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Modified the scaling values for plotting uncertainty ellipses to properly display 3 standard deviations for both 2D and 3D cases.

release/4.3a0
Calvin 2022-01-25 16:39:05 -06:00
parent f9d1af328f
commit d9a00ded23
1 changed files with 27 additions and 15 deletions
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42
python/gtsam/utils/plot.py
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@ -75,8 +75,9 @@ def plot_covariance_ellipse_3d(axes,
Plots a Gaussian as an uncertainty ellipse
Based on Maybeck Vol 1, page 366
k=2.296 corresponds to 1 std, 68.26% of all probability
k=11.82 corresponds to 3 std, 99.74% of all probability
For the 3D case:
k = 3.527 corresponds to 1 std, 68.26% of all probability
k = 14.157 corresponds to 3 std, 99.74% of all probability
Args:
axes (matplotlib.axes.Axes): Matplotlib axes.
@ -87,7 +88,7 @@ def plot_covariance_ellipse_3d(axes,
n: Defines the granularity of the ellipse. Higher values indicate finer ellipses.
alpha: Transparency value for the plotted surface in the range [0, 1].
"""
k = 11.82
k = np.sqrt(14.157)
U, S, _ = np.linalg.svd(P)
radii = k * np.sqrt(S)
@ -113,7 +114,14 @@ def plot_point2_on_axes(axes,
linespec: str,
P: Optional[np.ndarray] = None) -> None:
"""
Plot a 2D point on given axis `axes` with given `linespec`.
Plot a 2D point and its corresponding uncertainty ellipse on given axis
`axes` with given `linespec`.
Based on Stochastic Models, Estimation, and Control Vol 1 by Maybeck,
page 366
For the 2D case:
k = 2.296 corresponds to 1 std, 68.26% of all probability
k = 11.820 corresponds to 3 std, 99.74% of all probability
Args:
axes (matplotlib.axes.Axes): Matplotlib axes.
@ -125,16 +133,15 @@ def plot_point2_on_axes(axes,
if P is not None:
w, v = np.linalg.eig(P)
# "Sigma" value for drawing the uncertainty ellipse. 5 sigma corresponds
# to a 99.9999% confidence, i.e. assuming the estimation has been
# computed properly, there is a 99.999% chance that the true position
# of the point will lie within the uncertainty ellipse.
k = 5.0
# Scaling value for the uncertainty ellipse, we multiply by 2 because
# matplotlib takes the diameter and not the radius of the major and
# minor axes of the ellipse.
k = 2*np.sqrt(11.820)
angle = np.arctan2(v[1, 0], v[0, 0])
e1 = patches.Ellipse(point,
np.sqrt(w[0] * k),
np.sqrt(w[1] * k),
np.sqrt(w[0]) * k,
np.sqrt(w[1]) * k,
np.rad2deg(angle),
fill=False)
axes.add_patch(e1)
@ -178,6 +185,12 @@ def plot_pose2_on_axes(axes,
"""
Plot a 2D pose on given axis `axes` with given `axis_length`.
Based on Stochastic Models, Estimation, and Control Vol 1 by Maybeck,
page 366
For the 2D case:
k = 2.296 corresponds to 1 std, 68.26% of all probability
k = 11.820 corresponds to 3 std, 99.74% of all probability
Args:
axes (matplotlib.axes.Axes): Matplotlib axes.
pose: The pose to be plotted.
@ -205,13 +218,12 @@ def plot_pose2_on_axes(axes,
w, v = np.linalg.eig(gPp)
# k = 2.296
k = 5.0
k = 2*np.sqrt(11.820)
angle = np.arctan2(v[1, 0], v[0, 0])
e1 = patches.Ellipse(origin,
np.sqrt(w[0] * k),
np.sqrt(w[1] * k),
np.sqrt(w[0]) * k,
np.sqrt(w[1]) * k,
np.rad2deg(angle),
fill=False)
axes.add_patch(e1)