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# Source code for mpl_toolkits.mplot3d.axes3d

"""
axes3d.py, original mplot3d version by John Porter
Created: 23 Sep 2005

Parts fixed by Reinier Heeres <[email protected]>
Minor additions by Ben Axelrod <[email protected]>
Significant updates and revisions by Ben Root <[email protected]>

Module containing Axes3D, an object which can plot 3D objects on a
2D matplotlib figure.
"""
from collections import defaultdict
from functools import reduce
import math

import numpy as np

from matplotlib import artist
import matplotlib.axes as maxes
import matplotlib.cbook as cbook
import matplotlib.collections as mcoll
import matplotlib.colors as mcolors
import matplotlib.docstring as docstring
import matplotlib.projections as proj
import matplotlib.scale as mscale
import matplotlib.transforms as mtransforms
from matplotlib.axes import Axes, rcParams
from matplotlib.colors import Normalize, LightSource
from matplotlib.transforms import Bbox
from matplotlib.tri.triangulation import Triangulation

from . import art3d
from . import proj3d
from . import axis3d

def unit_bbox():
box = Bbox(np.array([[0, 0], [1, 1]]))
return box

[docs]class Axes3D(Axes):
"""
3D axes object.
"""
name = '3d'
_shared_z_axes = cbook.Grouper()

@docstring.dedent_interpd
def __init__(
self, fig, rect=None, *args,
azim=-60, elev=30, zscale=None, sharez=None, proj_type='persp',
**kwargs):
"""
Parameters
----------
fig : Figure
The parent figure.
rect : (float, float, float, float)
The (left, bottom, width, height) axes position.
azim : float, optional
Azimuthal viewing angle, defaults to -60.
elev : float, optional
Elevation viewing angle, defaults to 30.
zscale : [%(scale)s], optional
The z scale.  Note that currently, only a linear scale is
supported.
sharez : Axes3D, optional
Other axes to share z-limits with.
proj_type : {'persp', 'ortho'}
The projection type, default 'persp'.

Notes
-----
The *sharez* parameter.
"""

if rect is None:
rect = [0.0, 0.0, 1.0, 1.0]
self._cids = []

self.initial_azim = azim
self.initial_elev = elev
self.set_proj_type(proj_type)

self.xy_viewLim = unit_bbox()
self.zz_viewLim = unit_bbox()
self.xy_dataLim = unit_bbox()
self.zz_dataLim = unit_bbox()
# inhibit autoscale_view until the axes are defined
# they can't be defined until Axes.__init__ has been called
self.view_init(self.initial_elev, self.initial_azim)

self._sharez = sharez
if sharez is not None:
self._shared_z_axes.join(self, sharez)

super().__init__(fig, rect, frameon=True, *args, **kwargs)
# Disable drawing of axes by base class
super().set_axis_off()
# Enable drawing of axes by Axes3D class
self.set_axis_on()
self.M = None

# func used to format z -- fall back on major formatters
self.fmt_zdata = None

if zscale is not None:
self.set_zscale(zscale)

if self.zaxis is not None:
self._zcid = self.zaxis.callbacks.connect(
'units finalize', lambda: self._on_units_changed(scalez=True))
else:
self._zcid = None

self.mouse_init()
self.set_top_view()

self.patch.set_linewidth(0)
# Calculate the pseudo-data width and height
pseudo_bbox = self.transLimits.inverted().transform([(0, 0), (1, 1)])
self._pseudo_w, self._pseudo_h = pseudo_bbox[1] - pseudo_bbox[0]

# mplot3d currently manages its own spines and needs these turned off
# for bounding box calculations
for k in self.spines.keys():
self.spines[k].set_visible(False)

[docs]    def set_axis_off(self):
self._axis3don = False
self.stale = True

[docs]    def set_axis_on(self):
self._axis3don = True
self.stale = True

[docs]    def have_units(self):
"""
Return *True* if units are set on the *x*, *y*, or *z* axes

"""
return (self.xaxis.have_units() or self.yaxis.have_units() or
self.zaxis.have_units())

[docs]    def convert_zunits(self, z):
"""
For artists in an axes, if the zaxis has units support,
convert *z* using zaxis unit type

.. versionadded :: 1.2.1

"""
return self.zaxis.convert_units(z)

def _process_unit_info(self, xdata=None, ydata=None, zdata=None,
kwargs=None):
"""
Look for unit *kwargs* and update the axis instances as necessary

"""
super()._process_unit_info(xdata=xdata, ydata=ydata, kwargs=kwargs)

if self.xaxis is None or self.yaxis is None or self.zaxis is None:
return

if zdata is not None:
# we only need to update if there is nothing set yet.
if not self.zaxis.have_units():
self.zaxis.update_units(xdata)

# process kwargs 2nd since these will override default units
if kwargs is not None:
zunits = kwargs.pop('zunits', self.zaxis.units)
if zunits != self.zaxis.units:
self.zaxis.set_units(zunits)
# If the units being set imply a different converter,
# we need to update.
if zdata is not None:
self.zaxis.update_units(zdata)

[docs]    def set_top_view(self):
# this happens to be the right view for the viewing coordinates
# moved up and to the left slightly to fit labels and axes
xdwl = (0.95/self.dist)
xdw = (0.9/self.dist)
ydwl = (0.95/self.dist)
ydw = (0.9/self.dist)

# This is purposely using the 2D Axes's set_xlim and set_ylim,
# because we are trying to place our viewing pane.
super().set_xlim(-xdwl, xdw, auto=None)
super().set_ylim(-ydwl, ydw, auto=None)

def _init_axis(self):
'''Init 3D axes; overrides creation of regular X/Y axes'''
self.xaxis = axis3d.XAxis('x', self.xy_viewLim.intervalx,
self.xy_dataLim.intervalx, self)
self.yaxis = axis3d.YAxis('y', self.xy_viewLim.intervaly,
self.xy_dataLim.intervaly, self)
self.zaxis = axis3d.ZAxis('z', self.zz_viewLim.intervalx,
self.zz_dataLim.intervalx, self)
# Provide old aliases
self.w_xaxis = self.xaxis
self.w_yaxis = self.yaxis
self.w_zaxis = self.zaxis

for ax in self.xaxis, self.yaxis, self.zaxis:
ax.init3d()

[docs]    def get_zaxis(self):
'''Return the ZAxis (~.axis3d.Axis) instance.'''
return self.zaxis

def _get_axis_list(self):
return super()._get_axis_list() + (self.zaxis, )

[docs]    def unit_cube(self, vals=None):
minx, maxx, miny, maxy, minz, maxz = vals or self.get_w_lims()
return [(minx, miny, minz),
(maxx, miny, minz),
(maxx, maxy, minz),
(minx, maxy, minz),
(minx, miny, maxz),
(maxx, miny, maxz),
(maxx, maxy, maxz),
(minx, maxy, maxz)]

[docs]    def tunit_cube(self, vals=None, M=None):
if M is None:
M = self.M
xyzs = self.unit_cube(vals)
tcube = proj3d.proj_points(xyzs, M)
return tcube

[docs]    def tunit_edges(self, vals=None, M=None):
tc = self.tunit_cube(vals, M)
edges = [(tc[0], tc[1]),
(tc[1], tc[2]),
(tc[2], tc[3]),
(tc[3], tc[0]),

(tc[0], tc[4]),
(tc[1], tc[5]),
(tc[2], tc[6]),
(tc[3], tc[7]),

(tc[4], tc[5]),
(tc[5], tc[6]),
(tc[6], tc[7]),
(tc[7], tc[4])]
return edges

[docs]    @artist.allow_rasterization
def draw(self, renderer):
# draw the background patch
self.patch.draw(renderer)
self._frameon = False

# first, set the aspect
# this is duplicated from axes._base._AxesBase.draw
# but must be called before any of the artist are drawn as
# it adjusts the view limits and the size of the bounding box
# of the axes
locator = self.get_axes_locator()
if locator:
pos = locator(self, renderer)
self.apply_aspect(pos)
else:
self.apply_aspect()

# add the projection matrix to the renderer
self.M = self.get_proj()
renderer.M = self.M
renderer.vvec = self.vvec
renderer.eye = self.eye
renderer.get_axis_position = self.get_axis_position

# Calculate projection of collections and patches and zorder them.
# Make sure they are drawn above the grids.
zorder_offset = max(axis.get_zorder()
for axis in self._get_axis_list()) + 1
for i, col in enumerate(
sorted(self.collections,
key=lambda col: col.do_3d_projection(renderer),
reverse=True)):
col.zorder = zorder_offset + i
for i, patch in enumerate(
sorted(self.patches,
key=lambda patch: patch.do_3d_projection(renderer),
reverse=True)):
patch.zorder = zorder_offset + i

if self._axis3don:
# Draw panes first
for axis in self._get_axis_list():
axis.draw_pane(renderer)
# Then axes
for axis in self._get_axis_list():
axis.draw(renderer)

# Then rest
super().draw(renderer)

[docs]    def get_axis_position(self):
vals = self.get_w_lims()
tc = self.tunit_cube(vals, self.M)
xhigh = tc[1][2] > tc[2][2]
yhigh = tc[3][2] > tc[2][2]
zhigh = tc[0][2] > tc[2][2]
return xhigh, yhigh, zhigh

def _on_units_changed(self, scalex=False, scaley=False, scalez=False):
"""
Callback for processing changes to axis units.

Currently forces updates of data limits and view limits.
"""
self.relim()
self.autoscale_view(scalex=scalex, scaley=scaley, scalez=scalez)

[docs]    def update_datalim(self, xys, **kwargs):
pass

[docs]    def get_autoscale_on(self):
"""
Get whether autoscaling is applied for all axes on plot commands

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
return super().get_autoscale_on() and self.get_autoscalez_on()

[docs]    def get_autoscalez_on(self):
"""
Get whether autoscaling for the z-axis is applied on plot commands

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
return self._autoscaleZon

[docs]    def set_autoscale_on(self, b):
"""
Set whether autoscaling is applied on plot commands

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.

Parameters
----------
b : bool
"""
super().set_autoscale_on(b)
self.set_autoscalez_on(b)

[docs]    def set_autoscalez_on(self, b):
"""
Set whether autoscaling for the z-axis is applied on plot commands

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.

Parameters
----------
b : bool
"""
self._autoscaleZon = b

[docs]    def set_zmargin(self, m):
"""
Set padding of Z data limits prior to autoscaling.

*m* times the data interval will be added to each
end of that interval before it is used in autoscaling.

accepts: float in range 0 to 1

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
if m < 0 or m > 1:
raise ValueError("margin must be in range 0 to 1")
self._zmargin = m
self.stale = True

[docs]    def margins(self, *margins, x=None, y=None, z=None, tight=True):
"""
Convenience method to set or retrieve autoscaling margins.

signatures::
margins()

returns xmargin, ymargin, zmargin

::

margins(margin)

margins(xmargin, ymargin, zmargin)

margins(x=xmargin, y=ymargin, z=zmargin)

margins(..., tight=False)

All forms above set the xmargin, ymargin and zmargin
parameters. All keyword parameters are optional.  A single
positional argument specifies xmargin, ymargin and zmargin.
Passing both positional and keyword arguments for xmargin,
ymargin, and/or zmargin is invalid.

The *tight* parameter
is passed to :meth:autoscale_view, which is executed after
a margin is changed; the default here is *True*, on the
assumption that when margins are specified, no additional
padding to match tick marks is usually desired.  Setting
*tight* to *None* will preserve the previous setting.

Specifying any margin changes only the autoscaling; for example,
if *xmargin* is not None, then *xmargin* times the X data
interval will be added to each end of that interval before
it is used in autoscaling.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
if margins and x is not None and y is not None and z is not None:
raise TypeError('Cannot pass both positional and keyword '
'arguments for x, y, and/or z.')
elif len(margins) == 1:
x = y = z = margins[0]
elif len(margins) == 3:
x, y, z = margins
elif margins:
raise TypeError('Must pass a single positional argument for all '
'margins, or one for each margin (x, y, z).')

if x is None and y is None and z is None:
if tight is not True:
cbook._warn_external(f'ignoring tight={tight!r} in get mode')
return self._xmargin, self._ymargin, self._zmargin

if x is not None:
self.set_xmargin(x)
if y is not None:
self.set_ymargin(y)
if z is not None:
self.set_zmargin(z)

self.autoscale_view(
tight=tight, scalex=(x is not None), scaley=(y is not None),
scalez=(z is not None)
)

[docs]    def autoscale(self, enable=True, axis='both', tight=None):
"""
Convenience method for simple axis view autoscaling.
See :meth:matplotlib.axes.Axes.autoscale for full explanation.
Note that this function behaves the same, but for all
three axes.  Therefore, 'z' can be passed for *axis*,
and 'both' applies to all three axes.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
if enable is None:
scalex = True
scaley = True
scalez = True
else:
if axis in ['x', 'both']:
self._autoscaleXon = scalex = bool(enable)
else:
scalex = False
if axis in ['y', 'both']:
self._autoscaleYon = scaley = bool(enable)
else:
scaley = False
if axis in ['z', 'both']:
self._autoscaleZon = scalez = bool(enable)
else:
scalez = False
self.autoscale_view(tight=tight, scalex=scalex, scaley=scaley,
scalez=scalez)

[docs]    def auto_scale_xyz(self, X, Y, Z=None, had_data=None):
# This updates the bounding boxes as to keep a record as to what the
# minimum sized rectangular volume holds the data.
X = np.reshape(X, -1)
Y = np.reshape(Y, -1)
self.xy_dataLim.update_from_data_xy(
np.column_stack([X, Y]), not had_data)
if Z is not None:
Z = np.reshape(Z, -1)
self.zz_dataLim.update_from_data_xy(
np.column_stack([Z, Z]), not had_data)
# Let autoscale_view figure out how to use this data.
self.autoscale_view()

[docs]    def autoscale_view(self, tight=None, scalex=True, scaley=True,
scalez=True):
"""
Autoscale the view limits using the data limits.
See :meth:matplotlib.axes.Axes.autoscale_view for documentation.
Note that this function applies to the 3D axes, and as such
adds the *scalez* to the function arguments.

.. versionchanged :: 1.1.0
Function signature was changed to better match the 2D version.
*tight* is now explicitly a kwarg and placed first.

.. versionchanged :: 1.2.1
This is now fully functional.

"""
return

# This method looks at the rectangular volume (see above)
# of data and decides how to scale the view portal to fit it.
if tight is None:
# if image data only just use the datalim
_tight = self._tight or (
len(self.images) > 0
and len(self.lines) == len(self.patches) == 0)
else:
_tight = self._tight = bool(tight)

if scalex and self._autoscaleXon:
self._shared_x_axes.clean()
x0, x1 = self.xy_dataLim.intervalx
xlocator = self.xaxis.get_major_locator()
x0, x1 = xlocator.nonsingular(x0, x1)
if self._xmargin > 0:
delta = (x1 - x0) * self._xmargin
x0 -= delta
x1 += delta
if not _tight:
x0, x1 = xlocator.view_limits(x0, x1)
self.set_xbound(x0, x1)

if scaley and self._autoscaleYon:
self._shared_y_axes.clean()
y0, y1 = self.xy_dataLim.intervaly
ylocator = self.yaxis.get_major_locator()
y0, y1 = ylocator.nonsingular(y0, y1)
if self._ymargin > 0:
delta = (y1 - y0) * self._ymargin
y0 -= delta
y1 += delta
if not _tight:
y0, y1 = ylocator.view_limits(y0, y1)
self.set_ybound(y0, y1)

if scalez and self._autoscaleZon:
self._shared_z_axes.clean()
z0, z1 = self.zz_dataLim.intervalx
zlocator = self.zaxis.get_major_locator()
z0, z1 = zlocator.nonsingular(z0, z1)
if self._zmargin > 0:
delta = (z1 - z0) * self._zmargin
z0 -= delta
z1 += delta
if not _tight:
z0, z1 = zlocator.view_limits(z0, z1)
self.set_zbound(z0, z1)

[docs]    def get_w_lims(self):
'''Get 3D world limits.'''
minx, maxx = self.get_xlim3d()
miny, maxy = self.get_ylim3d()
minz, maxz = self.get_zlim3d()
return minx, maxx, miny, maxy, minz, maxz

def _determine_lims(self, xmin=None, xmax=None, *args, **kwargs):
if xmax is None and np.iterable(xmin):
xmin, xmax = xmin
if xmin == xmax:
xmin -= 0.05
xmax += 0.05
return (xmin, xmax)

[docs]    def set_xlim3d(self, left=None, right=None, emit=True, auto=False,
*, xmin=None, xmax=None):
"""
Set 3D x limits.

See :meth:matplotlib.axes.Axes.set_xlim for full documentation.

"""
if right is None and np.iterable(left):
left, right = left
if xmin is not None:
cbook.warn_deprecated('3.0', name='xmin',
alternative='left', obj_type='argument')
if left is not None:
raise TypeError('Cannot pass both xmin and left')
left = xmin
if xmax is not None:
cbook.warn_deprecated('3.0', name='xmax',
alternative='right', obj_type='argument')
if right is not None:
raise TypeError('Cannot pass both xmax and right')
right = xmax

self._process_unit_info(xdata=(left, right))
left = self._validate_converted_limits(left, self.convert_xunits)
right = self._validate_converted_limits(right, self.convert_xunits)

old_left, old_right = self.get_xlim()
if left is None:
left = old_left
if right is None:
right = old_right

if left == right:
cbook._warn_external(
f"Attempting to set identical left == right == {left} results "
f"in singular transformations; automatically expanding.")
left, right = self.xaxis.get_major_locator().nonsingular(left, right)
left, right = self.xaxis.limit_range_for_scale(left, right)
self.xy_viewLim.intervalx = (left, right)

if auto is not None:
self._autoscaleXon = bool(auto)

if emit:
self.callbacks.process('xlim_changed', self)
# Call all of the other x-axes that are shared with this one
for other in self._shared_x_axes.get_siblings(self):
if other is not self:
other.set_xlim(self.xy_viewLim.intervalx,
emit=False, auto=auto)
if other.figure != self.figure:
other.figure.canvas.draw_idle()
self.stale = True
return left, right
set_xlim = set_xlim3d

[docs]    def set_ylim3d(self, bottom=None, top=None, emit=True, auto=False,
*, ymin=None, ymax=None):
"""
Set 3D y limits.

See :meth:matplotlib.axes.Axes.set_ylim for full documentation.

"""
if top is None and np.iterable(bottom):
bottom, top = bottom
if ymin is not None:
cbook.warn_deprecated('3.0', name='ymin',
alternative='bottom', obj_type='argument')
if bottom is not None:
raise TypeError('Cannot pass both ymin and bottom')
bottom = ymin
if ymax is not None:
cbook.warn_deprecated('3.0', name='ymax',
alternative='top', obj_type='argument')
if top is not None:
raise TypeError('Cannot pass both ymax and top')
top = ymax

self._process_unit_info(ydata=(bottom, top))
bottom = self._validate_converted_limits(bottom, self.convert_yunits)
top = self._validate_converted_limits(top, self.convert_yunits)

old_bottom, old_top = self.get_ylim()
if bottom is None:
bottom = old_bottom
if top is None:
top = old_top

if bottom == top:
cbook._warn_external(
f"Attempting to set identical bottom == top == {bottom} "
f"results in singular transformations; automatically "
f"expanding.")
bottom, top = self.yaxis.get_major_locator().nonsingular(bottom, top)
bottom, top = self.yaxis.limit_range_for_scale(bottom, top)
self.xy_viewLim.intervaly = (bottom, top)

if auto is not None:
self._autoscaleYon = bool(auto)

if emit:
self.callbacks.process('ylim_changed', self)
# Call all of the other y-axes that are shared with this one
for other in self._shared_y_axes.get_siblings(self):
if other is not self:
other.set_ylim(self.xy_viewLim.intervaly,
emit=False, auto=auto)
if other.figure != self.figure:
other.figure.canvas.draw_idle()
self.stale = True
return bottom, top
set_ylim = set_ylim3d

[docs]    def set_zlim3d(self, bottom=None, top=None, emit=True, auto=False,
*, zmin=None, zmax=None):
"""
Set 3D z limits.

See :meth:matplotlib.axes.Axes.set_ylim for full documentation

"""
if top is None and np.iterable(bottom):
bottom, top = bottom
if zmin is not None:
cbook.warn_deprecated('3.0', name='zmin',
alternative='bottom', obj_type='argument')
if bottom is not None:
raise TypeError('Cannot pass both zmin and bottom')
bottom = zmin
if zmax is not None:
cbook.warn_deprecated('3.0', name='zmax',
alternative='top', obj_type='argument')
if top is not None:
raise TypeError('Cannot pass both zmax and top')
top = zmax

self._process_unit_info(zdata=(bottom, top))
bottom = self._validate_converted_limits(bottom, self.convert_zunits)
top = self._validate_converted_limits(top, self.convert_zunits)

old_bottom, old_top = self.get_zlim()
if bottom is None:
bottom = old_bottom
if top is None:
top = old_top

if bottom == top:
cbook._warn_external(
f"Attempting to set identical bottom == top == {bottom} "
f"results in singular transformations; automatically "
f"expanding.")
bottom, top = self.zaxis.get_major_locator().nonsingular(bottom, top)
bottom, top = self.zaxis.limit_range_for_scale(bottom, top)
self.zz_viewLim.intervalx = (bottom, top)

if auto is not None:
self._autoscaleZon = bool(auto)

if emit:
self.callbacks.process('zlim_changed', self)
# Call all of the other y-axes that are shared with this one
for other in self._shared_z_axes.get_siblings(self):
if other is not self:
other.set_zlim(self.zz_viewLim.intervalx,
emit=False, auto=auto)
if other.figure != self.figure:
other.figure.canvas.draw_idle()
self.stale = True
return bottom, top
set_zlim = set_zlim3d

[docs]    def get_xlim3d(self):
return tuple(self.xy_viewLim.intervalx)
get_xlim3d.__doc__ = maxes.Axes.get_xlim.__doc__
get_xlim = get_xlim3d
if get_xlim.__doc__ is not None:
get_xlim.__doc__ += """
.. versionchanged :: 1.1.0
This function now correctly refers to the 3D x-limits
"""

[docs]    def get_ylim3d(self):
return tuple(self.xy_viewLim.intervaly)
get_ylim3d.__doc__ = maxes.Axes.get_ylim.__doc__
get_ylim = get_ylim3d
if get_ylim.__doc__ is not None:
get_ylim.__doc__ += """
.. versionchanged :: 1.1.0
This function now correctly refers to the 3D y-limits.
"""

[docs]    def get_zlim3d(self):
'''Get 3D z limits.'''
return tuple(self.zz_viewLim.intervalx)
get_zlim = get_zlim3d

[docs]    def get_zscale(self):
"""
Return the zaxis scale string %s

""" % (", ".join(mscale.get_scale_names()))
return self.zaxis.get_scale()

# We need to slightly redefine these to pass scalez=False
# to their calls of autoscale_view.
[docs]    def set_xscale(self, value, **kwargs):
self.xaxis._set_scale(value, **kwargs)
self.autoscale_view(scaley=False, scalez=False)
self._update_transScale()
if maxes.Axes.set_xscale.__doc__ is not None:
set_xscale.__doc__ = maxes.Axes.set_xscale.__doc__ + """
.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""

[docs]    def set_yscale(self, value, **kwargs):
self.yaxis._set_scale(value, **kwargs)
self.autoscale_view(scalex=False, scalez=False)
self._update_transScale()
self.stale = True
if maxes.Axes.set_yscale.__doc__ is not None:
set_yscale.__doc__ = maxes.Axes.set_yscale.__doc__ + """
.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""

[docs]    def set_zscale(self, value, **kwargs):
"""
Set the z-axis scale.

Parameters
----------
value : {"linear", "log", "symlog", "logit", ...}
The axis scale type to apply.

**kwargs
Different keyword arguments are accepted, depending on the scale.
See the respective class keyword arguments:

- matplotlib.scale.LinearScale
- matplotlib.scale.LogScale
- matplotlib.scale.SymmetricalLogScale
- matplotlib.scale.LogitScale

Notes
-----
Currently, Axes3D objects only supports linear scales.
Other scales may or may not work, and support for these
is improving with each release.

By default, Matplotlib supports the above mentioned scales.
Additionally, custom scales may be registered using
matplotlib.scale.register_scale. These scales may then also
be used here as support is added.
"""
self.zaxis._set_scale(value, **kwargs)
self.autoscale_view(scalex=False, scaley=False)
self._update_transScale()
self.stale = True

[docs]    def set_zticks(self, *args, **kwargs):
"""
Set z-axis tick locations.
See :meth:matplotlib.axes.Axes.set_yticks for more details.

.. note::
Minor ticks are not supported.

"""
return self.zaxis.set_ticks(*args, **kwargs)

[docs]    def get_zticks(self, minor=False):
"""
Return the z ticks as a list of locations
See :meth:matplotlib.axes.Axes.get_yticks for more details.

.. note::
Minor ticks are not supported.

"""
return self.zaxis.get_ticklocs(minor=minor)

[docs]    def get_zmajorticklabels(self):
"""
Get the ztick labels as a list of Text instances

.. versionadded :: 1.1.0
"""
return cbook.silent_list('Text zticklabel',
self.zaxis.get_majorticklabels())

[docs]    def get_zminorticklabels(self):
"""
Get the ztick labels as a list of Text instances

.. note::
Minor ticks are not supported. This function was added
only for completeness.

.. versionadded :: 1.1.0
"""
return cbook.silent_list('Text zticklabel',
self.zaxis.get_minorticklabels())

[docs]    def set_zticklabels(self, *args, **kwargs):
"""
Set z-axis tick labels.
See :meth:matplotlib.axes.Axes.set_yticklabels for more details.

.. note::
Minor ticks are not supported by Axes3D objects.

"""
return self.zaxis.set_ticklabels(*args, **kwargs)

[docs]    def get_zticklabels(self, minor=False):
"""
Get ztick labels as a list of Text instances.
See :meth:matplotlib.axes.Axes.get_yticklabels for more details.

.. note::
Minor ticks are not supported.

"""
return cbook.silent_list('Text zticklabel',
self.zaxis.get_ticklabels(minor=minor))

[docs]    def zaxis_date(self, tz=None):
"""
Sets up z-axis ticks and labels that treat the z data as dates.

*tz* is a timezone string or :class:tzinfo instance.
Defaults to rc value.

.. note::
This function is merely provided for completeness.
Axes3D objects do not officially support dates for ticks,
and so this may or may not work as expected.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
self.zaxis.axis_date(tz)

[docs]    def get_zticklines(self):
"""
Get ztick lines as a list of Line2D instances.
Note that this function is provided merely for completeness.
These lines are re-calculated as the display changes.

"""
return self.zaxis.get_ticklines()

[docs]    def clabel(self, *args, **kwargs):
"""
This function is currently not implemented for 3D axes.
Returns *None*.
"""
return None

[docs]    def view_init(self, elev=None, azim=None):
"""
Set the elevation and azimuth of the axes.

This can be used to rotate the axes programmatically.

'elev' stores the elevation angle in the z plane.
'azim' stores the azimuth angle in the x,y plane.

if elev or azim are None (default), then the initial value
is used which was specified in the :class:Axes3D constructor.
"""

self.dist = 10

if elev is None:
self.elev = self.initial_elev
else:
self.elev = elev

if azim is None:
self.azim = self.initial_azim
else:
self.azim = azim

[docs]    def set_proj_type(self, proj_type):
"""
Set the projection type.

Parameters
----------
proj_type : str
Type of projection, accepts 'persp' and 'ortho'.

"""
if proj_type == 'persp':
self._projection = proj3d.persp_transformation
elif proj_type == 'ortho':
self._projection = proj3d.ortho_transformation
else:
raise ValueError("unrecognized projection: %s" % proj_type)

[docs]    def get_proj(self):
"""
Create the projection matrix from the current viewing position.

elev stores the elevation angle in the z plane
azim stores the azimuth angle in the x,y plane

dist is the distance of the eye viewing point from the object
point.

"""
relev, razim = np.pi * self.elev/180, np.pi * self.azim/180

xmin, xmax = self.get_xlim3d()
ymin, ymax = self.get_ylim3d()
zmin, zmax = self.get_zlim3d()

# transform to uniform world coordinates 0-1.0,0-1.0,0-1.0
worldM = proj3d.world_transformation(xmin, xmax,
ymin, ymax,
zmin, zmax)

# look into the middle of the new coordinates
R = np.array([0.5, 0.5, 0.5])

xp = R[0] + np.cos(razim) * np.cos(relev) * self.dist
yp = R[1] + np.sin(razim) * np.cos(relev) * self.dist
zp = R[2] + np.sin(relev) * self.dist
E = np.array((xp, yp, zp))

self.eye = E
self.vvec = R - E
self.vvec = self.vvec / np.linalg.norm(self.vvec)

if abs(relev) > np.pi/2:
# upside down
V = np.array((0, 0, -1))
else:
V = np.array((0, 0, 1))
zfront, zback = -self.dist, self.dist

viewM = proj3d.view_transformation(E, R, V)
projM = self._projection(zfront, zback)
M0 = np.dot(viewM, worldM)
M = np.dot(projM, M0)
return M

[docs]    def mouse_init(self, rotate_btn=1, zoom_btn=3):
"""
Initializes mouse button callbacks to enable 3D rotation of the axes.
Also optionally sets the mouse buttons for 3D rotation and zooming.

Parameters
----------
rotate_btn : int or list of int
The mouse button or buttons to use for 3D rotation of the axes;
defaults to 1.
zoom_btn : int or list of int
The mouse button or buttons to use to zoom the 3D axes; defaults to
3.
"""
self.button_pressed = None
self._cids = [
self.figure.canvas.mpl_connect(
'motion_notify_event', self._on_move),
self.figure.canvas.mpl_connect(
'button_press_event', self._button_press),
self.figure.canvas.mpl_connect(
'button_release_event', self._button_release),
]
# coerce scalars into array-like, then convert into
# a regular list to avoid comparisons against None
# which breaks in recent versions of numpy.
self._rotate_btn = np.atleast_1d(rotate_btn).tolist()
self._zoom_btn = np.atleast_1d(zoom_btn).tolist()

[docs]    def can_zoom(self):
"""
Return *True* if this axes supports the zoom box button functionality.

3D axes objects do not use the zoom box button.
"""
return False

[docs]    def can_pan(self):
"""
Return *True* if this axes supports the pan/zoom button functionality.

3D axes objects do not use the pan/zoom button.
"""
return False

[docs]    def cla(self):
"""
Clear axes
"""
# Disabling mouse interaction might have been needed a long
# time ago, but I can't find a reason for it now - BVR (2012-03)
#self.disable_mouse_rotation()
super().cla()
self.zaxis.cla()

if self._sharez is not None:
self.zaxis.major = self._sharez.zaxis.major
self.zaxis.minor = self._sharez.zaxis.minor
z0, z1 = self._sharez.get_zlim()
self.set_zlim(z0, z1, emit=False, auto=None)
self.zaxis._set_scale(self._sharez.zaxis.get_scale())
else:
self.zaxis._set_scale('linear')
try:
self.set_zlim(0, 1)
except TypeError:
pass

self._autoscaleZon = True
self._zmargin = 0

self.grid(rcParams['axes3d.grid'])

[docs]    def disable_mouse_rotation(self):
"""Disable mouse button callbacks.
"""
# Disconnect the various events we set.
for cid in self._cids:
self.figure.canvas.mpl_disconnect(cid)

self._cids = []

def _button_press(self, event):
if event.inaxes == self:
self.button_pressed = event.button
self.sx, self.sy = event.xdata, event.ydata

def _button_release(self, event):
self.button_pressed = None

[docs]    def format_zdata(self, z):
"""
Return *z* string formatted.  This function will use the
:attr:fmt_zdata attribute if it is callable, else will fall
back on the zaxis major formatter
"""
try:
return self.fmt_zdata(z)
except (AttributeError, TypeError):
func = self.zaxis.get_major_formatter().format_data_short
val = func(z)
return val

[docs]    def format_coord(self, xd, yd):
"""
Given the 2D view coordinates attempt to guess a 3D coordinate.
Looks for the nearest edge to the point and then assumes that
the point is at the same z location as the nearest point on the edge.
"""

if self.M is None:
return ''

if self.button_pressed in self._rotate_btn:
return 'azimuth={:.0f} deg, elevation={:.0f} deg '.format(
self.azim, self.elev)
# ignore xd and yd and display angles instead

# nearest edge
p0, p1 = min(self.tunit_edges(),
key=lambda edge: proj3d._line2d_seg_dist(
edge[0], edge[1], (xd, yd)))

# scale the z value to match
x0, y0, z0 = p0
x1, y1, z1 = p1
d0 = np.hypot(x0-xd, y0-yd)
d1 = np.hypot(x1-xd, y1-yd)
dt = d0+d1
z = d1/dt * z0 + d0/dt * z1

x, y, z = proj3d.inv_transform(xd, yd, z, self.M)

xs = self.format_xdata(x)
ys = self.format_ydata(y)
zs = self.format_zdata(z)
return 'x=%s, y=%s, z=%s' % (xs, ys, zs)

def _on_move(self, event):
"""Mouse moving

button-1 rotates by default.  Can be set explicitly in mouse_init().
button-3 zooms by default.  Can be set explicitly in mouse_init().
"""

if not self.button_pressed:
return

if self.M is None:
return

x, y = event.xdata, event.ydata
# In case the mouse is out of bounds.
if x is None:
return

dx, dy = x - self.sx, y - self.sy
w = self._pseudo_w
h = self._pseudo_h
self.sx, self.sy = x, y

# Rotation
if self.button_pressed in self._rotate_btn:
# rotate viewing point
# get the x and y pixel coords
if dx == 0 and dy == 0:
return
self.elev = art3d._norm_angle(self.elev - (dy/h)*180)
self.azim = art3d._norm_angle(self.azim - (dx/w)*180)
self.get_proj()
self.stale = True
self.figure.canvas.draw_idle()

#        elif self.button_pressed == 2:
# pan view
# project xv,yv,zv -> xw,yw,zw
# pan
#            pass

# Zoom
elif self.button_pressed in self._zoom_btn:
# zoom view
# hmmm..this needs some help from clipping....
minx, maxx, miny, maxy, minz, maxz = self.get_w_lims()
df = 1-((h - dy)/h)
dx = (maxx-minx)*df
dy = (maxy-miny)*df
dz = (maxz-minz)*df
self.set_xlim3d(minx - dx, maxx + dx)
self.set_ylim3d(miny - dy, maxy + dy)
self.set_zlim3d(minz - dz, maxz + dz)
self.get_proj()
self.figure.canvas.draw_idle()

[docs]    def set_zlabel(self, zlabel, fontdict=None, labelpad=None, **kwargs):
'''
Set zlabel.  See doc for :meth:set_ylabel for description.
'''
if labelpad is not None:
return self.zaxis.set_label_text(zlabel, fontdict, **kwargs)

[docs]    def get_zlabel(self):
"""
Get the z-label text string.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
label = self.zaxis.get_label()
return label.get_text()

#### Axes rectangle characteristics

[docs]    def get_frame_on(self):
"""
Get whether the 3D axes panels are drawn.

.. versionadded :: 1.1.0
"""
return self._frameon

[docs]    def set_frame_on(self, b):
"""
Set whether the 3D axes panels are drawn.

.. versionadded :: 1.1.0

Parameters
----------
b : bool
"""
self._frameon = bool(b)
self.stale = True

[docs]    def grid(self, b=True, **kwargs):
'''
Set / unset 3D grid.

.. note::

Currently, this function does not behave the same as
:meth:matplotlib.axes.Axes.grid, but it is intended to
eventually support that behavior.

.. versionchanged :: 1.1.0
This function was changed, but not tested. Please report any bugs.
'''
# TODO: Operate on each axes separately
if len(kwargs):
b = True
self._draw_grid = b
self.stale = True

[docs]    def ticklabel_format(
self, *, style='', scilimits=None, useOffset=None, axis='both'):
"""
Convenience method for manipulating the ScalarFormatter
used by default for linear axes in Axed3D objects.

See :meth:matplotlib.axes.Axes.ticklabel_format for full
documentation.  Note that this version applies to all three
axes of the Axes3D object.  Therefore, the *axis* argument
will also accept a value of 'z' and the value of 'both' will
apply to all three axes.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
style = style.lower()
axis = axis.lower()
if scilimits is not None:
try:
m, n = scilimits
m+n+1  # check that both are numbers
except (ValueError, TypeError):
raise ValueError("scilimits must be a sequence of 2 integers")
if style[:3] == 'sci':
sb = True
elif style == 'plain':
sb = False
elif style == '':
sb = None
else:
raise ValueError("%s is not a valid style value")
try:
if sb is not None:
if axis in ['both', 'z']:
self.xaxis.major.formatter.set_scientific(sb)
if axis in ['both', 'y']:
self.yaxis.major.formatter.set_scientific(sb)
if axis in ['both', 'z']:
self.zaxis.major.formatter.set_scientific(sb)
if scilimits is not None:
if axis in ['both', 'x']:
self.xaxis.major.formatter.set_powerlimits(scilimits)
if axis in ['both', 'y']:
self.yaxis.major.formatter.set_powerlimits(scilimits)
if axis in ['both', 'z']:
self.zaxis.major.formatter.set_powerlimits(scilimits)
if useOffset is not None:
if axis in ['both', 'x']:
self.xaxis.major.formatter.set_useOffset(useOffset)
if axis in ['both', 'y']:
self.yaxis.major.formatter.set_useOffset(useOffset)
if axis in ['both', 'z']:
self.zaxis.major.formatter.set_useOffset(useOffset)
except AttributeError:
raise AttributeError(
"This method only works with the ScalarFormatter.")

[docs]    def locator_params(self, axis='both', tight=None, **kwargs):
"""
Convenience method for controlling tick locators.

See :meth:matplotlib.axes.Axes.locator_params for full
documentation.  Note that this is for Axes3D objects,
therefore, setting *axis* to 'both' will result in the
parameters being set for all three axes.  Also, *axis*
can also take a value of 'z' to apply parameters to the
z axis.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
_x = axis in ['x', 'both']
_y = axis in ['y', 'both']
_z = axis in ['z', 'both']
if _x:
self.xaxis.get_major_locator().set_params(**kwargs)
if _y:
self.yaxis.get_major_locator().set_params(**kwargs)
if _z:
self.zaxis.get_major_locator().set_params(**kwargs)
self.autoscale_view(tight=tight, scalex=_x, scaley=_y, scalez=_z)

[docs]    def tick_params(self, axis='both', **kwargs):
"""
Convenience method for changing the appearance of ticks and
tick labels.

See :meth:matplotlib.axes.Axes.tick_params for more complete
documentation.

The only difference is that setting *axis* to 'both' will
mean that the settings are applied to all three axes. Also,
the *axis* parameter also accepts a value of 'z', which
would mean to apply to only the z-axis.

Also, because of how Axes3D objects are drawn very differently
from regular 2D axes, some of these settings may have
ambiguous meaning.  For simplicity, the 'z' axis will
accept settings as if it was like the 'y' axis.

.. note::
While this function is currently implemented, the core part
of the Axes3D object may ignore some of these settings.
Future releases will fix this. Priority will be given to
those who file bugs.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
cbook._check_in_list(['x', 'y', 'z', 'both'], axis=axis)
if axis in ['x', 'y', 'both']:
super().tick_params(axis, **kwargs)
if axis in ['z', 'both']:
zkw = dict(kwargs)
zkw.pop('top', None)
zkw.pop('bottom', None)
zkw.pop('labeltop', None)
zkw.pop('labelbottom', None)
self.zaxis.set_tick_params(**zkw)

### data limits, ticks, tick labels, and formatting

[docs]    def invert_zaxis(self):
"""
Invert the z-axis.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
bottom, top = self.get_zlim()
self.set_zlim(top, bottom, auto=None)

[docs]    def zaxis_inverted(self):
'''
Returns True if the z-axis is inverted.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
'''
bottom, top = self.get_zlim()

[docs]    def get_zbound(self):
"""
Returns the z-axis numerical bounds where::

lowerBound < upperBound

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
bottom, top = self.get_zlim()
if bottom < top:
return bottom, top
else:

[docs]    def set_zbound(self, lower=None, upper=None):
"""
Set the lower and upper numerical bounds of the z-axis.
This method will honor axes inversion regardless of parameter order.
It will not change the :attr:_autoscaleZon attribute.

.. versionadded :: 1.1.0
This function was added, but not tested. Please report any bugs.
"""
if upper is None and np.iterable(lower):
lower, upper = lower
old_lower, old_upper = self.get_zbound()
if lower is None:
lower = old_lower
if upper is None:
upper = old_upper

if self.zaxis_inverted():
if lower < upper:
self.set_zlim(upper, lower, auto=None)
else:
self.set_zlim(lower, upper, auto=None)
else:
if lower < upper:
self.set_zlim(lower, upper, auto=None)
else:
self.set_zlim(upper, lower, auto=None)

[docs]    def text(self, x, y, z, s, zdir=None, **kwargs):
'''
Add text to the plot. kwargs will be passed on to Axes.text,
except for the zdir keyword, which sets the direction to be
used as the z direction.
'''
text = super().text(x, y, s, **kwargs)
art3d.text_2d_to_3d(text, z, zdir)
return text

text3D = text
text2D = Axes.text

[docs]    def plot(self, xs, ys, *args, zdir='z', **kwargs):
"""
Plot 2D or 3D data.

Parameters
----------
xs : 1D array-like
x coordinates of vertices.
ys : 1D array-like
y coordinates of vertices.
zs : scalar or 1D array-like
z coordinates of vertices; either one for all points or one for
each point.
zdir : {'x', 'y', 'z'}
When plotting 2D data, the direction to use as z ('x', 'y' or 'z');
defaults to 'z'.
**kwargs
Other arguments are forwarded to matplotlib.axes.Axes.plot.
"""

# zs can be passed positionally or as keyword; checking whether
# args[0] is a string matches the behavior of 2D plot (via
# _process_plot_var_args).
if args and not isinstance(args[0], str):
zs = args[0]
args = args[1:]
if 'zs' in kwargs:
raise TypeError("plot() for multiple values for argument 'z'")
else:
zs = kwargs.pop('zs', 0)

# Match length
zs = np.broadcast_to(zs, len(xs))

lines = super().plot(xs, ys, *args, **kwargs)
for line in lines:
art3d.line_2d_to_3d(line, zs=zs, zdir=zdir)

xs, ys, zs = art3d.juggle_axes(xs, ys, zs, zdir)
self.auto_scale_xyz(xs, ys, zs, had_data)
return lines

plot3D = plot

[docs]    def plot_surface(self, X, Y, Z, *args, norm=None, vmin=None,
vmax=None, lightsource=None, **kwargs):
"""
Create a surface plot.

By default it will be colored in shades of a solid color, but it also
supports color mapping by supplying the *cmap* argument.

.. note::

The *rcount* and *ccount* kwargs, which both default to 50,
determine the maximum number of samples used in each direction.  If
the input data is larger, it will be downsampled (by slicing) to
these numbers of points.

Parameters
----------
X, Y, Z : 2d arrays
Data values.

rcount, ccount : int
Maximum number of samples used in each direction.  If the input
data is larger, it will be downsampled (by slicing) to these
numbers of points.  Defaults to 50.

rstride, cstride : int
Downsampling stride in each direction.  These arguments are
mutually exclusive with *rcount* and *ccount*.  If only one of
*rstride* or *cstride* is set, the other defaults to 10.

'classic' mode uses a default of rstride = cstride = 10 instead
of the new default of rcount = ccount = 50.

color : color-like
Color of the surface patches.

cmap : Colormap
Colormap of the surface patches.

facecolors : array-like of colors.
Colors of each individual patch.

norm : Normalize
Normalization for the colormap.

vmin, vmax : float
Bounds for the normalization.

Whether to shade the facecolors. Defaults to True. Shading is
always disabled when cmap is specified.

lightsource : ~matplotlib.colors.LightSource
The lightsource to use when shade is True.

**kwargs
Other arguments are forwarded to .Poly3DCollection.
"""

if Z.ndim != 2:
raise ValueError("Argument Z must be 2-dimensional.")
if np.any(np.isnan(Z)):
cbook._warn_external(
"Z contains NaN values. This may result in rendering "
"artifacts.")

# TODO: Support masked arrays
X, Y, Z = np.broadcast_arrays(X, Y, Z)
rows, cols = Z.shape

has_stride = 'rstride' in kwargs or 'cstride' in kwargs
has_count = 'rcount' in kwargs or 'ccount' in kwargs

if has_stride and has_count:
raise ValueError("Cannot specify both stride and count arguments")

rstride = kwargs.pop('rstride', 10)
cstride = kwargs.pop('cstride', 10)
rcount = kwargs.pop('rcount', 50)
ccount = kwargs.pop('ccount', 50)

if rcParams['_internal.classic_mode']:
# Strides have priority over counts in classic mode.
# So, only compute strides from counts
# if counts were explicitly given
compute_strides = has_count
else:
# If the strides are provided then it has priority.
# Otherwise, compute the strides from the counts.
compute_strides = not has_stride

if compute_strides:
rstride = int(max(np.ceil(rows / rcount), 1))
cstride = int(max(np.ceil(cols / ccount), 1))

if 'facecolors' in kwargs:
fcolors = kwargs.pop('facecolors')
else:
color = kwargs.pop('color', None)
if color is None:
color = self._get_lines.get_next_color()
color = np.array(mcolors.to_rgba(color))
fcolors = None

cmap = kwargs.get('cmap', None)
if shade is None:
cbook.warn_deprecated(
"3.1",
message="Passing shade=None to Axes3D.plot_surface() is "
"deprecated since matplotlib 3.1 and will change its "
"semantic or raise an error in matplotlib 3.3. "

# evenly spaced, and including both endpoints
row_inds = list(range(0, rows-1, rstride)) + [rows-1]
col_inds = list(range(0, cols-1, cstride)) + [cols-1]

colset = []  # the sampled facecolor
polys = []
for rs, rs_next in zip(row_inds[:-1], row_inds[1:]):
for cs, cs_next in zip(col_inds[:-1], col_inds[1:]):
ps = [
# +1 ensures we share edges between polygons
cbook._array_perimeter(a[rs:rs_next+1, cs:cs_next+1])
for a in (X, Y, Z)
]
# ps = np.stack(ps, axis=-1)
ps = np.array(ps).T
polys.append(ps)

if fcolors is not None:
colset.append(fcolors[rs][cs])

# note that the striding causes some polygons to have more coordinates
# than others
polyc = art3d.Poly3DCollection(polys, *args, **kwargs)

if fcolors is not None:
colset, self._generate_normals(polys), lightsource)
polyc.set_facecolors(colset)
polyc.set_edgecolors(colset)
elif cmap:
# doesn't vectorize because polys is jagged
avg_z = np.array([ps[:, 2].mean() for ps in polys])
polyc.set_array(avg_z)
if vmin is not None or vmax is not None:
polyc.set_clim(vmin, vmax)
if norm is not None:
polyc.set_norm(norm)
else:
color, self._generate_normals(polys), lightsource)
else:
colset = color
polyc.set_facecolors(colset)

self.auto_scale_xyz(X, Y, Z, had_data)

return polyc

def _generate_normals(self, polygons):
"""
Takes a list of polygons and return an array of their normals.

Normals point towards the viewer for a face with its vertices in
counterclockwise order, following the right hand rule.

Uses three points equally spaced around the polygon.
This normal of course might not make sense for polygons with more than
three points not lying in a plane, but it's a plausible and fast
approximation.

Parameters
----------
polygons: list of (M_i, 3) array_like, or (..., M, 3) array_like
A sequence of polygons to compute normals for, which can have
varying numbers of vertices. If the polygons all have the same
number of vertices and array is passed, then the operation will
be vectorized.

Returns
-------
normals: (..., 3) array_like
A normal vector estimated for the polygon.

"""
if isinstance(polygons, np.ndarray):
# optimization: polygons all have the same number of points, so can
# vectorize
n = polygons.shape[-2]
i1, i2, i3 = 0, n//3, 2*n//3
v1 = polygons[..., i1, :] - polygons[..., i2, :]
v2 = polygons[..., i2, :] - polygons[..., i3, :]
else:
# The subtraction doesn't vectorize because polygons is jagged.
v1 = np.empty((len(polygons), 3))
v2 = np.empty((len(polygons), 3))
for poly_i, ps in enumerate(polygons):
n = len(ps)
i1, i2, i3 = 0, n//3, 2*n//3
v1[poly_i, :] = ps[i1, :] - ps[i2, :]
v2[poly_i, :] = ps[i2, :] - ps[i3, :]
return np.cross(v1, v2)

def _shade_colors(self, color, normals, lightsource=None):
"""
Shade *color* using normal vectors given by *normals*.
*color* can also be an array of the same length as *normals*.
"""
if lightsource is None:
# chosen for backwards-compatibility
lightsource = LightSource(azdeg=225, altdeg=19.4712)

with np.errstate(invalid="ignore"):
shade = ((normals / np.linalg.norm(normals, axis=1, keepdims=True))
@ lightsource.direction)

# convert dot product to allowed shading fractions
in_norm = Normalize(-1, 1)
out_norm = Normalize(0.3, 1).inverse

def norm(x):
return out_norm(in_norm(x))

color = mcolors.to_rgba_array(color)
# shape of color should be (M, 4) (where M is number of faces)
# shape of shade should be (M,)
# colors should have final shape of (M, 4)
alpha = color[:, 3]
colors = norm(shade)[:, np.newaxis] * color
colors[:, 3] = alpha
else:
colors = np.asanyarray(color).copy()

return colors

[docs]    def plot_wireframe(self, X, Y, Z, *args, **kwargs):
"""
Plot a 3D wireframe.

.. note::

The *rcount* and *ccount* kwargs, which both default to 50,
determine the maximum number of samples used in each direction.  If
the input data is larger, it will be downsampled (by slicing) to
these numbers of points.

Parameters
----------
X, Y, Z : 2d arrays
Data values.

rcount, ccount : int
Maximum number of samples used in each direction.  If the input
data is larger, it will be downsampled (by slicing) to these
numbers of points.  Setting a count to zero causes the data to be
not sampled in the corresponding direction, producing a 3D line
plot rather than a wireframe plot.  Defaults to 50.

rstride, cstride : int
Downsampling stride in each direction.  These arguments are
mutually exclusive with *rcount* and *ccount*.  If only one of
*rstride* or *cstride* is set, the other defaults to 1.  Setting a
stride to zero causes the data to be not sampled in the
corresponding direction, producing a 3D line plot rather than a
wireframe plot.

'classic' mode uses a default of rstride = cstride = 1 instead
of the new default of rcount = ccount = 50.

**kwargs
Other arguments are forwarded to .Line3DCollection.
"""

if Z.ndim != 2:
raise ValueError("Argument Z must be 2-dimensional.")
# FIXME: Support masked arrays
X, Y, Z = np.broadcast_arrays(X, Y, Z)
rows, cols = Z.shape

has_stride = 'rstride' in kwargs or 'cstride' in kwargs
has_count = 'rcount' in kwargs or 'ccount' in kwargs

if has_stride and has_count:
raise ValueError("Cannot specify both stride and count arguments")

rstride = kwargs.pop('rstride', 1)
cstride = kwargs.pop('cstride', 1)
rcount = kwargs.pop('rcount', 50)
ccount = kwargs.pop('ccount', 50)

if rcParams['_internal.classic_mode']:
# Strides have priority over counts in classic mode.
# So, only compute strides from counts
# if counts were explicitly given
if has_count:
rstride = int(max(np.ceil(rows / rcount), 1)) if rcount else 0
cstride = int(max(np.ceil(cols / ccount), 1)) if ccount else 0
else:
# If the strides are provided then it has priority.
# Otherwise, compute the strides from the counts.
if not has_stride:
rstride = int(max(np.ceil(rows / rcount), 1)) if rcount else 0
cstride = int(max(np.ceil(cols / ccount), 1)) if ccount else 0

# We want two sets of lines, one running along the "rows" of
# Z and another set of lines running along the "columns" of Z.
# This transpose will make it easy to obtain the columns.
tX, tY, tZ = np.transpose(X), np.transpose(Y), np.transpose(Z)

if rstride:
rii = list(range(0, rows, rstride))
# Add the last index only if needed
if rows > 0 and rii[-1] != (rows - 1):
rii += [rows-1]
else:
rii = []
if cstride:
cii = list(range(0, cols, cstride))
# Add the last index only if needed
if cols > 0 and cii[-1] != (cols - 1):
cii += [cols-1]
else:
cii = []

if rstride == 0 and cstride == 0:
raise ValueError("Either rstride or cstride must be non zero")

# If the inputs were empty, then just
# reset everything.
if Z.size == 0:
rii = []
cii = []

xlines = [X[i] for i in rii]
ylines = [Y[i] for i in rii]
zlines = [Z[i] for i in rii]

txlines = [tX[i] for i in cii]
tylines = [tY[i] for i in cii]
tzlines = [tZ[i] for i in cii]

lines = ([list(zip(xl, yl, zl))
for xl, yl, zl in zip(xlines, ylines, zlines)]
+ [list(zip(xl, yl, zl))
for xl, yl, zl in zip(txlines, tylines, tzlines)])

linec = art3d.Line3DCollection(lines, *args, **kwargs)
self.auto_scale_xyz(X, Y, Z, had_data)

return linec

[docs]    def plot_trisurf(self, *args, color=None, norm=None, vmin=None, vmax=None,
lightsource=None, **kwargs):
"""
Plot a triangulated surface.

The (optional) triangulation can be specified in one of two ways;
either::

plot_trisurf(triangulation, ...)

where triangulation is a :class:~matplotlib.tri.Triangulation
object, or::

plot_trisurf(X, Y, ...)
plot_trisurf(X, Y, triangles, ...)
plot_trisurf(X, Y, triangles=triangles, ...)

in which case a Triangulation object will be created.  See
:class:~matplotlib.tri.Triangulation for a explanation of
these possibilities.

The remaining arguments are::

plot_trisurf(..., Z)

where *Z* is the array of values to contour, one per point
in the triangulation.

Parameters
----------
X, Y, Z : array-like
Data values as 1D arrays.
color
Color of the surface patches.
cmap
A colormap for the surface patches.
norm : Normalize
An instance of Normalize to map values to colors.
vmin, vmax : scalar, optional, default: None
Minimum and maximum value to map.
Whether to shade the facecolors. Defaults to True. Shading is
always disabled when *cmap* is specified.
lightsource : ~matplotlib.colors.LightSource
The lightsource to use when *shade* is True.
**kwargs
All other arguments are passed on to
:class:~mpl_toolkits.mplot3d.art3d.Poly3DCollection

Examples
--------

.. plot:: gallery/mplot3d/trisurf3d.py
.. plot:: gallery/mplot3d/trisurf3d_2.py

This plotting function was added for the v1.2.0 release.
"""

# TODO: Support custom face colours
if color is None:
color = self._get_lines.get_next_color()
color = np.array(mcolors.to_rgba(color))

cmap = kwargs.get('cmap', None)

tri, args, kwargs = \
Triangulation.get_from_args_and_kwargs(*args, **kwargs)
if 'Z' in kwargs:
z = np.asarray(kwargs.pop('Z'))
else:
z = np.asarray(args[0])
# We do this so Z doesn't get passed as an arg to PolyCollection
args = args[1:]

xt = tri.x[triangles]
yt = tri.y[triangles]
zt = z[triangles]
verts = np.stack((xt, yt, zt), axis=-1)

polyc = art3d.Poly3DCollection(verts, *args, **kwargs)

if cmap:
# average over the three points of each triangle
avg_z = verts[:, :, 2].mean(axis=1)
polyc.set_array(avg_z)
if vmin is not None or vmax is not None:
polyc.set_clim(vmin, vmax)
if norm is not None:
polyc.set_norm(norm)
else:
normals = self._generate_normals(verts)
colset = self._shade_colors(color, normals, lightsource)
else:
colset = color
polyc.set_facecolors(colset)

self.auto_scale_xyz(tri.x, tri.y, z, had_data)

return polyc

def _3d_extend_contour(self, cset, stride=5):
'''
Extend a contour in 3D by creating
'''

levels = cset.levels
colls = cset.collections
dz = (levels[1] - levels[0]) / 2

for z, linec in zip(levels, colls):
paths = linec.get_paths()
if not paths:
continue
topverts = art3d._paths_to_3d_segments(paths, z - dz)
botverts = art3d._paths_to_3d_segments(paths, z + dz)

color = linec.get_color()[0]

polyverts = []
normals = []
nsteps = np.round(len(topverts[0]) / stride)
if nsteps <= 1:
if len(topverts[0]) > 1:
nsteps = 2
else:
continue

stepsize = (len(topverts[0]) - 1) / (nsteps - 1)
for i in range(int(np.round(nsteps)) - 1):
i1 = int(np.round(i * stepsize))
i2 = int(np.round((i + 1) * stepsize))
polyverts.append([topverts[0][i1],
topverts[0][i2],
botverts[0][i2],
botverts[0][i1]])

# all polygons have 4 vertices, so vectorize
polyverts = np.array(polyverts)
normals = self._generate_normals(polyverts)

colors = self._shade_colors(color, normals)
colors2 = self._shade_colors(color, normals)
polycol = art3d.Poly3DCollection(polyverts,
facecolors=colors,
edgecolors=colors2)
polycol.set_sort_zpos(z)

for col in colls:
self.collections.remove(col)

self, cset, extend3d=False, stride=5, zdir='z', offset=None):
zdir = '-' + zdir
if extend3d:
self._3d_extend_contour(cset, stride)
else:
for z, linec in zip(cset.levels, cset.collections):
if offset is not None:
z = offset
art3d.line_collection_2d_to_3d(linec, z, zdir=zdir)

[docs]    def add_contourf_set(self, cset, zdir='z', offset=None):
zdir = '-' + zdir
for z, linec in zip(cset.levels, cset.collections):
if offset is not None:
z = offset
art3d.poly_collection_2d_to_3d(linec, z, zdir=zdir)
linec.set_sort_zpos(z)

[docs]    def contour(self, X, Y, Z, *args,
extend3d=False, stride=5, zdir='z', offset=None, **kwargs):
"""
Create a 3D contour plot.

Parameters
----------
X, Y, Z : array-likes
Input data.
extend3d : bool
Whether to extend contour in 3D; defaults to False.
stride : int
Step size for extending contour.
zdir : {'x', 'y', 'z'}
The direction to use; defaults to 'z'.
offset : scalar
If specified, plot a projection of the contour lines at this
position in a plane normal to zdir
*args, **kwargs
Other arguments are forwarded to matplotlib.axes.Axes.contour.

Returns
-------
"""

jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir)
cset = super().contour(jX, jY, jZ, *args, **kwargs)
self.add_contour_set(cset, extend3d, stride, zdir, offset)

self.auto_scale_xyz(X, Y, Z, had_data)
return cset

contour3D = contour

[docs]    def tricontour(self, *args,
extend3d=False, stride=5, zdir='z', offset=None, **kwargs):
"""
Create a 3D contour plot.

.. versionchanged:: 1.3.0
Added support for custom triangulations

.. note::
This method currently produces incorrect output due to a
longstanding bug in 3D PolyCollection rendering.

Parameters
----------
X, Y, Z : array-likes
Input data.
extend3d : bool
Whether to extend contour in 3D; defaults to False.
stride : int
Step size for extending contour.
zdir : {'x', 'y', 'z'}
The direction to use; defaults to 'z'.
offset : scalar
If specified, plot a projection of the contour lines at this
position in a plane normal to zdir
*args, **kwargs
Other arguments are forwarded to matplotlib.axes.Axes.tricontour.

Returns
-------
matplotlib.tri.tricontour.TriContourSet
"""

tri, args, kwargs = Triangulation.get_from_args_and_kwargs(
*args, **kwargs)
X = tri.x
Y = tri.y
if 'Z' in kwargs:
Z = kwargs.pop('Z')
else:
Z = args[0]
# We do this so Z doesn't get passed as an arg to Axes.tricontour
args = args[1:]

jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir)
tri = Triangulation(jX, jY, tri.triangles, tri.mask)

cset = super().tricontour(tri, jZ, *args, **kwargs)
self.add_contour_set(cset, extend3d, stride, zdir, offset)

self.auto_scale_xyz(X, Y, Z, had_data)
return cset

[docs]    def contourf(self, X, Y, Z, *args, zdir='z', offset=None, **kwargs):
"""
Create a 3D filled contour plot.

Parameters
----------
X, Y, Z : array-likes
Input data.
zdir : {'x', 'y', 'z'}
The direction to use; defaults to 'z'.
offset : scalar
If specified, plot a projection of the contour lines at this
position in a plane normal to zdir
*args, **kwargs
Other arguments are forwarded to matplotlib.axes.Axes.contourf.

Returns
-------

Notes
-----
The *zdir* and *offset* parameters.
"""

jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir)
cset = super().contourf(jX, jY, jZ, *args, **kwargs)

self.auto_scale_xyz(X, Y, Z, had_data)
return cset

contourf3D = contourf

[docs]    def tricontourf(self, *args, zdir='z', offset=None, **kwargs):
"""
Create a 3D filled contour plot.

.. note::
This method currently produces incorrect output due to a
longstanding bug in 3D PolyCollection rendering.

Parameters
----------
X, Y, Z : array-likes
Input data.
zdir : {'x', 'y', 'z'}
The direction to use; defaults to 'z'.
offset : scalar
If specified, plot a projection of the contour lines at this
position in a plane normal to zdir
*args, **kwargs
Other arguments are forwarded to
matplotlib.axes.Axes.tricontourf.

Returns
-------
matplotlib.tri.tricontour.TriContourSet

Notes
-----
The *zdir* and *offset* parameters.
.. versionchanged:: 1.3.0
Added support for custom triangulations
"""

tri, args, kwargs = Triangulation.get_from_args_and_kwargs(
*args, **kwargs)
X = tri.x
Y = tri.y
if 'Z' in kwargs:
Z = kwargs.pop('Z')
else:
Z = args[0]
# We do this so Z doesn't get passed as an arg to Axes.tricontourf
args = args[1:]

jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir)
tri = Triangulation(jX, jY, tri.triangles, tri.mask)

cset = super().tricontourf(tri, jZ, *args, **kwargs)

self.auto_scale_xyz(X, Y, Z, had_data)
return cset

[docs]    def add_collection3d(self, col, zs=0, zdir='z'):
'''
Add a 3D collection object to the plot.

2D collection types are converted to a 3D version by
modifying the object and adding z coordinate information.

Supported are:
- PolyCollection
- LineCollection
- PatchCollection
'''
zvals = np.atleast_1d(zs)
zsortval = (np.min(zvals) if zvals.size
else 0)  # FIXME: arbitrary default

# FIXME: use issubclass() (although, then a 3D collection
#       object would also pass.)  Maybe have a collection3d
#       abstract class to test for and exclude?
if type(col) is mcoll.PolyCollection:
art3d.poly_collection_2d_to_3d(col, zs=zs, zdir=zdir)
col.set_sort_zpos(zsortval)
elif type(col) is mcoll.LineCollection:
art3d.line_collection_2d_to_3d(col, zs=zs, zdir=zdir)
col.set_sort_zpos(zsortval)
elif type(col) is mcoll.PatchCollection:
art3d.patch_collection_2d_to_3d(col, zs=zs, zdir=zdir)
col.set_sort_zpos(zsortval)

[docs]    def scatter(self, xs, ys, zs=0, zdir='z', s=20, c=None, depthshade=True,
*args, **kwargs):
"""
Create a scatter plot.

Parameters
----------
xs, ys : array-like
The data positions.
zs : float or array-like, optional, default: 0
The z-positions. Either an array of the same length as *xs* and
*ys* or a single value to place all points in the same plane.
zdir : {'x', 'y', 'z', '-x', '-y', '-z'}, optional, default: 'z'
The axis direction for the *zs*. This is useful when plotting 2D
data on a 3D Axes. The data must be passed as *xs*, *ys*. Setting
*zdir* to 'y' then plots the data to the x-z-plane.

See also :doc:/gallery/mplot3d/2dcollections3d.

s : scalar or array-like, optional, default: 20
The marker size in points**2. Either an array of the same length
as *xs* and *ys* or a single value to make all markers the same
size.
c : color, sequence, or sequence of color, optional
The marker color. Possible values:

- A single color format string.
- A sequence of color specifications of length n.
- A sequence of n numbers to be mapped to colors using *cmap* and
*norm*.
- A 2-D array in which the rows are RGB or RGBA.

For more details see the *c* argument of ~.axes.Axes.scatter.
depthshade : bool, optional, default: True
Whether to shade the scatter markers to give the appearance of
depth.
**kwargs
All other arguments are passed on to ~.axes.Axes.scatter.

Returns
-------
paths : ~matplotlib.collections.PathCollection
"""

xs, ys, zs = np.broadcast_arrays(
*[np.ravel(np.ma.filled(t, np.nan)) for t in [xs, ys, zs]])
s = np.ma.ravel(s)  # This doesn't have to match x, y in size.

xs, ys, zs, s, c = cbook.delete_masked_points(xs, ys, zs, s, c)

patches = super().scatter(xs, ys, s=s, c=c, *args, **kwargs)
art3d.patch_collection_2d_to_3d(patches, zs=zs, zdir=zdir,

if self._zmargin < 0.05 and xs.size > 0:
self.set_zmargin(0.05)

self.auto_scale_xyz(xs, ys, zs, had_data)

return patches

scatter3D = scatter

[docs]    def bar(self, left, height, zs=0, zdir='z', *args, **kwargs):
"""

Parameters
----------
left : 1D array-like
The x coordinates of the left sides of the bars.
height : 1D array-like
The height of the bars.
zs : scalar or 1D array-like
Z coordinate of bars; if a single value is specified, it will be
used for all bars.
zdir : {'x', 'y', 'z'}
When plotting 2D data, the direction to use as z ('x', 'y' or 'z');
defaults to 'z'.
**kwargs
Other arguments are forwarded to matplotlib.axes.Axes.bar.

Returns
-------
mpl_toolkits.mplot3d.art3d.Patch3DCollection
"""

patches = super().bar(left, height, *args, **kwargs)

zs = np.broadcast_to(zs, len(left))

verts = []
verts_zs = []
for p, z in zip(patches, zs):
vs = art3d._get_patch_verts(p)
verts += vs.tolist()
verts_zs += [z] * len(vs)
art3d.patch_2d_to_3d(p, z, zdir)
if 'alpha' in kwargs:
p.set_alpha(kwargs['alpha'])

if len(verts) > 0:
# the following has to be skipped if verts is empty
# NOTE: Bugs could still occur if len(verts) > 0,
#       but the "2nd dimension" is empty.
xs, ys = zip(*verts)
else:
xs, ys = [], []

xs, ys, verts_zs = art3d.juggle_axes(xs, ys, verts_zs, zdir)
self.auto_scale_xyz(xs, ys, verts_zs, had_data)

return patches

[docs]    def bar3d(self, x, y, z, dx, dy, dz, color=None,
zsort='average', shade=True, *args, **kwargs):
"""Generate a 3D barplot.

This method creates three dimensional barplot where the width,
depth, height, and color of the bars can all be uniquely set.

Parameters
----------
x, y, z : array-like
The coordinates of the anchor point of the bars.

dx, dy, dz : scalar or array-like
The width, depth, and height of the bars, respectively.

color : sequence of valid color specifications, optional
The color of the bars can be specified globally or
individually. This parameter can be:

- A single color value, to color all bars the same color.
- An array of colors of length N bars, to color each bar
independently.
- An array of colors of length 6, to color the faces of the
bars similarly.
- An array of colors of length 6 * N bars, to color each face
independently.

When coloring the faces of the boxes specifically, this is
the order of the coloring:

1. -Z (bottom of box)
2. +Z (top of box)
3. -Y
4. +Y
5. -X
6. +X

zsort : str, optional
The z-axis sorting scheme passed onto ~.art3d.Poly3DCollection

shade : bool, optional (default = True)
When true, this shades the dark sides of the bars (relative
to the plot's source of light).

**kwargs
Any additional keyword arguments are passed onto
~.art3d.Poly3DCollection.

Returns
-------
collection : ~.art3d.Poly3DCollection
A collection of three dimensional polygons representing
the bars.
"""

x, y, z, dx, dy, dz = np.broadcast_arrays(
np.atleast_1d(x), y, z, dx, dy, dz)
minx = np.min(x)
maxx = np.max(x + dx)
miny = np.min(y)
maxy = np.max(y + dy)
minz = np.min(z)
maxz = np.max(z + dz)

# shape (6, 4, 3)
# All faces are oriented facing outwards - when viewed from the
# outside, their vertices are in a counterclockwise ordering.
cuboid = np.array([
# -z
(
(0, 0, 0),
(0, 1, 0),
(1, 1, 0),
(1, 0, 0),
),
# +z
(
(0, 0, 1),
(1, 0, 1),
(1, 1, 1),
(0, 1, 1),
),
# -y
(
(0, 0, 0),
(1, 0, 0),
(1, 0, 1),
(0, 0, 1),
),
# +y
(
(0, 1, 0),
(0, 1, 1),
(1, 1, 1),
(1, 1, 0),
),
# -x
(
(0, 0, 0),
(0, 0, 1),
(0, 1, 1),
(0, 1, 0),
),
# +x
(
(1, 0, 0),
(1, 1, 0),
(1, 1, 1),
(1, 0, 1),
),
])

# indexed by [bar, face, vertex, coord]
polys = np.empty(x.shape + cuboid.shape)

# handle each coordinate separately
for i, p, dp in [(0, x, dx), (1, y, dy), (2, z, dz)]:
p = p[..., np.newaxis, np.newaxis]
dp = dp[..., np.newaxis, np.newaxis]
polys[..., i] = p + dp * cuboid[..., i]

# collapse the first two axes
polys = polys.reshape((-1,) + polys.shape[2:])

facecolors = []
if color is None:
color = [self._get_patches_for_fill.get_next_color()]

if len(color) == len(x):
# bar colors specified, need to expand to number of faces
for c in color:
facecolors.extend([c] * 6)
else:
# a single color specified, or face colors specified explicitly
facecolors = list(mcolors.to_rgba_array(color))
if len(facecolors) < len(x):
facecolors *= (6 * len(x))

normals = self._generate_normals(polys)
sfacecolors = self._shade_colors(facecolors, normals)
else:
sfacecolors = facecolors

col = art3d.Poly3DCollection(polys,
zsort=zsort,
facecolor=sfacecolors,
*args, **kwargs)

self.auto_scale_xyz((minx, maxx), (miny, maxy), (minz, maxz), had_data)

return col

[docs]    def set_title(self, label, fontdict=None, loc='center', **kwargs):
# docstring inherited
ret = super().set_title(label, fontdict=fontdict, loc=loc, **kwargs)
(x, y) = self.title.get_position()
self.title.set_y(0.92 * y)
return ret

[docs]    def quiver(self, *args,
length=1, arrow_length_ratio=.3, pivot='tail', normalize=False,
**kwargs):
"""
ax.quiver(X, Y, Z, U, V, W, /, length=1, arrow_length_ratio=.3, \
pivot='tail', normalize=False, **kwargs)

Plot a 3D field of arrows.

The arguments could be array-like or scalars, so long as they
they can be broadcast together. The arguments can also be
masked arrays. If an element in any of argument is masked, then
that corresponding quiver element will not be plotted.

Parameters
----------
X, Y, Z : array-like
The x, y and z coordinates of the arrow locations (default is
tail of arrow; see *pivot* kwarg)

U, V, W : array-like
The x, y and z components of the arrow vectors

length : float
The length of each quiver, default to 1.0, the unit is
the same with the axes

arrow_length_ratio : float
The ratio of the arrow head with respect to the quiver,
default to 0.3

pivot : {'tail', 'middle', 'tip'}
The part of the arrow that is at the grid point; the arrow
Default is 'tail'

normalize : bool
When True, all of the arrows will be the same length. This
defaults to False, where the arrows will be different lengths
depending on the values of u,v,w.

**kwargs
Any additional keyword arguments are delegated to
:class:~matplotlib.collections.LineCollection
"""
def calc_arrow(uvw, angle=15):
"""
To calculate the arrow head. uvw should be a unit vector.
We normalize it here:
"""
# get unit direction vector perpendicular to (u,v,w)
norm = np.linalg.norm(uvw[:2])
if norm > 0:
x = uvw[1] / norm
y = -uvw[0] / norm
else:
x, y = 0, 1

# compute the two arrowhead direction unit vectors
c = math.cos(ra)
s = math.sin(ra)

# construct the rotation matrices
Rpos = np.array([[c+(x**2)*(1-c), x*y*(1-c), y*s],
[y*x*(1-c), c+(y**2)*(1-c), -x*s],
[-y*s, x*s, c]])
# opposite rotation negates all the sin terms
Rneg = Rpos.copy()
Rneg[[0, 1, 2, 2], [2, 2, 0, 1]] = \
-Rneg[[0, 1, 2, 2], [2, 2, 0, 1]]

# multiply them to get the rotated vector
return Rpos.dot(uvw), Rneg.dot(uvw)

# handle args
argi = 6
if len(args) < argi:
raise ValueError('Wrong number of arguments. Expected %d got %d' %
(argi, len(args)))

# first 6 arguments are X, Y, Z, U, V, W
input_args = args[:argi]

# extract the masks, if any
masks = [k.mask for k in input_args
# broadcast to match the shape
input_args = bcast[:argi]
# combine the masks into one
# put mask on and compress
for k in input_args]
else:
input_args = [np.ravel(k) for k in input_args]

if any(len(v) == 0 for v in input_args):
# No quivers, so just make an empty collection and return early
linec = art3d.Line3DCollection([], *args[argi:], **kwargs)
return linec

shaft_dt = np.array([0, length])
arrow_dt = shaft_dt * arrow_length_ratio

if pivot == 'tail':
shaft_dt -= length
elif pivot == 'middle':
shaft_dt -= length/2.
elif pivot != 'tip':
raise ValueError('Invalid pivot argument: ' + str(pivot))

XYZ = np.column_stack(input_args[:3])
UVW = np.column_stack(input_args[3:argi]).astype(float)

# Normalize rows of UVW
norm = np.linalg.norm(UVW, axis=1)

# If any row of UVW is all zeros, don't make a quiver for it
mask = norm > 0
if normalize:
else:

if len(XYZ) > 0:
# compute the shaft lines all at once with an outer product
shafts = (XYZ - np.multiply.outer(shaft_dt, UVW)).swapaxes(0, 1)
# compute head direction vectors, n heads x 2 sides x 3 dimensions
head_dirs = np.array([calc_arrow(d) for d in UVW])
# compute all head lines at once, starting from the shaft ends
heads = shafts[:, :1] - np.multiply.outer(arrow_dt, head_dirs)
# stack left and right head lines together
heads.shape = (len(arrow_dt), -1, 3)
# transpose to get a list of lines

lines = [*shafts, *heads]
else:
lines = []

linec = art3d.Line3DCollection(lines, *args[argi:], **kwargs)

self.auto_scale_xyz(XYZ[:, 0], XYZ[:, 1], XYZ[:, 2], had_data)

return linec

quiver3D = quiver

[docs]    def voxels(self, *args, facecolors=None, edgecolors=None, shade=True,
lightsource=None, **kwargs):
"""
ax.voxels([x, y, z,] /, filled, facecolors=None, edgecolors=None, \
**kwargs)

Plot a set of filled voxels

All voxels are plotted as 1x1x1 cubes on the axis, with filled[0,0,0]
placed with its lower corner at the origin. Occluded faces are not
plotted.

Parameters
----------
filled : 3D np.array of bool
A 3d array of values, with truthy values indicating which voxels
to fill

x, y, z : 3D np.array, optional
The coordinates of the corners of the voxels. This should broadcast
to a shape one larger in every dimension than the shape of
filled.  These can be used to plot non-cubic voxels.

If not specified, defaults to increasing integers along each axis,
like those returned by :func:~numpy.indices.
As indicated by the / in the function signature, these
arguments can only be passed positionally.

facecolors, edgecolors : array_like, optional
The color to draw the faces and edges of the voxels. Can only be
passed as keyword arguments.
This parameter can be:

- A single color value, to color all voxels the same color. This
can be either a string, or a 1D rgb/rgba array
- None, the default, to use a single color for the faces, and
the style default for the edges.
- A 3D ndarray of color names, with each item the color for the
corresponding voxel. The size must match the voxels.
- A 4D ndarray of rgb/rgba data, with the components along the
last axis.

Whether to shade the facecolors. Defaults to True. Shading is
always disabled when *cmap* is specified.

lightsource : ~matplotlib.colors.LightSource
The lightsource to use when *shade* is True.

**kwargs
Additional keyword arguments to pass onto
:func:~mpl_toolkits.mplot3d.art3d.Poly3DCollection

Returns
-------
faces : dict
A dictionary indexed by coordinate, where faces[i,j,k] is a
Poly3DCollection of the faces drawn for the voxel
filled[i,j,k]. If no faces were drawn for a given voxel, either
because it was not asked to be drawn, or it is fully occluded, then
(i,j,k) not in faces.

Examples
--------
.. plot:: gallery/mplot3d/voxels.py
.. plot:: gallery/mplot3d/voxels_rgb.py
.. plot:: gallery/mplot3d/voxels_torus.py
.. plot:: gallery/mplot3d/voxels_numpy_logo.py
"""

# work out which signature we should be using, and use it to parse
# the arguments. Name must be voxels for the correct error message
if len(args) >= 3:
# underscores indicate position only
def voxels(__x, __y, __z, filled, **kwargs):
return (__x, __y, __z), filled, kwargs
else:
def voxels(filled, **kwargs):
return None, filled, kwargs

xyz, filled, kwargs = voxels(*args, **kwargs)

# check dimensions
if filled.ndim != 3:
raise ValueError("Argument filled must be 3-dimensional")
size = np.array(filled.shape, dtype=np.intp)

# check xyz coordinates, which are one larger than the filled shape
coord_shape = tuple(size + 1)
if xyz is None:
x, y, z = np.indices(coord_shape)
else:
x, y, z = (np.broadcast_to(c, coord_shape) for c in xyz)

if np.ndim(color) in (0, 1):
# single color, like "red" or [1, 0, 0]
return np.broadcast_to(color, filled.shape + np.shape(color))
elif np.ndim(color) in (3, 4):
# 3D array of strings, or 4D array with last axis rgb
if np.shape(color)[:3] != filled.shape:
raise ValueError(
"When multidimensional, {} must match the shape of "
"filled".format(name))
return color
else:
raise ValueError("Invalid {} argument".format(name))

# broadcast and default on facecolors
if facecolors is None:
facecolors = self._get_patches_for_fill.get_next_color()
facecolors = _broadcast_color_arg(facecolors, 'facecolors')

# broadcast but no default on edgecolors
edgecolors = _broadcast_color_arg(edgecolors, 'edgecolors')

# scale to the full array, even if the data is only in the center
self.auto_scale_xyz(x, y, z)

# points lying on corners of a square
square = np.array([
[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0],
], dtype=np.intp)

voxel_faces = defaultdict(list)

def permutation_matrices(n):
"""Generator of cyclic permutation matrices."""
mat = np.eye(n, dtype=np.intp)
for i in range(n):
yield mat
mat = np.roll(mat, 1, axis=0)

# iterate over each of the YZ, ZX, and XY orientations, finding faces
# to render
for permute in permutation_matrices(3):
# find the set of ranges to iterate over
pc, qc, rc = permute.T.dot(size)
pinds = np.arange(pc)
qinds = np.arange(qc)
rinds = np.arange(rc)

square_rot_pos = square.dot(permute.T)
square_rot_neg = square_rot_pos[::-1]

# iterate within the current plane
for p in pinds:
for q in qinds:
# iterate perpendicularly to the current plane, handling
# boundaries. We only draw faces between a voxel and an
# empty space, to avoid drawing internal faces.

# draw lower faces
p0 = permute.dot([p, q, 0])
i0 = tuple(p0)
if filled[i0]:
voxel_faces[i0].append(p0 + square_rot_neg)

# draw middle faces
for r1, r2 in zip(rinds[:-1], rinds[1:]):
p1 = permute.dot([p, q, r1])
p2 = permute.dot([p, q, r2])

i1 = tuple(p1)
i2 = tuple(p2)

if filled[i1] and not filled[i2]:
voxel_faces[i1].append(p2 + square_rot_pos)
elif not filled[i1] and filled[i2]:
voxel_faces[i2].append(p2 + square_rot_neg)

# draw upper faces
pk = permute.dot([p, q, rc-1])
pk2 = permute.dot([p, q, rc])
ik = tuple(pk)
if filled[ik]:
voxel_faces[ik].append(pk2 + square_rot_pos)

# iterate over the faces, and generate a Poly3DCollection for each
# voxel
polygons = {}
for coord, faces_inds in voxel_faces.items():
# convert indices into 3D positions
if xyz is None:
faces = faces_inds
else:
faces = []
for face_inds in faces_inds:
ind = face_inds[:, 0], face_inds[:, 1], face_inds[:, 2]
face = np.empty(face_inds.shape)
face[:, 0] = x[ind]
face[:, 1] = y[ind]
face[:, 2] = z[ind]
faces.append(face)

# shade the faces
facecolor = facecolors[coord]
edgecolor = edgecolors[coord]
normals = self._generate_normals(faces)
facecolor = self._shade_colors(facecolor, normals, lightsource)
if edgecolor is not None:
edgecolor, normals, lightsource
)

poly = art3d.Poly3DCollection(faces,
facecolors=facecolor,
edgecolors=edgecolor,
**kwargs
)
polygons[coord] = poly

return polygons

def get_test_data(delta=0.05):
'''
Return a tuple X, Y, Z with a test data set.
'''
x = y = np.arange(-3.0, 3.0, delta)
X, Y = np.meshgrid(x, y)

Z1 = np.exp(-(X**2 + Y**2) / 2) / (2 * np.pi)
Z2 = (np.exp(-(((X - 1) / 1.5)**2 + ((Y - 1) / 0.5)**2) / 2) /
(2 * np.pi * 0.5 * 1.5))
Z = Z2 - Z1

X = X * 10
Y = Y * 10
Z = Z * 500
return X, Y, Z

########################################################
# Register Axes3D as a 'projection' object available
# for use just like any other axes
########################################################
proj.projection_registry.register(Axes3D)