# Source code for mpl_toolkits.mplot3d.art3d

# 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 matplotlib import (
artist, colors as mcolors, lines, text as mtext, path as mpath)
from matplotlib.collections import (
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

[docs]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 returned unchanged.

Returns
-------
x, y, z : array-like
The direction vector. This is either a numpy.array or *zdir* itself if
*zdir* is already a length-3 iterable.

"""
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 zdir
else:
raise ValueError("'x', 'y', 'z', None or vector of length 3 expected")

[docs]class Text3D(mtext.Text):
"""
Text object with 3D position and direction.

Parameters
----------
x, y, z
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.
"""

[docs]    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)

[docs]    def set_3d_properties(self, z=0, zdir='z'):
x, y = self.get_position()
self._position3d = np.array((x, y, z))
self._dir_vec = get_dir_vector(zdir)
self.stale = True

[docs]    @artist.allow_rasterization
def draw(self, renderer):
proj = proj3d.proj_trans_points(
[self._position3d, self._position3d + self._dir_vec], renderer.M)
dx = proj[0][1] - proj[0][0]
dy = proj[1][1] - proj[1][0]
angle = math.degrees(math.atan2(dy, dx))
self.set_position((proj[0][0], proj[1][0]))
self.set_rotation(_norm_text_angle(angle))
mtext.Text.draw(self, renderer)
self.stale = False

[docs]    def get_tightbbox(self, renderer):
# Overwriting the 2d Text behavior which is not valid for 3d.
# For now, just return None to exclude from layout calculation.
return None

[docs]def text_2d_to_3d(obj, z=0, zdir='z'):
"""Convert a Text to a Text3D object."""
obj.__class__ = Text3D
obj.set_3d_properties(z, zdir)

[docs]class Line3D(lines.Line2D):
"""
3D line object.
"""

[docs]    def __init__(self, xs, ys, zs, *args, **kwargs):
"""
Keyword arguments are passed onto :func:~matplotlib.lines.Line2D.
"""
lines.Line2D.__init__(self, [], [], *args, **kwargs)
self._verts3d = xs, ys, zs

[docs]    def set_3d_properties(self, zs=0, zdir='z'):
xs = self.get_xdata()
ys = self.get_ydata()
self._verts3d = juggle_axes(xs, ys, zs, zdir)
self.stale = True

[docs]    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:
self._verts3d = args[0]
else:
self._verts3d = args
self.stale = True

[docs]    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

[docs]    @artist.allow_rasterization
def draw(self, renderer):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
self.set_data(xs, ys)
lines.Line2D.draw(self, renderer)
self.stale = False

[docs]def line_2d_to_3d(line, zs=0, zdir='z'):
"""Convert a 2D line to 3D."""

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."""

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."""

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."""

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.
"""

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)

[docs]class Line3DCollection(LineCollection):
"""
A collection of 3D lines.
"""

[docs]    def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True

[docs]    def set_segments(self, segments):
"""
Set 3D segments.
"""
self._segments3d = segments
LineCollection.set_segments(self, [])

[docs]    def do_3d_projection(self, renderer):
"""
Project the points according to renderer matrix.
"""
xyslist = [
proj3d.proj_trans_points(points, renderer.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

[docs]    @artist.allow_rasterization
def draw(self, renderer, project=False):
if project:
self.do_3d_projection(renderer)
LineCollection.draw(self, renderer)

[docs]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)

[docs]class Patch3D(Patch):
"""
3D patch object.
"""

[docs]    def __init__(self, *args, zs=(), zdir='z', **kwargs):
Patch.__init__(self, *args, **kwargs)
self.set_3d_properties(zs, zdir)

[docs]    def set_3d_properties(self, verts, zs=0, zdir='z'):
self._segment3d = [juggle_axes(x, y, z, zdir)
for ((x, y), z) in zip(verts, zs)]
self._facecolor3d = Patch.get_facecolor(self)

[docs]    def get_path(self):
return self._path2d

[docs]    def get_facecolor(self):
return self._facecolor2d

[docs]    def do_3d_projection(self, renderer):
s = self._segment3d
xs, ys, zs = zip(*s)
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)
self._path2d = mpath.Path(np.column_stack([vxs, vys]))
# FIXME: coloring
self._facecolor2d = self._facecolor3d
return min(vzs)

[docs]class PathPatch3D(Patch3D):
"""
3D PathPatch object.
"""

[docs]    def __init__(self, path, *, zs=(), zdir='z', **kwargs):
Patch.__init__(self, **kwargs)
self.set_3d_properties(path, zs, zdir)

[docs]    def set_3d_properties(self, path, zs=0, zdir='z'):
Patch3D.set_3d_properties(self, path.vertices, zs=zs, zdir=zdir)
self._code3d = path.codes

[docs]    def do_3d_projection(self, renderer):
s = self._segment3d
xs, ys, zs = zip(*s)
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)
self._path2d = mpath.Path(np.column_stack([vxs, vys]), self._code3d)
# FIXME: coloring
self._facecolor2d = self._facecolor3d
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)
if len(polygons):
return polygons[0]
else:
return []

[docs]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)

[docs]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)

[docs]class Patch3DCollection(PatchCollection):
"""
A collection of 3D patches.
"""

[docs]    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 or not to shade the patches in order to
give the appearance of depth (default is *True*).
This is typically desired in scatter plots.
"""
super().__init__(*args, **kwargs)
self.set_3d_properties(zs, zdir)

[docs]    def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True

[docs]    def set_3d_properties(self, zs, zdir):
# 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._facecolor3d = self.get_facecolor()
self._edgecolor3d = self.get_edgecolor()
self.stale = True

[docs]    def do_3d_projection(self, renderer):
xs, ys, zs = self._offsets3d
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)

fcs = (_zalpha(self._facecolor3d, vzs) if self._depthshade else
self._facecolor3d)
fcs = mcolors.to_rgba_array(fcs, self._alpha)
self.set_facecolors(fcs)

ecs = (_zalpha(self._edgecolor3d, vzs) if self._depthshade else
self._edgecolor3d)
ecs = mcolors.to_rgba_array(ecs, self._alpha)
self.set_edgecolors(ecs)
PatchCollection.set_offsets(self, np.column_stack([vxs, vys]))

if vzs.size > 0:
return min(vzs)
else:
return np.nan

[docs]class Path3DCollection(PathCollection):
"""
A collection of 3D paths.
"""

[docs]    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 or not to shade the patches in order to
give the appearance of depth (default is *True*).
This is typically desired in scatter plots.
"""
super().__init__(*args, **kwargs)
self.set_3d_properties(zs, zdir)

[docs]    def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True

[docs]    def set_3d_properties(self, zs, zdir):
# 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._facecolor3d = self.get_facecolor()
self._edgecolor3d = self.get_edgecolor()
self._sizes3d = self.get_sizes()
self.stale = True

[docs]    def do_3d_projection(self, renderer):
xs, ys, zs = self._offsets3d
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)

fcs = (_zalpha(self._facecolor3d, vzs) if self._depthshade else
self._facecolor3d)
fcs = mcolors.to_rgba_array(fcs, self._alpha)
self.set_facecolors(fcs)

ecs = (_zalpha(self._edgecolor3d, vzs) if self._depthshade else
self._edgecolor3d)

sizes = self._sizes3d

# 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 = np.argsort(vzs)[::-1]

# Re-order items
vzs = vzs[z_markers_idx]
vxs = vxs[z_markers_idx]
vys = vys[z_markers_idx]
fcs = fcs[z_markers_idx]
ecs = ecs[z_markers_idx]
if len(sizes) > 1:
sizes = sizes[z_markers_idx]
vps = np.column_stack((vxs, vys))

fcs = mcolors.to_rgba_array(fcs, self._alpha)
ecs = mcolors.to_rgba_array(ecs, self._alpha)

self.set_edgecolors(ecs)
self.set_facecolors(fcs)
self.set_sizes(sizes)

PathCollection.set_offsets(self, vps)

return np.min(vzs) if vzs.size else np.nan

"""
Convert a :class:~matplotlib.collections.PatchCollection into a
:class:Patch3DCollection object
(or a :class:~matplotlib.collections.PathCollection into a
:class:Path3DCollection object).

Parameters
----------
za
The location or locations to place the patches in the collection along
the *zdir* axis. Default: 0.
zdir
The axis in which to place the patches. Default: "z".
Whether to shade the patches to give a sense of depth. Default: *True*.

"""
if isinstance(col, PathCollection):
col.__class__ = Path3DCollection
elif isinstance(col, PatchCollection):
col.__class__ = Patch3DCollection
col.set_3d_properties(zs, zdir)

[docs]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.
"""

[docs]    def __init__(self, verts, *args, zsort='average', **kwargs):
"""
Parameters
----------
verts : list of array-like Nx3
Each element describes a polygon as a sequence of N_i points
(x, y, z).
zsort : {'average', 'min', 'max'}, default: 'average'
The calculation method for the z-order.
See ~.Poly3DCollection.set_zsort for details.
*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.
"""
super().__init__(verts, *args, **kwargs)
self.set_zsort(zsort)
self._codes3d = None

_zsort_functions = {
'average': np.average,
'min': np.min,
'max': np.max,
}

[docs]    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

[docs]    def get_vector(self, segments3d):
"""Optimize points for projection."""
if len(segments3d):
xs, ys, zs = np.row_stack(segments3d).T
else:  # row_stack 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:])]

[docs]    def set_verts(self, verts, closed=True):
"""Set 3D vertices."""
self.get_vector(verts)
# 2D verts will be updated at draw time
PolyCollection.set_verts(self, [], False)
self._closed = closed

[docs]    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

[docs]    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._facecolors3d = PolyCollection.get_facecolor(self)
self._edgecolors3d = PolyCollection.get_edgecolor(self)
self._alpha3d = PolyCollection.get_alpha(self)
self.stale = True

[docs]    def set_sort_zpos(self, val):
"""Set the position to use for z-sorting."""
self._sort_zpos = val
self.stale = True

[docs]    def do_3d_projection(self, renderer):
"""
Perform the 3D projection for this object.
"""
# FIXME: This may no longer be needed?
if self._A is not None:
self.update_scalarmappable()
self._facecolors3d = self._facecolors

txs, tys, tzs = proj3d._proj_transform_vec(self._vec, renderer.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._facecolors3d
cedge = self._edgecolors3d
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)

# 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)

zzs, segments_2d, self._facecolors2d, self._edgecolors2d, idxs = \
zip(*z_segments_2d)

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._edgecolors3d) != len(cface):
self._edgecolors2d = self._edgecolors3d

# 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, renderer.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

[docs]    def set_facecolor(self, colors):
PolyCollection.set_facecolor(self, colors)
self._facecolors3d = PolyCollection.get_facecolor(self)

[docs]    def set_edgecolor(self, colors):
PolyCollection.set_edgecolor(self, colors)
self._edgecolors3d = PolyCollection.get_edgecolor(self)

[docs]    def set_alpha(self, alpha):
# docstring inherited
artist.Artist.set_alpha(self, alpha)
try:
self._facecolors3d = mcolors.to_rgba_array(
self._facecolors3d, self._alpha)
except (AttributeError, TypeError, IndexError):
pass
try:
self._edgecolors = mcolors.to_rgba_array(
self._edgecolors3d, self._alpha)
except (AttributeError, TypeError, IndexError):
pass
self.stale = True

[docs]    def get_facecolor(self):
return self._facecolors2d

[docs]    def get_edgecolor(self):
return self._edgecolors2d

[docs]def poly_collection_2d_to_3d(col, zs=0, zdir='z'):
"""Convert a PolyCollection to a Poly3DCollection object."""
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()

[docs]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

[docs]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 == 'x':
return ys, zs, xs
elif zdir == '-x':
return zs, xs, ys

elif zdir == 'y':
return zs, xs, ys
elif zdir == '-y':
return ys, zs, xs

else:
return xs, ys, zs

def _get_colors(c, num):
"""Stretch the color argument to provide the required number *num*."""
mcolors.to_rgba_array(c) if len(c) else [0, 0, 0, 0],
(num, 4))

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(zs) == 0:
return np.zeros((0, 4))
norm = Normalize(min(zs), max(zs))
sats = 1 - norm(zs) * 0.7