def plot(points,
ax=None,
space=None,
point_type='extrinsic',
**point_draw_kwargs):
"""Plot points in the 3D Special Euclidean Group.
Plot points in the 3D Special Euclidean Group,
by showing them as trihedrons.
"""
if space not in IMPLEMENTED:
raise NotImplementedError(
'The plot function is not implemented'
' for space {}. The spaces available for visualization'
' are: {}.'.format(space, IMPLEMENTED))
if points is None:
raise ValueError("No points given for plotting.")
points = gs.to_ndarray(points, to_ndim=2)
if space in ('SO3_GROUP', 'SE3_GROUP'):
if ax is None:
ax = plt.subplot(111, projection='3d')
if space == 'SE3_GROUP':
ax_s = AX_SCALE * gs.amax(gs.abs(points[:, 3:6]))
elif space == 'SO3_GROUP':
ax_s = AX_SCALE * gs.amax(gs.abs(points[:, :3]))
plt.setp(ax,
xlim=(-ax_s, ax_s),
ylim=(-ax_s, ax_s),
zlim=(-ax_s, ax_s),
xlabel='X',
ylabel='Y',
zlabel='Z')
trihedrons = convert_to_trihedron(points, space=space)
for t in trihedrons:
t.draw(ax, **point_draw_kwargs)
elif space == 'S1':
circle = Circle()
ax = circle.set_ax(ax=ax)
circle.add_points(points)
circle.draw(ax, **point_draw_kwargs)
elif space == 'S2':
sphere = Sphere()
ax = sphere.set_ax(ax=ax)
sphere.add_points(points)
sphere.draw(ax, **point_draw_kwargs)
elif space == 'H2_poincare_disk':
poincare_disk = PoincareDisk(point_type=point_type)
ax = poincare_disk.set_ax(ax=ax)
poincare_disk.add_points(points)
poincare_disk.draw(ax, **point_draw_kwargs)
elif space == 'poincare_polydisk':
n_disks = points.shape[1]
poincare_poly_disk = PoincarePolyDisk(point_type=point_type,
n_disks=n_disks)
n_columns = gs.ceil(n_disks**0.5)
n_rows = gs.ceil(n_disks / n_columns)
axis_list = []
for i_disk in range(n_disks):
axis_list.append(ax.add_subplot(n_rows, n_columns, i_disk + 1))
for i_disk, ax in enumerate(axis_list):
ax = poincare_poly_disk.set_ax(ax=ax)
poincare_poly_disk.clear_points()
poincare_poly_disk.add_points(points[:, i_disk, ...])
poincare_poly_disk.draw(ax, **point_draw_kwargs)
elif space == 'H2_poincare_half_plane':
poincare_half_plane = PoincareHalfPlane()
ax = poincare_half_plane.set_ax(ax=ax)
poincare_half_plane.add_points(points)
poincare_half_plane.draw(ax, **point_draw_kwargs)
elif space == 'H2_klein_disk':
klein_disk = KleinDisk()
ax = klein_disk.set_ax(ax=ax)
klein_disk.add_points(points)
klein_disk.draw(ax, **point_draw_kwargs)
return ax
def plot(points, ax=None, space=None, point_type=None, **point_draw_kwargs):
"""Plot points in one of the implemented manifolds.
The implemented manifolds are:
- the special orthogonal group SO(3)
- the special Euclidean group SE(3)
- the circle S1 and the sphere S2
- the hyperbolic plane (the Poincare disk, the Poincare
half plane and the Klein disk)
- the Poincare polydisk
- the Kendall shape space of 2D triangles
- the Kendall shape space of 3D triangles
Parameters
----------
points : array-like, shape=[..., dim]
Points to be plotted.
space: str, optional, {'SO3_GROUP', 'SE3_GROUP', 'S1', 'S2',
'H2_poincare_disk', 'H2_poincare_half_plane', 'H2_klein_disk',
'poincare_polydisk', 'S32', 'M32', 'S33', 'M33'}
point_type: str, optional, {'extrinsic', 'ball', 'half-space', 'pre-shape'}
"""
if space not in IMPLEMENTED:
raise NotImplementedError(
'The plot function is not implemented'
' for space {}. The spaces available for visualization'
' are: {}.'.format(space, IMPLEMENTED))
if points is None:
raise ValueError("No points given for plotting.")
if points.ndim < 2:
points = gs.expand_dims(points, 0)
if space in ('SO3_GROUP', 'SE3_GROUP'):
if ax is None:
ax = plt.subplot(111, projection='3d')
if space == 'SE3_GROUP':
ax_s = AX_SCALE * gs.amax(gs.abs(points[:, 3:6]))
elif space == 'SO3_GROUP':
ax_s = AX_SCALE * gs.amax(gs.abs(points[:, :3]))
ax_s = float(ax_s)
bounds = (-ax_s, ax_s)
plt.setp(ax,
xlim=bounds,
ylim=bounds,
zlim=bounds,
xlabel='X',
ylabel='Y',
zlabel='Z')
trihedrons = convert_to_trihedron(points, space=space)
for t in trihedrons:
t.draw(ax, **point_draw_kwargs)
elif space == 'S1':
circle = Circle()
ax = circle.set_ax(ax=ax)
circle.add_points(points)
circle.draw(ax, **point_draw_kwargs)
elif space == 'S2':
sphere = Sphere()
ax = sphere.set_ax(ax=ax)
sphere.add_points(points)
sphere.draw(ax, **point_draw_kwargs)
elif space == 'H2_poincare_disk':
if point_type is None:
point_type = 'extrinsic'
poincare_disk = PoincareDisk(point_type=point_type)
ax = poincare_disk.set_ax(ax=ax)
poincare_disk.add_points(points)
poincare_disk.draw(ax, **point_draw_kwargs)
plt.axis('off')
elif space == 'poincare_polydisk':
if point_type is None:
point_type = 'extrinsic'
n_disks = points.shape[1]
poincare_poly_disk = PoincarePolyDisk(point_type=point_type,
n_disks=n_disks)
n_columns = int(gs.ceil(n_disks**0.5))
n_rows = int(gs.ceil(n_disks / n_columns))
axis_list = []
for i_disk in range(n_disks):
axis_list.append(ax.add_subplot(n_rows, n_columns, i_disk + 1))
for i_disk, one_ax in enumerate(axis_list):
ax = poincare_poly_disk.set_ax(ax=one_ax)
poincare_poly_disk.clear_points()
poincare_poly_disk.add_points(points[:, i_disk, ...])
poincare_poly_disk.draw(ax, **point_draw_kwargs)
elif space == 'H2_poincare_half_plane':
if point_type is None:
point_type = 'half-space'
poincare_half_plane = PoincareHalfPlane(point_type=point_type)
ax = poincare_half_plane.set_ax(points=points, ax=ax)
poincare_half_plane.add_points(points)
poincare_half_plane.draw(ax, **point_draw_kwargs)
elif space == 'H2_klein_disk':
klein_disk = KleinDisk()
ax = klein_disk.set_ax(ax=ax)
klein_disk.add_points(points)
klein_disk.draw(ax, **point_draw_kwargs)
elif space == 'SE2_GROUP':
plane = SpecialEuclidean2()
ax = plane.set_ax(ax=ax)
plane.add_points(points)
plane.draw(ax, **point_draw_kwargs)
elif space == 'S32':
sphere = KendallSphere()
sphere.add_points(points)
sphere.draw()
sphere.draw_points()
ax = sphere.ax
elif space == 'M32':
sphere = KendallSphere(point_type='extrinsic')
sphere.add_points(points)
sphere.draw()
sphere.draw_points()
ax = sphere.ax
elif space == 'S33':
disk = KendallDisk()
disk.add_points(points)
disk.draw()
disk.draw_points()
ax = disk.ax
elif space == 'M33':
disk = KendallDisk(point_type='extrinsic')
disk.add_points(points)
disk.draw()
disk.draw_points()
ax = disk.ax
return ax