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# art3d.py, original mplot3d version by John Porter
# Parts rewritten by Reinier Heeres <[email protected]>
# Minor additions by Ben Axelrod <[email protected]>
"""
Module containing 3D artist code and functions to convert 2D
artists into 3D versions which can be added to an Axes3D.
"""
import math
import numpy as np
from contextlib import contextmanager
from matplotlib import (
artist, cbook, colors as mcolors, lines, text as mtext,
path as mpath)
from matplotlib.collections import (
Collection, LineCollection, PolyCollection, PatchCollection, PathCollection)
from matplotlib.colors import Normalize
from matplotlib.patches import Patch
from . import proj3d
def _norm_angle(a):
"""Return the given angle normalized to -180 < *a* <= 180 degrees."""
a = (a + 360) % 360
if a > 180:
a = a - 360
return a
def _norm_text_angle(a):
"""Return the given angle normalized to -90 < *a* <= 90 degrees."""
a = (a + 180) % 180
if a > 90:
a = a - 180
return a
def get_dir_vector(zdir):
"""
Return a direction vector.
Parameters
----------
zdir : {'x', 'y', 'z', None, 3-tuple}
The direction. Possible values are:
- 'x': equivalent to (1, 0, 0)
- 'y': equivalent to (0, 1, 0)
- 'z': equivalent to (0, 0, 1)
- *None*: equivalent to (0, 0, 0)
- an iterable (x, y, z) is converted to an array
Returns
-------
x, y, z : array
The direction vector.
"""
if zdir == 'x':
return np.array((1, 0, 0))
elif zdir == 'y':
return np.array((0, 1, 0))
elif zdir == 'z':
return np.array((0, 0, 1))
elif zdir is None:
return np.array((0, 0, 0))
elif np.iterable(zdir) and len(zdir) == 3:
return np.array(zdir)
else:
raise ValueError("'x', 'y', 'z', None or vector of length 3 expected")
class Text3D(mtext.Text):
"""
Text object with 3D position and direction.
Parameters
----------
x, y, z : float
The position of the text.
text : str
The text string to display.
zdir : {'x', 'y', 'z', None, 3-tuple}
The direction of the text. See `.get_dir_vector` for a description of
the values.
Other Parameters
----------------
**kwargs
All other parameters are passed on to `~matplotlib.text.Text`.
"""
def __init__(self, x=0, y=0, z=0, text='', zdir='z', **kwargs):
mtext.Text.__init__(self, x, y, text, **kwargs)
self.set_3d_properties(z, zdir)
def get_position_3d(self):
"""Return the (x, y, z) position of the text."""
return self._x, self._y, self._z
def set_position_3d(self, xyz, zdir=None):
"""
Set the (*x*, *y*, *z*) position of the text.
Parameters
----------
xyz : (float, float, float)
The position in 3D space.
zdir : {'x', 'y', 'z', None, 3-tuple}
The direction of the text. If unspecified, the *zdir* will not be
changed. See `.get_dir_vector` for a description of the values.
"""
super().set_position(xyz[:2])
self.set_z(xyz[2])
if zdir is not None:
self._dir_vec = get_dir_vector(zdir)
def set_z(self, z):
"""
Set the *z* position of the text.
Parameters
----------
z : float
"""
self._z = z
self.stale = True
def set_3d_properties(self, z=0, zdir='z'):
"""
Set the *z* position and direction of the text.
Parameters
----------
z : float
The z-position in 3D space.
zdir : {'x', 'y', 'z', 3-tuple}
The direction of the text. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
self._z = z
self._dir_vec = get_dir_vector(zdir)
self.stale = True
@artist.allow_rasterization
def draw(self, renderer):
position3d = np.array((self._x, self._y, self._z))
proj = proj3d._proj_trans_points(
[position3d, position3d + self._dir_vec], self.axes.M)
dx = proj[0][1] - proj[0][0]
dy = proj[1][1] - proj[1][0]
angle = math.degrees(math.atan2(dy, dx))
with cbook._setattr_cm(self, _x=proj[0][0], _y=proj[1][0],
_rotation=_norm_text_angle(angle)):
mtext.Text.draw(self, renderer)
self.stale = False
def get_tightbbox(self, renderer=None):
# Overwriting the 2d Text behavior which is not valid for 3d.
# For now, just return None to exclude from layout calculation.
return None
def text_2d_to_3d(obj, z=0, zdir='z'):
"""
Convert a `.Text` to a `.Text3D` object.
Parameters
----------
z : float
The z-position in 3D space.
zdir : {'x', 'y', 'z', 3-tuple}
The direction of the text. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
obj.__class__ = Text3D
obj.set_3d_properties(z, zdir)
class Line3D(lines.Line2D):
"""
3D line object.
.. note:: Use `get_data_3d` to obtain the data associated with the line.
`~.Line2D.get_data`, `~.Line2D.get_xdata`, and `~.Line2D.get_ydata` return
the x- and y-coordinates of the projected 2D-line, not the x- and y-data of
the 3D-line. Similarly, use `set_data_3d` to set the data, not
`~.Line2D.set_data`, `~.Line2D.set_xdata`, and `~.Line2D.set_ydata`.
"""
def __init__(self, xs, ys, zs, *args, **kwargs):
"""
Parameters
----------
xs : array-like
The x-data to be plotted.
ys : array-like
The y-data to be plotted.
zs : array-like
The z-data to be plotted.
*args, **kwargs
Additional arguments are passed to `~matplotlib.lines.Line2D`.
"""
super().__init__([], [], *args, **kwargs)
self.set_data_3d(xs, ys, zs)
def set_3d_properties(self, zs=0, zdir='z'):
"""
Set the *z* position and direction of the line.
Parameters
----------
zs : float or array of floats
The location along the *zdir* axis in 3D space to position the
line.
zdir : {'x', 'y', 'z'}
Plane to plot line orthogonal to. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
xs = self.get_xdata()
ys = self.get_ydata()
zs = cbook._to_unmasked_float_array(zs).ravel()
zs = np.broadcast_to(zs, len(xs))
self._verts3d = juggle_axes(xs, ys, zs, zdir)
self.stale = True
def set_data_3d(self, *args):
"""
Set the x, y and z data
Parameters
----------
x : array-like
The x-data to be plotted.
y : array-like
The y-data to be plotted.
z : array-like
The z-data to be plotted.
Notes
-----
Accepts x, y, z arguments or a single array-like (x, y, z)
"""
if len(args) == 1:
args = args[0]
for name, xyz in zip('xyz', args):
if not np.iterable(xyz):
raise RuntimeError(f'{name} must be a sequence')
self._verts3d = args
self.stale = True
def get_data_3d(self):
"""
Get the current data
Returns
-------
verts3d : length-3 tuple or array-like
The current data as a tuple or array-like.
"""
return self._verts3d
@artist.allow_rasterization
def draw(self, renderer):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, self.axes.M)
self.set_data(xs, ys)
super().draw(renderer)
self.stale = False
def line_2d_to_3d(line, zs=0, zdir='z'):
"""
Convert a `.Line2D` to a `.Line3D` object.
Parameters
----------
zs : float
The location along the *zdir* axis in 3D space to position the line.
zdir : {'x', 'y', 'z'}
Plane to plot line orthogonal to. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
line.__class__ = Line3D
line.set_3d_properties(zs, zdir)
def _path_to_3d_segment(path, zs=0, zdir='z'):
"""Convert a path to a 3D segment."""
zs = np.broadcast_to(zs, len(path))
pathsegs = path.iter_segments(simplify=False, curves=False)
seg = [(x, y, z) for (((x, y), code), z) in zip(pathsegs, zs)]
seg3d = [juggle_axes(x, y, z, zdir) for (x, y, z) in seg]
return seg3d
def _paths_to_3d_segments(paths, zs=0, zdir='z'):
"""Convert paths from a collection object to 3D segments."""
if not np.iterable(zs):
zs = np.broadcast_to(zs, len(paths))
else:
if len(zs) != len(paths):
raise ValueError('Number of z-coordinates does not match paths.')
segs = [_path_to_3d_segment(path, pathz, zdir)
for path, pathz in zip(paths, zs)]
return segs
def _path_to_3d_segment_with_codes(path, zs=0, zdir='z'):
"""Convert a path to a 3D segment with path codes."""
zs = np.broadcast_to(zs, len(path))
pathsegs = path.iter_segments(simplify=False, curves=False)
seg_codes = [((x, y, z), code) for ((x, y), code), z in zip(pathsegs, zs)]
if seg_codes:
seg, codes = zip(*seg_codes)
seg3d = [juggle_axes(x, y, z, zdir) for (x, y, z) in seg]
else:
seg3d = []
codes = []
return seg3d, list(codes)
def _paths_to_3d_segments_with_codes(paths, zs=0, zdir='z'):
"""
Convert paths from a collection object to 3D segments with path codes.
"""
zs = np.broadcast_to(zs, len(paths))
segments_codes = [_path_to_3d_segment_with_codes(path, pathz, zdir)
for path, pathz in zip(paths, zs)]
if segments_codes:
segments, codes = zip(*segments_codes)
else:
segments, codes = [], []
return list(segments), list(codes)
class Collection3D(Collection):
"""A collection of 3D paths."""
def do_3d_projection(self):
"""Project the points according to renderer matrix."""
xyzs_list = [proj3d.proj_transform(*vs.T, self.axes.M)
for vs, _ in self._3dverts_codes]
self._paths = [mpath.Path(np.column_stack([xs, ys]), cs)
for (xs, ys, _), (_, cs) in zip(xyzs_list, self._3dverts_codes)]
zs = np.concatenate([zs for _, _, zs in xyzs_list])
return zs.min() if len(zs) else 1e9
def collection_2d_to_3d(col, zs=0, zdir='z'):
"""Convert a `.Collection` to a `.Collection3D` object."""
zs = np.broadcast_to(zs, len(col.get_paths()))
col._3dverts_codes = [
(np.column_stack(juggle_axes(
*np.column_stack([p.vertices, np.broadcast_to(z, len(p.vertices))]).T,
zdir)),
p.codes)
for p, z in zip(col.get_paths(), zs)]
col.__class__ = cbook._make_class_factory(Collection3D, "{}3D")(type(col))
class Line3DCollection(LineCollection):
"""
A collection of 3D lines.
"""
def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True
def set_segments(self, segments):
"""
Set 3D segments.
"""
self._segments3d = segments
super().set_segments([])
def do_3d_projection(self):
"""
Project the points according to renderer matrix.
"""
xyslist = [proj3d._proj_trans_points(points, self.axes.M)
for points in self._segments3d]
segments_2d = [np.column_stack([xs, ys]) for xs, ys, zs in xyslist]
LineCollection.set_segments(self, segments_2d)
# FIXME
minz = 1e9
for xs, ys, zs in xyslist:
minz = min(minz, min(zs))
return minz
def line_collection_2d_to_3d(col, zs=0, zdir='z'):
"""Convert a `.LineCollection` to a `.Line3DCollection` object."""
segments3d = _paths_to_3d_segments(col.get_paths(), zs, zdir)
col.__class__ = Line3DCollection
col.set_segments(segments3d)
class Patch3D(Patch):
"""
3D patch object.
"""
def __init__(self, *args, zs=(), zdir='z', **kwargs):
"""
Parameters
----------
verts :
zs : float
The location along the *zdir* axis in 3D space to position the
patch.
zdir : {'x', 'y', 'z'}
Plane to plot patch orthogonal to. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
super().__init__(*args, **kwargs)
self.set_3d_properties(zs, zdir)
def set_3d_properties(self, verts, zs=0, zdir='z'):
"""
Set the *z* position and direction of the patch.
Parameters
----------
verts :
zs : float
The location along the *zdir* axis in 3D space to position the
patch.
zdir : {'x', 'y', 'z'}
Plane to plot patch orthogonal to. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
zs = np.broadcast_to(zs, len(verts))
self._segment3d = [juggle_axes(x, y, z, zdir)
for ((x, y), z) in zip(verts, zs)]
def get_path(self):
return self._path2d
def do_3d_projection(self):
s = self._segment3d
xs, ys, zs = zip(*s)
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs,
self.axes.M)
self._path2d = mpath.Path(np.column_stack([vxs, vys]))
return min(vzs)
class PathPatch3D(Patch3D):
"""
3D PathPatch object.
"""
def __init__(self, path, *, zs=(), zdir='z', **kwargs):
"""
Parameters
----------
path :
zs : float
The location along the *zdir* axis in 3D space to position the
path patch.
zdir : {'x', 'y', 'z', 3-tuple}
Plane to plot path patch orthogonal to. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
# Not super().__init__!
Patch.__init__(self, **kwargs)
self.set_3d_properties(path, zs, zdir)
def set_3d_properties(self, path, zs=0, zdir='z'):
"""
Set the *z* position and direction of the path patch.
Parameters
----------
path :
zs : float
The location along the *zdir* axis in 3D space to position the
path patch.
zdir : {'x', 'y', 'z', 3-tuple}
Plane to plot path patch orthogonal to. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
Patch3D.set_3d_properties(self, path.vertices, zs=zs, zdir=zdir)
self._code3d = path.codes
def do_3d_projection(self):
s = self._segment3d
xs, ys, zs = zip(*s)
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs,
self.axes.M)
self._path2d = mpath.Path(np.column_stack([vxs, vys]), self._code3d)
return min(vzs)
def _get_patch_verts(patch):
"""Return a list of vertices for the path of a patch."""
trans = patch.get_patch_transform()
path = patch.get_path()
polygons = path.to_polygons(trans)
return polygons[0] if len(polygons) else np.array([])
def patch_2d_to_3d(patch, z=0, zdir='z'):
"""Convert a `.Patch` to a `.Patch3D` object."""
verts = _get_patch_verts(patch)
patch.__class__ = Patch3D
patch.set_3d_properties(verts, z, zdir)
def pathpatch_2d_to_3d(pathpatch, z=0, zdir='z'):
"""Convert a `.PathPatch` to a `.PathPatch3D` object."""
path = pathpatch.get_path()
trans = pathpatch.get_patch_transform()
mpath = trans.transform_path(path)
pathpatch.__class__ = PathPatch3D
pathpatch.set_3d_properties(mpath, z, zdir)
class Patch3DCollection(PatchCollection):
"""
A collection of 3D patches.
"""
def __init__(self, *args, zs=0, zdir='z', depthshade=True, **kwargs):
"""
Create a collection of flat 3D patches with its normal vector
pointed in *zdir* direction, and located at *zs* on the *zdir*
axis. 'zs' can be a scalar or an array-like of the same length as
the number of patches in the collection.
Constructor arguments are the same as for
:class:`~matplotlib.collections.PatchCollection`. In addition,
keywords *zs=0* and *zdir='z'* are available.
Also, the keyword argument *depthshade* is available to indicate
whether to shade the patches in order to give the appearance of depth
(default is *True*). This is typically desired in scatter plots.
"""
self._depthshade = depthshade
super().__init__(*args, **kwargs)
self.set_3d_properties(zs, zdir)
def get_depthshade(self):
return self._depthshade
def set_depthshade(self, depthshade):
"""
Set whether depth shading is performed on collection members.
Parameters
----------
depthshade : bool
Whether to shade the patches in order to give the appearance of
depth.
"""
self._depthshade = depthshade
self.stale = True
def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True
def set_3d_properties(self, zs, zdir):
"""
Set the *z* positions and direction of the patches.
Parameters
----------
zs : float or array of floats
The location or locations to place the patches in the collection
along the *zdir* axis.
zdir : {'x', 'y', 'z'}
Plane to plot patches orthogonal to.
All patches must have the same direction.
See `.get_dir_vector` for a description of the values.
"""
# Force the collection to initialize the face and edgecolors
# just in case it is a scalarmappable with a colormap.
self.update_scalarmappable()
offsets = self.get_offsets()
if len(offsets) > 0:
xs, ys = offsets.T
else:
xs = []
ys = []
self._offsets3d = juggle_axes(xs, ys, np.atleast_1d(zs), zdir)
self._z_markers_idx = slice(-1)
self._vzs = None
self.stale = True
def do_3d_projection(self):
xs, ys, zs = self._offsets3d
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs,
self.axes.M)
self._vzs = vzs
super().set_offsets(np.column_stack([vxs, vys]))
if vzs.size > 0:
return min(vzs)
else:
return np.nan
def _maybe_depth_shade_and_sort_colors(self, color_array):
color_array = (
_zalpha(color_array, self._vzs)
if self._vzs is not None and self._depthshade
else color_array
)
if len(color_array) > 1:
color_array = color_array[self._z_markers_idx]
return mcolors.to_rgba_array(color_array, self._alpha)
def get_facecolor(self):
return self._maybe_depth_shade_and_sort_colors(super().get_facecolor())
def get_edgecolor(self):
# We need this check here to make sure we do not double-apply the depth
# based alpha shading when the edge color is "face" which means the
# edge colour should be identical to the face colour.
if cbook._str_equal(self._edgecolors, 'face'):
return self.get_facecolor()
return self._maybe_depth_shade_and_sort_colors(super().get_edgecolor())
class Path3DCollection(PathCollection):
"""
A collection of 3D paths.
"""
def __init__(self, *args, zs=0, zdir='z', depthshade=True, **kwargs):
"""
Create a collection of flat 3D paths with its normal vector
pointed in *zdir* direction, and located at *zs* on the *zdir*
axis. 'zs' can be a scalar or an array-like of the same length as
the number of paths in the collection.
Constructor arguments are the same as for
:class:`~matplotlib.collections.PathCollection`. In addition,
keywords *zs=0* and *zdir='z'* are available.
Also, the keyword argument *depthshade* is available to indicate
whether to shade the patches in order to give the appearance of depth
(default is *True*). This is typically desired in scatter plots.
"""
self._depthshade = depthshade
self._in_draw = False
super().__init__(*args, **kwargs)
self.set_3d_properties(zs, zdir)
self._offset_zordered = None
def draw(self, renderer):
with self._use_zordered_offset():
with cbook._setattr_cm(self, _in_draw=True):
super().draw(renderer)
def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True
def set_3d_properties(self, zs, zdir):
"""
Set the *z* positions and direction of the paths.
Parameters
----------
zs : float or array of floats
The location or locations to place the paths in the collection
along the *zdir* axis.
zdir : {'x', 'y', 'z'}
Plane to plot paths orthogonal to.
All paths must have the same direction.
See `.get_dir_vector` for a description of the values.
"""
# Force the collection to initialize the face and edgecolors
# just in case it is a scalarmappable with a colormap.
self.update_scalarmappable()
offsets = self.get_offsets()
if len(offsets) > 0:
xs, ys = offsets.T
else:
xs = []
ys = []
self._offsets3d = juggle_axes(xs, ys, np.atleast_1d(zs), zdir)
# In the base draw methods we access the attributes directly which
# means we cannot resolve the shuffling in the getter methods like
# we do for the edge and face colors.
#
# This means we need to carry around a cache of the unsorted sizes and
# widths (postfixed with 3d) and in `do_3d_projection` set the
# depth-sorted version of that data into the private state used by the
# base collection class in its draw method.
#
# Grab the current sizes and linewidths to preserve them.
self._sizes3d = self._sizes
self._linewidths3d = np.array(self._linewidths)
xs, ys, zs = self._offsets3d
# Sort the points based on z coordinates
# Performance optimization: Create a sorted index array and reorder
# points and point properties according to the index array
self._z_markers_idx = slice(-1)
self._vzs = None
self.stale = True
def set_sizes(self, sizes, dpi=72.0):
super().set_sizes(sizes, dpi)
if not self._in_draw:
self._sizes3d = sizes
def set_linewidth(self, lw):
super().set_linewidth(lw)
if not self._in_draw:
self._linewidths3d = np.array(self._linewidths)
def get_depthshade(self):
return self._depthshade
def set_depthshade(self, depthshade):
"""
Set whether depth shading is performed on collection members.
Parameters
----------
depthshade : bool
Whether to shade the patches in order to give the appearance of
depth.
"""
self._depthshade = depthshade
self.stale = True
def do_3d_projection(self):
xs, ys, zs = self._offsets3d
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs,
self.axes.M)
# Sort the points based on z coordinates
# Performance optimization: Create a sorted index array and reorder
# points and point properties according to the index array
z_markers_idx = self._z_markers_idx = np.argsort(vzs)[::-1]
self._vzs = vzs
# we have to special case the sizes because of code in collections.py
# as the draw method does
# self.set_sizes(self._sizes, self.figure.dpi)
# so we cannot rely on doing the sorting on the way out via get_*
if len(self._sizes3d) > 1:
self._sizes = self._sizes3d[z_markers_idx]
if len(self._linewidths3d) > 1:
self._linewidths = self._linewidths3d[z_markers_idx]
PathCollection.set_offsets(self, np.column_stack((vxs, vys)))
# Re-order items
vzs = vzs[z_markers_idx]
vxs = vxs[z_markers_idx]
vys = vys[z_markers_idx]
# Store ordered offset for drawing purpose
self._offset_zordered = np.column_stack((vxs, vys))
return np.min(vzs) if vzs.size else np.nan
@contextmanager
def _use_zordered_offset(self):
if self._offset_zordered is None:
# Do nothing
yield
else:
# Swap offset with z-ordered offset
old_offset = self._offsets
super().set_offsets(self._offset_zordered)
try:
yield
finally:
self._offsets = old_offset
def _maybe_depth_shade_and_sort_colors(self, color_array):
color_array = (
_zalpha(color_array, self._vzs)
if self._vzs is not None and self._depthshade
else color_array
)
if len(color_array) > 1:
color_array = color_array[self._z_markers_idx]
return mcolors.to_rgba_array(color_array, self._alpha)
def get_facecolor(self):
return self._maybe_depth_shade_and_sort_colors(super().get_facecolor())
def get_edgecolor(self):
# We need this check here to make sure we do not double-apply the depth
# based alpha shading when the edge color is "face" which means the
# edge colour should be identical to the face colour.
if cbook._str_equal(self._edgecolors, 'face'):
return self.get_facecolor()
return self._maybe_depth_shade_and_sort_colors(super().get_edgecolor())
def patch_collection_2d_to_3d(col, zs=0, zdir='z', depthshade=True):
"""
Convert a `.PatchCollection` into a `.Patch3DCollection` object
(or a `.PathCollection` into a `.Path3DCollection` object).
Parameters
----------
zs : float or array of floats
The location or locations to place the patches in the collection along
the *zdir* axis. Default: 0.
zdir : {'x', 'y', 'z'}
The axis in which to place the patches. Default: "z".
See `.get_dir_vector` for a description of the values.
depthshade
Whether to shade the patches to give a sense of depth. Default: *True*.
"""
if isinstance(col, PathCollection):
col.__class__ = Path3DCollection
col._offset_zordered = None
elif isinstance(col, PatchCollection):
col.__class__ = Patch3DCollection
col._depthshade = depthshade
col._in_draw = False
col.set_3d_properties(zs, zdir)
class Poly3DCollection(PolyCollection):
"""
A collection of 3D polygons.
.. note::
**Filling of 3D polygons**
There is no simple definition of the enclosed surface of a 3D polygon
unless the polygon is planar.
In practice, Matplotlib fills the 2D projection of the polygon. This
gives a correct filling appearance only for planar polygons. For all
other polygons, you'll find orientations in which the edges of the
polygon intersect in the projection. This will lead to an incorrect
visualization of the 3D area.
If you need filled areas, it is recommended to create them via
`~mpl_toolkits.mplot3d.axes3d.Axes3D.plot_trisurf`, which creates a
triangulation and thus generates consistent surfaces.
"""
def __init__(self, verts, *args, zsort='average', shade=False,
lightsource=None, **kwargs):
"""
Parameters
----------
verts : list of (N, 3) array-like
The sequence of polygons [*verts0*, *verts1*, ...] where each
element *verts_i* defines the vertices of polygon *i* as a 2D
array-like of shape (N, 3).
zsort : {'average', 'min', 'max'}, default: 'average'
The calculation method for the z-order.
See `~.Poly3DCollection.set_zsort` for details.
shade : bool, default: False
Whether to shade *facecolors* and *edgecolors*. When activating
*shade*, *facecolors* and/or *edgecolors* must be provided.
.. versionadded:: 3.7
lightsource : `~matplotlib.colors.LightSource`, optional
The lightsource to use when *shade* is True.
.. versionadded:: 3.7
*args, **kwargs
All other parameters are forwarded to `.PolyCollection`.
Notes
-----
Note that this class does a bit of magic with the _facecolors
and _edgecolors properties.
"""
if shade:
normals = _generate_normals(verts)
facecolors = kwargs.get('facecolors', None)
if facecolors is not None:
kwargs['facecolors'] = _shade_colors(
facecolors, normals, lightsource
)
edgecolors = kwargs.get('edgecolors', None)
if edgecolors is not None:
kwargs['edgecolors'] = _shade_colors(
edgecolors, normals, lightsource
)
if facecolors is None and edgecolors is None:
raise ValueError(
"You must provide facecolors, edgecolors, or both for "
"shade to work.")
super().__init__(verts, *args, **kwargs)
if isinstance(verts, np.ndarray):
if verts.ndim != 3:
raise ValueError('verts must be a list of (N, 3) array-like')
else:
if any(len(np.shape(vert)) != 2 for vert in verts):
raise ValueError('verts must be a list of (N, 3) array-like')
self.set_zsort(zsort)
self._codes3d = None
_zsort_functions = {
'average': np.average,
'min': np.min,
'max': np.max,
}
def set_zsort(self, zsort):
"""
Set the calculation method for the z-order.
Parameters
----------
zsort : {'average', 'min', 'max'}
The function applied on the z-coordinates of the vertices in the
viewer's coordinate system, to determine the z-order.
"""
self._zsortfunc = self._zsort_functions[zsort]
self._sort_zpos = None
self.stale = True
def get_vector(self, segments3d):
"""Optimize points for projection."""
if len(segments3d):
xs, ys, zs = np.vstack(segments3d).T
else: # vstack can't stack zero arrays.
xs, ys, zs = [], [], []
ones = np.ones(len(xs))
self._vec = np.array([xs, ys, zs, ones])
indices = [0, *np.cumsum([len(segment) for segment in segments3d])]
self._segslices = [*map(slice, indices[:-1], indices[1:])]
def set_verts(self, verts, closed=True):
"""
Set 3D vertices.
Parameters
----------
verts : list of (N, 3) array-like
The sequence of polygons [*verts0*, *verts1*, ...] where each
element *verts_i* defines the vertices of polygon *i* as a 2D
array-like of shape (N, 3).
closed : bool, default: True
Whether the polygon should be closed by adding a CLOSEPOLY
connection at the end.
"""
self.get_vector(verts)
# 2D verts will be updated at draw time
super().set_verts([], False)
self._closed = closed
def set_verts_and_codes(self, verts, codes):
"""Set 3D vertices with path codes."""
# set vertices with closed=False to prevent PolyCollection from
# setting path codes
self.set_verts(verts, closed=False)
# and set our own codes instead.
self._codes3d = codes
def set_3d_properties(self):
# Force the collection to initialize the face and edgecolors
# just in case it is a scalarmappable with a colormap.
self.update_scalarmappable()
self._sort_zpos = None
self.set_zsort('average')
self._facecolor3d = PolyCollection.get_facecolor(self)
self._edgecolor3d = PolyCollection.get_edgecolor(self)
self._alpha3d = PolyCollection.get_alpha(self)
self.stale = True
def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True
def do_3d_projection(self):
"""
Perform the 3D projection for this object.
"""
if self._A is not None:
# force update of color mapping because we re-order them
# below. If we do not do this here, the 2D draw will call
# this, but we will never port the color mapped values back
# to the 3D versions.
#
# We hold the 3D versions in a fixed order (the order the user
# passed in) and sort the 2D version by view depth.
self.update_scalarmappable()
if self._face_is_mapped:
self._facecolor3d = self._facecolors
if self._edge_is_mapped:
self._edgecolor3d = self._edgecolors
txs, tys, tzs = proj3d._proj_transform_vec(self._vec, self.axes.M)
xyzlist = [(txs[sl], tys[sl], tzs[sl]) for sl in self._segslices]
# This extra fuss is to re-order face / edge colors
cface = self._facecolor3d
cedge = self._edgecolor3d
if len(cface) != len(xyzlist):
cface = cface.repeat(len(xyzlist), axis=0)
if len(cedge) != len(xyzlist):
if len(cedge) == 0:
cedge = cface
else:
cedge = cedge.repeat(len(xyzlist), axis=0)
if xyzlist:
# sort by depth (furthest drawn first)
z_segments_2d = sorted(
((self._zsortfunc(zs), np.column_stack([xs, ys]), fc, ec, idx)
for idx, ((xs, ys, zs), fc, ec)
in enumerate(zip(xyzlist, cface, cedge))),
key=lambda x: x[0], reverse=True)
_, segments_2d, self._facecolors2d, self._edgecolors2d, idxs = \
zip(*z_segments_2d)
else:
segments_2d = []
self._facecolors2d = np.empty((0, 4))
self._edgecolors2d = np.empty((0, 4))
idxs = []
if self._codes3d is not None:
codes = [self._codes3d[idx] for idx in idxs]
PolyCollection.set_verts_and_codes(self, segments_2d, codes)
else:
PolyCollection.set_verts(self, segments_2d, self._closed)
if len(self._edgecolor3d) != len(cface):
self._edgecolors2d = self._edgecolor3d
# Return zorder value
if self._sort_zpos is not None:
zvec = np.array([[0], [0], [self._sort_zpos], [1]])
ztrans = proj3d._proj_transform_vec(zvec, self.axes.M)
return ztrans[2][0]
elif tzs.size > 0:
# FIXME: Some results still don't look quite right.
# In particular, examine contourf3d_demo2.py
# with az = -54 and elev = -45.
return np.min(tzs)
else:
return np.nan
def set_facecolor(self, colors):
# docstring inherited
super().set_facecolor(colors)
self._facecolor3d = PolyCollection.get_facecolor(self)
def set_edgecolor(self, colors):
# docstring inherited
super().set_edgecolor(colors)
self._edgecolor3d = PolyCollection.get_edgecolor(self)
def set_alpha(self, alpha):
# docstring inherited
artist.Artist.set_alpha(self, alpha)
try:
self._facecolor3d = mcolors.to_rgba_array(
self._facecolor3d, self._alpha)
except (AttributeError, TypeError, IndexError):
pass
try:
self._edgecolors = mcolors.to_rgba_array(
self._edgecolor3d, self._alpha)
except (AttributeError, TypeError, IndexError):
pass
self.stale = True
def get_facecolor(self):
# docstring inherited
# self._facecolors2d is not initialized until do_3d_projection
if not hasattr(self, '_facecolors2d'):
self.axes.M = self.axes.get_proj()
self.do_3d_projection()
return np.asarray(self._facecolors2d)
def get_edgecolor(self):
# docstring inherited
# self._edgecolors2d is not initialized until do_3d_projection
if not hasattr(self, '_edgecolors2d'):
self.axes.M = self.axes.get_proj()
self.do_3d_projection()
return np.asarray(self._edgecolors2d)
def poly_collection_2d_to_3d(col, zs=0, zdir='z'):
"""
Convert a `.PolyCollection` into a `.Poly3DCollection` object.
Parameters
----------
zs : float or array of floats
The location or locations to place the polygons in the collection along
the *zdir* axis. Default: 0.
zdir : {'x', 'y', 'z'}
The axis in which to place the patches. Default: 'z'.
See `.get_dir_vector` for a description of the values.
"""
segments_3d, codes = _paths_to_3d_segments_with_codes(
col.get_paths(), zs, zdir)
col.__class__ = Poly3DCollection
col.set_verts_and_codes(segments_3d, codes)
col.set_3d_properties()
def juggle_axes(xs, ys, zs, zdir):
"""
Reorder coordinates so that 2D *xs*, *ys* can be plotted in the plane
orthogonal to *zdir*. *zdir* is normally 'x', 'y' or 'z'. However, if
*zdir* starts with a '-' it is interpreted as a compensation for
`rotate_axes`.
"""
if zdir == 'x':
return zs, xs, ys
elif zdir == 'y':
return xs, zs, ys
elif zdir[0] == '-':
return rotate_axes(xs, ys, zs, zdir)
else:
return xs, ys, zs
def rotate_axes(xs, ys, zs, zdir):
"""
Reorder coordinates so that the axes are rotated with *zdir* along
the original z axis. Prepending the axis with a '-' does the
inverse transform, so *zdir* can be 'x', '-x', 'y', '-y', 'z' or '-z'.
"""
if zdir in ('x', '-y'):
return ys, zs, xs
elif zdir in ('-x', 'y'):
return zs, xs, ys
else:
return xs, ys, zs
def _zalpha(colors, zs):
"""Modify the alphas of the color list according to depth."""
# FIXME: This only works well if the points for *zs* are well-spaced
# in all three dimensions. Otherwise, at certain orientations,
# the min and max zs are very close together.
# Should really normalize against the viewing depth.
if len(colors) == 0 or len(zs) == 0:
return np.zeros((0, 4))
norm = Normalize(min(zs), max(zs))
sats = 1 - norm(zs) * 0.7
rgba = np.broadcast_to(mcolors.to_rgba_array(colors), (len(zs), 4))
return np.column_stack([rgba[:, :3], rgba[:, 3] * sats])
def _generate_normals(polygons):
"""
Compute the normals of a list of polygons, one normal per polygon.
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 method assumes
that the points are in a plane. Otherwise, more than one shade is required,
which is not supported.
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
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(color, normals, lightsource=None):
"""
Shade *color* using normal vectors given by *normals*,
assuming a *lightsource* (using default position if not given).
*color* can also be an array of the same length as *normals*.
"""
if lightsource is None:
# chosen for backwards-compatibility
lightsource = mcolors.LightSource(azdeg=225, altdeg=19.4712)
with np.errstate(invalid="ignore"):
shade = ((normals / np.linalg.norm(normals, axis=1, keepdims=True))
@ lightsource.direction)
mask = ~np.isnan(shade)
if mask.any():
# convert dot product to allowed shading fractions
in_norm = mcolors.Normalize(-1, 1)
out_norm = mcolors.Normalize(0.3, 1).inverse
def norm(x):
return out_norm(in_norm(x))
shade[~mask] = 0
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
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