""" axes3d.py, original mplot3d version by John Porter Created: 23 Sep 2005 Parts fixed by Reinier Heeres Minor additions by Ben Axelrod Significant updates and revisions by Ben Root Module containing Axes3D, an object which can plot 3D objects on a 2D matplotlib figure. """ from collections import defaultdict import itertools import math import textwrap import numpy as np import matplotlib as mpl from matplotlib import _api, cbook, _docstring, _preprocess_data import matplotlib.artist as martist import matplotlib.collections as mcoll import matplotlib.colors as mcolors import matplotlib.image as mimage import matplotlib.lines as mlines import matplotlib.patches as mpatches import matplotlib.container as mcontainer import matplotlib.transforms as mtransforms from matplotlib.axes import Axes from matplotlib.axes._base import _axis_method_wrapper, _process_plot_format from matplotlib.transforms import Bbox from matplotlib.tri._triangulation import Triangulation from . import art3d from . import proj3d from . import axis3d @_docstring.interpd @_api.define_aliases({ "xlim": ["xlim3d"], "ylim": ["ylim3d"], "zlim": ["zlim3d"]}) class Axes3D(Axes): """ 3D Axes object. .. note:: As a user, you do not instantiate Axes directly, but use Axes creation methods instead; e.g. from `.pyplot` or `.Figure`: `~.pyplot.subplots`, `~.pyplot.subplot_mosaic` or `.Figure.add_axes`. """ name = '3d' _axis_names = ("x", "y", "z") Axes._shared_axes["z"] = cbook.Grouper() Axes._shared_axes["view"] = cbook.Grouper() def __init__( self, fig, rect=None, *args, elev=30, azim=-60, roll=0, sharez=None, proj_type='persp', box_aspect=None, computed_zorder=True, focal_length=None, shareview=None, **kwargs): """ Parameters ---------- fig : Figure The parent figure. rect : tuple (left, bottom, width, height), default: None. The ``(left, bottom, width, height)`` Axes position. elev : float, default: 30 The elevation angle in degrees rotates the camera above and below the x-y plane, with a positive angle corresponding to a location above the plane. azim : float, default: -60 The azimuthal angle in degrees rotates the camera about the z axis, with a positive angle corresponding to a right-handed rotation. In other words, a positive azimuth rotates the camera about the origin from its location along the +x axis towards the +y axis. roll : float, default: 0 The roll angle in degrees rotates the camera about the viewing axis. A positive angle spins the camera clockwise, causing the scene to rotate counter-clockwise. sharez : Axes3D, optional Other Axes to share z-limits with. Note that it is not possible to unshare axes. proj_type : {'persp', 'ortho'} The projection type, default 'persp'. box_aspect : 3-tuple of floats, default: None Changes the physical dimensions of the Axes3D, such that the ratio of the axis lengths in display units is x:y:z. If None, defaults to 4:4:3 computed_zorder : bool, default: True If True, the draw order is computed based on the average position of the `.Artist`\\s along the view direction. Set to False if you want to manually control the order in which Artists are drawn on top of each other using their *zorder* attribute. This can be used for fine-tuning if the automatic order does not produce the desired result. Note however, that a manual zorder will only be correct for a limited view angle. If the figure is rotated by the user, it will look wrong from certain angles. focal_length : float, default: None For a projection type of 'persp', the focal length of the virtual camera. Must be > 0. If None, defaults to 1. For a projection type of 'ortho', must be set to either None or infinity (numpy.inf). If None, defaults to infinity. The focal length can be computed from a desired Field Of View via the equation: focal_length = 1/tan(FOV/2) shareview : Axes3D, optional Other Axes to share view angles with. Note that it is not possible to unshare axes. **kwargs Other optional keyword arguments: %(Axes3D:kwdoc)s """ if rect is None: rect = [0.0, 0.0, 1.0, 1.0] self.initial_azim = azim self.initial_elev = elev self.initial_roll = roll self.set_proj_type(proj_type, focal_length) self.computed_zorder = computed_zorder self.xy_viewLim = Bbox.unit() self.zz_viewLim = Bbox.unit() xymargin = 0.05 * 10/11 # match mpl3.8 appearance self.xy_dataLim = Bbox([[xymargin, xymargin], [1 - xymargin, 1 - xymargin]]) # z-limits are encoded in the x-component of the Bbox, y is un-used self.zz_dataLim = Bbox.unit() # inhibit autoscale_view until the axes are defined # they can't be defined until Axes.__init__ has been called self.view_init(self.initial_elev, self.initial_azim, self.initial_roll) self._sharez = sharez if sharez is not None: self._shared_axes["z"].join(self, sharez) self._adjustable = 'datalim' self._shareview = shareview if shareview is not None: self._shared_axes["view"].join(self, shareview) if kwargs.pop('auto_add_to_figure', False): raise AttributeError( 'auto_add_to_figure is no longer supported for Axes3D. ' 'Use fig.add_axes(ax) instead.' ) super().__init__( fig, rect, frameon=True, box_aspect=box_aspect, *args, **kwargs ) # Disable drawing of axes by base class super().set_axis_off() # Enable drawing of axes by Axes3D class self.set_axis_on() self.M = None self.invM = None self._view_margin = 1/48 # default value to match mpl3.8 self.autoscale_view() # func used to format z -- fall back on major formatters self.fmt_zdata = None self.mouse_init() self.figure.canvas.callbacks._connect_picklable( 'motion_notify_event', self._on_move) self.figure.canvas.callbacks._connect_picklable( 'button_press_event', self._button_press) self.figure.canvas.callbacks._connect_picklable( 'button_release_event', self._button_release) self.set_top_view() self.patch.set_linewidth(0) # Calculate the pseudo-data width and height pseudo_bbox = self.transLimits.inverted().transform([(0, 0), (1, 1)]) self._pseudo_w, self._pseudo_h = pseudo_bbox[1] - pseudo_bbox[0] # mplot3d currently manages its own spines and needs these turned off # for bounding box calculations self.spines[:].set_visible(False) def set_axis_off(self): self._axis3don = False self.stale = True def set_axis_on(self): self._axis3don = True self.stale = True def convert_zunits(self, z): """ For artists in an Axes, if the zaxis has units support, convert *z* using zaxis unit type """ return self.zaxis.convert_units(z) 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 # Set the viewing pane. self.viewLim.intervalx = (-xdwl, xdw) self.viewLim.intervaly = (-ydwl, ydw) self.stale = True def _init_axis(self): """Init 3D Axes; overrides creation of regular X/Y Axes.""" self.xaxis = axis3d.XAxis(self) self.yaxis = axis3d.YAxis(self) self.zaxis = axis3d.ZAxis(self) def get_zaxis(self): """Return the ``ZAxis`` (`~.axis3d.Axis`) instance.""" return self.zaxis get_zgridlines = _axis_method_wrapper("zaxis", "get_gridlines") get_zticklines = _axis_method_wrapper("zaxis", "get_ticklines") def _transformed_cube(self, vals): """Return cube with limits from *vals* transformed by self.M.""" minx, maxx, miny, maxy, minz, maxz = vals xyzs = [(minx, miny, minz), (maxx, miny, minz), (maxx, maxy, minz), (minx, maxy, minz), (minx, miny, maxz), (maxx, miny, maxz), (maxx, maxy, maxz), (minx, maxy, maxz)] return proj3d._proj_points(xyzs, self.M) def set_aspect(self, aspect, adjustable=None, anchor=None, share=False): """ Set the aspect ratios. Parameters ---------- aspect : {'auto', 'equal', 'equalxy', 'equalxz', 'equalyz'} Possible values: ========= ================================================== value description ========= ================================================== 'auto' automatic; fill the position rectangle with data. 'equal' adapt all the axes to have equal aspect ratios. 'equalxy' adapt the x and y axes to have equal aspect ratios. 'equalxz' adapt the x and z axes to have equal aspect ratios. 'equalyz' adapt the y and z axes to have equal aspect ratios. ========= ================================================== adjustable : None or {'box', 'datalim'}, optional If not *None*, this defines which parameter will be adjusted to meet the required aspect. See `.set_adjustable` for further details. anchor : None or str or 2-tuple of float, optional If not *None*, this defines where the Axes will be drawn if there is extra space due to aspect constraints. The most common way to specify the anchor are abbreviations of cardinal directions: ===== ===================== value description ===== ===================== 'C' centered 'SW' lower left corner 'S' middle of bottom edge 'SE' lower right corner etc. ===== ===================== See `~.Axes.set_anchor` for further details. share : bool, default: False If ``True``, apply the settings to all shared Axes. See Also -------- mpl_toolkits.mplot3d.axes3d.Axes3D.set_box_aspect """ _api.check_in_list(('auto', 'equal', 'equalxy', 'equalyz', 'equalxz'), aspect=aspect) super().set_aspect( aspect='auto', adjustable=adjustable, anchor=anchor, share=share) self._aspect = aspect if aspect in ('equal', 'equalxy', 'equalxz', 'equalyz'): ax_indices = self._equal_aspect_axis_indices(aspect) view_intervals = np.array([self.xaxis.get_view_interval(), self.yaxis.get_view_interval(), self.zaxis.get_view_interval()]) ptp = np.ptp(view_intervals, axis=1) if self._adjustable == 'datalim': mean = np.mean(view_intervals, axis=1) scale = max(ptp[ax_indices] / self._box_aspect[ax_indices]) deltas = scale * self._box_aspect for i, set_lim in enumerate((self.set_xlim3d, self.set_ylim3d, self.set_zlim3d)): if i in ax_indices: set_lim(mean[i] - deltas[i]/2., mean[i] + deltas[i]/2., auto=True, view_margin=None) else: # 'box' # Change the box aspect such that the ratio of the length of # the unmodified axis to the length of the diagonal # perpendicular to it remains unchanged. box_aspect = np.array(self._box_aspect) box_aspect[ax_indices] = ptp[ax_indices] remaining_ax_indices = {0, 1, 2}.difference(ax_indices) if remaining_ax_indices: remaining = remaining_ax_indices.pop() old_diag = np.linalg.norm(self._box_aspect[ax_indices]) new_diag = np.linalg.norm(box_aspect[ax_indices]) box_aspect[remaining] *= new_diag / old_diag self.set_box_aspect(box_aspect) def _equal_aspect_axis_indices(self, aspect): """ Get the indices for which of the x, y, z axes are constrained to have equal aspect ratios. Parameters ---------- aspect : {'auto', 'equal', 'equalxy', 'equalxz', 'equalyz'} See descriptions in docstring for `.set_aspect()`. """ ax_indices = [] # aspect == 'auto' if aspect == 'equal': ax_indices = [0, 1, 2] elif aspect == 'equalxy': ax_indices = [0, 1] elif aspect == 'equalxz': ax_indices = [0, 2] elif aspect == 'equalyz': ax_indices = [1, 2] return ax_indices def set_box_aspect(self, aspect, *, zoom=1): """ Set the Axes box aspect. The box aspect is the ratio of height to width in display units for each face of the box when viewed perpendicular to that face. This is not to be confused with the data aspect (see `~.Axes3D.set_aspect`). The default ratios are 4:4:3 (x:y:z). To simulate having equal aspect in data space, set the box aspect to match your data range in each dimension. *zoom* controls the overall size of the Axes3D in the figure. Parameters ---------- aspect : 3-tuple of floats or None Changes the physical dimensions of the Axes3D, such that the ratio of the axis lengths in display units is x:y:z. If None, defaults to (4, 4, 3). zoom : float, default: 1 Control overall size of the Axes3D in the figure. Must be > 0. """ if zoom <= 0: raise ValueError(f'Argument zoom = {zoom} must be > 0') if aspect is None: aspect = np.asarray((4, 4, 3), dtype=float) else: aspect = np.asarray(aspect, dtype=float) _api.check_shape((3,), aspect=aspect) # The scale 1.8294640721620434 is tuned to match the mpl3.2 appearance. # The 25/24 factor is to compensate for the change in automargin # behavior in mpl3.9. This comes from the padding of 1/48 on both sides # of the axes in mpl3.8. aspect *= 1.8294640721620434 * 25/24 * zoom / np.linalg.norm(aspect) self._box_aspect = self._roll_to_vertical(aspect, reverse=True) self.stale = True def apply_aspect(self, position=None): if position is None: position = self.get_position(original=True) # in the superclass, we would go through and actually deal with axis # scales and box/datalim. Those are all irrelevant - all we need to do # is make sure our coordinate system is square. trans = self.get_figure().transSubfigure bb = mtransforms.Bbox.unit().transformed(trans) # this is the physical aspect of the panel (or figure): fig_aspect = bb.height / bb.width box_aspect = 1 pb = position.frozen() pb1 = pb.shrunk_to_aspect(box_aspect, pb, fig_aspect) self._set_position(pb1.anchored(self.get_anchor(), pb), 'active') @martist.allow_rasterization def draw(self, renderer): if not self.get_visible(): return self._unstale_viewLim() # draw the background patch self.patch.draw(renderer) self._frameon = False # first, set the aspect # this is duplicated from `axes._base._AxesBase.draw` # but must be called before any of the artist are drawn as # it adjusts the view limits and the size of the bounding box # of the Axes locator = self.get_axes_locator() self.apply_aspect(locator(self, renderer) if locator else None) # add the projection matrix to the renderer self.M = self.get_proj() self.invM = np.linalg.inv(self.M) collections_and_patches = ( artist for artist in self._children if isinstance(artist, (mcoll.Collection, mpatches.Patch)) and artist.get_visible()) if self.computed_zorder: # Calculate projection of collections and patches and zorder # them. Make sure they are drawn above the grids. zorder_offset = max(axis.get_zorder() for axis in self._axis_map.values()) + 1 collection_zorder = patch_zorder = zorder_offset for artist in sorted(collections_and_patches, key=lambda artist: artist.do_3d_projection(), reverse=True): if isinstance(artist, mcoll.Collection): artist.zorder = collection_zorder collection_zorder += 1 elif isinstance(artist, mpatches.Patch): artist.zorder = patch_zorder patch_zorder += 1 else: for artist in collections_and_patches: artist.do_3d_projection() if self._axis3don: # Draw panes first for axis in self._axis_map.values(): axis.draw_pane(renderer) # Then gridlines for axis in self._axis_map.values(): axis.draw_grid(renderer) # Then axes, labels, text, and ticks for axis in self._axis_map.values(): axis.draw(renderer) # Then rest super().draw(renderer) def get_axis_position(self): tc = self._transformed_cube(self.get_w_lims()) 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): """ Not implemented in `~mpl_toolkits.mplot3d.axes3d.Axes3D`. """ pass get_autoscalez_on = _axis_method_wrapper("zaxis", "_get_autoscale_on") set_autoscalez_on = _axis_method_wrapper("zaxis", "_set_autoscale_on") def get_zmargin(self): """ Retrieve autoscaling margin of the z-axis. .. versionadded:: 3.9 Returns ------- zmargin : float See Also -------- mpl_toolkits.mplot3d.axes3d.Axes3D.set_zmargin """ return self._zmargin def set_zmargin(self, m): """ Set padding of Z data limits prior to autoscaling. *m* times the data interval will be added to each end of that interval before it is used in autoscaling. If *m* is negative, this will clip the data range instead of expanding it. For example, if your data is in the range [0, 2], a margin of 0.1 will result in a range [-0.2, 2.2]; a margin of -0.1 will result in a range of [0.2, 1.8]. Parameters ---------- m : float greater than -0.5 """ if m <= -0.5: raise ValueError("margin must be greater than -0.5") self._zmargin = m self._request_autoscale_view("z") self.stale = True def margins(self, *margins, x=None, y=None, z=None, tight=True): """ Set or retrieve autoscaling margins. See `.Axes.margins` for full documentation. Because this function applies to 3D Axes, it also takes a *z* argument, and returns ``(xmargin, ymargin, zmargin)``. """ if margins and (x is not None or y is not None or z is not None): raise TypeError('Cannot pass both positional and keyword ' 'arguments for x, y, and/or z.') elif len(margins) == 1: x = y = z = margins[0] elif len(margins) == 3: x, y, z = margins elif margins: raise TypeError('Must pass a single positional argument for all ' 'margins, or one for each margin (x, y, z).') if x is None and y is None and z is None: if tight is not True: _api.warn_external(f'ignoring tight={tight!r} in get mode') return self._xmargin, self._ymargin, self._zmargin if x is not None: self.set_xmargin(x) if y is not None: self.set_ymargin(y) if z is not None: self.set_zmargin(z) self.autoscale_view( tight=tight, scalex=(x is not None), scaley=(y is not None), scalez=(z is not None) ) def autoscale(self, enable=True, axis='both', tight=None): """ Convenience method for simple axis view autoscaling. See `.Axes.autoscale` for full documentation. Because this function applies to 3D Axes, *axis* can also be set to 'z', and setting *axis* to 'both' autoscales all three axes. """ if enable is None: scalex = True scaley = True scalez = True else: if axis in ['x', 'both']: self.set_autoscalex_on(enable) scalex = self.get_autoscalex_on() else: scalex = False if axis in ['y', 'both']: self.set_autoscaley_on(enable) scaley = self.get_autoscaley_on() else: scaley = False if axis in ['z', 'both']: self.set_autoscalez_on(enable) scalez = self.get_autoscalez_on() else: scalez = False if scalex: self._request_autoscale_view("x", tight=tight) if scaley: self._request_autoscale_view("y", tight=tight) if scalez: self._request_autoscale_view("z", tight=tight) def auto_scale_xyz(self, X, Y, Z=None, had_data=None): # This updates the bounding boxes as to keep a record as to what the # minimum sized rectangular volume holds the data. if np.shape(X) == np.shape(Y): self.xy_dataLim.update_from_data_xy( np.column_stack([np.ravel(X), np.ravel(Y)]), not had_data) else: self.xy_dataLim.update_from_data_x(X, not had_data) self.xy_dataLim.update_from_data_y(Y, not had_data) if Z is not None: self.zz_dataLim.update_from_data_x(Z, not had_data) # Let autoscale_view figure out how to use this data. self.autoscale_view() def autoscale_view(self, tight=None, scalex=True, scaley=True, scalez=True): """ Autoscale the view limits using the data limits. See `.Axes.autoscale_view` for full documentation. Because this function applies to 3D Axes, it also takes a *scalez* argument. """ # This method looks at the rectangular volume (see above) # of data and decides how to scale the view portal to fit it. if tight is None: _tight = self._tight if not _tight: # if image data only just use the datalim for artist in self._children: if isinstance(artist, mimage.AxesImage): _tight = True elif isinstance(artist, (mlines.Line2D, mpatches.Patch)): _tight = False break else: _tight = self._tight = bool(tight) if scalex and self.get_autoscalex_on(): x0, x1 = self.xy_dataLim.intervalx xlocator = self.xaxis.get_major_locator() x0, x1 = xlocator.nonsingular(x0, x1) if self._xmargin > 0: delta = (x1 - x0) * self._xmargin x0 -= delta x1 += delta if not _tight: x0, x1 = xlocator.view_limits(x0, x1) self.set_xbound(x0, x1, self._view_margin) if scaley and self.get_autoscaley_on(): y0, y1 = self.xy_dataLim.intervaly ylocator = self.yaxis.get_major_locator() y0, y1 = ylocator.nonsingular(y0, y1) if self._ymargin > 0: delta = (y1 - y0) * self._ymargin y0 -= delta y1 += delta if not _tight: y0, y1 = ylocator.view_limits(y0, y1) self.set_ybound(y0, y1, self._view_margin) if scalez and self.get_autoscalez_on(): z0, z1 = self.zz_dataLim.intervalx zlocator = self.zaxis.get_major_locator() z0, z1 = zlocator.nonsingular(z0, z1) if self._zmargin > 0: delta = (z1 - z0) * self._zmargin z0 -= delta z1 += delta if not _tight: z0, z1 = zlocator.view_limits(z0, z1) self.set_zbound(z0, z1, self._view_margin) 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 _set_bound3d(self, get_bound, set_lim, axis_inverted, lower=None, upper=None, view_margin=None): """ Set 3D axis bounds. """ if upper is None and np.iterable(lower): lower, upper = lower old_lower, old_upper = get_bound() if lower is None: lower = old_lower if upper is None: upper = old_upper set_lim(sorted((lower, upper), reverse=bool(axis_inverted())), auto=None, view_margin=view_margin) def set_xbound(self, lower=None, upper=None, view_margin=None): """ Set the lower and upper numerical bounds of the x-axis. This method will honor axis inversion regardless of parameter order. It will not change the autoscaling setting (`.get_autoscalex_on()`). Parameters ---------- lower, upper : float or None The lower and upper bounds. If *None*, the respective axis bound is not modified. view_margin : float or None The margin to apply to the bounds. If *None*, the margin is handled by `.set_xlim`. See Also -------- get_xbound get_xlim, set_xlim invert_xaxis, xaxis_inverted """ self._set_bound3d(self.get_xbound, self.set_xlim, self.xaxis_inverted, lower, upper, view_margin) def set_ybound(self, lower=None, upper=None, view_margin=None): """ Set the lower and upper numerical bounds of the y-axis. This method will honor axis inversion regardless of parameter order. It will not change the autoscaling setting (`.get_autoscaley_on()`). Parameters ---------- lower, upper : float or None The lower and upper bounds. If *None*, the respective axis bound is not modified. view_margin : float or None The margin to apply to the bounds. If *None*, the margin is handled by `.set_ylim`. See Also -------- get_ybound get_ylim, set_ylim invert_yaxis, yaxis_inverted """ self._set_bound3d(self.get_ybound, self.set_ylim, self.yaxis_inverted, lower, upper, view_margin) def set_zbound(self, lower=None, upper=None, view_margin=None): """ Set the lower and upper numerical bounds of the z-axis. This method will honor axis inversion regardless of parameter order. It will not change the autoscaling setting (`.get_autoscaley_on()`). Parameters ---------- lower, upper : float or None The lower and upper bounds. If *None*, the respective axis bound is not modified. view_margin : float or None The margin to apply to the bounds. If *None*, the margin is handled by `.set_zlim`. See Also -------- get_zbound get_zlim, set_zlim invert_zaxis, zaxis_inverted """ self._set_bound3d(self.get_zbound, self.set_zlim, self.zaxis_inverted, lower, upper, view_margin) def _set_lim3d(self, axis, lower=None, upper=None, *, emit=True, auto=False, view_margin=None, axmin=None, axmax=None): """ Set 3D axis limits. """ if upper is None: if np.iterable(lower): lower, upper = lower elif axmax is None: upper = axis.get_view_interval()[1] if lower is None and axmin is None: lower = axis.get_view_interval()[0] if axmin is not None: if lower is not None: raise TypeError("Cannot pass both 'lower' and 'min'") lower = axmin if axmax is not None: if upper is not None: raise TypeError("Cannot pass both 'upper' and 'max'") upper = axmax if np.isinf(lower) or np.isinf(upper): raise ValueError(f"Axis limits {lower}, {upper} cannot be infinite") if view_margin is None: if mpl.rcParams['axes3d.automargin']: view_margin = self._view_margin else: view_margin = 0 delta = (upper - lower) * view_margin lower -= delta upper += delta return axis._set_lim(lower, upper, emit=emit, auto=auto) def set_xlim(self, left=None, right=None, *, emit=True, auto=False, view_margin=None, xmin=None, xmax=None): """ Set the 3D x-axis view limits. Parameters ---------- left : float, optional The left xlim in data coordinates. Passing *None* leaves the limit unchanged. The left and right xlims may also be passed as the tuple (*left*, *right*) as the first positional argument (or as the *left* keyword argument). .. ACCEPTS: (left: float, right: float) right : float, optional The right xlim in data coordinates. Passing *None* leaves the limit unchanged. emit : bool, default: True Whether to notify observers of limit change. auto : bool or None, default: False Whether to turn on autoscaling of the x-axis. *True* turns on, *False* turns off, *None* leaves unchanged. view_margin : float, optional The additional margin to apply to the limits. xmin, xmax : float, optional They are equivalent to left and right respectively, and it is an error to pass both *xmin* and *left* or *xmax* and *right*. Returns ------- left, right : (float, float) The new x-axis limits in data coordinates. See Also -------- get_xlim set_xbound, get_xbound invert_xaxis, xaxis_inverted Notes ----- The *left* value may be greater than the *right* value, in which case the x-axis values will decrease from *left* to *right*. Examples -------- >>> set_xlim(left, right) >>> set_xlim((left, right)) >>> left, right = set_xlim(left, right) One limit may be left unchanged. >>> set_xlim(right=right_lim) Limits may be passed in reverse order to flip the direction of the x-axis. For example, suppose ``x`` represents depth of the ocean in m. The x-axis limits might be set like the following so 5000 m depth is at the left of the plot and the surface, 0 m, is at the right. >>> set_xlim(5000, 0) """ return self._set_lim3d(self.xaxis, left, right, emit=emit, auto=auto, view_margin=view_margin, axmin=xmin, axmax=xmax) def set_ylim(self, bottom=None, top=None, *, emit=True, auto=False, view_margin=None, ymin=None, ymax=None): """ Set the 3D y-axis view limits. Parameters ---------- bottom : float, optional The bottom ylim in data coordinates. Passing *None* leaves the limit unchanged. The bottom and top ylims may also be passed as the tuple (*bottom*, *top*) as the first positional argument (or as the *bottom* keyword argument). .. ACCEPTS: (bottom: float, top: float) top : float, optional The top ylim in data coordinates. Passing *None* leaves the limit unchanged. emit : bool, default: True Whether to notify observers of limit change. auto : bool or None, default: False Whether to turn on autoscaling of the y-axis. *True* turns on, *False* turns off, *None* leaves unchanged. view_margin : float, optional The additional margin to apply to the limits. ymin, ymax : float, optional They are equivalent to bottom and top respectively, and it is an error to pass both *ymin* and *bottom* or *ymax* and *top*. Returns ------- bottom, top : (float, float) The new y-axis limits in data coordinates. See Also -------- get_ylim set_ybound, get_ybound invert_yaxis, yaxis_inverted Notes ----- The *bottom* value may be greater than the *top* value, in which case the y-axis values will decrease from *bottom* to *top*. Examples -------- >>> set_ylim(bottom, top) >>> set_ylim((bottom, top)) >>> bottom, top = set_ylim(bottom, top) One limit may be left unchanged. >>> set_ylim(top=top_lim) Limits may be passed in reverse order to flip the direction of the y-axis. For example, suppose ``y`` represents depth of the ocean in m. The y-axis limits might be set like the following so 5000 m depth is at the bottom of the plot and the surface, 0 m, is at the top. >>> set_ylim(5000, 0) """ return self._set_lim3d(self.yaxis, bottom, top, emit=emit, auto=auto, view_margin=view_margin, axmin=ymin, axmax=ymax) def set_zlim(self, bottom=None, top=None, *, emit=True, auto=False, view_margin=None, zmin=None, zmax=None): """ Set the 3D z-axis view limits. Parameters ---------- bottom : float, optional The bottom zlim in data coordinates. Passing *None* leaves the limit unchanged. The bottom and top zlims may also be passed as the tuple (*bottom*, *top*) as the first positional argument (or as the *bottom* keyword argument). .. ACCEPTS: (bottom: float, top: float) top : float, optional The top zlim in data coordinates. Passing *None* leaves the limit unchanged. emit : bool, default: True Whether to notify observers of limit change. auto : bool or None, default: False Whether to turn on autoscaling of the z-axis. *True* turns on, *False* turns off, *None* leaves unchanged. view_margin : float, optional The additional margin to apply to the limits. zmin, zmax : float, optional They are equivalent to bottom and top respectively, and it is an error to pass both *zmin* and *bottom* or *zmax* and *top*. Returns ------- bottom, top : (float, float) The new z-axis limits in data coordinates. See Also -------- get_zlim set_zbound, get_zbound invert_zaxis, zaxis_inverted Notes ----- The *bottom* value may be greater than the *top* value, in which case the z-axis values will decrease from *bottom* to *top*. Examples -------- >>> set_zlim(bottom, top) >>> set_zlim((bottom, top)) >>> bottom, top = set_zlim(bottom, top) One limit may be left unchanged. >>> set_zlim(top=top_lim) Limits may be passed in reverse order to flip the direction of the z-axis. For example, suppose ``z`` represents depth of the ocean in m. The z-axis limits might be set like the following so 5000 m depth is at the bottom of the plot and the surface, 0 m, is at the top. >>> set_zlim(5000, 0) """ return self._set_lim3d(self.zaxis, bottom, top, emit=emit, auto=auto, view_margin=view_margin, axmin=zmin, axmax=zmax) set_xlim3d = set_xlim set_ylim3d = set_ylim set_zlim3d = set_zlim def get_xlim(self): # docstring inherited return tuple(self.xy_viewLim.intervalx) def get_ylim(self): # docstring inherited return tuple(self.xy_viewLim.intervaly) def get_zlim(self): """ Return the 3D z-axis view limits. Returns ------- left, right : (float, float) The current z-axis limits in data coordinates. See Also -------- set_zlim set_zbound, get_zbound invert_zaxis, zaxis_inverted Notes ----- The z-axis may be inverted, in which case the *left* value will be greater than the *right* value. """ return tuple(self.zz_viewLim.intervalx) get_zscale = _axis_method_wrapper("zaxis", "get_scale") # Redefine all three methods to overwrite their docstrings. set_xscale = _axis_method_wrapper("xaxis", "_set_axes_scale") set_yscale = _axis_method_wrapper("yaxis", "_set_axes_scale") set_zscale = _axis_method_wrapper("zaxis", "_set_axes_scale") set_xscale.__doc__, set_yscale.__doc__, set_zscale.__doc__ = map( """ Set the {}-axis scale. Parameters ---------- value : {{"linear"}} The axis scale type to apply. 3D Axes currently only support linear scales; other scales yield nonsensical results. **kwargs Keyword arguments are nominally forwarded to the scale class, but none of them is applicable for linear scales. """.format, ["x", "y", "z"]) get_zticks = _axis_method_wrapper("zaxis", "get_ticklocs") set_zticks = _axis_method_wrapper("zaxis", "set_ticks") get_zmajorticklabels = _axis_method_wrapper("zaxis", "get_majorticklabels") get_zminorticklabels = _axis_method_wrapper("zaxis", "get_minorticklabels") get_zticklabels = _axis_method_wrapper("zaxis", "get_ticklabels") set_zticklabels = _axis_method_wrapper( "zaxis", "set_ticklabels", doc_sub={"Axis.set_ticks": "Axes3D.set_zticks"}) zaxis_date = _axis_method_wrapper("zaxis", "axis_date") if zaxis_date.__doc__: zaxis_date.__doc__ += textwrap.dedent(""" Notes ----- This function is merely provided for completeness, but 3D Axes do not support dates for ticks, and so this may not work as expected. """) def clabel(self, *args, **kwargs): """Currently not implemented for 3D Axes, and returns *None*.""" return None def view_init(self, elev=None, azim=None, roll=None, vertical_axis="z", share=False): """ Set the elevation and azimuth of the Axes in degrees (not radians). This can be used to rotate the Axes programmatically. To look normal to the primary planes, the following elevation and azimuth angles can be used. A roll angle of 0, 90, 180, or 270 deg will rotate these views while keeping the axes at right angles. ========== ==== ==== view plane elev azim ========== ==== ==== XY 90 -90 XZ 0 -90 YZ 0 0 -XY -90 90 -XZ 0 90 -YZ 0 180 ========== ==== ==== Parameters ---------- elev : float, default: None The elevation angle in degrees rotates the camera above the plane pierced by the vertical axis, with a positive angle corresponding to a location above that plane. For example, with the default vertical axis of 'z', the elevation defines the angle of the camera location above the x-y plane. If None, then the initial value as specified in the `Axes3D` constructor is used. azim : float, default: None The azimuthal angle in degrees rotates the camera about the vertical axis, with a positive angle corresponding to a right-handed rotation. For example, with the default vertical axis of 'z', a positive azimuth rotates the camera about the origin from its location along the +x axis towards the +y axis. If None, then the initial value as specified in the `Axes3D` constructor is used. roll : float, default: None The roll angle in degrees rotates the camera about the viewing axis. A positive angle spins the camera clockwise, causing the scene to rotate counter-clockwise. If None, then the initial value as specified in the `Axes3D` constructor is used. vertical_axis : {"z", "x", "y"}, default: "z" The axis to align vertically. *azim* rotates about this axis. share : bool, default: False If ``True``, apply the settings to all Axes with shared views. """ self._dist = 10 # The camera distance from origin. Behaves like zoom if elev is None: elev = self.initial_elev if azim is None: azim = self.initial_azim if roll is None: roll = self.initial_roll vertical_axis = _api.check_getitem( {name: idx for idx, name in enumerate(self._axis_names)}, vertical_axis=vertical_axis, ) if share: axes = {sibling for sibling in self._shared_axes['view'].get_siblings(self)} else: axes = [self] for ax in axes: ax.elev = elev ax.azim = azim ax.roll = roll ax._vertical_axis = vertical_axis def set_proj_type(self, proj_type, focal_length=None): """ Set the projection type. Parameters ---------- proj_type : {'persp', 'ortho'} The projection type. focal_length : float, default: None For a projection type of 'persp', the focal length of the virtual camera. Must be > 0. If None, defaults to 1. The focal length can be computed from a desired Field Of View via the equation: focal_length = 1/tan(FOV/2) """ _api.check_in_list(['persp', 'ortho'], proj_type=proj_type) if proj_type == 'persp': if focal_length is None: focal_length = 1 elif focal_length <= 0: raise ValueError(f"focal_length = {focal_length} must be " "greater than 0") self._focal_length = focal_length else: # 'ortho': if focal_length not in (None, np.inf): raise ValueError(f"focal_length = {focal_length} must be " f"None for proj_type = {proj_type}") self._focal_length = np.inf def _roll_to_vertical( self, arr: "np.typing.ArrayLike", reverse: bool = False ) -> np.ndarray: """ Roll arrays to match the different vertical axis. Parameters ---------- arr : ArrayLike Array to roll. reverse : bool, default: False Reverse the direction of the roll. """ if reverse: return np.roll(arr, (self._vertical_axis - 2) * -1) else: return np.roll(arr, (self._vertical_axis - 2)) def get_proj(self): """Create the projection matrix from the current viewing position.""" # Transform to uniform world coordinates 0-1, 0-1, 0-1 box_aspect = self._roll_to_vertical(self._box_aspect) worldM = proj3d.world_transformation( *self.get_xlim3d(), *self.get_ylim3d(), *self.get_zlim3d(), pb_aspect=box_aspect, ) # Look into the middle of the world coordinates: R = 0.5 * box_aspect # elev: elevation angle in the z plane. # azim: azimuth angle in the xy plane. # Coordinates for a point that rotates around the box of data. # p0, p1 corresponds to rotating the box only around the vertical axis. # p2 corresponds to rotating the box only around the horizontal axis. elev_rad = np.deg2rad(self.elev) azim_rad = np.deg2rad(self.azim) p0 = np.cos(elev_rad) * np.cos(azim_rad) p1 = np.cos(elev_rad) * np.sin(azim_rad) p2 = np.sin(elev_rad) # When changing vertical axis the coordinates changes as well. # Roll the values to get the same behaviour as the default: ps = self._roll_to_vertical([p0, p1, p2]) # The coordinates for the eye viewing point. The eye is looking # towards the middle of the box of data from a distance: eye = R + self._dist * ps # Calculate the viewing axes for the eye position u, v, w = self._calc_view_axes(eye) self._view_u = u # _view_u is towards the right of the screen self._view_v = v # _view_v is towards the top of the screen self._view_w = w # _view_w is out of the screen # Generate the view and projection transformation matrices if self._focal_length == np.inf: # Orthographic projection viewM = proj3d._view_transformation_uvw(u, v, w, eye) projM = proj3d._ortho_transformation(-self._dist, self._dist) else: # Perspective projection # Scale the eye dist to compensate for the focal length zoom effect eye_focal = R + self._dist * ps * self._focal_length viewM = proj3d._view_transformation_uvw(u, v, w, eye_focal) projM = proj3d._persp_transformation(-self._dist, self._dist, self._focal_length) # Combine all the transformation matrices to get the final projection M0 = np.dot(viewM, worldM) M = np.dot(projM, M0) return M def mouse_init(self, rotate_btn=1, pan_btn=2, zoom_btn=3): """ Set the mouse buttons for 3D rotation and zooming. Parameters ---------- rotate_btn : int or list of int, default: 1 The mouse button or buttons to use for 3D rotation of the Axes. pan_btn : int or list of int, default: 2 The mouse button or buttons to use to pan the 3D Axes. zoom_btn : int or list of int, default: 3 The mouse button or buttons to use to zoom the 3D Axes. """ self.button_pressed = None # coerce scalars into array-like, then convert into # a regular list to avoid comparisons against None # which breaks in recent versions of numpy. self._rotate_btn = np.atleast_1d(rotate_btn).tolist() self._pan_btn = np.atleast_1d(pan_btn).tolist() self._zoom_btn = np.atleast_1d(zoom_btn).tolist() def disable_mouse_rotation(self): """Disable mouse buttons for 3D rotation, panning, and zooming.""" self.mouse_init(rotate_btn=[], pan_btn=[], zoom_btn=[]) def can_zoom(self): # doc-string inherited return True def can_pan(self): # doc-string inherited return True def sharez(self, other): """ Share the z-axis with *other*. This is equivalent to passing ``sharez=other`` when constructing the Axes, and cannot be used if the z-axis is already being shared with another Axes. Note that it is not possible to unshare axes. """ _api.check_isinstance(Axes3D, other=other) if self._sharez is not None and other is not self._sharez: raise ValueError("z-axis is already shared") self._shared_axes["z"].join(self, other) self._sharez = other self.zaxis.major = other.zaxis.major # Ticker instances holding self.zaxis.minor = other.zaxis.minor # locator and formatter. z0, z1 = other.get_zlim() self.set_zlim(z0, z1, emit=False, auto=other.get_autoscalez_on()) self.zaxis._scale = other.zaxis._scale def shareview(self, other): """ Share the view angles with *other*. This is equivalent to passing ``shareview=other`` when constructing the Axes, and cannot be used if the view angles are already being shared with another Axes. Note that it is not possible to unshare axes. """ _api.check_isinstance(Axes3D, other=other) if self._shareview is not None and other is not self._shareview: raise ValueError("view angles are already shared") self._shared_axes["view"].join(self, other) self._shareview = other vertical_axis = self._axis_names[other._vertical_axis] self.view_init(elev=other.elev, azim=other.azim, roll=other.roll, vertical_axis=vertical_axis, share=True) def clear(self): # docstring inherited. super().clear() if self._focal_length == np.inf: self._zmargin = mpl.rcParams['axes.zmargin'] else: self._zmargin = 0. xymargin = 0.05 * 10/11 # match mpl3.8 appearance self.xy_dataLim = Bbox([[xymargin, xymargin], [1 - xymargin, 1 - xymargin]]) # z-limits are encoded in the x-component of the Bbox, y is un-used self.zz_dataLim = Bbox.unit() self._view_margin = 1/48 # default value to match mpl3.8 self.autoscale_view() self.grid(mpl.rcParams['axes3d.grid']) def _button_press(self, event): if event.inaxes == self: self.button_pressed = event.button self._sx, self._sy = event.xdata, event.ydata toolbar = self.figure.canvas.toolbar if toolbar and toolbar._nav_stack() is None: toolbar.push_current() def _button_release(self, event): self.button_pressed = None toolbar = self.figure.canvas.toolbar # backend_bases.release_zoom and backend_bases.release_pan call # push_current, so check the navigation mode so we don't call it twice if toolbar and self.get_navigate_mode() is None: toolbar.push_current() def _get_view(self): # docstring inherited return { "xlim": self.get_xlim(), "autoscalex_on": self.get_autoscalex_on(), "ylim": self.get_ylim(), "autoscaley_on": self.get_autoscaley_on(), "zlim": self.get_zlim(), "autoscalez_on": self.get_autoscalez_on(), }, (self.elev, self.azim, self.roll) def _set_view(self, view): # docstring inherited props, (elev, azim, roll) = view self.set(**props) self.elev = elev self.azim = azim self.roll = roll def format_zdata(self, z): """ Return *z* string formatted. This function will use the :attr:`fmt_zdata` attribute if it is callable, else will fall back on the zaxis major formatter """ try: return self.fmt_zdata(z) except (AttributeError, TypeError): func = self.zaxis.get_major_formatter().format_data_short val = func(z) return val def format_coord(self, xv, yv, renderer=None): """ Return a string giving the current view rotation angles, or the x, y, z coordinates of the point on the nearest axis pane underneath the mouse cursor, depending on the mouse button pressed. """ coords = '' if self.button_pressed in self._rotate_btn: # ignore xv and yv and display angles instead coords = self._rotation_coords() elif self.M is not None: coords = self._location_coords(xv, yv, renderer) return coords def _rotation_coords(self): """ Return the rotation angles as a string. """ norm_elev = art3d._norm_angle(self.elev) norm_azim = art3d._norm_angle(self.azim) norm_roll = art3d._norm_angle(self.roll) coords = (f"elevation={norm_elev:.0f}\N{DEGREE SIGN}, " f"azimuth={norm_azim:.0f}\N{DEGREE SIGN}, " f"roll={norm_roll:.0f}\N{DEGREE SIGN}" ).replace("-", "\N{MINUS SIGN}") return coords def _location_coords(self, xv, yv, renderer): """ Return the location on the axis pane underneath the cursor as a string. """ p1, pane_idx = self._calc_coord(xv, yv, renderer) xs = self.format_xdata(p1[0]) ys = self.format_ydata(p1[1]) zs = self.format_zdata(p1[2]) if pane_idx == 0: coords = f'x pane={xs}, y={ys}, z={zs}' elif pane_idx == 1: coords = f'x={xs}, y pane={ys}, z={zs}' elif pane_idx == 2: coords = f'x={xs}, y={ys}, z pane={zs}' return coords def _get_camera_loc(self): """ Returns the current camera location in data coordinates. """ cx, cy, cz, dx, dy, dz = self._get_w_centers_ranges() c = np.array([cx, cy, cz]) r = np.array([dx, dy, dz]) if self._focal_length == np.inf: # orthographic projection focal_length = 1e9 # large enough to be effectively infinite else: # perspective projection focal_length = self._focal_length eye = c + self._view_w * self._dist * r / self._box_aspect * focal_length return eye def _calc_coord(self, xv, yv, renderer=None): """ Given the 2D view coordinates, find the point on the nearest axis pane that lies directly below those coordinates. Returns a 3D point in data coordinates. """ if self._focal_length == np.inf: # orthographic projection zv = 1 else: # perspective projection zv = -1 / self._focal_length # Convert point on view plane to data coordinates p1 = np.array(proj3d.inv_transform(xv, yv, zv, self.invM)).ravel() # Get the vector from the camera to the point on the view plane vec = self._get_camera_loc() - p1 # Get the pane locations for each of the axes pane_locs = [] for axis in self._axis_map.values(): xys, loc = axis.active_pane() pane_locs.append(loc) # Find the distance to the nearest pane by projecting the view vector scales = np.zeros(3) for i in range(3): if vec[i] == 0: scales[i] = np.inf else: scales[i] = (p1[i] - pane_locs[i]) / vec[i] pane_idx = np.argmin(abs(scales)) scale = scales[pane_idx] # Calculate the point on the closest pane p2 = p1 - scale*vec return p2, pane_idx def _on_move(self, event): """ Mouse moving. By default, button-1 rotates, button-2 pans, and button-3 zooms; these buttons can be modified via `mouse_init`. """ if not self.button_pressed: return if self.get_navigate_mode() is not None: # we don't want to rotate if we are zooming/panning # from the toolbar return if self.M is None: return x, y = event.xdata, event.ydata # In case the mouse is out of bounds. if x is None or event.inaxes != self: return dx, dy = x - self._sx, y - self._sy w = self._pseudo_w h = self._pseudo_h # 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 roll = np.deg2rad(self.roll) delev = -(dy/h)*180*np.cos(roll) + (dx/w)*180*np.sin(roll) dazim = -(dy/h)*180*np.sin(roll) - (dx/w)*180*np.cos(roll) elev = self.elev + delev azim = self.azim + dazim roll = self.roll vertical_axis = self._axis_names[self._vertical_axis] self.view_init( elev=elev, azim=azim, roll=roll, vertical_axis=vertical_axis, share=True, ) self.stale = True # Pan elif self.button_pressed in self._pan_btn: # Start the pan event with pixel coordinates px, py = self.transData.transform([self._sx, self._sy]) self.start_pan(px, py, 2) # pan view (takes pixel coordinate input) self.drag_pan(2, None, event.x, event.y) self.end_pan() # Zoom elif self.button_pressed in self._zoom_btn: # zoom view (dragging down zooms in) scale = h/(h - dy) self._scale_axis_limits(scale, scale, scale) # Store the event coordinates for the next time through. self._sx, self._sy = x, y # Always request a draw update at the end of interaction self.figure.canvas.draw_idle() def drag_pan(self, button, key, x, y): # docstring inherited # Get the coordinates from the move event p = self._pan_start (xdata, ydata), (xdata_start, ydata_start) = p.trans_inverse.transform( [(x, y), (p.x, p.y)]) self._sx, self._sy = xdata, ydata # Calling start_pan() to set the x/y of this event as the starting # move location for the next event self.start_pan(x, y, button) du, dv = xdata - xdata_start, ydata - ydata_start dw = 0 if key == 'x': dv = 0 elif key == 'y': du = 0 if du == 0 and dv == 0: return # Transform the pan from the view axes to the data axes R = np.array([self._view_u, self._view_v, self._view_w]) R = -R / self._box_aspect * self._dist duvw_projected = R.T @ np.array([du, dv, dw]) # Calculate pan distance minx, maxx, miny, maxy, minz, maxz = self.get_w_lims() dx = (maxx - minx) * duvw_projected[0] dy = (maxy - miny) * duvw_projected[1] dz = (maxz - minz) * duvw_projected[2] # Set the new axis limits self.set_xlim3d(minx + dx, maxx + dx, auto=None) self.set_ylim3d(miny + dy, maxy + dy, auto=None) self.set_zlim3d(minz + dz, maxz + dz, auto=None) def _calc_view_axes(self, eye): """ Get the unit vectors for the viewing axes in data coordinates. `u` is towards the right of the screen `v` is towards the top of the screen `w` is out of the screen """ elev_rad = np.deg2rad(art3d._norm_angle(self.elev)) roll_rad = np.deg2rad(art3d._norm_angle(self.roll)) # Look into the middle of the world coordinates R = 0.5 * self._roll_to_vertical(self._box_aspect) # Define which axis should be vertical. A negative value # indicates the plot is upside down and therefore the values # have been reversed: V = np.zeros(3) V[self._vertical_axis] = -1 if abs(elev_rad) > np.pi/2 else 1 u, v, w = proj3d._view_axes(eye, R, V, roll_rad) return u, v, w def _set_view_from_bbox(self, bbox, direction='in', mode=None, twinx=False, twiny=False): """ Zoom in or out of the bounding box. Will center the view in the center of the bounding box, and zoom by the ratio of the size of the bounding box to the size of the Axes3D. """ (start_x, start_y, stop_x, stop_y) = bbox if mode == 'x': start_y = self.bbox.min[1] stop_y = self.bbox.max[1] elif mode == 'y': start_x = self.bbox.min[0] stop_x = self.bbox.max[0] # Clip to bounding box limits start_x, stop_x = np.clip(sorted([start_x, stop_x]), self.bbox.min[0], self.bbox.max[0]) start_y, stop_y = np.clip(sorted([start_y, stop_y]), self.bbox.min[1], self.bbox.max[1]) # Move the center of the view to the center of the bbox zoom_center_x = (start_x + stop_x)/2 zoom_center_y = (start_y + stop_y)/2 ax_center_x = (self.bbox.max[0] + self.bbox.min[0])/2 ax_center_y = (self.bbox.max[1] + self.bbox.min[1])/2 self.start_pan(zoom_center_x, zoom_center_y, 2) self.drag_pan(2, None, ax_center_x, ax_center_y) self.end_pan() # Calculate zoom level dx = abs(start_x - stop_x) dy = abs(start_y - stop_y) scale_u = dx / (self.bbox.max[0] - self.bbox.min[0]) scale_v = dy / (self.bbox.max[1] - self.bbox.min[1]) # Keep aspect ratios equal scale = max(scale_u, scale_v) # Zoom out if direction == 'out': scale = 1 / scale self._zoom_data_limits(scale, scale, scale) def _zoom_data_limits(self, scale_u, scale_v, scale_w): """ Zoom in or out of a 3D plot. Will scale the data limits by the scale factors. These will be transformed to the x, y, z data axes based on the current view angles. A scale factor > 1 zooms out and a scale factor < 1 zooms in. For an Axes that has had its aspect ratio set to 'equal', 'equalxy', 'equalyz', or 'equalxz', the relevant axes are constrained to zoom equally. Parameters ---------- scale_u : float Scale factor for the u view axis (view screen horizontal). scale_v : float Scale factor for the v view axis (view screen vertical). scale_w : float Scale factor for the w view axis (view screen depth). """ scale = np.array([scale_u, scale_v, scale_w]) # Only perform frame conversion if unequal scale factors if not np.allclose(scale, scale_u): # Convert the scale factors from the view frame to the data frame R = np.array([self._view_u, self._view_v, self._view_w]) S = scale * np.eye(3) scale = np.linalg.norm(R.T @ S, axis=1) # Set the constrained scale factors to the factor closest to 1 if self._aspect in ('equal', 'equalxy', 'equalxz', 'equalyz'): ax_idxs = self._equal_aspect_axis_indices(self._aspect) min_ax_idxs = np.argmin(np.abs(scale[ax_idxs] - 1)) scale[ax_idxs] = scale[ax_idxs][min_ax_idxs] self._scale_axis_limits(scale[0], scale[1], scale[2]) def _scale_axis_limits(self, scale_x, scale_y, scale_z): """ Keeping the center of the x, y, and z data axes fixed, scale their limits by scale factors. A scale factor > 1 zooms out and a scale factor < 1 zooms in. Parameters ---------- scale_x : float Scale factor for the x data axis. scale_y : float Scale factor for the y data axis. scale_z : float Scale factor for the z data axis. """ # Get the axis centers and ranges cx, cy, cz, dx, dy, dz = self._get_w_centers_ranges() # Set the scaled axis limits self.set_xlim3d(cx - dx*scale_x/2, cx + dx*scale_x/2, auto=None) self.set_ylim3d(cy - dy*scale_y/2, cy + dy*scale_y/2, auto=None) self.set_zlim3d(cz - dz*scale_z/2, cz + dz*scale_z/2, auto=None) def _get_w_centers_ranges(self): """Get 3D world centers and axis ranges.""" # Calculate center of axis limits minx, maxx, miny, maxy, minz, maxz = self.get_w_lims() cx = (maxx + minx)/2 cy = (maxy + miny)/2 cz = (maxz + minz)/2 # Calculate range of axis limits dx = (maxx - minx) dy = (maxy - miny) dz = (maxz - minz) return cx, cy, cz, dx, dy, dz def set_zlabel(self, zlabel, fontdict=None, labelpad=None, **kwargs): """ Set zlabel. See doc for `.set_ylabel` for description. """ if labelpad is not None: self.zaxis.labelpad = labelpad return self.zaxis.set_label_text(zlabel, fontdict, **kwargs) def get_zlabel(self): """ Get the z-label text string. """ label = self.zaxis.get_label() return label.get_text() # Axes rectangle characteristics # The frame_on methods are not available for 3D axes. # Python will raise a TypeError if they are called. get_frame_on = None set_frame_on = None def grid(self, visible=True, **kwargs): """ Set / unset 3D grid. .. note:: Currently, this function does not behave the same as `.axes.Axes.grid`, but it is intended to eventually support that behavior. """ # TODO: Operate on each axes separately if len(kwargs): visible = True self._draw_grid = visible self.stale = True def tick_params(self, axis='both', **kwargs): """ Convenience method for changing the appearance of ticks and tick labels. See `.Axes.tick_params` for full documentation. Because this function applies to 3D Axes, *axis* can also be set to 'z', and setting *axis* to 'both' autoscales all three axes. Also, because of how Axes3D objects are drawn very differently from regular 2D Axes, some of these settings may have ambiguous meaning. For simplicity, the 'z' axis will accept settings as if it was like the 'y' axis. .. note:: Axes3D currently ignores some of these settings. """ _api.check_in_list(['x', 'y', 'z', 'both'], axis=axis) if axis in ['x', 'y', 'both']: super().tick_params(axis, **kwargs) if axis in ['z', 'both']: zkw = dict(kwargs) zkw.pop('top', None) zkw.pop('bottom', None) zkw.pop('labeltop', None) zkw.pop('labelbottom', None) self.zaxis.set_tick_params(**zkw) # data limits, ticks, tick labels, and formatting def invert_zaxis(self): """ Invert the z-axis. See Also -------- zaxis_inverted get_zlim, set_zlim get_zbound, set_zbound """ bottom, top = self.get_zlim() self.set_zlim(top, bottom, auto=None) zaxis_inverted = _axis_method_wrapper("zaxis", "get_inverted") def get_zbound(self): """ Return the lower and upper z-axis bounds, in increasing order. See Also -------- set_zbound get_zlim, set_zlim invert_zaxis, zaxis_inverted """ lower, upper = self.get_zlim() if lower < upper: return lower, upper else: return upper, lower def text(self, x, y, z, s, zdir=None, **kwargs): """ Add the text *s* to the 3D Axes at location *x*, *y*, *z* in data coordinates. Parameters ---------- x, y, z : float The position to place the text. s : str The text. zdir : {'x', 'y', 'z', 3-tuple}, optional The direction to be used as the z-direction. Default: 'z'. See `.get_dir_vector` for a description of the values. **kwargs Other arguments are forwarded to `matplotlib.axes.Axes.text`. Returns ------- `.Text3D` The created `.Text3D` instance. """ text = super().text(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, zdir='z', **kwargs): """ Plot 2D or 3D data. Parameters ---------- xs : 1D array-like x coordinates of vertices. ys : 1D array-like y coordinates of vertices. zs : float or 1D array-like z coordinates of vertices; either one for all points or one for each point. zdir : {'x', 'y', 'z'}, default: 'z' When plotting 2D data, the direction to use as z. **kwargs Other arguments are forwarded to `matplotlib.axes.Axes.plot`. """ had_data = self.has_data() # `zs` can be passed positionally or as keyword; checking whether # args[0] is a string matches the behavior of 2D `plot` (via # `_process_plot_var_args`). if args and not isinstance(args[0], str): zs, *args = args if 'zs' in kwargs: raise TypeError("plot() for multiple values for argument 'zs'") else: zs = kwargs.pop('zs', 0) xs, ys, zs = cbook._broadcast_with_masks(xs, ys, zs) lines = super().plot(xs, ys, *args, **kwargs) for line in lines: art3d.line_2d_to_3d(line, zs=zs, zdir=zdir) xs, ys, zs = art3d.juggle_axes(xs, ys, zs, zdir) self.auto_scale_xyz(xs, ys, zs, had_data) return lines plot3D = plot def plot_surface(self, X, Y, Z, *, norm=None, vmin=None, vmax=None, lightsource=None, **kwargs): """ Create a surface plot. By default, it will be colored in shades of a solid color, but it also supports colormapping by supplying the *cmap* argument. .. note:: The *rcount* and *ccount* kwargs, which both default to 50, determine the maximum number of samples used in each direction. If the input data is larger, it will be downsampled (by slicing) to these numbers of points. .. note:: To maximize rendering speed consider setting *rstride* and *cstride* to divisors of the number of rows minus 1 and columns minus 1 respectively. For example, given 51 rows rstride can be any of the divisors of 50. Similarly, a setting of *rstride* and *cstride* equal to 1 (or *rcount* and *ccount* equal the number of rows and columns) can use the optimized path. Parameters ---------- X, Y, Z : 2D arrays Data values. rcount, ccount : int Maximum number of samples used in each direction. If the input data is larger, it will be downsampled (by slicing) to these numbers of points. Defaults to 50. rstride, cstride : int Downsampling stride in each direction. These arguments are mutually exclusive with *rcount* and *ccount*. If only one of *rstride* or *cstride* is set, the other defaults to 10. 'classic' mode uses a default of ``rstride = cstride = 10`` instead of the new default of ``rcount = ccount = 50``. color : :mpltype:`color` Color of the surface patches. cmap : Colormap, optional Colormap of the surface patches. facecolors : list of :mpltype:`color` Colors of each individual patch. norm : `~matplotlib.colors.Normalize`, optional Normalization for the colormap. vmin, vmax : float, optional Bounds for the normalization. shade : bool, default: True Whether to shade the facecolors. Shading is always disabled when *cmap* is specified. lightsource : `~matplotlib.colors.LightSource`, optional The lightsource to use when *shade* is True. **kwargs Other keyword arguments are forwarded to `.Poly3DCollection`. """ had_data = self.has_data() if Z.ndim != 2: raise ValueError("Argument Z must be 2-dimensional.") Z = cbook._to_unmasked_float_array(Z) X, Y, Z = np.broadcast_arrays(X, Y, Z) rows, cols = Z.shape has_stride = 'rstride' in kwargs or 'cstride' in kwargs has_count = 'rcount' in kwargs or 'ccount' in kwargs if has_stride and has_count: raise ValueError("Cannot specify both stride and count arguments") rstride = kwargs.pop('rstride', 10) cstride = kwargs.pop('cstride', 10) rcount = kwargs.pop('rcount', 50) ccount = kwargs.pop('ccount', 50) if mpl.rcParams['_internal.classic_mode']: # Strides have priority over counts in classic mode. # So, only compute strides from counts # if counts were explicitly given compute_strides = has_count else: # If the strides are provided then it has priority. # Otherwise, compute the strides from the counts. compute_strides = not has_stride if compute_strides: rstride = int(max(np.ceil(rows / rcount), 1)) cstride = int(max(np.ceil(cols / ccount), 1)) fcolors = kwargs.pop('facecolors', None) cmap = kwargs.get('cmap', None) shade = kwargs.pop('shade', cmap is None) if shade is None: raise ValueError("shade cannot be None.") colset = [] # the sampled facecolor if (rows - 1) % rstride == 0 and \ (cols - 1) % cstride == 0 and \ fcolors is None: polys = np.stack( [cbook._array_patch_perimeters(a, rstride, cstride) for a in (X, Y, Z)], axis=-1) else: # evenly spaced, and including both endpoints row_inds = list(range(0, rows-1, rstride)) + [rows-1] col_inds = list(range(0, cols-1, cstride)) + [cols-1] polys = [] for rs, rs_next in zip(row_inds[:-1], row_inds[1:]): for cs, cs_next in zip(col_inds[:-1], col_inds[1:]): ps = [ # +1 ensures we share edges between polygons cbook._array_perimeter(a[rs:rs_next+1, cs:cs_next+1]) for a in (X, Y, Z) ] # ps = np.stack(ps, axis=-1) ps = np.array(ps).T polys.append(ps) if fcolors is not None: colset.append(fcolors[rs][cs]) # In cases where there are non-finite values in the data (possibly NaNs from # masked arrays), artifacts can be introduced. Here check whether such values # are present and remove them. if not isinstance(polys, np.ndarray) or not np.isfinite(polys).all(): new_polys = [] new_colset = [] # Depending on fcolors, colset is either an empty list or has as # many elements as polys. In the former case new_colset results in # a list with None entries, that is discarded later. for p, col in itertools.zip_longest(polys, colset): new_poly = np.array(p)[np.isfinite(p).all(axis=1)] if len(new_poly): new_polys.append(new_poly) new_colset.append(col) # Replace previous polys and, if fcolors is not None, colset polys = new_polys if fcolors is not None: colset = new_colset # note that the striding causes some polygons to have more coordinates # than others if fcolors is not None: polyc = art3d.Poly3DCollection( polys, edgecolors=colset, facecolors=colset, shade=shade, lightsource=lightsource, **kwargs) elif cmap: polyc = art3d.Poly3DCollection(polys, **kwargs) # can't always vectorize, because polys might be jagged if isinstance(polys, np.ndarray): avg_z = polys[..., 2].mean(axis=-1) else: avg_z = np.array([ps[:, 2].mean() for ps in polys]) polyc.set_array(avg_z) if vmin is not None or vmax is not None: polyc.set_clim(vmin, vmax) if norm is not None: polyc.set_norm(norm) else: color = kwargs.pop('color', None) if color is None: color = self._get_lines.get_next_color() color = np.array(mcolors.to_rgba(color)) polyc = art3d.Poly3DCollection( polys, facecolors=color, shade=shade, lightsource=lightsource, **kwargs) self.add_collection(polyc) self.auto_scale_xyz(X, Y, Z, had_data) return polyc def plot_wireframe(self, X, Y, Z, **kwargs): """ Plot a 3D wireframe. .. note:: The *rcount* and *ccount* kwargs, which both default to 50, determine the maximum number of samples used in each direction. If the input data is larger, it will be downsampled (by slicing) to these numbers of points. Parameters ---------- X, Y, Z : 2D arrays Data values. rcount, ccount : int Maximum number of samples used in each direction. If the input data is larger, it will be downsampled (by slicing) to these numbers of points. Setting a count to zero causes the data to be not sampled in the corresponding direction, producing a 3D line plot rather than a wireframe plot. Defaults to 50. rstride, cstride : int Downsampling stride in each direction. These arguments are mutually exclusive with *rcount* and *ccount*. If only one of *rstride* or *cstride* is set, the other defaults to 1. Setting a stride to zero causes the data to be not sampled in the corresponding direction, producing a 3D line plot rather than a wireframe plot. 'classic' mode uses a default of ``rstride = cstride = 1`` instead of the new default of ``rcount = ccount = 50``. **kwargs Other keyword arguments are forwarded to `.Line3DCollection`. """ had_data = self.has_data() if Z.ndim != 2: raise ValueError("Argument Z must be 2-dimensional.") # FIXME: Support masked arrays X, Y, Z = np.broadcast_arrays(X, Y, Z) rows, cols = Z.shape has_stride = 'rstride' in kwargs or 'cstride' in kwargs has_count = 'rcount' in kwargs or 'ccount' in kwargs if has_stride and has_count: raise ValueError("Cannot specify both stride and count arguments") rstride = kwargs.pop('rstride', 1) cstride = kwargs.pop('cstride', 1) rcount = kwargs.pop('rcount', 50) ccount = kwargs.pop('ccount', 50) if mpl.rcParams['_internal.classic_mode']: # Strides have priority over counts in classic mode. # So, only compute strides from counts # if counts were explicitly given if has_count: rstride = int(max(np.ceil(rows / rcount), 1)) if rcount else 0 cstride = int(max(np.ceil(cols / ccount), 1)) if ccount else 0 else: # If the strides are provided then it has priority. # Otherwise, compute the strides from the counts. if not has_stride: rstride = int(max(np.ceil(rows / rcount), 1)) if rcount else 0 cstride = int(max(np.ceil(cols / ccount), 1)) if ccount else 0 # We want two sets of lines, one running along the "rows" of # Z and another set of lines running along the "columns" of Z. # This transpose will make it easy to obtain the columns. tX, tY, tZ = np.transpose(X), np.transpose(Y), np.transpose(Z) if rstride: rii = list(range(0, rows, rstride)) # Add the last index only if needed if rows > 0 and rii[-1] != (rows - 1): rii += [rows-1] else: rii = [] if cstride: cii = list(range(0, cols, cstride)) # Add the last index only if needed if cols > 0 and cii[-1] != (cols - 1): cii += [cols-1] else: cii = [] if rstride == 0 and cstride == 0: raise ValueError("Either rstride or cstride must be non zero") # If the inputs were empty, then just # reset everything. if Z.size == 0: rii = [] cii = [] xlines = [X[i] for i in rii] ylines = [Y[i] for i in rii] zlines = [Z[i] for i in rii] txlines = [tX[i] for i in cii] tylines = [tY[i] for i in cii] tzlines = [tZ[i] for i in cii] lines = ([list(zip(xl, yl, zl)) for xl, yl, zl in zip(xlines, ylines, zlines)] + [list(zip(xl, yl, zl)) for xl, yl, zl in zip(txlines, tylines, tzlines)]) linec = art3d.Line3DCollection(lines, **kwargs) self.add_collection(linec) self.auto_scale_xyz(X, Y, Z, had_data) return linec def plot_trisurf(self, *args, color=None, norm=None, vmin=None, vmax=None, lightsource=None, **kwargs): """ Plot a triangulated surface. The (optional) triangulation can be specified in one of two ways; either:: plot_trisurf(triangulation, ...) where triangulation is a `~matplotlib.tri.Triangulation` object, or:: plot_trisurf(X, Y, ...) plot_trisurf(X, Y, triangles, ...) plot_trisurf(X, Y, triangles=triangles, ...) in which case a Triangulation object will be created. See `.Triangulation` for an explanation of these possibilities. The remaining arguments are:: plot_trisurf(..., Z) where *Z* is the array of values to contour, one per point in the triangulation. Parameters ---------- X, Y, Z : array-like Data values as 1D arrays. color Color of the surface patches. cmap A colormap for the surface patches. norm : `~matplotlib.colors.Normalize`, optional An instance of Normalize to map values to colors. vmin, vmax : float, optional Minimum and maximum value to map. shade : bool, default: True Whether to shade the facecolors. Shading is always disabled when *cmap* is specified. lightsource : `~matplotlib.colors.LightSource`, optional The lightsource to use when *shade* is True. **kwargs All other keyword arguments are passed on to :class:`~mpl_toolkits.mplot3d.art3d.Poly3DCollection` Examples -------- .. plot:: gallery/mplot3d/trisurf3d.py .. plot:: gallery/mplot3d/trisurf3d_2.py """ had_data = self.has_data() # TODO: Support custom face colours if color is None: color = self._get_lines.get_next_color() color = np.array(mcolors.to_rgba(color)) cmap = kwargs.get('cmap', None) shade = kwargs.pop('shade', cmap is None) tri, args, kwargs = \ Triangulation.get_from_args_and_kwargs(*args, **kwargs) try: z = kwargs.pop('Z') except KeyError: # We do this so Z doesn't get passed as an arg to PolyCollection z, *args = args z = np.asarray(z) triangles = tri.get_masked_triangles() xt = tri.x[triangles] yt = tri.y[triangles] zt = z[triangles] verts = np.stack((xt, yt, zt), axis=-1) if cmap: polyc = art3d.Poly3DCollection(verts, *args, **kwargs) # average over the three points of each triangle avg_z = verts[:, :, 2].mean(axis=1) polyc.set_array(avg_z) if vmin is not None or vmax is not None: polyc.set_clim(vmin, vmax) if norm is not None: polyc.set_norm(norm) else: polyc = art3d.Poly3DCollection( verts, *args, shade=shade, lightsource=lightsource, facecolors=color, **kwargs) self.add_collection(polyc) self.auto_scale_xyz(tri.x, tri.y, z, had_data) return polyc def _3d_extend_contour(self, cset, stride=5): """ Extend a contour in 3D by creating """ dz = (cset.levels[1] - cset.levels[0]) / 2 polyverts = [] colors = [] for idx, level in enumerate(cset.levels): path = cset.get_paths()[idx] subpaths = [*path._iter_connected_components()] color = cset.get_edgecolor()[idx] top = art3d._paths_to_3d_segments(subpaths, level - dz) bot = art3d._paths_to_3d_segments(subpaths, level + dz) if not len(top[0]): continue nsteps = max(round(len(top[0]) / stride), 2) stepsize = (len(top[0]) - 1) / (nsteps - 1) polyverts.extend([ (top[0][round(i * stepsize)], top[0][round((i + 1) * stepsize)], bot[0][round((i + 1) * stepsize)], bot[0][round(i * stepsize)]) for i in range(round(nsteps) - 1)]) colors.extend([color] * (round(nsteps) - 1)) self.add_collection3d(art3d.Poly3DCollection( np.array(polyverts), # All polygons have 4 vertices, so vectorize. facecolors=colors, edgecolors=colors, shade=True)) cset.remove() def add_contour_set( self, cset, extend3d=False, stride=5, zdir='z', offset=None): zdir = '-' + zdir if extend3d: self._3d_extend_contour(cset, stride) else: art3d.collection_2d_to_3d( cset, zs=offset if offset is not None else cset.levels, zdir=zdir) def add_contourf_set(self, cset, zdir='z', offset=None): self._add_contourf_set(cset, zdir=zdir, offset=offset) def _add_contourf_set(self, cset, zdir='z', offset=None): """ Returns ------- levels : `numpy.ndarray` Levels at which the filled contours are added. """ zdir = '-' + zdir midpoints = cset.levels[:-1] + np.diff(cset.levels) / 2 # Linearly interpolate to get levels for any extensions if cset._extend_min: min_level = cset.levels[0] - np.diff(cset.levels[:2]) / 2 midpoints = np.insert(midpoints, 0, min_level) if cset._extend_max: max_level = cset.levels[-1] + np.diff(cset.levels[-2:]) / 2 midpoints = np.append(midpoints, max_level) art3d.collection_2d_to_3d( cset, zs=offset if offset is not None else midpoints, zdir=zdir) return midpoints @_preprocess_data() def contour(self, X, Y, Z, *args, extend3d=False, stride=5, zdir='z', offset=None, **kwargs): """ Create a 3D contour plot. Parameters ---------- X, Y, Z : array-like, Input data. See `.Axes.contour` for supported data shapes. extend3d : bool, default: False Whether to extend contour in 3D. stride : int, default: 5 Step size for extending contour. zdir : {'x', 'y', 'z'}, default: 'z' The direction to use. offset : float, optional If specified, plot a projection of the contour lines at this position in a plane normal to *zdir*. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER *args, **kwargs Other arguments are forwarded to `matplotlib.axes.Axes.contour`. Returns ------- matplotlib.contour.QuadContourSet """ had_data = self.has_data() jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir) cset = super().contour(jX, jY, jZ, *args, **kwargs) self.add_contour_set(cset, extend3d, stride, zdir, offset) self.auto_scale_xyz(X, Y, Z, had_data) return cset contour3D = contour @_preprocess_data() def tricontour(self, *args, extend3d=False, stride=5, zdir='z', offset=None, **kwargs): """ Create a 3D contour plot. .. note:: This method currently produces incorrect output due to a longstanding bug in 3D PolyCollection rendering. Parameters ---------- X, Y, Z : array-like Input data. See `.Axes.tricontour` for supported data shapes. extend3d : bool, default: False Whether to extend contour in 3D. stride : int, default: 5 Step size for extending contour. zdir : {'x', 'y', 'z'}, default: 'z' The direction to use. offset : float, optional If specified, plot a projection of the contour lines at this position in a plane normal to *zdir*. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER *args, **kwargs Other arguments are forwarded to `matplotlib.axes.Axes.tricontour`. Returns ------- matplotlib.tri._tricontour.TriContourSet """ had_data = self.has_data() tri, args, kwargs = Triangulation.get_from_args_and_kwargs( *args, **kwargs) X = tri.x Y = tri.y if 'Z' in kwargs: Z = kwargs.pop('Z') else: # We do this so Z doesn't get passed as an arg to Axes.tricontour Z, *args = args jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir) tri = Triangulation(jX, jY, tri.triangles, tri.mask) cset = super().tricontour(tri, jZ, *args, **kwargs) self.add_contour_set(cset, extend3d, stride, zdir, offset) self.auto_scale_xyz(X, Y, Z, had_data) return cset def _auto_scale_contourf(self, X, Y, Z, zdir, levels, had_data): # Autoscale in the zdir based on the levels added, which are # different from data range if any contour extensions are present dim_vals = {'x': X, 'y': Y, 'z': Z, zdir: levels} # Input data and levels have different sizes, but auto_scale_xyz # expected same-size input, so manually take min/max limits limits = [(np.nanmin(dim_vals[dim]), np.nanmax(dim_vals[dim])) for dim in ['x', 'y', 'z']] self.auto_scale_xyz(*limits, had_data) @_preprocess_data() def contourf(self, X, Y, Z, *args, zdir='z', offset=None, **kwargs): """ Create a 3D filled contour plot. Parameters ---------- X, Y, Z : array-like Input data. See `.Axes.contourf` for supported data shapes. zdir : {'x', 'y', 'z'}, default: 'z' The direction to use. offset : float, optional If specified, plot a projection of the contour lines at this position in a plane normal to *zdir*. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER *args, **kwargs Other arguments are forwarded to `matplotlib.axes.Axes.contourf`. Returns ------- matplotlib.contour.QuadContourSet """ had_data = self.has_data() jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir) cset = super().contourf(jX, jY, jZ, *args, **kwargs) levels = self._add_contourf_set(cset, zdir, offset) self._auto_scale_contourf(X, Y, Z, zdir, levels, had_data) return cset contourf3D = contourf @_preprocess_data() def tricontourf(self, *args, zdir='z', offset=None, **kwargs): """ Create a 3D filled contour plot. .. note:: This method currently produces incorrect output due to a longstanding bug in 3D PolyCollection rendering. Parameters ---------- X, Y, Z : array-like Input data. See `.Axes.tricontourf` for supported data shapes. zdir : {'x', 'y', 'z'}, default: 'z' The direction to use. offset : float, optional If specified, plot a projection of the contour lines at this position in a plane normal to zdir. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER *args, **kwargs Other arguments are forwarded to `matplotlib.axes.Axes.tricontourf`. Returns ------- matplotlib.tri._tricontour.TriContourSet """ had_data = self.has_data() tri, args, kwargs = Triangulation.get_from_args_and_kwargs( *args, **kwargs) X = tri.x Y = tri.y if 'Z' in kwargs: Z = kwargs.pop('Z') else: # We do this so Z doesn't get passed as an arg to Axes.tricontourf Z, *args = args jX, jY, jZ = art3d.rotate_axes(X, Y, Z, zdir) tri = Triangulation(jX, jY, tri.triangles, tri.mask) cset = super().tricontourf(tri, jZ, *args, **kwargs) levels = self._add_contourf_set(cset, zdir, offset) self._auto_scale_contourf(X, Y, Z, zdir, levels, had_data) return cset def add_collection3d(self, col, zs=0, zdir='z', autolim=True): """ 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, *zs* and *zdir*. Supported 2D collection types are: - `.PolyCollection` - `.LineCollection` - `.PatchCollection` (currently not supporting *autolim*) Parameters ---------- col : `.Collection` A 2D collection object. zs : float or array-like, default: 0 The z-positions to be used for the 2D objects. zdir : {'x', 'y', 'z'}, default: 'z' The direction to use for the z-positions. autolim : bool, default: True Whether to update the data limits. """ had_data = self.has_data() zvals = np.atleast_1d(zs) zsortval = (np.min(zvals) if zvals.size else 0) # FIXME: arbitrary default # FIXME: use issubclass() (although, then a 3D collection # object would also pass.) Maybe have a collection3d # abstract class to test for and exclude? if type(col) is mcoll.PolyCollection: art3d.poly_collection_2d_to_3d(col, zs=zs, zdir=zdir) col.set_sort_zpos(zsortval) elif type(col) is mcoll.LineCollection: art3d.line_collection_2d_to_3d(col, zs=zs, zdir=zdir) col.set_sort_zpos(zsortval) elif type(col) is mcoll.PatchCollection: art3d.patch_collection_2d_to_3d(col, zs=zs, zdir=zdir) col.set_sort_zpos(zsortval) if autolim: if isinstance(col, art3d.Line3DCollection): self.auto_scale_xyz(*np.array(col._segments3d).transpose(), had_data=had_data) elif isinstance(col, art3d.Poly3DCollection): self.auto_scale_xyz(*col._vec[:-1], had_data=had_data) elif isinstance(col, art3d.Patch3DCollection): pass # FIXME: Implement auto-scaling function for Patch3DCollection # Currently unable to do so due to issues with Patch3DCollection # See https://github.com/matplotlib/matplotlib/issues/14298 for details collection = super().add_collection(col) return collection @_preprocess_data(replace_names=["xs", "ys", "zs", "s", "edgecolors", "c", "facecolor", "facecolors", "color"]) def scatter(self, xs, ys, zs=0, zdir='z', s=20, c=None, depthshade=True, *args, **kwargs): """ Create a scatter plot. Parameters ---------- xs, ys : array-like The data positions. zs : float or array-like, default: 0 The z-positions. Either an array of the same length as *xs* and *ys* or a single value to place all points in the same plane. zdir : {'x', 'y', 'z', '-x', '-y', '-z'}, default: 'z' The axis direction for the *zs*. This is useful when plotting 2D data on a 3D Axes. The data must be passed as *xs*, *ys*. Setting *zdir* to 'y' then plots the data to the x-z-plane. See also :doc:`/gallery/mplot3d/2dcollections3d`. s : float or array-like, default: 20 The marker size in points**2. Either an array of the same length as *xs* and *ys* or a single value to make all markers the same size. c : :mpltype:`color`, sequence, or sequence of colors, optional The marker color. Possible values: - A single color format string. - A sequence of colors of length n. - A sequence of n numbers to be mapped to colors using *cmap* and *norm*. - A 2D array in which the rows are RGB or RGBA. For more details see the *c* argument of `~.axes.Axes.scatter`. depthshade : bool, default: True Whether to shade the scatter markers to give the appearance of depth. Each call to ``scatter()`` will perform its depthshading independently. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER **kwargs All other keyword arguments are passed on to `~.axes.Axes.scatter`. Returns ------- paths : `~matplotlib.collections.PathCollection` """ had_data = self.has_data() zs_orig = zs xs, ys, zs = cbook._broadcast_with_masks(xs, ys, zs) s = np.ma.ravel(s) # This doesn't have to match x, y in size. xs, ys, zs, s, c, color = cbook.delete_masked_points( xs, ys, zs, s, c, kwargs.get('color', None) ) if kwargs.get("color") is not None: kwargs['color'] = color # For xs and ys, 2D scatter() will do the copying. if np.may_share_memory(zs_orig, zs): # Avoid unnecessary copies. zs = zs.copy() patches = super().scatter(xs, ys, s=s, c=c, *args, **kwargs) art3d.patch_collection_2d_to_3d(patches, zs=zs, zdir=zdir, depthshade=depthshade) if self._zmargin < 0.05 and xs.size > 0: self.set_zmargin(0.05) self.auto_scale_xyz(xs, ys, zs, had_data) return patches scatter3D = scatter @_preprocess_data() def bar(self, left, height, zs=0, zdir='z', *args, **kwargs): """ Add 2D bar(s). Parameters ---------- left : 1D array-like The x coordinates of the left sides of the bars. height : 1D array-like The height of the bars. zs : float or 1D array-like, default: 0 Z coordinate of bars; if a single value is specified, it will be used for all bars. zdir : {'x', 'y', 'z'}, default: 'z' When plotting 2D data, the direction to use as z ('x', 'y' or 'z'). data : indexable object, optional DATA_PARAMETER_PLACEHOLDER **kwargs Other keyword arguments are forwarded to `matplotlib.axes.Axes.bar`. Returns ------- mpl_toolkits.mplot3d.art3d.Patch3DCollection """ had_data = self.has_data() patches = super().bar(left, height, *args, **kwargs) zs = np.broadcast_to(zs, len(left), subok=True) verts = [] verts_zs = [] for p, z in zip(patches, zs): vs = art3d._get_patch_verts(p) verts += vs.tolist() verts_zs += [z] * len(vs) art3d.patch_2d_to_3d(p, z, zdir) if 'alpha' in kwargs: p.set_alpha(kwargs['alpha']) if len(verts) > 0: # the following has to be skipped if verts is empty # NOTE: Bugs could still occur if len(verts) > 0, # but the "2nd dimension" is empty. xs, ys = zip(*verts) else: xs, ys = [], [] xs, ys, verts_zs = art3d.juggle_axes(xs, ys, verts_zs, zdir) self.auto_scale_xyz(xs, ys, verts_zs, had_data) return patches @_preprocess_data() def bar3d(self, x, y, z, dx, dy, dz, color=None, zsort='average', shade=True, lightsource=None, *args, **kwargs): """ Generate a 3D barplot. This method creates three-dimensional barplot where the width, depth, height, and color of the bars can all be uniquely set. Parameters ---------- x, y, z : array-like The coordinates of the anchor point of the bars. dx, dy, dz : float or array-like The width, depth, and height of the bars, respectively. color : sequence of colors, optional The color of the bars can be specified globally or individually. This parameter can be: - A single color, to color all bars the same color. - An array of colors of length N bars, to color each bar independently. - An array of colors of length 6, to color the faces of the bars similarly. - An array of colors of length 6 * N bars, to color each face independently. When coloring the faces of the boxes specifically, this is the order of the coloring: 1. -Z (bottom of box) 2. +Z (top of box) 3. -Y 4. +Y 5. -X 6. +X zsort : {'average', 'min', 'max'}, default: 'average' The z-axis sorting scheme passed onto `~.art3d.Poly3DCollection` shade : bool, default: True When true, this shades the dark sides of the bars (relative to the plot's source of light). lightsource : `~matplotlib.colors.LightSource`, optional The lightsource to use when *shade* is True. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER **kwargs Any additional keyword arguments are passed onto `~.art3d.Poly3DCollection`. Returns ------- collection : `~.art3d.Poly3DCollection` A collection of three-dimensional polygons representing the bars. """ had_data = self.has_data() x, y, z, dx, dy, dz = np.broadcast_arrays( np.atleast_1d(x), y, z, dx, dy, dz) minx = np.min(x) maxx = np.max(x + dx) miny = np.min(y) maxy = np.max(y + dy) minz = np.min(z) maxz = np.max(z + dz) # shape (6, 4, 3) # All faces are oriented facing outwards - when viewed from the # outside, their vertices are in a counterclockwise ordering. cuboid = np.array([ # -z ( (0, 0, 0), (0, 1, 0), (1, 1, 0), (1, 0, 0), ), # +z ( (0, 0, 1), (1, 0, 1), (1, 1, 1), (0, 1, 1), ), # -y ( (0, 0, 0), (1, 0, 0), (1, 0, 1), (0, 0, 1), ), # +y ( (0, 1, 0), (0, 1, 1), (1, 1, 1), (1, 1, 0), ), # -x ( (0, 0, 0), (0, 0, 1), (0, 1, 1), (0, 1, 0), ), # +x ( (1, 0, 0), (1, 1, 0), (1, 1, 1), (1, 0, 1), ), ]) # indexed by [bar, face, vertex, coord] polys = np.empty(x.shape + cuboid.shape) # handle each coordinate separately for i, p, dp in [(0, x, dx), (1, y, dy), (2, z, dz)]: p = p[..., np.newaxis, np.newaxis] dp = dp[..., np.newaxis, np.newaxis] polys[..., i] = p + dp * cuboid[..., i] # collapse the first two axes polys = polys.reshape((-1,) + polys.shape[2:]) facecolors = [] if color is None: color = [self._get_patches_for_fill.get_next_color()] color = list(mcolors.to_rgba_array(color)) if len(color) == len(x): # bar colors specified, need to expand to number of faces for c in color: facecolors.extend([c] * 6) else: # a single color specified, or face colors specified explicitly facecolors = color if len(facecolors) < len(x): facecolors *= (6 * len(x)) col = art3d.Poly3DCollection(polys, zsort=zsort, facecolors=facecolors, shade=shade, lightsource=lightsource, *args, **kwargs) self.add_collection(col) self.auto_scale_xyz((minx, maxx), (miny, maxy), (minz, maxz), had_data) return col def set_title(self, label, fontdict=None, loc='center', **kwargs): # docstring inherited ret = super().set_title(label, fontdict=fontdict, loc=loc, **kwargs) (x, y) = self.title.get_position() self.title.set_y(0.92 * y) return ret @_preprocess_data() def quiver(self, X, Y, Z, U, V, W, *, length=1, arrow_length_ratio=.3, pivot='tail', normalize=False, **kwargs): """ Plot a 3D field of arrows. The arguments can be array-like or scalars, so long as they can be broadcast together. The arguments can also be masked arrays. If an element in any of argument is masked, then that corresponding quiver element will not be plotted. Parameters ---------- X, Y, Z : array-like The x, y and z coordinates of the arrow locations (default is tail of arrow; see *pivot* kwarg). U, V, W : array-like The x, y and z components of the arrow vectors. length : float, default: 1 The length of each quiver. arrow_length_ratio : float, default: 0.3 The ratio of the arrow head with respect to the quiver. pivot : {'tail', 'middle', 'tip'}, default: 'tail' The part of the arrow that is at the grid point; the arrow rotates about this point, hence the name *pivot*. normalize : bool, default: False Whether all arrows are normalized to have the same length, or keep the lengths defined by *u*, *v*, and *w*. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER **kwargs Any additional keyword arguments are delegated to :class:`.Line3DCollection` """ def calc_arrows(UVW): # get unit direction vector perpendicular to (u, v, w) x = UVW[:, 0] y = UVW[:, 1] norm = np.linalg.norm(UVW[:, :2], axis=1) x_p = np.divide(y, norm, where=norm != 0, out=np.zeros_like(x)) y_p = np.divide(-x, norm, where=norm != 0, out=np.ones_like(x)) # compute the two arrowhead direction unit vectors rangle = math.radians(15) c = math.cos(rangle) s = math.sin(rangle) # construct the rotation matrices of shape (3, 3, n) r13 = y_p * s r32 = x_p * s r12 = x_p * y_p * (1 - c) Rpos = np.array( [[c + (x_p ** 2) * (1 - c), r12, r13], [r12, c + (y_p ** 2) * (1 - c), -r32], [-r13, r32, np.full_like(x_p, c)]]) # opposite rotation negates all the sin terms Rneg = Rpos.copy() Rneg[[0, 1, 2, 2], [2, 2, 0, 1]] *= -1 # Batch n (3, 3) x (3) matrix multiplications ((3, 3, n) x (n, 3)). Rpos_vecs = np.einsum("ij...,...j->...i", Rpos, UVW) Rneg_vecs = np.einsum("ij...,...j->...i", Rneg, UVW) # Stack into (n, 2, 3) result. return np.stack([Rpos_vecs, Rneg_vecs], axis=1) had_data = self.has_data() input_args = cbook._broadcast_with_masks(X, Y, Z, U, V, W, compress=True) if any(len(v) == 0 for v in input_args): # No quivers, so just make an empty collection and return early linec = art3d.Line3DCollection([], **kwargs) self.add_collection(linec) return linec shaft_dt = np.array([0., length], dtype=float) arrow_dt = shaft_dt * arrow_length_ratio _api.check_in_list(['tail', 'middle', 'tip'], pivot=pivot) if pivot == 'tail': shaft_dt -= length elif pivot == 'middle': shaft_dt -= length / 2 XYZ = np.column_stack(input_args[:3]) UVW = np.column_stack(input_args[3:]).astype(float) # Normalize rows of UVW if normalize: norm = np.linalg.norm(UVW, axis=1) norm[norm == 0] = 1 UVW = UVW / norm.reshape((-1, 1)) if len(XYZ) > 0: # compute the shaft lines all at once with an outer product shafts = (XYZ - np.multiply.outer(shaft_dt, UVW)).swapaxes(0, 1) # compute head direction vectors, n heads x 2 sides x 3 dimensions head_dirs = calc_arrows(UVW) # compute all head lines at once, starting from the shaft ends heads = shafts[:, :1] - np.multiply.outer(arrow_dt, head_dirs) # stack left and right head lines together heads = heads.reshape((len(arrow_dt), -1, 3)) # transpose to get a list of lines heads = heads.swapaxes(0, 1) lines = [*shafts, *heads[::2], *heads[1::2]] else: lines = [] linec = art3d.Line3DCollection(lines, **kwargs) self.add_collection(linec) self.auto_scale_xyz(XYZ[:, 0], XYZ[:, 1], XYZ[:, 2], had_data) return linec quiver3D = quiver def voxels(self, *args, facecolors=None, edgecolors=None, shade=True, lightsource=None, **kwargs): """ ax.voxels([x, y, z,] /, filled, facecolors=None, edgecolors=None, \ **kwargs) Plot a set of filled voxels All voxels are plotted as 1x1x1 cubes on the axis, with ``filled[0, 0, 0]`` placed with its lower corner at the origin. Occluded faces are not plotted. Parameters ---------- filled : 3D np.array of bool A 3D array of values, with truthy values indicating which voxels to fill x, y, z : 3D np.array, optional The coordinates of the corners of the voxels. This should broadcast to a shape one larger in every dimension than the shape of *filled*. These can be used to plot non-cubic voxels. If not specified, defaults to increasing integers along each axis, like those returned by :func:`~numpy.indices`. As indicated by the ``/`` in the function signature, these arguments can only be passed positionally. facecolors, edgecolors : array-like, optional The color to draw the faces and edges of the voxels. Can only be passed as keyword arguments. These parameters can be: - A single color value, to color all voxels the same color. This can be either a string, or a 1D RGB/RGBA array - ``None``, the default, to use a single color for the faces, and the style default for the edges. - A 3D `~numpy.ndarray` of color names, with each item the color for the corresponding voxel. The size must match the voxels. - A 4D `~numpy.ndarray` of RGB/RGBA data, with the components along the last axis. shade : bool, default: True Whether to shade the facecolors. lightsource : `~matplotlib.colors.LightSource`, optional The lightsource to use when *shade* is True. **kwargs Additional keyword arguments to pass onto `~mpl_toolkits.mplot3d.art3d.Poly3DCollection`. Returns ------- faces : dict A dictionary indexed by coordinate, where ``faces[i, j, k]`` is a `.Poly3DCollection` of the faces drawn for the voxel ``filled[i, j, k]``. If no faces were drawn for a given voxel, either because it was not asked to be drawn, or it is fully occluded, then ``(i, j, k) not in faces``. Examples -------- .. plot:: gallery/mplot3d/voxels.py .. plot:: gallery/mplot3d/voxels_rgb.py .. plot:: gallery/mplot3d/voxels_torus.py .. plot:: gallery/mplot3d/voxels_numpy_logo.py """ # work out which signature we should be using, and use it to parse # the arguments. Name must be voxels for the correct error message if len(args) >= 3: # underscores indicate position only def voxels(__x, __y, __z, filled, **kwargs): return (__x, __y, __z), filled, kwargs else: def voxels(filled, **kwargs): return None, filled, kwargs xyz, filled, kwargs = voxels(*args, **kwargs) # check dimensions if filled.ndim != 3: raise ValueError("Argument filled must be 3-dimensional") size = np.array(filled.shape, dtype=np.intp) # check xyz coordinates, which are one larger than the filled shape coord_shape = tuple(size + 1) if xyz is None: x, y, z = np.indices(coord_shape) else: x, y, z = (np.broadcast_to(c, coord_shape) for c in xyz) def _broadcast_color_arg(color, name): if np.ndim(color) in (0, 1): # single color, like "red" or [1, 0, 0] return np.broadcast_to(color, filled.shape + np.shape(color)) elif np.ndim(color) in (3, 4): # 3D array of strings, or 4D array with last axis rgb if np.shape(color)[:3] != filled.shape: raise ValueError( f"When multidimensional, {name} must match the shape " "of filled") return color else: raise ValueError(f"Invalid {name} argument") # broadcast and default on facecolors if facecolors is None: facecolors = self._get_patches_for_fill.get_next_color() facecolors = _broadcast_color_arg(facecolors, 'facecolors') # broadcast but no default on edgecolors edgecolors = _broadcast_color_arg(edgecolors, 'edgecolors') # scale to the full array, even if the data is only in the center self.auto_scale_xyz(x, y, z) # points lying on corners of a square square = np.array([ [0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], ], dtype=np.intp) voxel_faces = defaultdict(list) def permutation_matrices(n): """Generate cyclic permutation matrices.""" mat = np.eye(n, dtype=np.intp) for i in range(n): yield mat mat = np.roll(mat, 1, axis=0) # iterate over each of the YZ, ZX, and XY orientations, finding faces # to render for permute in permutation_matrices(3): # find the set of ranges to iterate over pc, qc, rc = permute.T.dot(size) pinds = np.arange(pc) qinds = np.arange(qc) rinds = np.arange(rc) square_rot_pos = square.dot(permute.T) square_rot_neg = square_rot_pos[::-1] # iterate within the current plane for p in pinds: for q in qinds: # iterate perpendicularly to the current plane, handling # boundaries. We only draw faces between a voxel and an # empty space, to avoid drawing internal faces. # draw lower faces p0 = permute.dot([p, q, 0]) i0 = tuple(p0) if filled[i0]: voxel_faces[i0].append(p0 + square_rot_neg) # draw middle faces for r1, r2 in zip(rinds[:-1], rinds[1:]): p1 = permute.dot([p, q, r1]) p2 = permute.dot([p, q, r2]) i1 = tuple(p1) i2 = tuple(p2) if filled[i1] and not filled[i2]: voxel_faces[i1].append(p2 + square_rot_pos) elif not filled[i1] and filled[i2]: voxel_faces[i2].append(p2 + square_rot_neg) # draw upper faces pk = permute.dot([p, q, rc-1]) pk2 = permute.dot([p, q, rc]) ik = tuple(pk) if filled[ik]: voxel_faces[ik].append(pk2 + square_rot_pos) # iterate over the faces, and generate a Poly3DCollection for each # voxel polygons = {} for coord, faces_inds in voxel_faces.items(): # convert indices into 3D positions if xyz is None: faces = faces_inds else: faces = [] for face_inds in faces_inds: ind = face_inds[:, 0], face_inds[:, 1], face_inds[:, 2] face = np.empty(face_inds.shape) face[:, 0] = x[ind] face[:, 1] = y[ind] face[:, 2] = z[ind] faces.append(face) # shade the faces facecolor = facecolors[coord] edgecolor = edgecolors[coord] poly = art3d.Poly3DCollection( faces, facecolors=facecolor, edgecolors=edgecolor, shade=shade, lightsource=lightsource, **kwargs) self.add_collection3d(poly) polygons[coord] = poly return polygons @_preprocess_data(replace_names=["x", "y", "z", "xerr", "yerr", "zerr"]) def errorbar(self, x, y, z, zerr=None, yerr=None, xerr=None, fmt='', barsabove=False, errorevery=1, ecolor=None, elinewidth=None, capsize=None, capthick=None, xlolims=False, xuplims=False, ylolims=False, yuplims=False, zlolims=False, zuplims=False, **kwargs): """ Plot lines and/or markers with errorbars around them. *x*/*y*/*z* define the data locations, and *xerr*/*yerr*/*zerr* define the errorbar sizes. By default, this draws the data markers/lines as well the errorbars. Use fmt='none' to draw errorbars only. Parameters ---------- x, y, z : float or array-like The data positions. xerr, yerr, zerr : float or array-like, shape (N,) or (2, N), optional The errorbar sizes: - scalar: Symmetric +/- values for all data points. - shape(N,): Symmetric +/-values for each data point. - shape(2, N): Separate - and + values for each bar. First row contains the lower errors, the second row contains the upper errors. - *None*: No errorbar. Note that all error arrays should have *positive* values. fmt : str, default: '' The format for the data points / data lines. See `.plot` for details. Use 'none' (case-insensitive) to plot errorbars without any data markers. ecolor : :mpltype:`color`, default: None The color of the errorbar lines. If None, use the color of the line connecting the markers. elinewidth : float, default: None The linewidth of the errorbar lines. If None, the linewidth of the current style is used. capsize : float, default: :rc:`errorbar.capsize` The length of the error bar caps in points. capthick : float, default: None An alias to the keyword argument *markeredgewidth* (a.k.a. *mew*). This setting is a more sensible name for the property that controls the thickness of the error bar cap in points. For backwards compatibility, if *mew* or *markeredgewidth* are given, then they will over-ride *capthick*. This may change in future releases. barsabove : bool, default: False If True, will plot the errorbars above the plot symbols. Default is below. xlolims, ylolims, zlolims : bool, default: False These arguments can be used to indicate that a value gives only lower limits. In that case a caret symbol is used to indicate this. *lims*-arguments may be scalars, or array-likes of the same length as the errors. To use limits with inverted axes, `~.set_xlim`, `~.set_ylim`, or `~.set_zlim` must be called before `errorbar`. Note the tricky parameter names: setting e.g. *ylolims* to True means that the y-value is a *lower* limit of the True value, so, only an *upward*-pointing arrow will be drawn! xuplims, yuplims, zuplims : bool, default: False Same as above, but for controlling the upper limits. errorevery : int or (int, int), default: 1 draws error bars on a subset of the data. *errorevery* =N draws error bars on the points (x[::N], y[::N], z[::N]). *errorevery* =(start, N) draws error bars on the points (x[start::N], y[start::N], z[start::N]). e.g. *errorevery* =(6, 3) adds error bars to the data at (x[6], x[9], x[12], x[15], ...). Used to avoid overlapping error bars when two series share x-axis values. Returns ------- errlines : list List of `~mpl_toolkits.mplot3d.art3d.Line3DCollection` instances each containing an errorbar line. caplines : list List of `~mpl_toolkits.mplot3d.art3d.Line3D` instances each containing a capline object. limmarks : list List of `~mpl_toolkits.mplot3d.art3d.Line3D` instances each containing a marker with an upper or lower limit. Other Parameters ---------------- data : indexable object, optional DATA_PARAMETER_PLACEHOLDER **kwargs All other keyword arguments for styling errorbar lines are passed `~mpl_toolkits.mplot3d.art3d.Line3DCollection`. Examples -------- .. plot:: gallery/mplot3d/errorbar3d.py """ had_data = self.has_data() kwargs = cbook.normalize_kwargs(kwargs, mlines.Line2D) # Drop anything that comes in as None to use the default instead. kwargs = {k: v for k, v in kwargs.items() if v is not None} kwargs.setdefault('zorder', 2) self._process_unit_info([("x", x), ("y", y), ("z", z)], kwargs, convert=False) # make sure all the args are iterable; use lists not arrays to # preserve units x = x if np.iterable(x) else [x] y = y if np.iterable(y) else [y] z = z if np.iterable(z) else [z] if not len(x) == len(y) == len(z): raise ValueError("'x', 'y', and 'z' must have the same size") everymask = self._errorevery_to_mask(x, errorevery) label = kwargs.pop("label", None) kwargs['label'] = '_nolegend_' # Create the main line and determine overall kwargs for child artists. # We avoid calling self.plot() directly, or self._get_lines(), because # that would call self._process_unit_info again, and do other indirect # data processing. (data_line, base_style), = self._get_lines._plot_args( self, (x, y) if fmt == '' else (x, y, fmt), kwargs, return_kwargs=True) art3d.line_2d_to_3d(data_line, zs=z) # Do this after creating `data_line` to avoid modifying `base_style`. if barsabove: data_line.set_zorder(kwargs['zorder'] - .1) else: data_line.set_zorder(kwargs['zorder'] + .1) # Add line to plot, or throw it away and use it to determine kwargs. if fmt.lower() != 'none': self.add_line(data_line) else: data_line = None # Remove alpha=0 color that _process_plot_format returns. base_style.pop('color') if 'color' not in base_style: base_style['color'] = 'C0' if ecolor is None: ecolor = base_style['color'] # Eject any line-specific information from format string, as it's not # needed for bars or caps. for key in ['marker', 'markersize', 'markerfacecolor', 'markeredgewidth', 'markeredgecolor', 'markevery', 'linestyle', 'fillstyle', 'drawstyle', 'dash_capstyle', 'dash_joinstyle', 'solid_capstyle', 'solid_joinstyle']: base_style.pop(key, None) # Make the style dict for the line collections (the bars). eb_lines_style = {**base_style, 'color': ecolor} if elinewidth: eb_lines_style['linewidth'] = elinewidth elif 'linewidth' in kwargs: eb_lines_style['linewidth'] = kwargs['linewidth'] for key in ('transform', 'alpha', 'zorder', 'rasterized'): if key in kwargs: eb_lines_style[key] = kwargs[key] # Make the style dict for caps (the "hats"). eb_cap_style = {**base_style, 'linestyle': 'None'} if capsize is None: capsize = mpl.rcParams["errorbar.capsize"] if capsize > 0: eb_cap_style['markersize'] = 2. * capsize if capthick is not None: eb_cap_style['markeredgewidth'] = capthick eb_cap_style['color'] = ecolor def _apply_mask(arrays, mask): # Return, for each array in *arrays*, the elements for which *mask* # is True, without using fancy indexing. return [[*itertools.compress(array, mask)] for array in arrays] def _extract_errs(err, data, lomask, himask): # For separate +/- error values we need to unpack err if len(err.shape) == 2: low_err, high_err = err else: low_err, high_err = err, err lows = np.where(lomask | ~everymask, data, data - low_err) highs = np.where(himask | ~everymask, data, data + high_err) return lows, highs # collect drawn items while looping over the three coordinates errlines, caplines, limmarks = [], [], [] # list of endpoint coordinates, used for auto-scaling coorderrs = [] # define the markers used for errorbar caps and limits below # the dictionary key is mapped by the `i_xyz` helper dictionary capmarker = {0: '|', 1: '|', 2: '_'} i_xyz = {'x': 0, 'y': 1, 'z': 2} # Calculate marker size from points to quiver length. Because these are # not markers, and 3D Axes do not use the normal transform stack, this # is a bit involved. Since the quiver arrows will change size as the # scene is rotated, they are given a standard size based on viewing # them directly in planar form. quiversize = eb_cap_style.get('markersize', mpl.rcParams['lines.markersize']) ** 2 quiversize *= self.figure.dpi / 72 quiversize = self.transAxes.inverted().transform([ (0, 0), (quiversize, quiversize)]) quiversize = np.mean(np.diff(quiversize, axis=0)) # quiversize is now in Axes coordinates, and to convert back to data # coordinates, we need to run it through the inverse 3D transform. For # consistency, this uses a fixed elevation, azimuth, and roll. with cbook._setattr_cm(self, elev=0, azim=0, roll=0): invM = np.linalg.inv(self.get_proj()) # elev=azim=roll=0 produces the Y-Z plane, so quiversize in 2D 'x' is # 'y' in 3D, hence the 1 index. quiversize = np.dot(invM, [quiversize, 0, 0, 0])[1] # Quivers use a fixed 15-degree arrow head, so scale up the length so # that the size corresponds to the base. In other words, this constant # corresponds to the equation tan(15) = (base / 2) / (arrow length). quiversize *= 1.8660254037844388 eb_quiver_style = {**eb_cap_style, 'length': quiversize, 'arrow_length_ratio': 1} eb_quiver_style.pop('markersize', None) # loop over x-, y-, and z-direction and draw relevant elements for zdir, data, err, lolims, uplims in zip( ['x', 'y', 'z'], [x, y, z], [xerr, yerr, zerr], [xlolims, ylolims, zlolims], [xuplims, yuplims, zuplims]): dir_vector = art3d.get_dir_vector(zdir) i_zdir = i_xyz[zdir] if err is None: continue if not np.iterable(err): err = [err] * len(data) err = np.atleast_1d(err) # arrays fine here, they are booleans and hence not units lolims = np.broadcast_to(lolims, len(data)).astype(bool) uplims = np.broadcast_to(uplims, len(data)).astype(bool) # a nested list structure that expands to (xl,xh),(yl,yh),(zl,zh), # where x/y/z and l/h correspond to dimensions and low/high # positions of errorbars in a dimension we're looping over coorderr = [ _extract_errs(err * dir_vector[i], coord, lolims, uplims) for i, coord in enumerate([x, y, z])] (xl, xh), (yl, yh), (zl, zh) = coorderr # draws capmarkers - flat caps orthogonal to the error bars nolims = ~(lolims | uplims) if nolims.any() and capsize > 0: lo_caps_xyz = _apply_mask([xl, yl, zl], nolims & everymask) hi_caps_xyz = _apply_mask([xh, yh, zh], nolims & everymask) # setting '_' for z-caps and '|' for x- and y-caps; # these markers will rotate as the viewing angle changes cap_lo = art3d.Line3D(*lo_caps_xyz, ls='', marker=capmarker[i_zdir], **eb_cap_style) cap_hi = art3d.Line3D(*hi_caps_xyz, ls='', marker=capmarker[i_zdir], **eb_cap_style) self.add_line(cap_lo) self.add_line(cap_hi) caplines.append(cap_lo) caplines.append(cap_hi) if lolims.any(): xh0, yh0, zh0 = _apply_mask([xh, yh, zh], lolims & everymask) self.quiver(xh0, yh0, zh0, *dir_vector, **eb_quiver_style) if uplims.any(): xl0, yl0, zl0 = _apply_mask([xl, yl, zl], uplims & everymask) self.quiver(xl0, yl0, zl0, *-dir_vector, **eb_quiver_style) errline = art3d.Line3DCollection(np.array(coorderr).T, **eb_lines_style) self.add_collection(errline) errlines.append(errline) coorderrs.append(coorderr) coorderrs = np.array(coorderrs) def _digout_minmax(err_arr, coord_label): return (np.nanmin(err_arr[:, i_xyz[coord_label], :, :]), np.nanmax(err_arr[:, i_xyz[coord_label], :, :])) minx, maxx = _digout_minmax(coorderrs, 'x') miny, maxy = _digout_minmax(coorderrs, 'y') minz, maxz = _digout_minmax(coorderrs, 'z') self.auto_scale_xyz((minx, maxx), (miny, maxy), (minz, maxz), had_data) # Adapting errorbar containers for 3d case, assuming z-axis points "up" errorbar_container = mcontainer.ErrorbarContainer( (data_line, tuple(caplines), tuple(errlines)), has_xerr=(xerr is not None or yerr is not None), has_yerr=(zerr is not None), label=label) self.containers.append(errorbar_container) return errlines, caplines, limmarks @_api.make_keyword_only("3.8", "call_axes_locator") def get_tightbbox(self, renderer=None, call_axes_locator=True, bbox_extra_artists=None, *, for_layout_only=False): ret = super().get_tightbbox(renderer, call_axes_locator=call_axes_locator, bbox_extra_artists=bbox_extra_artists, for_layout_only=for_layout_only) batch = [ret] if self._axis3don: for axis in self._axis_map.values(): if axis.get_visible(): axis_bb = martist._get_tightbbox_for_layout_only( axis, renderer) if axis_bb: batch.append(axis_bb) return mtransforms.Bbox.union(batch) @_preprocess_data() def stem(self, x, y, z, *, linefmt='C0-', markerfmt='C0o', basefmt='C3-', bottom=0, label=None, orientation='z'): """ Create a 3D stem plot. A stem plot draws lines perpendicular to a baseline, and places markers at the heads. By default, the baseline is defined by *x* and *y*, and stems are drawn vertically from *bottom* to *z*. Parameters ---------- x, y, z : array-like The positions of the heads of the stems. The stems are drawn along the *orientation*-direction from the baseline at *bottom* (in the *orientation*-coordinate) to the heads. By default, the *x* and *y* positions are used for the baseline and *z* for the head position, but this can be changed by *orientation*. linefmt : str, default: 'C0-' A string defining the properties of the vertical lines. Usually, this will be a color or a color and a linestyle: ========= ============= Character Line Style ========= ============= ``'-'`` solid line ``'--'`` dashed line ``'-.'`` dash-dot line ``':'`` dotted line ========= ============= Note: While it is technically possible to specify valid formats other than color or color and linestyle (e.g. 'rx' or '-.'), this is beyond the intention of the method and will most likely not result in a reasonable plot. markerfmt : str, default: 'C0o' A string defining the properties of the markers at the stem heads. basefmt : str, default: 'C3-' A format string defining the properties of the baseline. bottom : float, default: 0 The position of the baseline, in *orientation*-coordinates. label : str, optional The label to use for the stems in legends. orientation : {'x', 'y', 'z'}, default: 'z' The direction along which stems are drawn. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER Returns ------- `.StemContainer` The container may be treated like a tuple (*markerline*, *stemlines*, *baseline*) Examples -------- .. plot:: gallery/mplot3d/stem3d_demo.py """ from matplotlib.container import StemContainer had_data = self.has_data() _api.check_in_list(['x', 'y', 'z'], orientation=orientation) xlim = (np.min(x), np.max(x)) ylim = (np.min(y), np.max(y)) zlim = (np.min(z), np.max(z)) # Determine the appropriate plane for the baseline and the direction of # stemlines based on the value of orientation. if orientation == 'x': basex, basexlim = y, ylim basey, baseylim = z, zlim lines = [[(bottom, thisy, thisz), (thisx, thisy, thisz)] for thisx, thisy, thisz in zip(x, y, z)] elif orientation == 'y': basex, basexlim = x, xlim basey, baseylim = z, zlim lines = [[(thisx, bottom, thisz), (thisx, thisy, thisz)] for thisx, thisy, thisz in zip(x, y, z)] else: basex, basexlim = x, xlim basey, baseylim = y, ylim lines = [[(thisx, thisy, bottom), (thisx, thisy, thisz)] for thisx, thisy, thisz in zip(x, y, z)] # Determine style for stem lines. linestyle, linemarker, linecolor = _process_plot_format(linefmt) if linestyle is None: linestyle = mpl.rcParams['lines.linestyle'] # Plot everything in required order. baseline, = self.plot(basex, basey, basefmt, zs=bottom, zdir=orientation, label='_nolegend_') stemlines = art3d.Line3DCollection( lines, linestyles=linestyle, colors=linecolor, label='_nolegend_') self.add_collection(stemlines) markerline, = self.plot(x, y, z, markerfmt, label='_nolegend_') stem_container = StemContainer((markerline, stemlines, baseline), label=label) self.add_container(stem_container) jx, jy, jz = art3d.juggle_axes(basexlim, baseylim, [bottom, bottom], orientation) self.auto_scale_xyz([*jx, *xlim], [*jy, *ylim], [*jz, *zlim], had_data) return stem_container stem3D = stem def get_test_data(delta=0.05): """Return a tuple X, Y, Z with a test data set.""" x = y = np.arange(-3.0, 3.0, delta) X, Y = np.meshgrid(x, y) Z1 = np.exp(-(X**2 + Y**2) / 2) / (2 * np.pi) Z2 = (np.exp(-(((X - 1) / 1.5)**2 + ((Y - 1) / 0.5)**2) / 2) / (2 * np.pi * 0.5 * 1.5)) Z = Z2 - Z1 X = X * 10 Y = Y * 10 Z = Z * 500 return X, Y, Z