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#!/usr/bin/python
# art3d.py, original mplot3d version by John Porter
# Parts rewritten by Reinier Heeres <reinier@heeres.eu>
# Minor additions by Ben Axelrod <baxelrod@coroware.com>
'''
Module containing 3D artist code and functions to convert 2D
artists into 3D versions which can be added to an Axes3D.
'''
from matplotlib import lines, text as mtext, path as mpath, colors as mcolors
from matplotlib.collections import Collection, LineCollection, \
PolyCollection, PatchCollection
from matplotlib.cm import ScalarMappable
from matplotlib.patches import Patch
from matplotlib.colors import Normalize
from matplotlib.cbook import iterable
import warnings
import numpy as np
import math
import proj3d
def norm_angle(a):
"""Return angle between -180 and +180"""
a = (a + 360) % 360
if a > 180:
a = a - 360
return a
def norm_text_angle(a):
"""Return angle between -90 and +90"""
a = (a + 180) % 180
if a > 90:
a = a - 180
return a
def get_dir_vector(zdir):
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 == None:
return np.array((0, 0, 0))
elif iterable(zdir) and len(zdir) == 3:
return zdir
else:
raise ValueError("'x', 'y', 'z', None or vector of length 3 expected")
class Text3D(mtext.Text):
'''
Text object with 3D position and (in the future) direction.
'''
def __init__(self, x=0, y=0, z=0, text='', zdir='z', **kwargs):
'''
*x*, *y*, *z* Position of text
*text* Text string to display
*zdir* Direction of text
Keyword arguments are passed onto :func:`~matplotlib.text.Text`.
'''
mtext.Text.__init__(self, x, y, text, **kwargs)
self.set_3d_properties(z, zdir)
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)
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]
if dx==0. and dy==0.:
# atan2 raises ValueError: math domain error on 0,0
angle = 0.
else:
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)
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)
class Line3D(lines.Line2D):
'''
3D line object.
'''
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
def set_3d_properties(self, zs=0, zdir='z'):
xs = self.get_xdata()
ys = self.get_ydata()
try:
zs = float(zs)
zs = [zs for x in xs]
except:
pass
self._verts3d = juggle_axes(xs, ys, zs, zdir)
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)
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.'''
if not iterable(zs):
zs = np.ones(len(path)) * zs
seg = []
pathsegs = path.iter_segments(simplify=False, curves=False)
for (((x, y), code), z) in zip(pathsegs, zs):
seg.append((x, y, z))
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 iterable(zs):
zs = np.ones(len(paths)) * zs
segments = []
for path, pathz in zip(paths, zs):
segments.append(path_to_3d_segment(path, pathz, zdir))
return segments
class Line3DCollection(LineCollection):
'''
A collection of 3D lines.
'''
def __init__(self, segments, *args, **kwargs):
'''
Keyword arguments are passed onto :func:`~matplotlib.collections.LineCollection`.
'''
LineCollection.__init__(self, segments, *args, **kwargs)
def set_segments(self, segments):
'''
Set 3D segments
'''
self._segments3d = segments
LineCollection.set_segments(self, [])
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 = [zip(xs, ys) for (xs, ys, zs) in xyslist]
LineCollection.set_segments(self, segments_2d)
minz = 1e9
for (xs, ys, zs) in xyslist:
minz = min(minz, min(zs))
return minz
def draw(self, renderer, project=False):
if project:
self.do_3d_projection(renderer)
LineCollection.draw(self, renderer)
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, **kwargs):
zs = kwargs.pop('zs', [])
zdir = kwargs.pop('zdir', 'z')
Patch.__init__(self, *args, **kwargs)
self.set_3d_properties(zs, zdir)
def set_3d_properties(self, verts, zs=0, zdir='z'):
if not iterable(zs):
zs = np.ones(len(verts)) * zs
self._segment3d = [juggle_axes(x, y, z, zdir) \
for ((x, y), z) in zip(verts, zs)]
self._facecolor3d = Patch.get_facecolor(self)
def get_path(self):
return self._path2d
def get_facecolor(self):
return self._facecolor2d
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(zip(vxs, vys))
# FIXME: coloring
self._facecolor2d = self._facecolor3d
return min(vzs)
def draw(self, renderer):
Patch.draw(self, renderer)
class PathPatch3D(Patch3D):
'''
3D PathPatch object.
'''
def __init__(self, path, **kwargs):
zs = kwargs.pop('zs', [])
zdir = kwargs.pop('zdir', 'z')
Patch.__init__(self, **kwargs)
self.set_3d_properties(path, zs, zdir)
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
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(zip(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 []
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, **kwargs):
PatchCollection.__init__(self, *args, **kwargs)
self._old_draw = lambda x: PatchCollection.draw(self, x)
def set_3d_properties(self, zs, zdir):
xs, ys = zip(*self.get_offsets())
self._offsets3d = juggle_axes(xs, ys, zs, zdir)
self._facecolor3d = self.get_facecolor()
self._edgecolor3d = self.get_edgecolor()
def do_3d_projection(self, renderer):
xs, ys, zs = self._offsets3d
vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)
#FIXME: mpl allows us no way to unset the collection alpha value
self._alpha = None
self.set_facecolors(zalpha(self._facecolor3d, vzs))
self.set_edgecolors(zalpha(self._edgecolor3d, vzs))
PatchCollection.set_offsets(self, zip(vxs, vys))
return min(vzs)
def draw(self, renderer):
self._old_draw(renderer)
def patch_collection_2d_to_3d(col, zs=0, zdir='z'):
"""Convert a PatchCollection to a Patch3DCollection object."""
# The tricky part here is that there are several classes that are
# derived from PatchCollection. We need to use the right draw method.
col._old_draw = col.draw
col.__class__ = Patch3DCollection
col.set_3d_properties(zs, zdir)
class Poly3DCollection(PolyCollection):
'''
A collection of 3D polygons.
'''
def __init__(self, verts, *args, **kwargs):
'''
Create a Poly3DCollection.
*verts* should contain 3D coordinates.
Keyword arguments:
zsort, see set_zsort for options.
Note that this class does a bit of magic with the _facecolors
and _edgecolors properties.
'''
self.set_zsort(kwargs.pop('zsort', True))
PolyCollection.__init__(self, verts, *args, **kwargs)
_zsort_functions = {
'average': np.average,
'min': np.min,
'max': np.max,
}
def set_zsort(self, zsort):
'''
Set z-sorting behaviour:
boolean: if True use default 'average'
string: 'average', 'min' or 'max'
'''
if zsort is True:
zsort = 'average'
if zsort is not False:
if zsort in self._zsort_functions:
zsortfunc = self._zsort_functions[zsort]
else:
return False
else:
zsortfunc = None
self._zsort = zsort
self._sort_zpos = None
self._zsortfunc = zsortfunc
def get_vector(self, segments3d):
"""Optimize points for projection"""
si = 0
ei = 0
segis = []
points = []
for p in segments3d:
points.extend(p)
ei = si+len(p)
segis.append((si, ei))
si = ei
xs, ys, zs = zip(*points)
ones = np.ones(len(xs))
self._vec = np.array([xs, ys, zs, ones])
self._segis = segis
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, [], closed)
def set_3d_properties(self):
self._sort_zpos = None
self.set_zsort(True)
self._facecolors3d = PolyCollection.get_facecolors(self)
self._edgecolors3d = PolyCollection.get_edgecolors(self)
def set_sort_zpos(self,val):
'''Set the position to use for z-sorting.'''
self._sort_zpos = val
def do_3d_projection(self, renderer):
'''
Perform the 3D projection for this object.
'''
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[si:ei], tys[si:ei], tzs[si:ei]) \
for si, ei in self._segis]
# 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
cedge = cedge.repeat(len(xyzlist), axis=0)
# if required sort by depth (furthest drawn first)
if self._zsort:
z_segments_2d = [(self._zsortfunc(zs), zip(xs, ys), fc, ec) for
(xs, ys, zs), fc, ec in zip(xyzlist, cface, cedge)]
z_segments_2d.sort(cmp=lambda x, y: cmp(y[0], x[0]))
else:
raise ValueError, "whoops"
segments_2d = [s for z, s, fc, ec in z_segments_2d]
PolyCollection.set_verts(self, segments_2d)
self._facecolors2d = [fc for z, s, fc, ec in z_segments_2d]
if len(self._edgecolors3d) == len(cface):
self._edgecolors2d = [ec for z, s, fc, ec in z_segments_2d]
else:
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]
else:
return np.min(tzs)
def set_facecolor(self, colors):
PolyCollection.set_facecolor(self, colors)
self._facecolors3d = PolyCollection.get_facecolor(self)
set_facecolors = set_facecolor
def set_edgecolor(self, colors):
PolyCollection.set_edgecolor(self, colors)
self._edgecolors3d = PolyCollection.get_edgecolor(self)
set_edgecolors = set_edgecolor
def get_facecolors(self):
return self._facecolors2d
get_facecolor = get_facecolors
def get_edgecolors(self):
return self._edgecolors2d
get_edgecolor = get_edgecolors
def draw(self, renderer):
return Collection.draw(self, renderer)
def poly_collection_2d_to_3d(col, zs=0, zdir='z'):
"""Convert a PolyCollection to a Poly3DCollection object."""
segments_3d = paths_to_3d_segments(col.get_paths(), zs, zdir)
col.__class__ = Poly3DCollection
col.set_verts(segments_3d)
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 == '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 iscolor(c):
try:
if len(c) == 4 or len(c) == 3:
if iterable(c[0]):
return False
if hasattr(c[0], '__float__'):
return True
except:
return False
return False
def get_colors(c, num):
"""Stretch the color argument to provide the required number num"""
if type(c) == type("string"):
c = mcolors.colorConverter.to_rgba(c)
if iscolor(c):
return [c] * num
if len(c) == num:
return c
elif iscolor(c):
return [c] * num
elif len(c) == 0: #if edgecolor or facecolor is specified as 'none'
return [[0,0,0,0]] * num
elif iscolor(c[0]):
return [c[0]] * num
else:
raise ValueError, 'unknown color format %s' % c
def zalpha(colors, zs):
"""Modify the alphas of the color list according to depth"""
colors = get_colors(colors, len(zs))
norm = Normalize(min(zs), max(zs))
sats = 1 - norm(zs) * 0.7
colors = [(c[0], c[1], c[2], c[3] * s) for c, s in zip(colors, sats)]
return colors