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Copy pathgraphics.py
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1391 lines (1129 loc) · 42.8 KB
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import math
from itertools import product
from collections.abc import Iterable
import warnings
import numpy as np
import scipy as sp
from matplotlib import colors
from spatialmath import base as smbase
try:
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
from mpl_toolkits.mplot3d.art3d import (
Poly3DCollection,
Line3DCollection,
pathpatch_2d_to_3d,
)
_matplotlib_exists = True
except ImportError: # pragma: no cover
_matplotlib_exists = False
"""
Set of functions to draw 2D and 3D graphical primitives using matplotlib.
The 2D functions all allow color and line style to be specified by a fmt string
like, 'r' or 'b--'.
The 3D functions require explicity arguments to set properties, like color='b'
All return a list of the graphic objects they create.
"""
# TODO
# return a redrawer object, that can be used for animation
# =========================== 2D shapes =================================== #
def plot_text(pos, text=None, ax=None, color=None, **kwargs):
"""
Plot text using matplotlib
:param pos: position of text
:type pos: array_like(2)
:param text: text
:type text: str
:param ax: axes to draw in, defaults to ``gca()``
:type ax: Axis, optional
:param color: text color, defaults to None
:type color: str or array_like(3), optional
:param kwargs: additional arguments passed to ``pyplot.text()``
:return: the matplotlib object
:rtype: list of Text instance
Example:
.. runblock:: pycon
>>> from spatialmath.base import plotvol2, plot_text
>>> plotvol2(5)
>>> plot_text((1,3), 'foo')
>>> plot_text((2,2), 'bar', 'b')
>>> plot_text((2,2), 'baz', fontsize=14, horizontalalignment='centre')
"""
defaults = {"horizontalalignment": "left", "verticalalignment": "center"}
for k, v in defaults.items():
if k not in kwargs:
kwargs[k] = v
if ax is None:
ax = plt.gca()
handle = plt.text(pos[0], pos[1], text, color=color, **kwargs)
return [handle]
def plot_point(pos, marker="bs", text=None, ax=None, textargs=None, textcolor=None, **kwargs):
"""
Plot a point using matplotlib
:param pos: position of marker
:type pos: array_like(2), ndarray(2,n), list of 2-tuples
:param marker: matplotlub marker style, defaults to 'bs'
:type marker: str or list of str, optional
:param text: text label, defaults to None
:type text: str, optional
:param ax: axes to plot in, defaults to ``gca()``
:type ax: Axis, optional
:return: the matplotlib object
:rtype: list of Text and Line2D instances
Plot one or more points, with optional text label.
- The color of the marker can be different to the color of the text, the
marker color is specified by a single letter in the marker string.
- A point can have multiple markers, given as a list, which will be
overlaid, for instance ``["rx", "ro"]`` will give a ⨂ symbol.
- The optional text label is placed to the right of the marker, and
vertically aligned.
- Multiple points can be marked if ``pos`` is a 2xn array or a list of
coordinate pairs. In this case:
- all points have the same ``text`` label
- ``text`` can include the format string {} which is susbstituted for the
point index, starting at zero
- ``text`` can be a tuple containing a format string followed by vectors
of shape(n). For example::
``("#{0} a={1:.1f}, b={2:.1f}", a, b)``
will label each point with its index (argument 0) and consecutive
elements of ``a`` and ``b`` which are arguments 1 and 2 respectively.
Examples:
- ``plot_point((1,2))`` plot default marker at coordinate (1,2)
- ``plot_point((1,2), 'r*')`` plot red star at coordinate (1,2)
- ``plot_point((1,2), 'r*', 'foo')`` plot red star at coordinate (1,2) and
label it as 'foo'
- ``plot_point(p, 'r*')`` plot red star at points defined by columns of
``p``.
- ``plot_point(p, 'r*', 'foo')`` plot red star at points defined by columns
of ``p`` and label them all as 'foo'
- ``plot_point(p, 'r*', '{0}')`` plot red star at points defined by columns
of ``p`` and label them sequentially from 0
- ``plot_point(p, 'r*', ('{1:.1f}', z))`` plot red star at points defined by
columns of ``p`` and label them all with successive elements of ``z``.
"""
if isinstance(pos, np.ndarray):
if pos.ndim == 1:
x = pos[0]
y = pos[1]
elif pos.ndim == 2 and pos.shape[0] == 2:
x = pos[0, :]
y = pos[1, :]
elif isinstance(pos, (tuple, list)):
# [x, y]
# [(x,y), (x,y), ...]
# [xlist, ylist]
# [xarray, yarray]
if smbase.islistof(pos, (tuple, list)):
x = [z[0] for z in pos]
y = [z[1] for z in pos]
elif smbase.islistof(pos, np.ndarray):
x = pos[0]
y = pos[1]
else:
x = pos[0]
y = pos[1]
textopts = {
"fontsize": 12,
"horizontalalignment": "left",
"verticalalignment": "center",
}
if textargs is not None:
textopts = {**textopts, **textargs}
if textcolor is not None and "color" not in textopts:
textopts["color"] = textcolor
if ax is None:
ax = plt.gca()
handles = []
if isinstance(marker, (list, tuple)):
for m in marker:
handles.append(plt.plot(x, y, m, **kwargs))
else:
handles.append(plt.plot(x, y, marker, **kwargs))
if text is not None:
try:
xy = zip(x, y)
except TypeError:
xy = [(x, y)]
if isinstance(text, str):
# simple string, but might have format chars
for i, (x, y) in enumerate(xy):
handles.append(plt.text(x, y, " " + text.format(i), **textopts))
elif isinstance(text, (tuple, list)):
for i, (x, y) in enumerate(xy):
handles.append(
plt.text(
x,
y,
" " + text[0].format(i, *[d[i] for d in text[1:]]),
**textopts
)
)
return handles
def plot_homline(lines, *args, ax=None, xlim=None, ylim=None, **kwargs):
r"""
Plot a homogeneous line using matplotlib
:param lines: homgeneous lines
:type lines: array_like(3), ndarray(3,N)
:param ax: axes to plot in, defaults to ``gca()``
:type ax: Axis, optional
:param kwargs: arguments passed to ``plot``
:return: matplotlib object
:rtype: list of Line2D instances
Draws the 2D line given in homogeneous form :math:`\ell[0] x + \ell[1] y + \ell[2] = 0` in the current
2D axes.
.. warning: A set of 2D axes must exist in order that the axis limits can
be obtained. The line is drawn from edge to edge.
If ``lines`` is a 3xN array then ``N`` lines are drawn, one per column.
Example:
.. runblock:: pycon
>>> from spatialmath.base import plotvol2, plot_homline
>>> plotvol2(5)
>>> plot_homline((1, -2, 3))
>>> plot_homline((1, -2, 3), 'k--') # dashed black line
"""
ax = axes_logic(ax, 2)
# get plot limits from current graph
if xlim is None:
xlim = np.r_[ax.get_xlim()]
if ylim is None:
ylim = np.r_[ax.get_ylim()]
# if lines.ndim == 1:
# lines = lines.
lines = smbase.getmatrix(lines, (3, None))
handles = []
for line in lines.T: # for each column
if abs(line[1]) > abs(line[0]):
y = (-line[2] - line[0] * xlim) / line[1]
ax.plot(xlim, y, *args, **kwargs)
else:
x = (-line[2] - line[1] * ylim) / line[0]
handles.append(ax.plot(x, ylim, *args, **kwargs))
return handles
def plot_box(
*fmt,
lbrt=None,
lrbt=None,
lbwh=None,
bbox=None,
ltrb=None,
lb=None,
lt=None,
rb=None,
rt=None,
wh=None,
centre=None,
w=None,
h=None,
ax=None,
filled=False,
**kwargs
):
"""
Plot a 2D box using matplotlib
:param bl: bottom-left corner, defaults to None
:type bl: array_like(2), optional
:param tl: top-left corner, defaults to None
:type tl: [array_like(2), optional
:param br: bottom-right corner, defaults to None
:type br: array_like(2), optional
:param tr: top-right corner, defaults to None
:type tr: array_like(2), optional
:param wh: width and height, if both are the same provide scalar, defaults to None
:type wh: scalar, array_like(2), optional
:param centre: centre of box, defaults to None
:type centre: array_like(2), optional
:param w: width of box, defaults to None
:type w: float, optional
:param h: height of box, defaults to None
:type h: float, optional
:param ax: the axes to draw on, defaults to ``gca()``
:type ax: Axis, optional
:param bbox: bounding box matrix, defaults to None
:type bbox: ndarray(2,2), optional
:param color: box outline color
:type color: array_like(3) or str
:param fillcolor: box fill color
:type fillcolor: array_like(3) or str
:param alpha: transparency, defaults to 1
:type alpha: float, optional
:param thickness: line thickness, defaults to None
:type thickness: float, optional
:return: the matplotlib object
:rtype: list of Line2D or Patch.Rectangle instance
The box can be specified in many ways:
- bounding box which is a 2x2 matrix [xmin, xmax, ymin, ymax]
- bounding box [xmin, xmax, ymin, ymax]
- alternative box [xmin, ymin, xmax, ymax]
- centre and width+height
- bottom-left and top-right corners
- bottom-left corner and width+height
- top-right corner and width+height
- top-left corner and width+height
For plots where the y-axis is inverted (eg. for images) then top is the
smaller vertical coordinate.
Example:
.. runblock:: pycon
>>> from spatialmath.base import plotvol2, plot_box
>>> plotvol2(5)
>>> plot_box('r', centre=(2,3), wh=1) # w=h=1
>>> plot_box(tl=(1,1), br=(0,2), filled=True, color='b')
"""
if wh is not None:
if smbase.isscalar(wh):
w, h = wh, wh
else:
w, h = wh
# test for various 4-coordinate versions
if bbox is not None:
lb = bbox[:2]
w, h = bbox[2:]
elif lbwh is not None:
lb = lbwh[:2]
w, h = lbwh[2:]
elif lbrt is not None:
lb = lbrt[:2]
rt = lbrt[2:]
w, h = rt[0] - lb[0], rt[1] - lb[1]
elif lrbt is not None:
lb = (lrbt[0], lrbt[2])
rt = (lrbt[1], lrbt[3])
w, h = rt[0] - lb[0], rt[1] - lb[1]
elif ltrb is not None:
lb = (ltrb[0], ltrb[3])
rt = (ltrb[2], ltrb[1])
w, h = rt[0] - lb[0], rt[1] - lb[1]
elif w is not None and h is not None:
# we have width & height, one corner is enough
if centre is not None:
lb = (centre[0] - w/2, centre[1] - h/2)
elif lt is not None:
lb = (lt[0], lt[1] - h)
elif rt is not None:
lb = (rt[0] - w, rt[1] - h)
elif rb is not None:
lb = (rb[0] - w, rb[1])
else:
# we need two opposite corners
if lb is not None and rt is not None:
w = rt[0] - lb[0]
h = rt[1] - lb[1]
elif lt is not None and rb is not None:
lb = (lt[0], rb[1])
w = rb[0] - lt[0]
h = lt[1] - rb[1]
else:
raise ValueError('cant compute box')
if w < 0:
raise ValueError("width must be positive")
if h < 0:
raise ValueError("height must be positive")
# we only need lb, wh
ax = axes_logic(ax, 2)
if filled:
r = plt.Rectangle(lb, w, h, clip_on=True, **kwargs)
else:
if 'color' in kwargs:
kwargs['edgecolor'] = kwargs['color']
del kwargs['color']
r = plt.Rectangle(lb, w, h, clip_on=True, facecolor='None', **kwargs)
ax.add_patch(r)
return r
def plot_arrow(start, end, ax=None, **kwargs):
"""
Plot 2D arrow
:param start: start point, arrow tail
:type start: array_like(2)
:param end: end point, arrow head
:type end: array_like(2)
:param ax: axes to draw into, defaults to None
:type ax: Axes, optional
:param kwargs: argumetns to pass to :class:`matplotlib.patches.Arrow`
Example:
.. runblock:: pycon
>>> from spatialmath.base import plotvol2, plot_arrow
>>> plotvol2(5)
>>> plot_arrow((-2, 2), (3, 4), color='r', width=0.1) # red arrow
"""
ax = axes_logic(ax, 2)
ax.arrow(start[0], start[1], end[0] - start[0], end[1] - start[1], length_includes_head=True, **kwargs)
def plot_polygon(vertices, *fmt, close=False, **kwargs):
"""
Plot polygon
:param vertices: vertices
:type vertices: ndarray(2,N)
:param close: close the polygon, defaults to False
:type close: bool, optional
:param kwargs: arguments passed to Patch
:return: Matplotlib artist
:rtype: line or patch
Example:
.. runblock:: pycon
>>> from spatialmath.base import plotvol2, plot_polygon
>>> plotvol2(5)
>>> vertices = np.array([[-1, 2, -1], [1, 0, -1]])
>>> plot_polygon(vertices, filled=True, facecolor='g') # green filled triangle
"""
if close:
vertices = np.hstack((vertices, vertices[:, [0]]))
return _render2D(vertices, fmt=fmt, **kwargs)
def _render2D(vertices, pose=None, filled=False, color=None, ax=None, fmt=(), **kwargs):
ax = axes_logic(ax, 2)
if pose is not None:
vertices = pose * vertices
if filled:
if color is not None:
kwargs['facecolor'] = color
kwargs['edgecolor'] = color
r = plt.Polygon(vertices.T, closed=True, **kwargs)
ax.add_patch(r)
else:
r = plt.plot(vertices[0, :], vertices[1, :], *fmt, color=color, **kwargs)
return r
def circle(centre=(0, 0), radius=1, resolution=50, closed=False):
"""
Points on a circle
:param centre: centre of circle, defaults to (0, 0)
:type centre: array_like(2), optional
:param radius: radius of circle, defaults to 1
:type radius: float, optional
:param resolution: number of points on circumferece, defaults to 50
:type resolution: int, optional
:return: points on circumference
:rtype: ndarray(2,N) or ndarray(3,N)
Returns a set of ``resolution`` that lie on the circumference of a circle
of given ``center`` and ``radius``.
If ``len(centre)==3`` then the 3D coordinates are returned, where the
circle lies in the xy-plane and the z-coordinate comes from ``centre[2]``.
"""
if closed:
resolution += 1
u = np.linspace(0.0, 2.0 * np.pi, resolution, endpoint=closed)
x = radius * np.cos(u) + centre[0]
y = radius * np.sin(u) + centre[1]
if len(centre) == 3:
z = np.full(x.shape, centre[2])
return np.array((x, y, z))
else:
return np.array((x, y))
def plot_circle(
radius, centre, *fmt, resolution=50, ax=None, filled=False, **kwargs
):
"""
Plot a circle using matplotlib
:param centre: centre of circle, defaults to (0,0)
:type centre: array_like(2), optional
:param args:
:param radius: radius of circle
:type radius: float
:param resolution: number of points on circumference, defaults to 50
:type resolution: int, optional
:return: the matplotlib object
:rtype: list of Line2D or Patch.Polygon
Plot or more circles. If ``centre`` is a 3xN array, then each column is
taken as the centre of a circle. All circles have the same radius, color
etc.
Example:
.. runblock:: pycon
>>> from spatialmath.base import plotvol2, plot_circle
>>> plotvol2(5)
>>> plot_circle(1, 'r') # red circle
>>> plot_circle(2, 'b--') # blue dashed circle
>>> plot_circle(0.5, filled=True, facecolor='y') # yellow filled circle
"""
centres = smbase.getmatrix(centre, (2, None))
ax = axes_logic(ax, 2)
handles = []
for centre in centres.T:
xy = circle(centre, radius, resolution, closed=not filled)
if filled:
patch = plt.Polygon(xy.T, **kwargs)
handles.append(ax.add_patch(patch))
else:
handles.append(ax.plot(xy[0, :], xy[1, :], *fmt, **kwargs))
return handles
def ellipse(E, centre=(0, 0), scale=1, confidence=None, resolution=40, inverted=False, closed=False):
r"""
Points on ellipse
:param E: ellipse
:type E: ndarray(2,2)
:param centre: ellipse centre, defaults to (0,0,0)
:type centre: tuple, optional
:param scale: scale factor for the ellipse radii
:type scale: float
:param confidence: if E is an inverse covariance matrix plot an ellipse
for this confidence interval in the range [0,1], defaults to None
:type confidence: float, optional
:param resolution: number of points on circumferance, defaults to 40
:type resolution: int, optional
:param inverted: if :math:`\mat{E}^{-1}` is provided, defaults to False
:type inverted: bool, optional
:raises ValueError: [description]
:return: points on circumference
:rtype: ndarray(2,N)
The ellipse is defined by :math:`x^T \mat{E} x = s^2` where :math:`x \in
\mathbb{R}^2` and :math:`s` is the scale factor.
.. note:: For some common cases we require :math:`\mat{E}^{-1}`, for example
- for robot manipulability
:math:`\nu (\mat{J} \mat{J}^T)^{-1} \nu` i
- a covariance matrix
:math:`(x - \mu)^T \mat{P}^{-1} (x - \mu)`
so to avoid inverting ``E`` twice to compute the ellipse, we flag that
the inverse is provided using ``inverted``.
"""
if E.shape != (2, 2):
raise ValueError("ellipse is defined by a 2x2 matrix")
if confidence:
from scipy.stats.distributions import chi2
# process the probability
s = math.sqrt(chi2.ppf(confidence, df=2)) * scale
else:
s = scale
xy = circle(resolution=resolution, closed=closed) # unit circle
if not inverted:
E = np.linalg.inv(E)
e = s * sp.linalg.sqrtm(E) @ xy + np.array(centre, ndmin=2).T
return e
def plot_ellipse(
E,
*fmt,
centre=(0, 0),
scale=1,
confidence=None,
resolution=40,
inverted=False,
ax=None,
filled=False,
**kwargs
):
r"""
Plot an ellipse using matplotlib
:param E: matrix describing ellipse
:type E: ndarray(2,2)
:param centre: centre of ellipse, defaults to (0, 0)
:type centre: array_like(2), optional
:param scale: scale factor for the ellipse radii
:type scale: float
:param resolution: number of points on circumferece, defaults to 40
:type resolution: int, optional
:return: the matplotlib object
:rtype: Line2D or Patch.Polygon
The ellipse is defined by :math:`x^T \mat{E} x = s^2` where :math:`x \in
\mathbb{R}^2` and :math:`s` is the scale factor.
.. note:: For some common cases we require :math:`\mat{E}^{-1}`, for example
- for robot manipulability
:math:`\nu (\mat{J} \mat{J}^T)^{-1} \nu` i
- a covariance matrix
:math:`(x - \mu)^T \mat{P}^{-1} (x - \mu)`
so to avoid inverting ``E`` twice to compute the ellipse, we flag that
the inverse is provided using ``inverted``.
Returns a set of ``resolution`` that lie on the circumference of a circle
of given ``center`` and ``radius``.
Example:
.. runblock:: pycon
>>> from spatialmath.base import plotvol2, plot_circle
>>> plotvol2(5)
>>> plot_ellipse(np.diag((1,2)), 'r') # red ellipse
>>> plot_ellipse(np.diag((1,2)), 'b--') # blue dashed ellipse
>>> plot_ellipse(np.diag((1,2)), filled=True, facecolor='y') # yellow filled ellipse
"""
# allow for centre[2] to plot ellipse in a plane in a 3D plot
xy = ellipse(E, centre, scale, confidence, resolution, inverted, closed=True)
ax = axes_logic(ax, 2)
if filled:
patch = plt.Polygon(xy.T, **kwargs)
ax.add_patch(patch)
else:
plt.plot(xy[0, :], xy[1, :], *fmt, **kwargs)
# =========================== 3D shapes =================================== #
def sphere(radius=1, centre=(0, 0, 0), resolution=50):
"""
Points on a sphere
:param centre: centre of sphere, defaults to (0, 0, 0)
:type centre: array_like(3), optional
:param radius: radius of sphere, defaults to 1
:type radius: float, optional
:param resolution: number of points ``N`` on circumferece, defaults to 50
:type resolution: int, optional
:return: X, Y and Z braid matrices
:rtype: 3 x ndarray(N, N)
:seealso: :func:`plot_sphere`, :func:`~matplotlib.pyplot.plot_surface`, :func:`~matplotlib.pyplot.plot_wireframe`
"""
theta_range = np.linspace(0, np.pi, resolution)
phi_range = np.linspace(-np.pi, np.pi, resolution)
Phi, Theta = np.meshgrid(phi_range, theta_range)
x = radius * np.sin(Theta) * np.cos(Phi) + centre[0]
y = radius * np.sin(Theta) * np.sin(Phi) + centre[1]
z = radius * np.cos(Theta) + centre[2]
return (x, y, z)
def plot_sphere(radius, centre=(0, 0, 0), pose=None, resolution=50, ax=None, **kwargs):
"""
Plot a sphere using matplotlib
:param centre: centre of sphere, defaults to (0, 0, 0)
:type centre: array_like(3), ndarray(3,N), optional
:param radius: radius of sphere, defaults to 1
:type radius: float, optional
:param resolution: number of points on circumferece, defaults to 50
:type resolution: int, optional
:param pose: pose of sphere, defaults to None
:type pose: SE3, optional
:param ax: axes to draw into, defaults to None
:type ax: Axes3D, optional
:param filled: draw filled polygon, else wireframe, defaults to False
:type filled: bool, optional
:param kwargs: arguments passed to ``plot_wireframe`` or ``plot_surface``
:return: matplotlib collection
:rtype: list of Line3DCollection or Poly3DCollection
Plot one or more spheres. If ``centre`` is a 3xN array, then each column is
taken as the centre of a sphere. All spheres have the same radius, color
etc.
Example:
.. runblock:: pycon
>>> from spatialmath.base import plot_sphere
>>> plot_sphere(radius=1, color='r') # red sphere wireframe
>>> plot_sphere(radius=1, centre=(1,1,1), filled=True, facecolor='b')
:seealso: :func:`~matplotlib.pyplot.plot_surface`, :func:`~matplotlib.pyplot.plot_wireframe`
"""
ax = axes_logic(ax, 3)
centre = smbase.getmatrix(centre, (3, None))
handles = []
for c in centre.T:
X, Y, Z = sphere(centre=c, radius=radius, resolution=resolution)
handles.append(_render3D(ax, X, Y, Z, **kwargs))
return handles
def ellipsoid(
E, centre=(0, 0, 0), scale=1, confidence=None, resolution=40, inverted=False
):
r"""
rPoints on an ellipsoid
:param centre: centre of ellipsoid, defaults to (0, 0, 0)
:type centre: array_like(3), optional
:param scale: scale factor for the ellipse radii
:type scale: float
:param confidence: confidence interval, range 0 to 1
:type confidence: float
:param resolution: number of points ``N`` on circumferece, defaults to 40
:type resolution: int, optional
:param inverted: :math:`E^{-1}` rather than :math:`E` provided, defaults to False
:type inverted: bool, optional
:return: X, Y and Z braid matrices
:rtype: 3 x ndarray(N, N)
The ellipse is defined by :math:`x^T \mat{E} x = s^2` where :math:`x \in
\mathbb{R}^3` and :math:`s` is the scale factor.
.. note:: For some common cases we require :math:`\mat{E}^{-1}`, for example
- for robot manipulability
:math:`\nu (\mat{J} \mat{J}^T)^{-1} \nu` i
- a covariance matrix
:math:`(x - \mu)^T \mat{P}^{-1} (x - \mu)`
so to avoid inverting ``E`` twice to compute the ellipse, we flag that
the inverse is provided using ``inverted``.
:seealso: :func:`plot_ellipsoid`, :func:`~matplotlib.pyplot.plot_surface`, :func:`~matplotlib.pyplot.plot_wireframe`
"""
if E.shape != (3, 3):
raise ValueError("ellipsoid is defined by a 3x3 matrix")
if confidence:
# process the probability
from scipy.stats.distributions import chi2
s = math.sqrt(chi2.ppf(confidence, df=3)) * scale
else:
s = scale
if not inverted:
E = np.linalg.inv(E)
x, y, z = sphere() # unit sphere
e = (
s * sp.linalg.sqrtm(E) @ np.array([x.flatten(), y.flatten(), z.flatten()])
+ np.c_[centre].T
)
return e[0, :].reshape(x.shape), e[1, :].reshape(x.shape), e[2, :].reshape(x.shape)
def plot_ellipsoid(
E,
centre=(0, 0, 0),
scale=1,
confidence=None,
resolution=40,
inverted=False,
ax=None,
**kwargs
):
r"""
Draw an ellipsoid using matplotlib
:param E: ellipsoid
:type E: ndarray(3,3)
:param centre: [description], defaults to (0,0,0)
:type centre: tuple, optional
:param scale:
:type scale:
:param confidence: confidence interval, range 0 to 1
:type confidence: float
:param resolution: number of points on circumferece, defaults to 40
:type resolution: int, optional
:param inverted: :math:`E^{-1}` rather than :math:`E` provided, defaults to False
:type inverted: bool, optional
:param ax: [description], defaults to None
:type ax: [type], optional
:param wireframe: [description], defaults to False
:type wireframe: bool, optional
:param stride: [description], defaults to 1
:type stride: int, optional
``plot_ellipse(E)`` draws the ellipsoid defined by :math:`x^T \mat{E} x = 0`
on the current plot.
Example::
H = plot_ellipse(diag([1 2]), [3 4]', 'r'); % draw red ellipse
plot_ellipse(diag([1 2]), [5 6]', 'alter', H); % move the ellipse
plot_ellipse(diag([1 2]), [5 6]', 'alter', H, 'LineColor', 'k'); % change color
plot_ellipse(COVAR, 'confidence', 0.95); % draw 95% confidence ellipse
.. note::
- If a confidence interval is given then ``E`` is interpretted as a covariance
matrix and the ellipse size is computed using an inverse chi-squared function.
:seealso: :func:`~matplotlib.pyplot.plot_surface`, :func:`~matplotlib.pyplot.plot_wireframe`
"""
X, Y, Z = ellipsoid(E, centre, scale, confidence, resolution, inverted)
ax = axes_logic(ax, 3)
handle = _render3D(ax, X, Y, Z, **kwargs)
return [handle]
# TODO, get cylinder, cuboid, cone working
def cylinder(center_x, center_y, radius, height_z, resolution=50):
Z = np.linspace(0, height_z, radius)
theta = np.linspace(0, 2 * np.pi, radius)
theta_grid, z_grid = np.meshgrid(theta, z)
X = radius * np.cos(theta_grid) + center_x
Y = radius * np.sin(theta_grid) + center_y
return X, Y, Z
# https://stackoverflow.com/questions/30715083/python-plotting-a-wireframe-3d-cuboid
# https://stackoverflow.com/questions/26874791/disconnected-surfaces-when-plotting-cones
def plot_cylinder(
radius,
height,
resolution=50,
centre=(0, 0, 0),
ends=False,
ax=None,
filled=False,
**kwargs
):
"""
Plot a cylinder using matplotlib
:param radius: radius of sphere
:type radius: float
:param height: height of cylinder in the z-direction
:type height: float or array_like(2)
:param resolution: number of points on circumferece, defaults to 50
:type resolution: int, optional
:param pose: pose of sphere, defaults to None
:type pose: SE3, optional
:param ax: axes to draw into, defaults to None
:type ax: Axes3D, optional
:param filled: draw filled polygon, else wireframe, defaults to False
:type filled: bool, optional
:param kwargs: arguments passed to ``plot_wireframe`` or ``plot_surface``
:return: matplotlib objects
:rtype: list of matplotlib object types
The axis of the cylinder is parallel to the z-axis and extends from z=0
to z=height, or z=height[0] to z=height[1].
The cylinder can be positioned by setting ``centre``, or positioned
and orientated by setting ``pose``.
:seealso: :func:`~matplotlib.pyplot.plot_surface`, :func:`~matplotlib.pyplot.plot_wireframe`
"""
if smbase.isscalar(height):
height = [0, height]
ax = axes_logic(ax, 3)
x = np.linspace(centre[0] - radius, centre[0] + radius, resolution)
z = height
X, Z = np.meshgrid(x, z)
Y = np.sqrt(radius ** 2 - (X - centre[0]) ** 2) + centre[1] # Pythagorean theorem
handles = []
handles.append(_render3D(ax, X, Y, Z, filled=filled, **kwargs))
handles.append(_render3D(ax, X, (2 * centre[1] - Y), Z, filled=filled, **kwargs))
if ends and kwargs.get("filled", default=False):
floor = Circle(centre[:2], radius, **kwargs)
handles.append(ax.add_patch(floor))
pathpatch_2d_to_3d(floor, z=height[0], zdir="z")
ceiling = Circle(centre[:2], radius, **kwargs)
handles.append(ax.add_patch(ceiling))
pathpatch_2d_to_3d(ceiling, z=height[1], zdir="z")
return handles
def plot_cone(
radius,
height,
resolution=50,
flip=False,
centre=(0, 0, 0),
ends=False,
ax=None,
filled=False,
**kwargs
):
"""
Plot a cone using matplotlib
:param radius: radius of cone at open end
:type radius: float
:param height: height of cone in the z-direction
:type height: float
:param resolution: number of points on circumferece, defaults to 50
:type resolution: int, optional
:param flip: cone faces upward, defaults to False
:type flip: bool, optional
:param pose: pose of cone, defaults to None
:type pose: SE3, optional
:param ax: axes to draw into, defaults to None
:type ax: Axes3D, optional
:param filled: draw filled polygon, else wireframe, defaults to False
:type filled: bool, optional
:param kwargs: arguments passed to ``plot_wireframe`` or ``plot_surface``
:return: matplotlib objects
:rtype: list of matplotlib object types
The axis of the cone is parallel to the z-axis and it is drawn pointing
down. The point is at z=0 and the open end at z= ``height``. If ``flip`` is
True then the cone faces upwards, the point is at z= ``height`` and the open
end at z=0.
The cylinder can be positioned by setting ``centre``, or positioned
and orientated by setting ``pose``.
:seealso: :func:`~matplotlib.pyplot.plot_surface`, :func:`~matplotlib.pyplot.plot_wireframe`
"""
ax = axes_logic(ax, 3)
# https://stackoverflow.com/questions/26874791/disconnected-surfaces-when-plotting-cones
# Set up the grid in polar coords
theta = np.linspace(0, 2 * np.pi, resolution)
r = np.linspace(0, radius, resolution)
T, R = np.meshgrid(theta, r)
# Then calculate X, Y, and Z
X = R * np.cos(T) + centre[0]
Y = R * np.sin(T) + centre[1]
Z = np.sqrt(X ** 2 + Y ** 2) / radius * height + centre[2]
if flip:
Z = height - Z
handles = []
handles.append(_render3D(ax, X, Y, Z, filled=filled, **kwargs))
handles.append(_render3D(ax, X, (2 * centre[1] - Y), Z, filled=filled, **kwargs))
if ends and kwargs.get("filled", default=False):
floor = Circle(centre[:2], radius, **kwargs)
handles.append(ax.add_patch(floor))
pathpatch_2d_to_3d(floor, z=height[0], zdir="z")
ceiling = Circle(centre[:2], radius, **kwargs)
handles.append(ax.add_patch(ceiling))
pathpatch_2d_to_3d(ceiling, z=height[1], zdir="z")
return handles
def plot_cuboid(
sides=[1, 1, 1], centre=(0, 0, 0), pose=None, ax=None, filled=False, **kwargs
):