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#!/usr/bin/python
# axes3d.py, original mplot3d version by John Porter
# Created: 23 Sep 2005
# Parts fixed by Reinier Heeres <reinier@heeres.eu>
# Minor additions by Ben Axelrod <baxelrod@coroware.com>
"""
Module containing Axes3D, an object which can plot 3D objects on a
2D matplotlib figure.
"""
import warnings
from matplotlib.axes import Axes, rcParams
from matplotlib import cbook
from matplotlib.transforms import Bbox
from matplotlib import collections
import numpy as np
from matplotlib.colors import Normalize, colorConverter, LightSource
import art3d
import proj3d
import axis3d
def sensible_format_data(self, value):
"""Used to generate more comprehensible numbers in status bar"""
if abs(value) > 1e4 or abs(value)<1e-3:
s = '%1.4e' % value
return self._formatSciNotation(s)
else:
return '%4.3f' % value
def unit_bbox():
box = Bbox(np.array([[0, 0], [1, 1]]))
return box
class Axes3D(Axes):
"""
3D axes object.
"""
name = '3d'
def __init__(self, fig, rect=None, *args, **kwargs):
'''
Build an :class:`Axes3D` instance in
:class:`~matplotlib.figure.Figure` *fig* with
*rect=[left, bottom, width, height]* in
:class:`~matplotlib.figure.Figure` coordinates
Optional keyword arguments:
================ =========================================
Keyword Description
================ =========================================
*azim* Azimuthal viewing angle (default -60)
*elev* Elevation viewing angle (default 30)
================ =========================================
'''
if rect is None:
rect = [0.0, 0.0, 1.0, 1.0]
self.fig = fig
self._cids = []
self.initial_azim = kwargs.pop('azim', -60)
self.initial_elev = kwargs.pop('elev', 30)
self.xy_viewLim = unit_bbox()
self.zz_viewLim = unit_bbox()
self.xy_dataLim = unit_bbox()
self.zz_dataLim = unit_bbox()
# inihibit 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._ready = 0
Axes.__init__(self, self.fig, rect,
frameon=True,
xticks=[], yticks=[], *args, **kwargs)
self.M = None
self._ready = 1
self.mouse_init()
self.create_axes()
self.set_top_view()
self.axesPatch.set_linewidth(0)
self.fig.add_axes(self)
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)
Axes.set_xlim(self, -xdwl, xdw, auto=None)
Axes.set_ylim(self, -ydwl, ydw, auto=None)
def create_axes(self):
self.w_xaxis = axis3d.XAxis('x', self.xy_viewLim.intervalx,
self.xy_dataLim.intervalx, self)
self.w_yaxis = axis3d.YAxis('y', self.xy_viewLim.intervaly,
self.xy_dataLim.intervaly, self)
self.w_zaxis = axis3d.ZAxis('z', self.zz_viewLim.intervalx,
self.zz_dataLim.intervalx, self)
def unit_cube(self, vals=None):
minx, maxx, miny, maxy, minz, maxz = vals or self.get_w_lims()
xs, ys, zs = ([minx, maxx, maxx, minx, minx, maxx, maxx, minx],
[miny, miny, maxy, maxy, miny, miny, maxy, maxy],
[minz, minz, minz, minz, maxz, maxz, maxz, maxz])
return zip(xs, ys, zs)
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
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
def draw(self, renderer):
# draw the background patch
self.axesPatch.draw(renderer)
self._frameon = False
# 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 zorder them
zlist = [(col.do_3d_projection(renderer), col) \
for col in self.collections]
zlist.sort()
zlist.reverse()
for i, (z, col) in enumerate(zlist):
col.zorder = i
# Calculate projection of patches and zorder them
zlist = [(patch.do_3d_projection(renderer), patch) \
for patch in self.patches]
zlist.sort()
zlist.reverse()
for i, (z, patch) in enumerate(zlist):
patch.zorder = i
axes = (self.w_xaxis, self.w_yaxis, self.w_zaxis)
for ax in axes:
ax.draw_pane(renderer)
for ax in axes:
ax.draw(renderer)
Axes.draw(self, renderer)
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 update_datalim(self, xys, **kwargs):
pass
def auto_scale_xyz(self, X, Y, Z=None, had_data=None):
x, y, z = map(np.asarray, (X, Y, Z))
try:
x, y = x.flatten(), y.flatten()
if Z is not None:
z = z.flatten()
except AttributeError:
raise
# This updates the bounding boxes as to keep a record as
# to what the minimum sized rectangular volume holds the
# data.
self.xy_dataLim.update_from_data_xy(np.array([x, y]).T, not had_data)
if z is not None:
self.zz_dataLim.update_from_data_xy(np.array([z, z]).T, not had_data)
# Let autoscale_view figure out how to use this data.
self.autoscale_view()
def autoscale_view(self, scalex=True, scaley=True, scalez=True, **kw):
# This method looks at the rectanglular volume (see above)
# of data and decides how to scale the view portal to fit it.
self.set_top_view()
if not self._ready:
return
if not self.get_autoscale_on():
return
if scalex:
self.set_xlim3d(self.xy_dataLim.intervalx)
if scaley:
self.set_ylim3d(self.xy_dataLim.intervaly)
if scalez:
self.set_zlim3d(self.zz_dataLim.intervalx)
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 cbook.iterable(xmin):
xmin, xmax = xmin
if xmin == xmax:
xmin -= 0.5
xmax += 0.5
return (xmin, xmax)
def set_xlim3d(self, *args, **kwargs):
'''Set 3D x limits.'''
lims = self._determine_lims(*args, **kwargs)
self.xy_viewLim.intervalx = lims
return lims
def set_ylim3d(self, *args, **kwargs):
'''Set 3D y limits.'''
lims = self._determine_lims(*args, **kwargs)
self.xy_viewLim.intervaly = lims
return lims
def set_zlim3d(self, *args, **kwargs):
'''Set 3D z limits.'''
lims = self._determine_lims(*args, **kwargs)
self.zz_viewLim.intervalx = lims
return lims
def get_xlim3d(self):
'''Get 3D x limits.'''
return self.xy_viewLim.intervalx
def get_ylim3d(self):
'''Get 3D y limits.'''
return self.xy_viewLim.intervaly
def get_zlim3d(self):
'''Get 3D z limits.'''
return self.zz_viewLim.intervalx
def clabel(self, *args, **kwargs):
return None
def pany(self, numsteps):
print 'numsteps', numsteps
def panpy(self, numsteps):
print 'numsteps', numsteps
def view_init(self, elev=None, azim=None):
"""
Set the elevation and azimuth of the axes.
This can be used to rotate the axes programatically.
'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
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 / proj3d.mod(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)
perspM = proj3d.persp_transformation(zfront, zback)
M0 = np.dot(viewM, worldM)
M = np.dot(perspM, M0)
return M
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.
============ =======================================================
Argument Description
============ =======================================================
*rotate_btn* The integer or list of integers specifying which mouse
button or buttons to use for 3D rotation of the axes.
Default = 1.
*zoom_btn* The integer or list of integers specifying which mouse
button or buttons to use to zoom the 3D axes.
Default = 3.
============ =======================================================
"""
self.button_pressed = None
canv = self.figure.canvas
if canv != None:
c1 = canv.mpl_connect('motion_notify_event', self._on_move)
c2 = canv.mpl_connect('button_press_event', self._button_press)
c3 = canv.mpl_connect('button_release_event', self._button_release)
self._cids = [c1, c2, c3]
else:
warnings.warn('Axes3D.figure.canvas is \'None\', mouse rotation disabled. Set canvas then call Axes3D.mouse_init().')
self._rotate_btn = np.atleast_1d(rotate_btn)
self._zoom_btn = np.atleast_1d(zoom_btn)
def cla(self):
"""Clear axes and disable mouse button callbacks.
"""
self.disable_mouse_rotation()
Axes.cla(self)
self.grid(rcParams['axes3d.grid'])
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
def format_xdata(self, x):
"""
Return x string formatted. This function will use the attribute
self.fmt_xdata if it is callable, else will fall back on the xaxis
major formatter
"""
try:
return self.fmt_xdata(x)
except TypeError:
fmt = self.w_xaxis.get_major_formatter()
return sensible_format_data(fmt, x)
def format_ydata(self, y):
"""
Return y string formatted. This function will use the attribute
self.fmt_ydata if it is callable, else will fall back on the yaxis
major formatter
"""
try:
return self.fmt_ydata(y)
except TypeError:
fmt = self.w_yaxis.get_major_formatter()
return sensible_format_data(fmt, y)
def format_zdata(self, z):
"""
Return z string formatted. This function will use the attribute
self.fmt_zdata if it is callable, else will fall back on the yaxis
major formatter
"""
try:
return self.fmt_zdata(z)
except (AttributeError, TypeError):
fmt = self.w_zaxis.get_major_formatter()
return sensible_format_data(fmt, z)
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=%d deg, elevation=%d deg ' % (self.azim, self.elev)
# ignore xd and yd and display angles instead
p = (xd, yd)
edges = self.tunit_edges()
#lines = [proj3d.line2d(p0,p1) for (p0,p1) in edges]
ldists = [(proj3d.line2d_seg_dist(p0, p1, p), i) for \
i, (p0, p1) in enumerate(edges)]
ldists.sort()
# nearest edge
edgei = ldists[0][1]
p0, p1 = edges[edgei]
# 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_ydata(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 == None:
return
dx, dy = x - self.sx, y - self.sy
x0, x1 = self.get_xlim()
y0, y1 = self.get_ylim()
w = (x1-x0)
h = (y1-y0)
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.figure.canvas.draw()
# 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()
def set_xlabel(self, xlabel, fontdict=None, **kwargs):
'''Set xlabel.'''
label = self.w_xaxis.get_label()
label.set_text(xlabel)
if fontdict is not None:
label.update(fontdict)
label.update(kwargs)
return label
def set_ylabel(self, ylabel, fontdict=None, **kwargs):
'''Set ylabel.'''
label = self.w_yaxis.get_label()
label.set_text(ylabel)
if fontdict is not None:
label.update(fontdict)
label.update(kwargs)
return label
def set_zlabel(self, zlabel, fontdict=None, **kwargs):
'''Set zlabel.'''
label = self.w_zaxis.get_label()
label.set_text(zlabel)
if fontdict is not None:
label.update(fontdict)
label.update(kwargs)
return label
def grid(self, on=True, **kwargs):
'''
Set / unset 3D grid.
'''
self._draw_grid = on
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 = Axes.text(self, x, y, s, **kwargs)
art3d.text_2d_to_3d(text, z, zdir)
return text
text3D = text
text2D = Axes.text
def plot(self, xs, ys, *args, **kwargs):
'''
Plot 2D or 3D data.
========== ================================================
Argument Description
========== ================================================
*xs*, *ys* X, y coordinates of vertices
*zs* z value(s), either one for all points or one for
each point.
*zdir* Which direction to use as z ('x', 'y' or 'z')
when plotting a 2d set.
========== ================================================
Other arguments are passed on to
:func:`~matplotlib.axes.Axes.plot`
'''
had_data = self.has_data()
zs = kwargs.pop('zs', 0)
zdir = kwargs.pop('zdir', 'z')
argsi = 0
# First argument is array of zs
if len(args) > 0 and cbook.iterable(args[0]) and \
len(xs) == len(args[0]) and cbook.is_scalar(args[0][0]):
zs = args[argsi]
argsi += 1
# First argument is z value
elif len(args) > 0 and cbook.is_scalar(args[0]):
zs = args[argsi]
argsi += 1
# Match length
if not cbook.iterable(zs):
zs = np.ones(len(xs)) * zs
lines = Axes.plot(self, xs, ys, *args[argsi:], **kwargs)
for line in lines:
art3d.line_2d_to_3d(line, zs=zs, zdir=zdir)
self.auto_scale_xyz(xs, ys, zs, had_data)
return lines
plot3D = plot
def plot_surface(self, X, Y, Z, *args, **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.
============= ================================================
Argument Description
============= ================================================
*X*, *Y*, *Z* Data values as numpy.arrays
*rstride* Array row stride (step size)
*cstride* Array column stride (step size)
*color* Color of the surface patches
*cmap* A colormap for the surface patches.
*facecolors* Face colors for the individual patches
*norm* An instance of Normalize to map values to colors
*vmin* Minimum value to map
*vmax* Maximum value to map
*shade* Whether to shade the facecolors
============= ================================================
Other arguments are passed on to
:func:`~mpl_toolkits.mplot3d.art3d.Poly3DCollection.__init__`
'''
had_data = self.has_data()
rows, cols = Z.shape
tX, tY, tZ = np.transpose(X), np.transpose(Y), np.transpose(Z)
rstride = kwargs.pop('rstride', 10)
cstride = kwargs.pop('cstride', 10)
if 'facecolors' in kwargs:
fcolors = kwargs.pop('facecolors')
else:
color = np.array(colorConverter.to_rgba(kwargs.pop('color', 'b')))
fcolors = None
cmap = kwargs.get('cmap', None)
norm = kwargs.pop('norm', None)
vmin = kwargs.pop('vmin', None)
vmax = kwargs.pop('vmax', None)
linewidth = kwargs.get('linewidth', None)
shade = kwargs.pop('shade', cmap is None)
lightsource = kwargs.pop('lightsource', None)
# Shade the data
if shade and cmap is not None and fcolors is not None:
fcolors = self._shade_colors_lightsource(Z, cmap, lightsource)
polys = []
normals = []
#colset contains the data for coloring: either average z or the facecolor
colset = []
for rs in np.arange(0, rows-1, rstride):
for cs in np.arange(0, cols-1, cstride):
ps = []
corners = []
for a, ta in [(X, tX), (Y, tY), (Z, tZ)]:
ztop = a[rs][cs:min(cols, cs+cstride+1)]
zleft = ta[min(cols-1, cs+cstride)][rs:min(rows, rs+rstride+1)]
zbase = a[min(rows-1, rs+rstride)][cs:min(cols, cs+cstride+1):]
zbase = zbase[::-1]
zright = ta[cs][rs:min(rows, rs+rstride+1):]
zright = zright[::-1]
corners.append([ztop[0], ztop[-1], zbase[0], zbase[-1]])
z = np.concatenate((ztop, zleft, zbase, zright))
ps.append(z)
# The construction leaves the array with duplicate points, which
# are removed here.
ps = zip(*ps)
lastp = np.array([])
ps2 = []
avgzsum = 0.0
for p in ps:
if p != lastp:
ps2.append(p)
lastp = p
avgzsum += p[2]
polys.append(ps2)
if fcolors is not None:
colset.append(fcolors[rs][cs])
else:
colset.append(avgzsum / len(ps2))
# Only need vectors to shade if no cmap
if cmap is None and shade:
v1 = np.array(ps2[0]) - np.array(ps2[1])
v2 = np.array(ps2[2]) - np.array(ps2[0])
normals.append(np.cross(v1, v2))
polyc = art3d.Poly3DCollection(polys, *args, **kwargs)
if fcolors is not None:
if shade:
colset = self._shade_colors(colset, normals)
polyc.set_facecolors(colset)
polyc.set_edgecolors(colset)
elif cmap:
colset = np.array(colset)
polyc.set_array(colset)
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:
if shade:
colset = self._shade_colors(color, normals)
else:
colset = color
polyc.set_facecolors(colset)
self.add_collection(polyc)
self.auto_scale_xyz(X, Y, Z, had_data)
return polyc
def _generate_normals(self, polygons):
'''
Generate normals for polygons by using the first three points.
This normal of course might not make sense for polygons with
more than three points not lying in a plane.
'''
normals = []
for verts in polygons:
v1 = np.array(verts[0]) - np.array(verts[1])
v2 = np.array(verts[2]) - np.array(verts[0])
normals.append(np.cross(v1, v2))
return normals
def _shade_colors(self, color, normals):
'''
Shade *color* using normal vectors given by *normals*.
*color* can also be an array of the same length as *normals*.
'''
shade = []
for n in normals:
n = n / proj3d.mod(n)
shade.append(np.dot(n, [-1, -1, 0.5]))
shade = np.array(shade)
mask = ~np.isnan(shade)
if len(shade[mask]) > 0:
norm = Normalize(min(shade[mask]), max(shade[mask]))
if art3d.iscolor(color):
color = color.copy()
color[3] = 1
colors = [color * (0.5 + norm(v) * 0.5) for v in shade]
else:
colors = [np.array(colorConverter.to_rgba(c)) * \
(0.5 + norm(v) * 0.5) \
for c, v in zip(color, shade)]
else:
colors = color.copy()
return colors
def _shade_colors_lightsource(self, data, cmap, lightsource):
if lightsource is None:
lightsource = LightSource(azdeg=135, altdeg=55)
return lightsource.shade(data, cmap)
def plot_wireframe(self, X, Y, Z, *args, **kwargs):
'''
Plot a 3D wireframe.
========== ================================================
Argument Description
========== ================================================
*X*, *Y*, Data values as numpy.arrays
*Z*
*rstride* Array row stride (step size)
*cstride* Array column stride (step size)
========== ================================================
Keyword arguments are passed on to
:func:`matplotlib.collections.LineCollection.__init__`.
Returns a :class:`~mpl_toolkits.mplot3d.art3d.Line3DCollection`
'''
rstride = kwargs.pop("rstride", 1)
cstride = kwargs.pop("cstride", 1)
had_data = self.has_data()
rows, cols = Z.shape
tX, tY, tZ = np.transpose(X), np.transpose(Y), np.transpose(Z)
rii = [i for i in range(0, rows, rstride)]+[rows-1]
cii = [i for i in range(0, cols, cstride)]+[cols-1]
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 = [zip(xl, yl, zl) for xl, yl, zl in \
zip(xlines, ylines, zlines)]
lines += [zip(xl, yl, zl) for xl, yl, zl in \
zip(txlines, tylines, tzlines)]
linec = art3d.Line3DCollection(lines, *args, **kwargs)
self.add_collection(linec)
self.auto_scale_xyz(X, Y, Z, had_data)
return linec
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):
topverts = art3d.paths_to_3d_segments(linec.get_paths(), z - dz)
botverts = art3d.paths_to_3d_segments(linec.get_paths(), z + dz)
color = linec.get_color()[0]
polyverts = []
normals = []
nsteps = 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(round(nsteps)) - 1):
i1 = int(round(i * stepsize))
i2 = int(round((i + 1) * stepsize))
polyverts.append([topverts[0][i1],
topverts[0][i2],
botverts[0][i2],
botverts[0][i1]])
v1 = np.array(topverts[0][i1]) - np.array(topverts[0][i2])
v2 = np.array(topverts[0][i1]) - np.array(botverts[0][i1])
normals.append(np.cross(v1, v2))
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)
self.add_collection3d(polycol)
for col in colls:
self.collections.remove(col)
def contour(self, X, Y, Z, *args, **kwargs):
'''
Create a 3D contour plot.
========== ================================================
Argument Description
========== ================================================
*X*, *Y*, Data values as numpy.arrays
*Z*
*extend3d* Whether to extend contour in 3D (default: False)
*stride* Stride (step size) for extending contour
*zdir* The direction to use: x, y or z (default)
*offset* If specified plot a projection of the contour
lines on this position in plane normal to zdir
========== ================================================
The positional and other keyword arguments are passed on to
:func:`~matplotlib.axes.Axes.contour`
Returns a :class:`~matplotlib.axes.Axes.contour`
'''
extend3d = kwargs.pop('extend3d', False)
stride = kwargs.pop('stride', 5)
zdir = kwargs.pop('zdir', 'z')
offset = kwargs.pop('offset', None)
had_data = self.has_data()
jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir)
cset = Axes.contour(self, jX, jY, jZ, *args, **kwargs)
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)
self.auto_scale_xyz(X, Y, Z, had_data)
return cset
contour3D = contour
def contourf(self, X, Y, Z, *args, **kwargs):
'''
Plot filled 3D contours.
*X*, *Y*, *Z*: data points.
The positional and keyword arguments are passed on to
:func:`~matplotlib.axes.Axes.contourf`
Returns a :class:`~matplotlib.axes.Axes.contourf`
'''
had_data = self.has_data()
cset = Axes.contourf(self, X, Y, Z, *args, **kwargs)
levels = cset.levels
colls = cset.collections
for z1, z2, linec in zip(levels, levels[1:], colls):
art3d.poly_collection_2d_to_3d(linec, z1)
linec.set_sort_zpos(z1)
self.auto_scale_xyz(X, Y, Z, had_data)
return cset
contourf3D = contourf
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
- LineColleciton
- PatchCollection
'''
if type(col) is collections.PolyCollection:
art3d.poly_collection_2d_to_3d(col, zs=zs, zdir=zdir)
col.set_sort_zpos(min(zs))
elif type(col) is collections.LineCollection:
art3d.line_collection_2d_to_3d(col, zs=zs, zdir=zdir)
col.set_sort_zpos(min(zs))
elif type(col) is collections.PatchCollection:
art3d.patch_collection_2d_to_3d(col, zs=zs, zdir=zdir)
col.set_sort_zpos(min(zs))
Axes.add_collection(self, col)
def scatter(self, xs, ys, zs=0, zdir='z', *args, **kwargs):
'''
Create a scatter plot.
========== ================================================
Argument Description
========== ================================================
*xs*, *ys* Positions of data points.
*zs* Either an array of the same length as *xs* and
*ys* or a single value to place all points in
the same plane. Default is 0.
*zdir* Which direction to use as z ('x', 'y' or 'z')
when plotting a 2d set.
========== ================================================
Keyword arguments are passed on to
:func:`~matplotlib.axes.Axes.scatter`.
Returns a :class:`~mpl_toolkits.mplot3d.art3d.Patch3DCollection`
'''
had_data = self.has_data()
patches = Axes.scatter(self, xs, ys, *args, **kwargs)
if not cbook.iterable(zs):
is_2d = True
zs = np.ones(len(xs)) * zs
else:
is_2d = False
art3d.patch_collection_2d_to_3d(patches, zs=zs, zdir=zdir)
#FIXME: why is this necessary?
if not is_2d:
self.auto_scale_xyz(xs, ys, zs, had_data)
return patches
scatter3D = scatter
def bar(self, left, height, zs=0, zdir='z', *args, **kwargs):
'''
Add 2D bar(s).
========== ================================================
Argument Description
========== ================================================
*left* The x coordinates of the left sides of the bars.
*height* The height of the bars.
*zs* Z coordinate of bars, if one value is specified
they will all be placed at the same z.
*zdir* Which direction to use as z ('x', 'y' or 'z')
when plotting a 2d set.
========== ================================================
Keyword arguments are passed onto :func:`~matplotlib.axes.Axes.bar`.
Returns a :class:`~mpl_toolkits.mplot3d.art3d.Patch3DCollection`
'''
had_data = self.has_data()
patches = Axes.bar(self, left, height, *args, **kwargs)
if not cbook.iterable(zs):
zs = np.ones(len(left)) * zs
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, zs, zdir)
if 'alpha' in kwargs:
p.set_alpha(kwargs['alpha'])
xs, ys = zip(*verts)
xs, ys, verts_zs = art3d.juggle_axes(xs, ys, verts_zs, zdir)
self.auto_scale_xyz(xs, ys, verts_zs, had_data)
return patches
def bar3d(self, x, y, z, dx, dy, dz, color='b',
zsort='average', *args, **kwargs):
'''
Generate a 3D bar, or multiple bars.
When generating multiple bars, x, y, z have to be arrays.
dx, dy, dz can be arrays or scalars.
*color* 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
Keyword arguments are passed onto
:func:`~mpl_toolkits.mplot3d.art3d.Poly3DCollection`
'''
had_data = self.has_data()
if not cbook.iterable(x):
x = [x]
if not cbook.iterable(y):
y = [y]
if not cbook.iterable(z):
z = [z]
if not cbook.iterable(dx):
dx = [dx]
if not cbook.iterable(dy):
dy = [dy]
if not cbook.iterable(dz):
dz = [dz]
if len(dx) == 1:
dx = dx * len(x)
if len(dy) == 1:
dy = dy * len(y)
if len(dz) == 1:
dz = dz * len(z)
if len(x) != len(y) or len(x) != len(z):
warnings.warn('x, y, and z must be the same length.')
minx, miny, minz = 1e20, 1e20, 1e20
maxx, maxy, maxz = -1e20, -1e20, -1e20
polys = []
for xi, yi, zi, dxi, dyi, dzi in zip(x, y, z, dx, dy, dz):
minx = min(xi, minx)
maxx = max(xi + dxi, maxx)
miny = min(yi, miny)
maxy = max(yi + dyi, maxy)
minz = min(zi, minz)
maxz = max(zi + dzi, maxz)
polys.extend([
((xi, yi, zi), (xi + dxi, yi, zi),
(xi + dxi, yi + dyi, zi), (xi, yi + dyi, zi)),
((xi, yi, zi + dzi), (xi + dxi, yi, zi + dzi),
(xi + dxi, yi + dyi, zi + dzi), (xi, yi + dyi, zi + dzi)),
((xi, yi, zi), (xi + dxi, yi, zi),
(xi + dxi, yi, zi + dzi), (xi, yi, zi + dzi)),
((xi, yi + dyi, zi), (xi + dxi, yi + dyi, zi),
(xi + dxi, yi + dyi, zi + dzi), (xi, yi + dyi, zi + dzi)),
((xi, yi, zi), (xi, yi + dyi, zi),
(xi, yi + dyi, zi + dzi), (xi, yi, zi + dzi)),
((xi + dxi, yi, zi), (xi + dxi, yi + dyi, zi),
(xi + dxi, yi + dyi, zi + dzi), (xi + dxi, yi, zi + dzi)),
])
facecolors = []
if color is None:
# no color specified
facecolors = [None] * len(x)
elif 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(colorConverter.to_rgba_array(color))
if len(facecolors) < len(x):
facecolors *= (6 * len(x))
normals = self._generate_normals(polys)
sfacecolors = self._shade_colors(facecolors, normals)
col = art3d.Poly3DCollection(polys,
zsort=zsort,
facecolor=sfacecolors,
*args, **kwargs)
self.add_collection(col)
self.auto_scale_xyz((minx, maxx), (miny, maxy), (minz, maxz), had_data)
def set_title(self, label, fontdict=None, **kwargs):
Axes.set_title(self, label, fontdict, **kwargs)
(x, y) = self.title.get_position()
self.title.set_y(0.92 * y)
def get_test_data(delta=0.05):
'''
Return a tuple X, Y, Z with a test data set.
'''
from matplotlib.mlab import bivariate_normal
x = y = np.arange(-3.0, 3.0, delta)
X, Y = np.meshgrid(x, y)
Z1 = bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
Z2 = bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
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
########################################################
import matplotlib.projections as proj
proj.projection_registry.register(Axes3D)