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1428 lines
49 KiB
Python
1428 lines
49 KiB
Python
# art3d.py, original mplot3d version by John Porter
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# Parts rewritten by Reinier Heeres <reinier@heeres.eu>
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# Minor additions by Ben Axelrod <baxelrod@coroware.com>
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"""
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Module containing 3D artist code and functions to convert 2D
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artists into 3D versions which can be added to an Axes3D.
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"""
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import math
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import numpy as np
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from contextlib import contextmanager
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from matplotlib import (
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_api, artist, cbook, colors as mcolors, lines, text as mtext,
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path as mpath)
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from matplotlib.collections import (
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Collection, LineCollection, PolyCollection, PatchCollection, PathCollection)
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from matplotlib.colors import Normalize
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from matplotlib.patches import Patch
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from . import proj3d
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def _norm_angle(a):
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"""Return the given angle normalized to -180 < *a* <= 180 degrees."""
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a = (a + 360) % 360
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if a > 180:
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a = a - 360
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return a
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def _norm_text_angle(a):
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"""Return the given angle normalized to -90 < *a* <= 90 degrees."""
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a = (a + 180) % 180
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if a > 90:
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a = a - 180
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return a
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def get_dir_vector(zdir):
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"""
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Return a direction vector.
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Parameters
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----------
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zdir : {'x', 'y', 'z', None, 3-tuple}
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The direction. Possible values are:
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- 'x': equivalent to (1, 0, 0)
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- 'y': equivalent to (0, 1, 0)
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- 'z': equivalent to (0, 0, 1)
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- *None*: equivalent to (0, 0, 0)
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- an iterable (x, y, z) is converted to an array
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Returns
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-------
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x, y, z : array
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The direction vector.
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"""
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if zdir == 'x':
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return np.array((1, 0, 0))
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elif zdir == 'y':
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return np.array((0, 1, 0))
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elif zdir == 'z':
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return np.array((0, 0, 1))
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elif zdir is None:
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return np.array((0, 0, 0))
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elif np.iterable(zdir) and len(zdir) == 3:
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return np.array(zdir)
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else:
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raise ValueError("'x', 'y', 'z', None or vector of length 3 expected")
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def _viewlim_mask(xs, ys, zs, axes):
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"""
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Return original points with points outside the axes view limits masked.
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Parameters
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----------
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xs, ys, zs : array-like
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The points to mask.
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axes : Axes3D
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The axes to use for the view limits.
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Returns
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-------
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xs_masked, ys_masked, zs_masked : np.ma.array
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The masked points.
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"""
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mask = np.logical_or.reduce((xs < axes.xy_viewLim.xmin,
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xs > axes.xy_viewLim.xmax,
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ys < axes.xy_viewLim.ymin,
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ys > axes.xy_viewLim.ymax,
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zs < axes.zz_viewLim.xmin,
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zs > axes.zz_viewLim.xmax))
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xs_masked = np.ma.array(xs, mask=mask)
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ys_masked = np.ma.array(ys, mask=mask)
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zs_masked = np.ma.array(zs, mask=mask)
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return xs_masked, ys_masked, zs_masked
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class Text3D(mtext.Text):
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"""
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Text object with 3D position and direction.
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Parameters
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----------
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x, y, z : float
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The position of the text.
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text : str
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The text string to display.
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zdir : {'x', 'y', 'z', None, 3-tuple}
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The direction of the text. See `.get_dir_vector` for a description of
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the values.
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axlim_clip : bool, default: False
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Whether to hide text outside the axes view limits.
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Other Parameters
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----------------
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**kwargs
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All other parameters are passed on to `~matplotlib.text.Text`.
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"""
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def __init__(self, x=0, y=0, z=0, text='', zdir='z', axlim_clip=False,
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**kwargs):
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mtext.Text.__init__(self, x, y, text, **kwargs)
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self.set_3d_properties(z, zdir, axlim_clip)
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def get_position_3d(self):
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"""Return the (x, y, z) position of the text."""
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return self._x, self._y, self._z
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def set_position_3d(self, xyz, zdir=None):
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"""
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Set the (*x*, *y*, *z*) position of the text.
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Parameters
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----------
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xyz : (float, float, float)
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The position in 3D space.
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zdir : {'x', 'y', 'z', None, 3-tuple}
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The direction of the text. If unspecified, the *zdir* will not be
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changed. See `.get_dir_vector` for a description of the values.
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"""
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super().set_position(xyz[:2])
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self.set_z(xyz[2])
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if zdir is not None:
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self._dir_vec = get_dir_vector(zdir)
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def set_z(self, z):
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"""
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Set the *z* position of the text.
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Parameters
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----------
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z : float
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"""
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self._z = z
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self.stale = True
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def set_3d_properties(self, z=0, zdir='z', axlim_clip=False):
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"""
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Set the *z* position and direction of the text.
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Parameters
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----------
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z : float
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The z-position in 3D space.
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zdir : {'x', 'y', 'z', 3-tuple}
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The direction of the text. Default: 'z'.
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See `.get_dir_vector` for a description of the values.
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axlim_clip : bool, default: False
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Whether to hide text outside the axes view limits.
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"""
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self._z = z
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self._dir_vec = get_dir_vector(zdir)
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self._axlim_clip = axlim_clip
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self.stale = True
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@artist.allow_rasterization
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def draw(self, renderer):
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if self._axlim_clip:
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xs, ys, zs = _viewlim_mask(self._x, self._y, self._z, self.axes)
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position3d = np.ma.row_stack((xs, ys, zs)).ravel().filled(np.nan)
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else:
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xs, ys, zs = self._x, self._y, self._z
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position3d = np.asanyarray([xs, ys, zs])
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proj = proj3d._proj_trans_points(
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[position3d, position3d + self._dir_vec], self.axes.M)
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dx = proj[0][1] - proj[0][0]
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dy = proj[1][1] - proj[1][0]
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angle = math.degrees(math.atan2(dy, dx))
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with cbook._setattr_cm(self, _x=proj[0][0], _y=proj[1][0],
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_rotation=_norm_text_angle(angle)):
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mtext.Text.draw(self, renderer)
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self.stale = False
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def get_tightbbox(self, renderer=None):
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# Overwriting the 2d Text behavior which is not valid for 3d.
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# For now, just return None to exclude from layout calculation.
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return None
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def text_2d_to_3d(obj, z=0, zdir='z', axlim_clip=False):
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"""
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Convert a `.Text` to a `.Text3D` object.
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Parameters
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----------
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z : float
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The z-position in 3D space.
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zdir : {'x', 'y', 'z', 3-tuple}
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The direction of the text. Default: 'z'.
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See `.get_dir_vector` for a description of the values.
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axlim_clip : bool, default: False
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Whether to hide text outside the axes view limits.
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"""
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obj.__class__ = Text3D
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obj.set_3d_properties(z, zdir, axlim_clip)
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class Line3D(lines.Line2D):
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"""
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3D line object.
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.. note:: Use `get_data_3d` to obtain the data associated with the line.
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`~.Line2D.get_data`, `~.Line2D.get_xdata`, and `~.Line2D.get_ydata` return
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the x- and y-coordinates of the projected 2D-line, not the x- and y-data of
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the 3D-line. Similarly, use `set_data_3d` to set the data, not
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`~.Line2D.set_data`, `~.Line2D.set_xdata`, and `~.Line2D.set_ydata`.
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"""
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def __init__(self, xs, ys, zs, *args, axlim_clip=False, **kwargs):
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"""
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Parameters
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----------
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xs : array-like
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The x-data to be plotted.
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ys : array-like
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The y-data to be plotted.
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zs : array-like
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The z-data to be plotted.
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*args, **kwargs
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Additional arguments are passed to `~matplotlib.lines.Line2D`.
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"""
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super().__init__([], [], *args, **kwargs)
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self.set_data_3d(xs, ys, zs)
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self._axlim_clip = axlim_clip
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def set_3d_properties(self, zs=0, zdir='z', axlim_clip=False):
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"""
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Set the *z* position and direction of the line.
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Parameters
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----------
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zs : float or array of floats
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The location along the *zdir* axis in 3D space to position the
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line.
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zdir : {'x', 'y', 'z'}
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Plane to plot line orthogonal to. Default: 'z'.
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See `.get_dir_vector` for a description of the values.
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axlim_clip : bool, default: False
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Whether to hide lines with an endpoint outside the axes view limits.
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"""
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xs = self.get_xdata()
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ys = self.get_ydata()
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zs = cbook._to_unmasked_float_array(zs).ravel()
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zs = np.broadcast_to(zs, len(xs))
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self._verts3d = juggle_axes(xs, ys, zs, zdir)
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self._axlim_clip = axlim_clip
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self.stale = True
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def set_data_3d(self, *args):
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"""
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Set the x, y and z data
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Parameters
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----------
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x : array-like
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The x-data to be plotted.
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y : array-like
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The y-data to be plotted.
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z : array-like
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The z-data to be plotted.
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Notes
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-----
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Accepts x, y, z arguments or a single array-like (x, y, z)
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"""
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if len(args) == 1:
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args = args[0]
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for name, xyz in zip('xyz', args):
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if not np.iterable(xyz):
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raise RuntimeError(f'{name} must be a sequence')
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self._verts3d = args
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self.stale = True
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def get_data_3d(self):
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"""
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Get the current data
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Returns
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-------
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verts3d : length-3 tuple or array-like
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The current data as a tuple or array-like.
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"""
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return self._verts3d
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@artist.allow_rasterization
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def draw(self, renderer):
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if self._axlim_clip:
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xs3d, ys3d, zs3d = _viewlim_mask(*self._verts3d, self.axes)
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else:
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xs3d, ys3d, zs3d = self._verts3d
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xs, ys, zs, tis = proj3d._proj_transform_clip(xs3d, ys3d, zs3d,
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self.axes.M,
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self.axes._focal_length)
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self.set_data(xs, ys)
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super().draw(renderer)
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self.stale = False
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def line_2d_to_3d(line, zs=0, zdir='z', axlim_clip=False):
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"""
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Convert a `.Line2D` to a `.Line3D` object.
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Parameters
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----------
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zs : float
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The location along the *zdir* axis in 3D space to position the line.
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zdir : {'x', 'y', 'z'}
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Plane to plot line orthogonal to. Default: 'z'.
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See `.get_dir_vector` for a description of the values.
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axlim_clip : bool, default: False
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Whether to hide lines with an endpoint outside the axes view limits.
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"""
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line.__class__ = Line3D
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line.set_3d_properties(zs, zdir, axlim_clip)
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def _path_to_3d_segment(path, zs=0, zdir='z'):
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"""Convert a path to a 3D segment."""
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zs = np.broadcast_to(zs, len(path))
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pathsegs = path.iter_segments(simplify=False, curves=False)
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seg = [(x, y, z) for (((x, y), code), z) in zip(pathsegs, zs)]
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seg3d = [juggle_axes(x, y, z, zdir) for (x, y, z) in seg]
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return seg3d
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def _paths_to_3d_segments(paths, zs=0, zdir='z'):
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"""Convert paths from a collection object to 3D segments."""
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if not np.iterable(zs):
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zs = np.broadcast_to(zs, len(paths))
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else:
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if len(zs) != len(paths):
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raise ValueError('Number of z-coordinates does not match paths.')
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segs = [_path_to_3d_segment(path, pathz, zdir)
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for path, pathz in zip(paths, zs)]
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return segs
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def _path_to_3d_segment_with_codes(path, zs=0, zdir='z'):
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"""Convert a path to a 3D segment with path codes."""
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zs = np.broadcast_to(zs, len(path))
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pathsegs = path.iter_segments(simplify=False, curves=False)
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seg_codes = [((x, y, z), code) for ((x, y), code), z in zip(pathsegs, zs)]
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if seg_codes:
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seg, codes = zip(*seg_codes)
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seg3d = [juggle_axes(x, y, z, zdir) for (x, y, z) in seg]
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else:
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seg3d = []
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codes = []
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return seg3d, list(codes)
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def _paths_to_3d_segments_with_codes(paths, zs=0, zdir='z'):
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"""
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Convert paths from a collection object to 3D segments with path codes.
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"""
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zs = np.broadcast_to(zs, len(paths))
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segments_codes = [_path_to_3d_segment_with_codes(path, pathz, zdir)
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for path, pathz in zip(paths, zs)]
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if segments_codes:
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segments, codes = zip(*segments_codes)
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else:
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segments, codes = [], []
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return list(segments), list(codes)
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class Collection3D(Collection):
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"""A collection of 3D paths."""
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def do_3d_projection(self):
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"""Project the points according to renderer matrix."""
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vs_list = [vs for vs, _ in self._3dverts_codes]
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if self._axlim_clip:
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vs_list = [np.ma.row_stack(_viewlim_mask(*vs.T, self.axes)).T
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for vs in vs_list]
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xyzs_list = [proj3d.proj_transform(*vs.T, self.axes.M) for vs in vs_list]
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self._paths = [mpath.Path(np.ma.column_stack([xs, ys]), cs)
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for (xs, ys, _), (_, cs) in zip(xyzs_list, self._3dverts_codes)]
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zs = np.concatenate([zs for _, _, zs in xyzs_list])
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return zs.min() if len(zs) else 1e9
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def collection_2d_to_3d(col, zs=0, zdir='z', axlim_clip=False):
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"""Convert a `.Collection` to a `.Collection3D` object."""
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zs = np.broadcast_to(zs, len(col.get_paths()))
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col._3dverts_codes = [
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(np.column_stack(juggle_axes(
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*np.column_stack([p.vertices, np.broadcast_to(z, len(p.vertices))]).T,
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zdir)),
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p.codes)
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for p, z in zip(col.get_paths(), zs)]
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col.__class__ = cbook._make_class_factory(Collection3D, "{}3D")(type(col))
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col._axlim_clip = axlim_clip
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class Line3DCollection(LineCollection):
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"""
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A collection of 3D lines.
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"""
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def __init__(self, lines, axlim_clip=False, **kwargs):
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super().__init__(lines, **kwargs)
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self._axlim_clip = axlim_clip
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def set_sort_zpos(self, val):
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"""Set the position to use for z-sorting."""
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self._sort_zpos = val
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self.stale = True
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def set_segments(self, segments):
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"""
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Set 3D segments.
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"""
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self._segments3d = segments
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super().set_segments([])
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def do_3d_projection(self):
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"""
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Project the points according to renderer matrix.
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"""
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segments = self._segments3d
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if self._axlim_clip:
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all_points = np.ma.vstack(segments)
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masked_points = np.ma.column_stack([*_viewlim_mask(*all_points.T,
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self.axes)])
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segment_lengths = [np.shape(segment)[0] for segment in segments]
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segments = np.split(masked_points, np.cumsum(segment_lengths[:-1]))
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xyslist = [proj3d._proj_trans_points(points, self.axes.M)
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for points in segments]
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segments_2d = [np.ma.column_stack([xs, ys]) for xs, ys, zs in xyslist]
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LineCollection.set_segments(self, segments_2d)
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# FIXME
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minz = 1e9
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for xs, ys, zs in xyslist:
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minz = min(minz, min(zs))
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return minz
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def line_collection_2d_to_3d(col, zs=0, zdir='z', axlim_clip=False):
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"""Convert a `.LineCollection` to a `.Line3DCollection` object."""
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segments3d = _paths_to_3d_segments(col.get_paths(), zs, zdir)
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col.__class__ = Line3DCollection
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col.set_segments(segments3d)
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col._axlim_clip = axlim_clip
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class Patch3D(Patch):
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"""
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3D patch object.
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"""
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def __init__(self, *args, zs=(), zdir='z', axlim_clip=False, **kwargs):
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"""
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Parameters
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----------
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verts :
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zs : float
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The location along the *zdir* axis in 3D space to position the
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patch.
|
|
zdir : {'x', 'y', 'z'}
|
|
Plane to plot patch orthogonal to. Default: 'z'.
|
|
See `.get_dir_vector` for a description of the values.
|
|
axlim_clip : bool, default: False
|
|
Whether to hide patches with a vertex outside the axes view limits.
|
|
"""
|
|
super().__init__(*args, **kwargs)
|
|
self.set_3d_properties(zs, zdir, axlim_clip)
|
|
|
|
def set_3d_properties(self, verts, zs=0, zdir='z', axlim_clip=False):
|
|
"""
|
|
Set the *z* position and direction of the patch.
|
|
|
|
Parameters
|
|
----------
|
|
verts :
|
|
zs : float
|
|
The location along the *zdir* axis in 3D space to position the
|
|
patch.
|
|
zdir : {'x', 'y', 'z'}
|
|
Plane to plot patch orthogonal to. Default: 'z'.
|
|
See `.get_dir_vector` for a description of the values.
|
|
axlim_clip : bool, default: False
|
|
Whether to hide patches with a vertex outside the axes view limits.
|
|
"""
|
|
zs = np.broadcast_to(zs, len(verts))
|
|
self._segment3d = [juggle_axes(x, y, z, zdir)
|
|
for ((x, y), z) in zip(verts, zs)]
|
|
self._axlim_clip = axlim_clip
|
|
|
|
def get_path(self):
|
|
# docstring inherited
|
|
# self._path2d is not initialized until do_3d_projection
|
|
if not hasattr(self, '_path2d'):
|
|
self.axes.M = self.axes.get_proj()
|
|
self.do_3d_projection()
|
|
return self._path2d
|
|
|
|
def do_3d_projection(self):
|
|
s = self._segment3d
|
|
if self._axlim_clip:
|
|
xs, ys, zs = _viewlim_mask(*zip(*s), self.axes)
|
|
else:
|
|
xs, ys, zs = zip(*s)
|
|
vxs, vys, vzs, vis = proj3d._proj_transform_clip(xs, ys, zs,
|
|
self.axes.M,
|
|
self.axes._focal_length)
|
|
self._path2d = mpath.Path(np.ma.column_stack([vxs, vys]))
|
|
return min(vzs)
|
|
|
|
|
|
class PathPatch3D(Patch3D):
|
|
"""
|
|
3D PathPatch object.
|
|
"""
|
|
|
|
def __init__(self, path, *, zs=(), zdir='z', axlim_clip=False, **kwargs):
|
|
"""
|
|
Parameters
|
|
----------
|
|
path :
|
|
zs : float
|
|
The location along the *zdir* axis in 3D space to position the
|
|
path patch.
|
|
zdir : {'x', 'y', 'z', 3-tuple}
|
|
Plane to plot path patch orthogonal to. Default: 'z'.
|
|
See `.get_dir_vector` for a description of the values.
|
|
axlim_clip : bool, default: False
|
|
Whether to hide path patches with a point outside the axes view limits.
|
|
"""
|
|
# Not super().__init__!
|
|
Patch.__init__(self, **kwargs)
|
|
self.set_3d_properties(path, zs, zdir, axlim_clip)
|
|
|
|
def set_3d_properties(self, path, zs=0, zdir='z', axlim_clip=False):
|
|
"""
|
|
Set the *z* position and direction of the path patch.
|
|
|
|
Parameters
|
|
----------
|
|
path :
|
|
zs : float
|
|
The location along the *zdir* axis in 3D space to position the
|
|
path patch.
|
|
zdir : {'x', 'y', 'z', 3-tuple}
|
|
Plane to plot path patch orthogonal to. Default: 'z'.
|
|
See `.get_dir_vector` for a description of the values.
|
|
axlim_clip : bool, default: False
|
|
Whether to hide path patches with a point outside the axes view limits.
|
|
"""
|
|
Patch3D.set_3d_properties(self, path.vertices, zs=zs, zdir=zdir,
|
|
axlim_clip=axlim_clip)
|
|
self._code3d = path.codes
|
|
|
|
def do_3d_projection(self):
|
|
s = self._segment3d
|
|
if self._axlim_clip:
|
|
xs, ys, zs = _viewlim_mask(*zip(*s), self.axes)
|
|
else:
|
|
xs, ys, zs = zip(*s)
|
|
vxs, vys, vzs, vis = proj3d._proj_transform_clip(xs, ys, zs,
|
|
self.axes.M,
|
|
self.axes._focal_length)
|
|
self._path2d = mpath.Path(np.ma.column_stack([vxs, vys]), self._code3d)
|
|
return min(vzs)
|
|
|
|
|
|
def _get_patch_verts(patch):
|
|
"""Return a list of vertices for the path of a patch."""
|
|
trans = patch.get_patch_transform()
|
|
path = patch.get_path()
|
|
polygons = path.to_polygons(trans)
|
|
return polygons[0] if len(polygons) else np.array([])
|
|
|
|
|
|
def patch_2d_to_3d(patch, z=0, zdir='z', axlim_clip=False):
|
|
"""Convert a `.Patch` to a `.Patch3D` object."""
|
|
verts = _get_patch_verts(patch)
|
|
patch.__class__ = Patch3D
|
|
patch.set_3d_properties(verts, z, zdir, axlim_clip)
|
|
|
|
|
|
def pathpatch_2d_to_3d(pathpatch, z=0, zdir='z'):
|
|
"""Convert a `.PathPatch` to a `.PathPatch3D` object."""
|
|
path = pathpatch.get_path()
|
|
trans = pathpatch.get_patch_transform()
|
|
|
|
mpath = trans.transform_path(path)
|
|
pathpatch.__class__ = PathPatch3D
|
|
pathpatch.set_3d_properties(mpath, z, zdir)
|
|
|
|
|
|
class Patch3DCollection(PatchCollection):
|
|
"""
|
|
A collection of 3D patches.
|
|
"""
|
|
|
|
def __init__(self, *args,
|
|
zs=0, zdir='z', depthshade=True, axlim_clip=False, **kwargs):
|
|
"""
|
|
Create a collection of flat 3D patches with its normal vector
|
|
pointed in *zdir* direction, and located at *zs* on the *zdir*
|
|
axis. 'zs' can be a scalar or an array-like of the same length as
|
|
the number of patches in the collection.
|
|
|
|
Constructor arguments are the same as for
|
|
:class:`~matplotlib.collections.PatchCollection`. In addition,
|
|
keywords *zs=0* and *zdir='z'* are available.
|
|
|
|
Also, the keyword argument *depthshade* is available to indicate
|
|
whether to shade the patches in order to give the appearance of depth
|
|
(default is *True*). This is typically desired in scatter plots.
|
|
"""
|
|
self._depthshade = depthshade
|
|
super().__init__(*args, **kwargs)
|
|
self.set_3d_properties(zs, zdir, axlim_clip)
|
|
|
|
def get_depthshade(self):
|
|
return self._depthshade
|
|
|
|
def set_depthshade(self, depthshade):
|
|
"""
|
|
Set whether depth shading is performed on collection members.
|
|
|
|
Parameters
|
|
----------
|
|
depthshade : bool
|
|
Whether to shade the patches in order to give the appearance of
|
|
depth.
|
|
"""
|
|
self._depthshade = depthshade
|
|
self.stale = True
|
|
|
|
def set_sort_zpos(self, val):
|
|
"""Set the position to use for z-sorting."""
|
|
self._sort_zpos = val
|
|
self.stale = True
|
|
|
|
def set_3d_properties(self, zs, zdir, axlim_clip=False):
|
|
"""
|
|
Set the *z* positions and direction of the patches.
|
|
|
|
Parameters
|
|
----------
|
|
zs : float or array of floats
|
|
The location or locations to place the patches in the collection
|
|
along the *zdir* axis.
|
|
zdir : {'x', 'y', 'z'}
|
|
Plane to plot patches orthogonal to.
|
|
All patches must have the same direction.
|
|
See `.get_dir_vector` for a description of the values.
|
|
axlim_clip : bool, default: False
|
|
Whether to hide patches with a vertex outside the axes view limits.
|
|
"""
|
|
# Force the collection to initialize the face and edgecolors
|
|
# just in case it is a scalarmappable with a colormap.
|
|
self.update_scalarmappable()
|
|
offsets = self.get_offsets()
|
|
if len(offsets) > 0:
|
|
xs, ys = offsets.T
|
|
else:
|
|
xs = []
|
|
ys = []
|
|
self._offsets3d = juggle_axes(xs, ys, np.atleast_1d(zs), zdir)
|
|
self._z_markers_idx = slice(-1)
|
|
self._vzs = None
|
|
self._axlim_clip = axlim_clip
|
|
self.stale = True
|
|
|
|
def do_3d_projection(self):
|
|
if self._axlim_clip:
|
|
xs, ys, zs = _viewlim_mask(*self._offsets3d, self.axes)
|
|
else:
|
|
xs, ys, zs = self._offsets3d
|
|
vxs, vys, vzs, vis = proj3d._proj_transform_clip(xs, ys, zs,
|
|
self.axes.M,
|
|
self.axes._focal_length)
|
|
self._vzs = vzs
|
|
super().set_offsets(np.ma.column_stack([vxs, vys]))
|
|
|
|
if vzs.size > 0:
|
|
return min(vzs)
|
|
else:
|
|
return np.nan
|
|
|
|
def _maybe_depth_shade_and_sort_colors(self, color_array):
|
|
color_array = (
|
|
_zalpha(color_array, self._vzs)
|
|
if self._vzs is not None and self._depthshade
|
|
else color_array
|
|
)
|
|
if len(color_array) > 1:
|
|
color_array = color_array[self._z_markers_idx]
|
|
return mcolors.to_rgba_array(color_array, self._alpha)
|
|
|
|
def get_facecolor(self):
|
|
return self._maybe_depth_shade_and_sort_colors(super().get_facecolor())
|
|
|
|
def get_edgecolor(self):
|
|
# We need this check here to make sure we do not double-apply the depth
|
|
# based alpha shading when the edge color is "face" which means the
|
|
# edge colour should be identical to the face colour.
|
|
if cbook._str_equal(self._edgecolors, 'face'):
|
|
return self.get_facecolor()
|
|
return self._maybe_depth_shade_and_sort_colors(super().get_edgecolor())
|
|
|
|
|
|
class Path3DCollection(PathCollection):
|
|
"""
|
|
A collection of 3D paths.
|
|
"""
|
|
|
|
def __init__(self, *args,
|
|
zs=0, zdir='z', depthshade=True, axlim_clip=False, **kwargs):
|
|
"""
|
|
Create a collection of flat 3D paths with its normal vector
|
|
pointed in *zdir* direction, and located at *zs* on the *zdir*
|
|
axis. 'zs' can be a scalar or an array-like of the same length as
|
|
the number of paths in the collection.
|
|
|
|
Constructor arguments are the same as for
|
|
:class:`~matplotlib.collections.PathCollection`. In addition,
|
|
keywords *zs=0* and *zdir='z'* are available.
|
|
|
|
Also, the keyword argument *depthshade* is available to indicate
|
|
whether to shade the patches in order to give the appearance of depth
|
|
(default is *True*). This is typically desired in scatter plots.
|
|
"""
|
|
self._depthshade = depthshade
|
|
self._in_draw = False
|
|
super().__init__(*args, **kwargs)
|
|
self.set_3d_properties(zs, zdir, axlim_clip)
|
|
self._offset_zordered = None
|
|
|
|
def draw(self, renderer):
|
|
with self._use_zordered_offset():
|
|
with cbook._setattr_cm(self, _in_draw=True):
|
|
super().draw(renderer)
|
|
|
|
def set_sort_zpos(self, val):
|
|
"""Set the position to use for z-sorting."""
|
|
self._sort_zpos = val
|
|
self.stale = True
|
|
|
|
def set_3d_properties(self, zs, zdir, axlim_clip=False):
|
|
"""
|
|
Set the *z* positions and direction of the paths.
|
|
|
|
Parameters
|
|
----------
|
|
zs : float or array of floats
|
|
The location or locations to place the paths in the collection
|
|
along the *zdir* axis.
|
|
zdir : {'x', 'y', 'z'}
|
|
Plane to plot paths orthogonal to.
|
|
All paths must have the same direction.
|
|
See `.get_dir_vector` for a description of the values.
|
|
axlim_clip : bool, default: False
|
|
Whether to hide paths with a vertex outside the axes view limits.
|
|
"""
|
|
# Force the collection to initialize the face and edgecolors
|
|
# just in case it is a scalarmappable with a colormap.
|
|
self.update_scalarmappable()
|
|
offsets = self.get_offsets()
|
|
if len(offsets) > 0:
|
|
xs, ys = offsets.T
|
|
else:
|
|
xs = []
|
|
ys = []
|
|
self._zdir = zdir
|
|
self._offsets3d = juggle_axes(xs, ys, np.atleast_1d(zs), zdir)
|
|
# In the base draw methods we access the attributes directly which
|
|
# means we cannot resolve the shuffling in the getter methods like
|
|
# we do for the edge and face colors.
|
|
#
|
|
# This means we need to carry around a cache of the unsorted sizes and
|
|
# widths (postfixed with 3d) and in `do_3d_projection` set the
|
|
# depth-sorted version of that data into the private state used by the
|
|
# base collection class in its draw method.
|
|
#
|
|
# Grab the current sizes and linewidths to preserve them.
|
|
self._sizes3d = self._sizes
|
|
self._linewidths3d = np.array(self._linewidths)
|
|
xs, ys, zs = self._offsets3d
|
|
|
|
# Sort the points based on z coordinates
|
|
# Performance optimization: Create a sorted index array and reorder
|
|
# points and point properties according to the index array
|
|
self._z_markers_idx = slice(-1)
|
|
self._vzs = None
|
|
|
|
self._axlim_clip = axlim_clip
|
|
self.stale = True
|
|
|
|
def set_sizes(self, sizes, dpi=72.0):
|
|
super().set_sizes(sizes, dpi)
|
|
if not self._in_draw:
|
|
self._sizes3d = sizes
|
|
|
|
def set_linewidth(self, lw):
|
|
super().set_linewidth(lw)
|
|
if not self._in_draw:
|
|
self._linewidths3d = np.array(self._linewidths)
|
|
|
|
def get_depthshade(self):
|
|
return self._depthshade
|
|
|
|
def set_depthshade(self, depthshade):
|
|
"""
|
|
Set whether depth shading is performed on collection members.
|
|
|
|
Parameters
|
|
----------
|
|
depthshade : bool
|
|
Whether to shade the patches in order to give the appearance of
|
|
depth.
|
|
"""
|
|
self._depthshade = depthshade
|
|
self.stale = True
|
|
|
|
def do_3d_projection(self):
|
|
if self._axlim_clip:
|
|
xs, ys, zs = _viewlim_mask(*self._offsets3d, self.axes)
|
|
else:
|
|
xs, ys, zs = self._offsets3d
|
|
vxs, vys, vzs, vis = proj3d._proj_transform_clip(xs, ys, zs,
|
|
self.axes.M,
|
|
self.axes._focal_length)
|
|
# Sort the points based on z coordinates
|
|
# Performance optimization: Create a sorted index array and reorder
|
|
# points and point properties according to the index array
|
|
z_markers_idx = self._z_markers_idx = np.ma.argsort(vzs)[::-1]
|
|
self._vzs = vzs
|
|
|
|
# we have to special case the sizes because of code in collections.py
|
|
# as the draw method does
|
|
# self.set_sizes(self._sizes, self.figure.dpi)
|
|
# so we cannot rely on doing the sorting on the way out via get_*
|
|
|
|
if len(self._sizes3d) > 1:
|
|
self._sizes = self._sizes3d[z_markers_idx]
|
|
|
|
if len(self._linewidths3d) > 1:
|
|
self._linewidths = self._linewidths3d[z_markers_idx]
|
|
|
|
PathCollection.set_offsets(self, np.ma.column_stack((vxs, vys)))
|
|
|
|
# Re-order items
|
|
vzs = vzs[z_markers_idx]
|
|
vxs = vxs[z_markers_idx]
|
|
vys = vys[z_markers_idx]
|
|
|
|
# Store ordered offset for drawing purpose
|
|
self._offset_zordered = np.ma.column_stack((vxs, vys))
|
|
|
|
return np.min(vzs) if vzs.size else np.nan
|
|
|
|
@contextmanager
|
|
def _use_zordered_offset(self):
|
|
if self._offset_zordered is None:
|
|
# Do nothing
|
|
yield
|
|
else:
|
|
# Swap offset with z-ordered offset
|
|
old_offset = self._offsets
|
|
super().set_offsets(self._offset_zordered)
|
|
try:
|
|
yield
|
|
finally:
|
|
self._offsets = old_offset
|
|
|
|
def _maybe_depth_shade_and_sort_colors(self, color_array):
|
|
color_array = (
|
|
_zalpha(color_array, self._vzs)
|
|
if self._vzs is not None and self._depthshade
|
|
else color_array
|
|
)
|
|
if len(color_array) > 1:
|
|
color_array = color_array[self._z_markers_idx]
|
|
return mcolors.to_rgba_array(color_array, self._alpha)
|
|
|
|
def get_facecolor(self):
|
|
return self._maybe_depth_shade_and_sort_colors(super().get_facecolor())
|
|
|
|
def get_edgecolor(self):
|
|
# We need this check here to make sure we do not double-apply the depth
|
|
# based alpha shading when the edge color is "face" which means the
|
|
# edge colour should be identical to the face colour.
|
|
if cbook._str_equal(self._edgecolors, 'face'):
|
|
return self.get_facecolor()
|
|
return self._maybe_depth_shade_and_sort_colors(super().get_edgecolor())
|
|
|
|
|
|
def patch_collection_2d_to_3d(col, zs=0, zdir='z', depthshade=True, axlim_clip=False):
|
|
"""
|
|
Convert a `.PatchCollection` into a `.Patch3DCollection` object
|
|
(or a `.PathCollection` into a `.Path3DCollection` object).
|
|
|
|
Parameters
|
|
----------
|
|
col : `~matplotlib.collections.PatchCollection` or \
|
|
`~matplotlib.collections.PathCollection`
|
|
The collection to convert.
|
|
zs : float or array of floats
|
|
The location or locations to place the patches in the collection along
|
|
the *zdir* axis. Default: 0.
|
|
zdir : {'x', 'y', 'z'}
|
|
The axis in which to place the patches. Default: "z".
|
|
See `.get_dir_vector` for a description of the values.
|
|
depthshade : bool, default: True
|
|
Whether to shade the patches to give a sense of depth.
|
|
axlim_clip : bool, default: False
|
|
Whether to hide patches with a vertex outside the axes view limits.
|
|
"""
|
|
if isinstance(col, PathCollection):
|
|
col.__class__ = Path3DCollection
|
|
col._offset_zordered = None
|
|
elif isinstance(col, PatchCollection):
|
|
col.__class__ = Patch3DCollection
|
|
col._depthshade = depthshade
|
|
col._in_draw = False
|
|
col.set_3d_properties(zs, zdir, axlim_clip)
|
|
|
|
|
|
class Poly3DCollection(PolyCollection):
|
|
"""
|
|
A collection of 3D polygons.
|
|
|
|
.. note::
|
|
**Filling of 3D polygons**
|
|
|
|
There is no simple definition of the enclosed surface of a 3D polygon
|
|
unless the polygon is planar.
|
|
|
|
In practice, Matplotlib fills the 2D projection of the polygon. This
|
|
gives a correct filling appearance only for planar polygons. For all
|
|
other polygons, you'll find orientations in which the edges of the
|
|
polygon intersect in the projection. This will lead to an incorrect
|
|
visualization of the 3D area.
|
|
|
|
If you need filled areas, it is recommended to create them via
|
|
`~mpl_toolkits.mplot3d.axes3d.Axes3D.plot_trisurf`, which creates a
|
|
triangulation and thus generates consistent surfaces.
|
|
"""
|
|
|
|
def __init__(self, verts, *args, zsort='average', shade=False,
|
|
lightsource=None, axlim_clip=False, **kwargs):
|
|
"""
|
|
Parameters
|
|
----------
|
|
verts : list of (N, 3) array-like
|
|
The sequence of polygons [*verts0*, *verts1*, ...] where each
|
|
element *verts_i* defines the vertices of polygon *i* as a 2D
|
|
array-like of shape (N, 3).
|
|
zsort : {'average', 'min', 'max'}, default: 'average'
|
|
The calculation method for the z-order.
|
|
See `~.Poly3DCollection.set_zsort` for details.
|
|
shade : bool, default: False
|
|
Whether to shade *facecolors* and *edgecolors*. When activating
|
|
*shade*, *facecolors* and/or *edgecolors* must be provided.
|
|
|
|
.. versionadded:: 3.7
|
|
|
|
lightsource : `~matplotlib.colors.LightSource`, optional
|
|
The lightsource to use when *shade* is True.
|
|
|
|
.. versionadded:: 3.7
|
|
|
|
axlim_clip : bool, default: False
|
|
Whether to hide polygons with a vertex outside the view limits.
|
|
|
|
*args, **kwargs
|
|
All other parameters are forwarded to `.PolyCollection`.
|
|
|
|
Notes
|
|
-----
|
|
Note that this class does a bit of magic with the _facecolors
|
|
and _edgecolors properties.
|
|
"""
|
|
if shade:
|
|
normals = _generate_normals(verts)
|
|
facecolors = kwargs.get('facecolors', None)
|
|
if facecolors is not None:
|
|
kwargs['facecolors'] = _shade_colors(
|
|
facecolors, normals, lightsource
|
|
)
|
|
|
|
edgecolors = kwargs.get('edgecolors', None)
|
|
if edgecolors is not None:
|
|
kwargs['edgecolors'] = _shade_colors(
|
|
edgecolors, normals, lightsource
|
|
)
|
|
if facecolors is None and edgecolors is None:
|
|
raise ValueError(
|
|
"You must provide facecolors, edgecolors, or both for "
|
|
"shade to work.")
|
|
super().__init__(verts, *args, **kwargs)
|
|
if isinstance(verts, np.ndarray):
|
|
if verts.ndim != 3:
|
|
raise ValueError('verts must be a list of (N, 3) array-like')
|
|
else:
|
|
if any(len(np.shape(vert)) != 2 for vert in verts):
|
|
raise ValueError('verts must be a list of (N, 3) array-like')
|
|
self.set_zsort(zsort)
|
|
self._codes3d = None
|
|
self._axlim_clip = axlim_clip
|
|
|
|
_zsort_functions = {
|
|
'average': np.average,
|
|
'min': np.min,
|
|
'max': np.max,
|
|
}
|
|
|
|
def set_zsort(self, zsort):
|
|
"""
|
|
Set the calculation method for the z-order.
|
|
|
|
Parameters
|
|
----------
|
|
zsort : {'average', 'min', 'max'}
|
|
The function applied on the z-coordinates of the vertices in the
|
|
viewer's coordinate system, to determine the z-order.
|
|
"""
|
|
self._zsortfunc = self._zsort_functions[zsort]
|
|
self._sort_zpos = None
|
|
self.stale = True
|
|
|
|
@_api.deprecated("3.10")
|
|
def get_vector(self, segments3d):
|
|
return self._get_vector(segments3d)
|
|
|
|
def _get_vector(self, segments3d):
|
|
"""Optimize points for projection."""
|
|
if len(segments3d):
|
|
xs, ys, zs = np.vstack(segments3d).T
|
|
else: # vstack can't stack zero arrays.
|
|
xs, ys, zs = [], [], []
|
|
ones = np.ones(len(xs))
|
|
self._vec = np.array([xs, ys, zs, ones])
|
|
|
|
indices = [0, *np.cumsum([len(segment) for segment in segments3d])]
|
|
self._segslices = [*map(slice, indices[:-1], indices[1:])]
|
|
|
|
def set_verts(self, verts, closed=True):
|
|
"""
|
|
Set 3D vertices.
|
|
|
|
Parameters
|
|
----------
|
|
verts : list of (N, 3) array-like
|
|
The sequence of polygons [*verts0*, *verts1*, ...] where each
|
|
element *verts_i* defines the vertices of polygon *i* as a 2D
|
|
array-like of shape (N, 3).
|
|
closed : bool, default: True
|
|
Whether the polygon should be closed by adding a CLOSEPOLY
|
|
connection at the end.
|
|
"""
|
|
self._get_vector(verts)
|
|
# 2D verts will be updated at draw time
|
|
super().set_verts([], False)
|
|
self._closed = closed
|
|
|
|
def set_verts_and_codes(self, verts, codes):
|
|
"""Set 3D vertices with path codes."""
|
|
# set vertices with closed=False to prevent PolyCollection from
|
|
# setting path codes
|
|
self.set_verts(verts, closed=False)
|
|
# and set our own codes instead.
|
|
self._codes3d = codes
|
|
|
|
def set_3d_properties(self, axlim_clip=False):
|
|
# Force the collection to initialize the face and edgecolors
|
|
# just in case it is a scalarmappable with a colormap.
|
|
self.update_scalarmappable()
|
|
self._sort_zpos = None
|
|
self.set_zsort('average')
|
|
self._facecolor3d = PolyCollection.get_facecolor(self)
|
|
self._edgecolor3d = PolyCollection.get_edgecolor(self)
|
|
self._alpha3d = PolyCollection.get_alpha(self)
|
|
self.stale = True
|
|
|
|
def set_sort_zpos(self, val):
|
|
"""Set the position to use for z-sorting."""
|
|
self._sort_zpos = val
|
|
self.stale = True
|
|
|
|
def do_3d_projection(self):
|
|
"""
|
|
Perform the 3D projection for this object.
|
|
"""
|
|
if self._A is not None:
|
|
# force update of color mapping because we re-order them
|
|
# below. If we do not do this here, the 2D draw will call
|
|
# this, but we will never port the color mapped values back
|
|
# to the 3D versions.
|
|
#
|
|
# We hold the 3D versions in a fixed order (the order the user
|
|
# passed in) and sort the 2D version by view depth.
|
|
self.update_scalarmappable()
|
|
if self._face_is_mapped:
|
|
self._facecolor3d = self._facecolors
|
|
if self._edge_is_mapped:
|
|
self._edgecolor3d = self._edgecolors
|
|
if self._axlim_clip:
|
|
xs, ys, zs = _viewlim_mask(*self._vec[0:3], self.axes)
|
|
if self._vec.shape[0] == 4: # Will be 3 (xyz) or 4 (xyzw)
|
|
w_masked = np.ma.masked_where(zs.mask, self._vec[3])
|
|
vec = np.ma.array([xs, ys, zs, w_masked])
|
|
else:
|
|
vec = np.ma.array([xs, ys, zs])
|
|
else:
|
|
vec = self._vec
|
|
txs, tys, tzs = proj3d._proj_transform_vec(vec, self.axes.M)
|
|
xyzlist = [(txs[sl], tys[sl], tzs[sl]) for sl in self._segslices]
|
|
|
|
# This extra fuss is to re-order face / edge colors
|
|
cface = self._facecolor3d
|
|
cedge = self._edgecolor3d
|
|
if len(cface) != len(xyzlist):
|
|
cface = cface.repeat(len(xyzlist), axis=0)
|
|
if len(cedge) != len(xyzlist):
|
|
if len(cedge) == 0:
|
|
cedge = cface
|
|
else:
|
|
cedge = cedge.repeat(len(xyzlist), axis=0)
|
|
|
|
if xyzlist:
|
|
# sort by depth (furthest drawn first)
|
|
z_segments_2d = sorted(
|
|
((self._zsortfunc(zs.data), np.ma.column_stack([xs, ys]), fc, ec, idx)
|
|
for idx, ((xs, ys, zs), fc, ec)
|
|
in enumerate(zip(xyzlist, cface, cedge))),
|
|
key=lambda x: x[0], reverse=True)
|
|
|
|
_, segments_2d, self._facecolors2d, self._edgecolors2d, idxs = \
|
|
zip(*z_segments_2d)
|
|
else:
|
|
segments_2d = []
|
|
self._facecolors2d = np.empty((0, 4))
|
|
self._edgecolors2d = np.empty((0, 4))
|
|
idxs = []
|
|
|
|
if self._codes3d is not None:
|
|
codes = [self._codes3d[idx] for idx in idxs]
|
|
PolyCollection.set_verts_and_codes(self, segments_2d, codes)
|
|
else:
|
|
PolyCollection.set_verts(self, segments_2d, self._closed)
|
|
|
|
if len(self._edgecolor3d) != len(cface):
|
|
self._edgecolors2d = self._edgecolor3d
|
|
|
|
# Return zorder value
|
|
if self._sort_zpos is not None:
|
|
zvec = np.array([[0], [0], [self._sort_zpos], [1]])
|
|
ztrans = proj3d._proj_transform_vec(zvec, self.axes.M)
|
|
return ztrans[2][0]
|
|
elif tzs.size > 0:
|
|
# FIXME: Some results still don't look quite right.
|
|
# In particular, examine contourf3d_demo2.py
|
|
# with az = -54 and elev = -45.
|
|
return np.min(tzs)
|
|
else:
|
|
return np.nan
|
|
|
|
def set_facecolor(self, colors):
|
|
# docstring inherited
|
|
super().set_facecolor(colors)
|
|
self._facecolor3d = PolyCollection.get_facecolor(self)
|
|
|
|
def set_edgecolor(self, colors):
|
|
# docstring inherited
|
|
super().set_edgecolor(colors)
|
|
self._edgecolor3d = PolyCollection.get_edgecolor(self)
|
|
|
|
def set_alpha(self, alpha):
|
|
# docstring inherited
|
|
artist.Artist.set_alpha(self, alpha)
|
|
try:
|
|
self._facecolor3d = mcolors.to_rgba_array(
|
|
self._facecolor3d, self._alpha)
|
|
except (AttributeError, TypeError, IndexError):
|
|
pass
|
|
try:
|
|
self._edgecolors = mcolors.to_rgba_array(
|
|
self._edgecolor3d, self._alpha)
|
|
except (AttributeError, TypeError, IndexError):
|
|
pass
|
|
self.stale = True
|
|
|
|
def get_facecolor(self):
|
|
# docstring inherited
|
|
# self._facecolors2d is not initialized until do_3d_projection
|
|
if not hasattr(self, '_facecolors2d'):
|
|
self.axes.M = self.axes.get_proj()
|
|
self.do_3d_projection()
|
|
return np.asarray(self._facecolors2d)
|
|
|
|
def get_edgecolor(self):
|
|
# docstring inherited
|
|
# self._edgecolors2d is not initialized until do_3d_projection
|
|
if not hasattr(self, '_edgecolors2d'):
|
|
self.axes.M = self.axes.get_proj()
|
|
self.do_3d_projection()
|
|
return np.asarray(self._edgecolors2d)
|
|
|
|
|
|
def poly_collection_2d_to_3d(col, zs=0, zdir='z', axlim_clip=False):
|
|
"""
|
|
Convert a `.PolyCollection` into a `.Poly3DCollection` object.
|
|
|
|
Parameters
|
|
----------
|
|
col : `~matplotlib.collections.PolyCollection`
|
|
The collection to convert.
|
|
zs : float or array of floats
|
|
The location or locations to place the polygons in the collection along
|
|
the *zdir* axis. Default: 0.
|
|
zdir : {'x', 'y', 'z'}
|
|
The axis in which to place the patches. Default: 'z'.
|
|
See `.get_dir_vector` for a description of the values.
|
|
"""
|
|
segments_3d, codes = _paths_to_3d_segments_with_codes(
|
|
col.get_paths(), zs, zdir)
|
|
col.__class__ = Poly3DCollection
|
|
col.set_verts_and_codes(segments_3d, codes)
|
|
col.set_3d_properties()
|
|
col._axlim_clip = axlim_clip
|
|
|
|
|
|
def juggle_axes(xs, ys, zs, zdir):
|
|
"""
|
|
Reorder coordinates so that 2D *xs*, *ys* can be plotted in the plane
|
|
orthogonal to *zdir*. *zdir* is normally 'x', 'y' or 'z'. However, if
|
|
*zdir* starts with a '-' it is interpreted as a compensation for
|
|
`rotate_axes`.
|
|
"""
|
|
if zdir == 'x':
|
|
return zs, xs, ys
|
|
elif zdir == 'y':
|
|
return xs, zs, ys
|
|
elif zdir[0] == '-':
|
|
return rotate_axes(xs, ys, zs, zdir)
|
|
else:
|
|
return xs, ys, zs
|
|
|
|
|
|
def rotate_axes(xs, ys, zs, zdir):
|
|
"""
|
|
Reorder coordinates so that the axes are rotated with *zdir* along
|
|
the original z axis. Prepending the axis with a '-' does the
|
|
inverse transform, so *zdir* can be 'x', '-x', 'y', '-y', 'z' or '-z'.
|
|
"""
|
|
if zdir in ('x', '-y'):
|
|
return ys, zs, xs
|
|
elif zdir in ('-x', 'y'):
|
|
return zs, xs, ys
|
|
else:
|
|
return xs, ys, zs
|
|
|
|
|
|
def _zalpha(colors, zs):
|
|
"""Modify the alphas of the color list according to depth."""
|
|
# FIXME: This only works well if the points for *zs* are well-spaced
|
|
# in all three dimensions. Otherwise, at certain orientations,
|
|
# the min and max zs are very close together.
|
|
# Should really normalize against the viewing depth.
|
|
if len(colors) == 0 or len(zs) == 0:
|
|
return np.zeros((0, 4))
|
|
norm = Normalize(min(zs), max(zs))
|
|
sats = 1 - norm(zs) * 0.7
|
|
rgba = np.broadcast_to(mcolors.to_rgba_array(colors), (len(zs), 4))
|
|
return np.column_stack([rgba[:, :3], rgba[:, 3] * sats])
|
|
|
|
|
|
def _all_points_on_plane(xs, ys, zs, atol=1e-8):
|
|
"""
|
|
Check if all points are on the same plane. Note that NaN values are
|
|
ignored.
|
|
|
|
Parameters
|
|
----------
|
|
xs, ys, zs : array-like
|
|
The x, y, and z coordinates of the points.
|
|
atol : float, default: 1e-8
|
|
The tolerance for the equality check.
|
|
"""
|
|
xs, ys, zs = np.asarray(xs), np.asarray(ys), np.asarray(zs)
|
|
points = np.column_stack([xs, ys, zs])
|
|
points = points[~np.isnan(points).any(axis=1)]
|
|
# Check for the case where we have less than 3 unique points
|
|
points = np.unique(points, axis=0)
|
|
if len(points) <= 3:
|
|
return True
|
|
# Calculate the vectors from the first point to all other points
|
|
vs = (points - points[0])[1:]
|
|
vs = vs / np.linalg.norm(vs, axis=1)[:, np.newaxis]
|
|
# Filter out parallel vectors
|
|
vs = np.unique(vs, axis=0)
|
|
if len(vs) <= 2:
|
|
return True
|
|
# Filter out parallel and antiparallel vectors to the first vector
|
|
cross_norms = np.linalg.norm(np.cross(vs[0], vs[1:]), axis=1)
|
|
zero_cross_norms = np.where(np.isclose(cross_norms, 0, atol=atol))[0] + 1
|
|
vs = np.delete(vs, zero_cross_norms, axis=0)
|
|
if len(vs) <= 2:
|
|
return True
|
|
# Calculate the normal vector from the first three points
|
|
n = np.cross(vs[0], vs[1])
|
|
n = n / np.linalg.norm(n)
|
|
# If the dot product of the normal vector and all other vectors is zero,
|
|
# all points are on the same plane
|
|
dots = np.dot(n, vs.transpose())
|
|
return np.allclose(dots, 0, atol=atol)
|
|
|
|
|
|
def _generate_normals(polygons):
|
|
"""
|
|
Compute the normals of a list of polygons, one normal per polygon.
|
|
|
|
Normals point towards the viewer for a face with its vertices in
|
|
counterclockwise order, following the right hand rule.
|
|
|
|
Uses three points equally spaced around the polygon. This method assumes
|
|
that the points are in a plane. Otherwise, more than one shade is required,
|
|
which is not supported.
|
|
|
|
Parameters
|
|
----------
|
|
polygons : list of (M_i, 3) array-like, or (..., M, 3) array-like
|
|
A sequence of polygons to compute normals for, which can have
|
|
varying numbers of vertices. If the polygons all have the same
|
|
number of vertices and array is passed, then the operation will
|
|
be vectorized.
|
|
|
|
Returns
|
|
-------
|
|
normals : (..., 3) array
|
|
A normal vector estimated for the polygon.
|
|
"""
|
|
if isinstance(polygons, np.ndarray):
|
|
# optimization: polygons all have the same number of points, so can
|
|
# vectorize
|
|
n = polygons.shape[-2]
|
|
i1, i2, i3 = 0, n//3, 2*n//3
|
|
v1 = polygons[..., i1, :] - polygons[..., i2, :]
|
|
v2 = polygons[..., i2, :] - polygons[..., i3, :]
|
|
else:
|
|
# The subtraction doesn't vectorize because polygons is jagged.
|
|
v1 = np.empty((len(polygons), 3))
|
|
v2 = np.empty((len(polygons), 3))
|
|
for poly_i, ps in enumerate(polygons):
|
|
n = len(ps)
|
|
ps = np.asarray(ps)
|
|
i1, i2, i3 = 0, n//3, 2*n//3
|
|
v1[poly_i, :] = ps[i1, :] - ps[i2, :]
|
|
v2[poly_i, :] = ps[i2, :] - ps[i3, :]
|
|
return np.cross(v1, v2)
|
|
|
|
|
|
def _shade_colors(color, normals, lightsource=None):
|
|
"""
|
|
Shade *color* using normal vectors given by *normals*,
|
|
assuming a *lightsource* (using default position if not given).
|
|
*color* can also be an array of the same length as *normals*.
|
|
"""
|
|
if lightsource is None:
|
|
# chosen for backwards-compatibility
|
|
lightsource = mcolors.LightSource(azdeg=225, altdeg=19.4712)
|
|
|
|
with np.errstate(invalid="ignore"):
|
|
shade = ((normals / np.linalg.norm(normals, axis=1, keepdims=True))
|
|
@ lightsource.direction)
|
|
mask = ~np.isnan(shade)
|
|
|
|
if mask.any():
|
|
# convert dot product to allowed shading fractions
|
|
in_norm = mcolors.Normalize(-1, 1)
|
|
out_norm = mcolors.Normalize(0.3, 1).inverse
|
|
|
|
def norm(x):
|
|
return out_norm(in_norm(x))
|
|
|
|
shade[~mask] = 0
|
|
|
|
color = mcolors.to_rgba_array(color)
|
|
# shape of color should be (M, 4) (where M is number of faces)
|
|
# shape of shade should be (M,)
|
|
# colors should have final shape of (M, 4)
|
|
alpha = color[:, 3]
|
|
colors = norm(shade)[:, np.newaxis] * color
|
|
colors[:, 3] = alpha
|
|
else:
|
|
colors = np.asanyarray(color).copy()
|
|
|
|
return colors
|