def voronoi_plot_no_points(vor, ax=None):
"""
Plot the given Voronoi diagram in 2-D
Parameters
----------
vor : scipy.spatial.Voronoi instance
Diagram to plot
ax : matplotlib.axes.Axes instance, optional
Axes to plot on
Returns
-------
fig : matplotlib.figure.Figure instance
Figure for the plot
See Also
--------
Voronoi
Notes
-----
Requires Matplotlib.
"""
if vor.points.shape[1] != 2:
raise ValueError("Voronoi diagram is not 2-D")
# ax.plot(vor.points[:, 0], vor.points[:, 1], 'o')
# ax.plot(vor.vertices[:,0], vor.vertices[:,1], 'o')
for simplex in vor.ridge_vertices:
simplex = np.asarray(simplex)
if np.all(simplex >= 0):
ax.plot(vor.vertices[simplex, 0], vor.vertices[simplex, 1], 'k-')
ptp_bound = vor.points.ptp(axis=0)
center = vor.points.mean(axis=0)
for pointidx, simplex in zip(vor.ridge_points, vor.ridge_vertices):
simplex = np.asarray(simplex)
if np.any(simplex < 0):
i = simplex[simplex >= 0][0] # finite end Voronoi vertex
t = vor.points[pointidx[1]] - vor.points[pointidx[0]] # tangent
t /= np.linalg.norm(t)
n = np.array([-t[1], t[0]]) # normal
midpoint = vor.points[pointidx].mean(axis=0)
direction = np.sign(np.dot(midpoint - center, n)) * n
far_point = vor.vertices[i] + direction * ptp_bound.max()
ax.plot([vor.vertices[i, 0], far_point[0]],
[vor.vertices[i, 1], far_point[1]], 'k--')
_adjust_bounds(ax, vor.points)
return ax.figure
def hull_without_points(hull, ax=None):
"""
modified from scipy.spatial.convex_hull_plot_2d
"""
if ax is None:
ax = pyplot.gcf().gca()
if hull.points.shape[1] != 2:
raise ValueError("Convex hull is not 2-D")
for simplex in hull.simplices:
ax.plot(hull.points[simplex, 0], hull.points[simplex, 1], 'k-')
_adjust_bounds(ax, hull.points)
return ax.figure
def hull_without_points(hull, ax=None):
"""
modified from scipy.spatial.convex_hull_plot_2d
"""
if ax is None:
ax = pyplot.gcf().gca()
if hull.points.shape[1] != 2:
raise ValueError("Convex hull is not 2-D")
for simplex in hull.simplices:
ax.plot(hull.points[simplex,0], hull.points[simplex,1], 'k-')
_adjust_bounds(ax, hull.points)
return ax.figure
def cone_rays(angles, ai, hull, which=None, ax=None, fill_args={}, plot=True):
"""
draw the cone rays
"""
angles = np.sort(angles)
points = np.array([np.cos(angles), np.sin(angles)]).T
vor = Voronoi(points)
if vor.points.shape[1] != 2:
raise ValueError("Voronoi diagram is not 2-D")
if ax is None:
ax = pyplot.gca()
rays = np.array([(np.cos(_angle), np.sin(_angle)) for _angle in angles])
for i in range(rays.shape[0]):
rays[i] /= np.linalg.norm(rays[i])
if plot:
for ray in rays:
ax.plot([0, 100 * ray[0]], [0, 100 * ray[1]], 'k--')
if which is not None:
if which < rays.shape[0] - 1:
active_rays = [100 * rays[which], 100 * rays[which + 1]]
else:
active_rays = [100 * rays[0], 100 * rays[-1]]
poly = np.vstack([
active_rays[0],
np.zeros(2), active_rays[1],
100 * (active_rays[0] + active_rays[1])
])
dual_rays = np.linalg.pinv(np.array(active_rays))
angle1 = angle(dual_rays[:, 0])
angle2 = angle(dual_rays[:, 1])
else:
poly = None
active_rays = None
dual_rays = None
_adjust_bounds(ax, vor.points)
ax.set_xticks([])
ax.set_yticks([])
return ax, poly, dual_rays, np.array(active_rays)
def voronoi_plot_2d(vor, ax=None, **kw):
"""
Plot the given Voronoi diagram in 2-D
Parameters
----------
vor : scipy.spatial.Voronoi instance
Diagram to plot
ax : matplotlib.axes.Axes instance, optional
Axes to plot on
show_points: bool, optional
Add the Voronoi points to the plot.
show_vertices : bool, optional
Add the Voronoi vertices to the plot.
line_colors : string, optional
Specifies the line color for polygon boundaries
line_width : float, optional
Specifies the line width for polygon boundaries
line_alpha: float, optional
Specifies the line alpha for polygon boundaries
point_size: float, optional
Specifies the size of points
Returns
-------
fig : matplotlib.figure.Figure instance
Figure for the plot
See Also
--------
Voronoi
Notes
-----
Requires Matplotlib.
Examples
--------
Set of point:
>>> import matplotlib.pyplot as plt
>>> points = np.random.rand(10,2) #random
Voronoi diagram of the points:
>>> from scipy.spatial import Voronoi, voronoi_plot_2d
>>> vor = Voronoi(points)
using `voronoi_plot_2d` for visualisation:
>>> fig = voronoi_plot_2d(vor)
using `voronoi_plot_2d` for visualisation with enhancements:
>>> fig = voronoi_plot_2d(vor, show_vertices=False, line_colors='orange',
... line_width=2, line_alpha=0.6, point_size=2)
>>> plt.show()
"""
from matplotlib.collections import LineCollection
if vor.points.shape[1] != 2:
raise ValueError("Voronoi diagram is not 2-D")
if kw.get('show_points', True):
point_size = kw.get('point_size', None)
ax.plot(vor.points[:, 0],
vor.points[:, 1],
'.',
markersize=point_size,
frameon=False)
if kw.get('show_vertices', True):
ax.plot(vor.vertices[:, 0], vor.vertices[:, 1], 'o', frameon=False)
line_colors = kw.get('line_colors', 'k')
line_width = kw.get('line_width', 1.0)
line_alpha = kw.get('line_alpha', 1.0)
center = vor.points.mean(axis=0)
ptp_bound = vor.points.ptp(axis=0)
finite_segments = []
infinite_segments = []
for pointidx, simplex in zip(vor.ridge_points, vor.ridge_vertices):
simplex = np.asarray(simplex)
if np.all(simplex >= 0):
finite_segments.append(vor.vertices[simplex])
else:
i = simplex[simplex >= 0][0] # finite end Voronoi vertex
t = vor.points[pointidx[1]] - vor.points[pointidx[0]] # tangent
t /= np.linalg.norm(t)
n = np.array([-t[1], t[0]]) # normal
midpoint = vor.points[pointidx].mean(axis=0)
direction = np.sign(np.dot(midpoint - center, n)) * n
# if (vor.furthest_site): Had to comment this out to bypass error
if hasattr(vor, 'furthest_site'):
direction = -direction
far_point = vor.vertices[i] + direction * ptp_bound.max()
infinite_segments.append([vor.vertices[i], far_point])
ax.add_collection(
LineCollection(finite_segments,
colors=line_colors,
lw=line_width,
alpha=line_alpha,
linestyle='solid'))
ax.add_collection(
LineCollection(infinite_segments,
colors=line_colors,
lw=line_width,
alpha=line_alpha,
linestyle='solid'))
_adjust_bounds(ax, vor.points)
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
return ax.figure
def cone_rays(angles, which=None, ax=None, fill_args={}):
"""
Plot the given Voronoi diagram in 2-D based on a set of directions
Parameters
----------
vor : scipy.spatial.Voronoi instance
Diagram to plot
ax : matplotlib.axes.Axes instance, optional
Axes to plot on
Returns
-------
fig : matplotlib.figure.Figure instance
Figure for the plot
See Also
--------
Voronoi
Notes
-----
Requires Matplotlib.
"""
angles = np.sort(angles)
points = np.array([np.cos(angles), np.sin(angles)]).T
vor = Voronoi(points)
if vor.points.shape[1] != 2:
raise ValueError("Voronoi diagram is not 2-D")
if ax is None:
ax = pyplot.gca()
rays = np.array([(np.cos(angle), np.sin(angle)) for angle in angles])
for i in range(rays.shape[0]):
rays[i] /= np.linalg.norm(rays[i])
rays *= 100
for ray in rays:
ax.plot([0, ray[0]], [0, ray[1]], 'k--')
if which is not None:
if which < rays.shape[0] - 1:
active_rays = [rays[which], rays[which + 1]]
else:
active_rays = [rays[0], rays[-1]]
poly = np.vstack([
active_rays[0],
np.zeros(2), active_rays[1],
100 * (active_rays[0] + active_rays[1])
])
dual_rays = np.linalg.pinv(np.array(active_rays))
else:
poly = None
active_rays = None
dual_rays = None
_adjust_bounds(ax, vor.points)
ax.set_xticks([])
ax.set_yticks([])
return ax, poly, dual_rays, np.array(active_rays)
def cone_rays(angles, ai, hull, which=None, ax=None, fill_args={},
plot=True):
"""
Plot the given Voronoi diagram in 2-D based on a set of directions
Parameters
----------
vor : scipy.spatial.Voronoi instance
Diagram to plot
ax : matplotlib.axes.Axes instance, optional
Axes to plot on
Returns
-------
fig : matplotlib.figure.Figure instance
Figure for the plot
See Also
--------
Voronoi
Notes
-----
Requires Matplotlib.
"""
angles = np.sort(angles)
points = np.array([np.cos(angles), np.sin(angles)]).T
vor = Voronoi(points)
if vor.points.shape[1] != 2:
raise ValueError("Voronoi diagram is not 2-D")
if ax is None:
ax = pyplot.gca()
rays = np.array([(np.cos(_angle), np.sin(_angle)) for _angle in angles])
for i in range(rays.shape[0]):
rays[i] /= np.linalg.norm(rays[i])
rays *= 100
if plot:
for ray in rays:
ax.plot([0,ray[0]],[0,ray[1]], 'k--')
if which is not None:
if which < rays.shape[0]-1:
active_rays = [rays[which], rays[which+1]]
else:
active_rays = [rays[0], rays[-1]]
poly = np.vstack([active_rays[0], np.zeros(2), active_rays[1], 100*(active_rays[0]+active_rays[1])])
dual_rays = np.linalg.pinv(np.array(active_rays))
angle1 = angle(dual_rays[:,0])
angle2 = angle(dual_rays[:,1])
else:
poly = None
active_rays = None
dual_rays = None
_adjust_bounds(ax, vor.points)
ax.set_xticks([])
ax.set_yticks([])
return ax, poly, dual_rays, np.array(active_rays)