:`x1` <
:attr:`x0`.""")
def _get_height(self):
points = self.get_points()
return points[1, 1] - points[0, 1]
height = property(_get_height, None, None, """
(property) The height of the bounding box. It may be negative if :attr:`y1` <
:attr:`y0`.""")
def _get_size(self):
points = self.get_points()
return points[1] - points[0]
size = property(_get_size, None, None, """
(property) The width and height of the bounding box. May be negative, in the same
way as :attr:`width` and :attr:`height`.""")
def _get_bounds(self):
x0, y0, x1, y1 = self.get_points().flatten()
return (x0, y0, x1 - x0, y1 - y0)
bounds = property(_get_bounds, None, None, """
(property) Returns (:attr:`x0`, :attr:`y0`, :attr:`width`, :attr:`height`).""")
def _get_extents(self):
return self.get_points().flatten().copy()
extents = property(_get_extents, None, None, """
(property) Returns (:attr:`x0`, :attr:`y0`, :attr:`x1`, :attr:`y1`).""")
def get_points(self):
return NotImplementedError()
00368 def containsx(self, x):
"""
Returns True if x is between or equal to :attr:`x0` and
:attr:`x1`.
"""
x0, x1 = self.intervalx
return ((x0 < x1
and (x >= x0 and x <= x1))
or (x >= x1 and x <= x0))
00378 def containsy(self, y):
"""
Returns True if y is between or equal to :attr:`y0` and
:attr:`y1`.
"""
y0, y1 = self.intervaly
return ((y0 < y1
and (y >= y0 and y <= y1))
or (y >= y1 and y <= y0))
00388 def contains(self, x, y):
"""
Returns True if (x, y) is a coordinate inside the bounding
box or on its edge.
"""
return self.containsx(x) and self.containsy(y)
00395 def overlaps(self, other):
"""
Returns True if this bounding box overlaps with the given
bounding box *other*.
"""
ax1, ay1, ax2, ay2 = self._get_extents()
bx1, by1, bx2, by2 = other._get_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 not ((bx2 < ax1) or
(by2 < ay1) or
(bx1 > ax2) or
(by1 > ay2))
00417 def fully_containsx(self, x):
"""
Returns True if x is between but not equal to :attr:`x0` and
:attr:`x1`.
"""
x0, x1 = self.intervalx
return ((x0 < x1
and (x > x0 and x < x1))
or (x > x1 and x < x0))
00427 def fully_containsy(self, y):
"""
Returns True if y is between but not equal to :attr:`y0` and
:attr:`y1`.
"""
y0, y1 = self.intervaly
return ((y0 < y1
and (x > y0 and x < y1))
or (x > y1 and x < y0))
00437 def fully_contains(self, x, y):
"""
Returns True if (x, y) is a coordinate inside the bounding
box, but not on its edge.
"""
return self.fully_containsx(x) \
and self.fully_containsy(y)
00445 def fully_overlaps(self, other):
"""
Returns True if this bounding box overlaps with the given
bounding box *other*, but not on its edge alone."""
ax1, ay1, ax2, ay2 = self._get_extents()
bx1, by1, bx2, by2 = other._get_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 not ((bx2 <= ax1) or
(by2 <= ay1) or
(bx1 >= ax2) or
(by1 >= ay2))
00466 def transformed(self, transform):
"""
Return a new :class:`Bbox` object, statically transformed by
the given transform.
"""
return Bbox(transform.transform(self.get_points()))
00473 def inverse_transformed(self, transform):
"""
Return a new :class:`Bbox` object, statically transformed by
the inverse of the given transform.
"""
return Bbox(transform.inverted().transform(self.get_points()))
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)}
00489 def anchored(self, c, container = None):
"""
Return a copy of the Bbox, shifted to position c within a
container.
c: may be either:
* a sequence (cx, cy) where cx, 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.
Optional argument *container* is 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])
00521 def shrunk(self, mx, my):
"""
Return a copy of the :class:`Bbox`, shurnk 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]])
00532 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.
"""
assert box_aspect > 0 and fig_aspect > 0
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)])
00555 def splitx(self, *args):
"""
e.g., ``bbox.splitx(f1, f2, ...)``
Returns a list of new :class:`Bbox` objects formed by
splitting the original one with vertical lines at fractional
positions *f1*, *f2*, ...
"""
boxes = []
xf = [0] + list(args) + [1]
x0, y0, x1, y1 = self._get_extents()
w = x1 - x0
for xf0, xf1 in zip(xf[:-1], xf[1:]):
boxes.append(Bbox([[x0 + xf0 * w, y0], [x0 + xf1 * w, y1]]))
return boxes
00571 def splity(self, *args):
"""
e.g., ``bbox.splitx(f1, f2, ...)``
Returns a list of new :class:`Bbox` objects formed by
splitting the original one with horizontal lines at fractional
positions *f1*, *f2*, ...
"""
boxes = []
yf = [0] + list(args) + [1]
x0, y0, x1, y1 = self._get_extents()
h = y1 - y0
for yf0, yf1 in zip(yf[:-1], yf[1:]):
boxes.append(Bbox([[x0, y0 + yf0 * h], [x1, y0 + yf1 * h]]))
return boxes
00587 def count_contains(self, vertices):
"""
Count the number of vertices contained in the Bbox.
vertices is a Nx2 numpy array.
"""
if len(vertices) == 0:
return 0
vertices = np.asarray(vertices)
x0, y0, x1, y1 = self._get_extents()
dx0 = np.sign(vertices[:, 0] - x0)
dy0 = np.sign(vertices[:, 1] - y0)
dx1 = np.sign(vertices[:, 0] - x1)
dy1 = np.sign(vertices[:, 1] - y1)
inside = (abs(dx0 + dx1) + abs(dy0 + dy1)) <= 2
return N.sum(inside)
00604 def count_overlaps(self, bboxes):
"""
Count the number of bounding boxes that overlap this one.
bboxes is a sequence of :class:`BboxBase` objects
"""
return count_bboxes_overlapping_bbox(self, bboxes)
00612 def expanded(self, sw, sh):
"""
Return a new :class:`Bbox` which is this :class:`Bbox`
expanded around its center by the given 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)
00625 def padded(self, p):
"""
Return a new :class:`Bbox` that is padded on all four sides by
the given value.
"""
points = self._points
return Bbox(points + [[-p, -p], [p, p]])
00633 def translated(self, tx, ty):
"""
Return a copy of the :class:`Bbox`, statically translated by
tx and ty.
"""
return Bbox(self._points + (tx, ty))
00640 def corners(self):
"""
Return an array of points which are the four corners of this
rectangle. For example, if this :class:`Bbox` is defined by
the points (*a*, *b*) and (*c*, *d*), :meth:`corners` returns
(*a*, *b*), (*a*, *d*), (*c*, *b*) and (*c*, *d*).
"""
l, b, r, t = self.get_points().flatten()
return np.array([[l, b], [l, t], [r, b], [r, t]])
00650 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
00663 def union(bboxes):
"""
Return a :class:`Bbox` that contains all of the given bboxes.
"""
assert(len(bboxes))
if len(bboxes) == 1:
return bboxes[0]
x0 = np.inf
y0 = np.inf
x1 = -np.inf
y1 = -np.inf
for bbox in bboxes:
points = bbox.get_points()
xs = points[:, 0]
ys = points[:, 1]
x0 = min(x0, np.min(xs))
y0 = min(y0, np.min(ys))
x1 = max(x1, np.max(xs))
y1 = max(y1, np.max(ys))
return Bbox.from_extents(x0, y0, x1, y1)
union = staticmethod(union)
00690 class Bbox(BboxBase):
"""
A mutable bounding box.
"""
00695 def __init__(self, points):
"""
points: a 2x2 numpy array of the form [[x0, y0], [x1, y1]]
If you need to create a :class:`Bbox` object from another form
of data, consider the static methods unit, from_bounds and
from_extents.
"""
BboxBase.__init__(self)
self._points = np.asarray(points, np.float_)
self._minpos = np.array([0.0000001, 0.0000001])
self._ignore = True
if DEBUG:
___init__ = __init__
def __init__(self, points):
self._check(points)
self.___init__(points)
00714 def invalidate(self):
self._check(self._points)
TransformNode.invalidate(self)
_unit_values = np.array([[0.0, 0.0], [1.0, 1.0]], np.float_)
00720 def unit():
"""
(staticmethod) Create a new unit :class:`Bbox` from (0, 0) to
(1, 1).
"""
return Bbox(Bbox._unit_values.copy())
unit = staticmethod(unit)
00729 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)
from_bounds = staticmethod(from_bounds)
00740 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=np.float_).reshape(2, 2)
return Bbox(points)
from_extents = staticmethod(from_extents)
def __repr__(self):
return 'Bbox(%s)' % repr(self._points)
__str__ = __repr__
00755 def ignore(self, value):
"""
Set whether the existing bounds of the box should be ignored
by subsequent calls to :meth:`update_from_data` or
:meth:`update_from_data_xy`.
value:
- When True, subsequent calls to :meth:`update_from_data`
will ignore the existing bounds of the :class:`Bbox`.
- When False, subsequent calls to :meth:`update_from_data`
will include the existing bounds of the :class:`Bbox`.
"""
self._ignore = value
00771 def update_from_data(self, x, y, ignore=None):
"""
Update the bounds of the :class:`Bbox` based on the passed in
data.
x: a numpy array of x-values
y: a numpy array of y-values
ignore:
- 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 :meth:`ignore`.
"""
warnings.warn("update_from_data requires a memory copy -- please replace with update_from_data_xy")
xy = np.hstack((x.reshape((len(x), 1)), y.reshape((len(y), 1))))
return self.update_from_data_xy(xy, ignore)
00789 def update_from_data_xy(self, xy, ignore=None):
"""
Update the bounds of the :class:`Bbox` based on the passed in
data.
xy: a numpy array of 2D points
ignore:
- 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 :meth:`ignore`.
"""
if ignore is None:
ignore = self._ignore
if len(xy) == 0:
return
xym = ma.masked_invalid(xy)
if (xym.count(axis=1)!=2).all():
return
points, minpos, changed = update_path_extents(
Path(xy), None, self._points, self._minpos, ignore)
if changed:
self._points = points
self._minpos = minpos
self.invalidate()
def _set_x0(self, val):
self._points[0, 0] = val
self.invalidate()
x0 = property(BboxBase._get_x0, _set_x0)
def _set_y0(self, val):
self._points[0, 1] = val
self.invalidate()
y0 = property(BboxBase._get_y0, _set_y0)
def _set_x1(self, val):
self._points[1, 0] = val
self.invalidate()
x1 = property(BboxBase._get_x1, _set_x1)
def _set_y1(self, val):
self._points[1, 1] = val
self.invalidate()
y1 = property(BboxBase._get_y1, _set_y1)
def _set_p0(self, val):
self._points[0] = val
self.invalidate()
p0 = property(BboxBase._get_p0, _set_p0)
def _set_p1(self, val):
self._points[1] = val
self.invalidate()
p1 = property(BboxBase._get_p1, _set_p1)
def _set_intervalx(self, interval):
self._points[:, 0] = interval
self.invalidate()
intervalx = property(BboxBase._get_intervalx, _set_intervalx)
def _set_intervaly(self, interval):
self._points[:, 1] = interval
self.invalidate()
intervaly = property(BboxBase._get_intervaly, _set_intervaly)
def _set_bounds(self, bounds):
l, b, w, h = bounds
points = np.array([[l, b], [l+w, b+h]], np.float_)
if np.any(self._points != points):
self._points = points
self.invalidate()
bounds = property(BboxBase._get_bounds, _set_bounds)
def _get_minpos(self):
return self._minpos
minpos = property(_get_minpos)
def _get_minposx(self):
return self._minpos[0]
minposx = property(_get_minposx)
def _get_minposy(self):
return self._minpos[1]
minposy = property(_get_minposy)
00878 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
00886 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()
00896 def set(self, other):
"""
Set this bounding box from the "frozen" bounds of another Bbox.
"""
if np.any(self._points != other.get_points()):
self._points = other.get_points()
self.invalidate()
00905 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.
"""
00911 def __init__(self, bbox, transform):
"""
bbox: a child bbox
transform: a 2D transform
"""
assert bbox.is_bbox
assert isinstance(transform, Transform)
assert transform.input_dims == 2
assert transform.output_dims == 2
BboxBase.__init__(self)
self._bbox = bbox
self._transform = transform
self.set_children(bbox, transform)
self._points = None
def __repr__(self):
return "TransformedBbox(%s, %s)" % (self._bbox, self._transform)
__str__ = __repr__
def get_points(self):
if self._invalid:
points = self._transform.transform(self._bbox.get_points())
if ma.isMaskedArray(points):
points.putmask(0.0)
points = np.asarray(points)
self._points = points
self._invalid = 0
return self._points
get_points.__doc__ = Bbox.get_points.__doc__
if DEBUG:
_get_points = get_points
def get_points(self):
points = self._get_points()
self._check(points)
return points
00950 class Transform(TransformNode):
"""
The base class of all TransformNodes 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 :meth:`has_inverse` can return True)
If the transform needs to do something non-standard with
:class:`mathplotlib.path.Path` objects, such as adding curves
where there were once line segments, it should override:
- :meth:`transform_path`
"""
input_dims = None
output_dims = None
has_inverse = False
is_separable = False
00991 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))
01000 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))
01009 def __array__(self, *args, **kwargs):
"""
Used by C/C++ -based backends to get at the array matrix data.
"""
return self.frozen().__array__()
01015 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`).
"""
raise NotImplementedError()
01024 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`).
"""
return values
01041 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`).
"""
return self.transform(points)
01057 def get_affine(self):
"""
Get the affine part of this transform.
"""
return IdentityTransform()
01063 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`.
"""
assert len(point) == self.input_dims
return self.transform(np.asarray([point]))[0]
01075 def transform_path(self, path):
"""
Returns a transformed copy of path.
path: a Path instance.
In some cases, this transform may insert curves into the path
that began as line segments.
"""
return Path(self.transform(path.vertices), path.codes)
01086 def transform_path_affine(self, path):
"""
Returns a copy of path, transformed only by the affine part of
this transform.
path: a Path instance
``transform_path(path)`` is equivalent to
``transform_path_affine(transform_path_non_affine(values))``.
"""
return path
01098 def transform_path_non_affine(self, path):
"""
Returns a copy of path, transformed only by the non-affine
part of this transform.
path: a Path instance
``transform_path(path)`` is equivalent to
``transform_path_affine(transform_path_non_affine(values))``.
"""
return Path(self.transform_non_affine(path.vertices), path.codes)
01110 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()
01123 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
01139 def __init__(self, child):
"""
child: A Transform instance. This child may later be replaced
with :meth:`set`.
"""
assert isinstance(child, Transform)
Transform.__init__(self)
self.input_dims = child.input_dims
self.output_dims = child.output_dims
self._set(child)
self._invalid = 0
def __repr__(self):
return "TransformWrapper(%r)" % self._child
__str__ = __repr__
01156 def frozen(self):
return self._child.frozen()
frozen.__doc__ = Transform.frozen.__doc__
def _set(self, child):
self._child = child
self.set_children(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
01173 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.
"""
assert child.input_dims == self.input_dims
assert child.output_dims == self.output_dims
self._set(child)
self._invalid = 0
self.invalidate()
self._invalid = 0
def _get_is_affine(self):
return self._child.is_affine
is_affine = property(_get_is_affine)
def _get_is_separable(self):
return self._child.is_separable
is_separable = property(_get_is_separable)
def _get_has_inverse(self):
return self._child.has_inverse
has_inverse = property(_get_has_inverse)
01202 class AffineBase(Transform):
"""
The base class of all affine transformations of any number of
dimensions.
"""
is_affine = True
01209 def __init__(self):
Transform.__init__(self)
self._inverted = None
01213 def __array__(self, *args, **kwargs):
return self.get_matrix()
01217 def _concat(a, b):
"""
Concatenates two transformation matrices (represented as numpy
arrays) together.
"""
return np.dot(b, a)
_concat = staticmethod(_concat)
01225 def get_matrix(self):
"""
Get the underlying transformation matrix as a numpy array.
"""
raise NotImplementedError()
01231 def transform_non_affine(self, points):
return points
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
01235 def transform_path_affine(self, path):
return self.transform_path(path)
transform_path_affine.__doc__ = Transform.transform_path_affine.__doc__
01239 def transform_path_non_affine(self, path):
return path
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
01243 def get_affine(self):
return self
get_affine.__doc__ = Transform.get_affine.__doc__
01248 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 'get_matrix' that generates a custom 3x3 matrix.
"""
input_dims = 2
output_dims = 2
01273 def frozen(self):
return Affine2D(self.get_matrix().copy())
frozen.__doc__ = AffineBase.frozen.__doc__
def _get_is_separable(self):
mtx = self.get_matrix()
return mtx[0, 1] == 0.0 and mtx[1, 0] == 0.0
is_separable = property(_get_is_separable)
01282 def __array__(self, *args, **kwargs):
return self.get_matrix()
01285 def to_values(self):
"""
Return the values of the matrix as a sequence (a,b,c,d,e,f)
"""
mtx = self.get_matrix()
return tuple(mtx[:2].swapaxes(0, 1).flatten())
01293 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]], np.float_)
matrix_from_values = staticmethod(matrix_from_values)
01305 def transform(self, points):
mtx = self.get_matrix()
if isinstance(points, MaskedArray):
tpoints = affine_transform(points.data, mtx)
return ma.MaskedArray(tpoints, mask=ma.getmask(points))
return affine_transform(points, mtx)
01312 def transform_point(self, point):
mtx = self.get_matrix()
return affine_transform(point, mtx)
transform_point.__doc__ = AffineBase.transform_point.__doc__
if DEBUG:
_transform = transform
01319 def transform(self, points):
if (not ma.isMaskedArray(points) and
not isinstance(points, np.ndarray)):
warnings.warn(
('A non-numpy array of type %s was passed in for ' +
'transformation. Please correct this.')
% type(values))
return self._transform(points)
transform.__doc__ = AffineBase.transform.__doc__
transform_affine = transform
transform_affine.__doc__ = AffineBase.transform_affine.__doc__
01335 def inverted(self):
if self._inverted is None or self._invalid:
mtx = self.get_matrix()
self._inverted = Affine2D(inv(mtx))
self._invalid = 0
return self._inverted
inverted.__doc__ = AffineBase.inverted.__doc__
01344 class Affine2D(Affine2DBase):
"""
A mutable 2D affine transformation.
"""
01349 def __init__(self, matrix = None):
"""
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)
if matrix is None:
matrix = np.identity(3)
elif DEBUG:
matrix = np.asarray(matrix, np.float_)
assert matrix.shape == (3, 3)
self._mtx = matrix
self._invalid = 0
def __repr__(self):
return "Affine2D(%s)" % repr(self._mtx)
__str__ = __repr__
def __cmp__(self, other):
if (isinstance(other, Affine2D) and
(self.get_matrix() == other.get_matrix()).all()):
return 0
return -1
01379 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], np.float_)
.reshape((3,3)))
from_values = staticmethod(from_values)
01393 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
01404 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()
01415 def set(self, other):
"""
Set this transformation from the frozen copy of another
:class:`Affine2DBase` object.
"""
assert isinstance(other, Affine2DBase)
self._mtx = other.get_matrix()
self.invalidate()
01425 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(np.identity(3))
identity = staticmethod(identity)
01436 def clear(self):
"""
Reset the underlying matrix to the identity transform.
"""
self._mtx = np.identity(3)
self.invalidate()
return self
01444 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]],
np.float_)
self._mtx = np.dot(rotate_mtx, self._mtx)
self.invalidate()
return self
01461 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(degrees*np.pi/180.)
01471 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)
01481 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`.
"""
return self.translate(-x, -y).rotate_deg(degrees).translate(x, y)
01491 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]],
np.float_)
self._mtx = np.dot(translate_mtx, self._mtx)
self.invalidate()
return self
01506 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]],
np.float_)
self._mtx = np.dot(scale_mtx, self._mtx)
self.invalidate()
return self
def _get_is_separable(self):
mtx = self.get_matrix()
return mtx[0, 1] == 0.0 and mtx[1, 0] == 0.0
is_separable = property(_get_is_separable)
01532 class IdentityTransform(Affine2DBase):
"""
A special class that does on thing, the identity transform, in a
fast way.
"""
_mtx = np.identity(3)
01539 def frozen(self):
return self
frozen.__doc__ = Affine2DBase.frozen.__doc__
def __repr__(self):
return "IdentityTransform()"
__str__ = __repr__
01547 def get_matrix(self):
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
01551 def transform(self, points):
return points
transform.__doc__ = Affine2DBase.transform.__doc__
transform_affine = transform
transform_affine.__doc__ = Affine2DBase.transform_affine.__doc__
transform_non_affine = transform
transform_non_affine.__doc__ = Affine2DBase.transform_non_affine.__doc__
01561 def transform_path(self, path):
return path
transform_path.__doc__ = Affine2DBase.transform_path.__doc__
transform_path_affine = transform_path
transform_path_affine.__doc__ = Affine2DBase.transform_path_affine.__doc__
transform_path_non_affine = transform_path
transform_path_non_affine.__doc__ = Affine2DBase.transform_path_non_affine.__doc__
01571 def get_affine(self):
return self
get_affine.__doc__ = Affine2DBase.get_affine.__doc__
inverted = get_affine
inverted.__doc__ = Affine2DBase.inverted.__doc__
01579 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
01592 def __init__(self, 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.
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.
"""
Transform.__init__(self)
self._x = x_transform
self._y = y_transform
self.set_children(x_transform, y_transform)
self._affine = None
def _get_is_affine(self):
return self._x.is_affine and self._y.is_affine
is_affine = property(_get_is_affine)
01614 def frozen(self):
return blended_transform_factory(self._x.frozen(), self._y.frozen())
frozen.__doc__ = Transform.frozen.__doc__
def __repr__(self):
return "BlendedGenericTransform(%s,%s)" % (self._x, self._y)
__str__ = __repr__
01622 def transform(self, points):
x = self._x
y = self._y
if x is y and x.input_dims == 2:
return x.transform(points)
if x.input_dims == 2:
x_points = x.transform(points)[:, 0:1]
else:
x_points = x.transform(points[:, 0])
x_points = x_points.reshape((len(x_points), 1))
if y.input_dims == 2:
y_points = y.transform(points)[:, 1:]
else:
y_points = y.transform(points[:, 1])
y_points = y_points.reshape((len(y_points), 1))
if isinstance(x_points, MaskedArray) or isinstance(y_points, MaskedArray):
return ma.concatenate((x_points, y_points), 1)
else:
return np.concatenate((x_points, y_points), 1)
transform.__doc__ = Transform.transform.__doc__
01647 def transform_affine(self, points):
return self.get_affine().transform(points)
transform_affine.__doc__ = Transform.transform_affine.__doc__
01651 def transform_non_affine(self, points):
if self._x.is_affine and self._y.is_affine:
return points
return self.transform(points)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
01657 def inverted(self):
return BlendedGenericTransform(self._x.inverted(), self._y.inverted())
inverted.__doc__ = Transform.inverted.__doc__
01661 def get_affine(self):
if self._invalid or self._affine is None:
if self._x.is_affine and self._y.is_affine:
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()
mtx = np.vstack((x_mtx[0], y_mtx[1], [0.0, 0.0, 1.0]))
self._affine = Affine2D(mtx)
else:
self._affine = IdentityTransform()
self._invalid = 0
return self._affine
get_affine.__doc__ = Transform.get_affine.__doc__
01681 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 Affine2DBase.
"""
is_separable = True
01691 def __init__(self, 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.
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.
"""
assert x_transform.is_affine
assert y_transform.is_affine
assert x_transform.is_separable
assert y_transform.is_separable
Transform.__init__(self)
self._x = x_transform
self._y = y_transform
self.set_children(x_transform, y_transform)
Affine2DBase.__init__(self)
self._mtx = None
def __repr__(self):
return "BlendedAffine2D(%s,%s)" % (self._x, self._y)
__str__ = __repr__
01720 def get_matrix(self):
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()
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
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
01737 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)
01751 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
01759 def __init__(self, a, b):
"""
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.
"""
assert a.output_dims == b.input_dims
self.input_dims = a.input_dims
self.output_dims = b.output_dims
Transform.__init__(self)
self._a = a
self._b = b
self.set_children(a, b)
01778 def frozen(self):
self._invalid = 0
frozen = composite_transform_factory(self._a.frozen(), self._b.frozen())
if not isinstance(frozen, CompositeGenericTransform):
return frozen.frozen()
return frozen
frozen.__doc__ = Transform.frozen.__doc__
def _get_is_affine(self):
return self._a.is_affine and self._b.is_affine
is_affine = property(_get_is_affine)
def _get_is_separable(self):
return self._a.is_separable and self._b.is_separable
is_separable = property(_get_is_separable)
def __repr__(self):
return "CompositeGenericTransform(%s, %s)" % (self._a, self._b)
__str__ = __repr__
01798 def transform(self, points):
return self._b.transform(
self._a.transform(points))
transform.__doc__ = Transform.transform.__doc__
01803 def transform_affine(self, points):
return self.get_affine().transform(points)
transform_affine.__doc__ = Transform.transform_affine.__doc__
01807 def transform_non_affine(self, points):
if self._a.is_affine and self._b.is_affine:
return points
return self._b.transform_non_affine(
self._a.transform(points))
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
01814 def transform_path(self, path):
return self._b.transform_path(
self._a.transform_path(path))
transform_path.__doc__ = Transform.transform_path.__doc__
01819 def transform_path_affine(self, path):
return self._b.transform_path_affine(
self._a.transform_path(path))
transform_path_affine.__doc__ = Transform.transform_path_affine.__doc__
01824 def transform_path_non_affine(self, path):
if self._a.is_affine and self._b.is_affine:
return path
return self._b.transform_path_non_affine(
self._a.transform_path(path))
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
01831 def get_affine(self):
if self._a.is_affine and self._b.is_affine:
return Affine2D(np.dot(self._b.get_affine().get_matrix(),
self._a.get_affine().get_matrix()))
else:
return self._b.get_affine()
get_affine.__doc__ = Transform.get_affine.__doc__
01839 def inverted(self):
return CompositeGenericTransform(self._b.inverted(), self._a.inverted())
inverted.__doc__ = Transform.inverted.__doc__
01844 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.
"""
01851 def __init__(self, a, b):
"""
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.
"""
assert a.output_dims == b.input_dims
self.input_dims = a.input_dims
self.output_dims = b.output_dims
assert a.is_affine
assert b.is_affine
Affine2DBase.__init__(self)
self._a = a
self._b = b
self.set_children(a, b)
self._mtx = None
def __repr__(self):
return "CompositeAffine2D(%s, %s)" % (self._a, self._b)
__str__ = __repr__
01879 def get_matrix(self):
if self._invalid:
self._mtx = np.dot(
self._b.get_matrix(),
self._a.get_matrix())
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
01890 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
"""
if isinstance(a, IdentityTransform):
return b
elif isinstance(b, IdentityTransform):
return a
elif isinstance(a, AffineBase) and isinstance(b, AffineBase):
return CompositeAffine2D(a, b)
return CompositeGenericTransform(a, b)
01913 class BboxTransform(Affine2DBase):
"""
BboxTransform linearly transforms points from one Bbox to another Bbox.
"""
is_separable = True
01919 def __init__(self, boxin, boxout):
"""
Create a new BboxTransform that linearly transforms points
from boxin to boxout.
"""
assert boxin.is_bbox
assert boxout.is_bbox
Affine2DBase.__init__(self)
self._boxin = boxin
self._boxout = boxout
self.set_children(boxin, boxout)
self._mtx = None
self._inverted = None
def __repr__(self):
return "BboxTransform(%s, %s)" % (self._boxin, self._boxout)
__str__ = __repr__
01938 def get_matrix(self):
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 ]],
np.float_)
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
01956 class BboxTransformTo(Affine2DBase):
"""
BboxTransformTo is a transformation that linearly transforms
points from the unit bounding box to a given :class:`Bbox`.
"""
is_separable = True
01963 def __init__(self, boxout):
"""
Create a new :class:`BboxTransformTo` that linearly transforms
points from the unit bounding box to boxout.
"""
assert boxout.is_bbox
Affine2DBase.__init__(self)
self._boxout = boxout
self.set_children(boxout)
self._mtx = None
self._inverted = None
def __repr__(self):
return "BboxTransformTo(%s)" % (self._boxout)
__str__ = __repr__
01980 def get_matrix(self):
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]],
np.float_)
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
01995 class BboxTransformFrom(Affine2DBase):
"""
BboxTransform linearly transforms points from a given
:class:`Bbox` to the unit bounding box.
"""
is_separable = True
def __init__(self, boxin):
assert boxin.is_bbox
Affine2DBase.__init__(self)
self._boxin = boxin
self.set_children(boxin)
self._mtx = None
self._inverted = None
def __repr__(self):
return "BboxTransformFrom(%s)" % (self._boxin)
__str__ = __repr__
02015 def get_matrix(self):
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 ]],
np.float_)
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
02032 class ScaledTranslation(Affine2DBase):
"""
A transformation that translates by xt and yt, after xt and yt
have been transformaed by the given transform scale_trans.
"""
def __init__(self, xt, yt, scale_trans):
Affine2DBase.__init__(self)
self._t = (xt, yt)
self._scale_trans = scale_trans
self.set_children(scale_trans)
self._mtx = None
self._inverted = None
def __repr__(self):
return "ScaledTranslation(%s)" % (self._t,)
__str__ = __repr__
02049 def get_matrix(self):
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]],
np.float_)
self._invalid = 0
self._inverted = None
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
02062 class TransformedPath(TransformNode):
"""
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.
"""
02068 def __init__(self, path, transform):
"""
Create a new TransformedPath from the given path and transform.
"""
assert isinstance(transform, Transform)
TransformNode.__init__(self)
self._path = path
self._transform = transform
self.set_children(transform)
self._transformed_path = None
02080 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.
"""
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._invalid = 0
return self._transformed_path, self.get_affine()
02093 def get_fully_transformed_path(self):
"""
Return a fully-transformed copy of the child path.
"""
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._invalid = 0
return self._transform.transform_path_affine(self._transformed_path)
def get_affine(self):
return self._transform.get_affine()
02108 def nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True):
'''
Ensure the endpoints of a range are not too close together.
"too close" means the interval is smaller than 'tiny' times
the maximum absolute value.
If they are too close, each will be moved by the 'expander'.
If 'increasing' is True and vmin > vmax, they will be swapped,
regardless of whether they are too close.
'''
swapped = False
if vmax < vmin:
vmin, vmax = vmax, vmin
swapped = True
if vmax - vmin <= max(abs(vmin), abs(vmax)) * tiny:
if vmin == 0.0:
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
def interval_contains(interval, val):
a, b = interval
return (
((a < b) and (a <= val and b >= val))
or (b <= val and a >= val))
def interval_contains_open(interval, val):
a, b = interval
return (
((a < b) and (a < val and b > val))
or (b < val and a > val))
if __name__ == '__main__':
import copy
from random import random
import timeit
bbox = Bbox.from_extents(10., 15., 20., 25.)
assert bbox.x0 == 10
assert bbox.y0 == 15
assert bbox.x1 == 20
assert bbox.y1 == 25
assert np.all(bbox.min == [10, 15])
assert np.all(bbox.max == [20, 25])
assert np.all(bbox.intervalx == (10, 20))
assert np.all(bbox.intervaly == (15, 25))
assert bbox.width == 10
assert bbox.height == 10
assert bbox.bounds == (10, 15, 10, 10)
assert tuple(np.asarray(bbox).flatten()) == (10, 15, 20, 25)
bbox.intervalx = (11, 21)
bbox.intervaly = (16, 26)
assert bbox.bounds == (11, 16, 10, 10)
bbox.x0 = 12
bbox.y0 = 17
bbox.x1 = 22
bbox.y1 = 27
assert bbox.bounds == (12, 17, 10, 10)
bbox = Bbox.from_bounds(10, 11, 12, 13)
assert bbox.bounds == (10, 11, 12, 13)
bbox_copy = copy.deepcopy(bbox)
assert (bbox.extents == bbox_copy.extents).all()
bbox_copy.p1 = (14, 15)
assert bbox.bounds == (10, 11, 12, 13)
assert bbox_copy.bounds == (10, 11, 4, 4)
bbox1 = Bbox([[10., 15.], [20., 25.]])
bbox2 = Bbox([[30., 35.], [40., 45.]])
trans = BboxTransform(bbox1, bbox2)
bbox3 = bbox1.transformed(trans)
assert (bbox3.extents == bbox2.extents).all()
translation = Affine2D().translate(10, 20)
assert translation.to_values() == (1, 0, 0, 1, 10, 20)
scale = Affine2D().scale(10, 20)
assert scale.to_values() == (10, 0, 0, 20, 0, 0)
rotation = Affine2D().rotate_deg(30)
assert rotation.to_values() == (0.86602540378443871, 0.49999999999999994,
-0.49999999999999994, 0.86602540378443871,
0.0, 0.0)
points = np.array([[1, 2], [3, 4], [5, 6], [7, 8]], np.float_)
translated_points = translation.transform(points)
assert (translated_points == [[11., 22.], [13., 24.], [15., 26.], [17., 28.]]).all()
scaled_points = scale.transform(points)
print scaled_points
rotated_points = rotation.transform(points)
print rotated_points
tpoints1 = rotation.transform(translation.transform(scale.transform(points)))
trans_sum = scale + translation + rotation
tpoints2 = trans_sum.transform(points)
assert (tpoints1.round() == tpoints2.round()).all()
print points
points = np.asarray([(random(), random()) for i in xrange(10000)])
t = timeit.Timer("trans_sum.transform(points)", "from __main__ import trans_sum, points")
print "Time to transform 10000 x 10 points:", t.timeit(10)