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spv_plot.py
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spv_plot.py
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import numpy as np
import os
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi, voronoi_plot_2d
from matplotlib.patches import Polygon
from matplotlib.collections import PatchCollection
def _voronoi_finite_polygons_2d(vor, radius=None):
"""
Reconstruct infinite voronoi regions in a 2D diagram to finite
regions.
Parameters
----------
vor : Voronoi
Input diagram
radius : float, optional
Distance to 'points at infinity'.
Returns
-------
regions : list of tuples
Indices of vertices in each revised Voronoi regions.
vertices : list of tuples
Coordinates for revised Voronoi vertices. Same as coordinates
of input vertices, with 'points at infinity' appended to the
end.
"""
if vor.points.shape[1] != 2:
raise ValueError("Requires 2D input")
new_regions = []
new_vertices = vor.vertices.tolist()
center = vor.points.mean(axis=0)
if radius is None:
radius = vor.points.ptp().max()
# Construct a map containing all ridges for a given point
all_ridges = {}
for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):
all_ridges.setdefault(p1, []).append((p2, v1, v2))
all_ridges.setdefault(p2, []).append((p1, v1, v2))
# Reconstruct infinite regions
for p1, region in enumerate(vor.point_region):
vertices = vor.regions[region]
if all(v >= 0 for v in vertices):
# finite region
new_regions.append(vertices)
continue
# reconstruct a non-finite region
ridges = all_ridges[p1]
new_region = [v for v in vertices if v >= 0]
for p2, v1, v2 in ridges:
if v2 < 0:
v1, v2 = v2, v1
if v1 >= 0:
# finite ridge: already in the region
continue
# Compute the missing endpoint of an infinite ridge
t = vor.points[p2] - vor.points[p1] # tangent
t /= np.linalg.norm(t)
n = np.array([-t[1], t[0]]) # normal
midpoint = vor.points[[p1, p2]].mean(axis=0)
direction = np.sign(np.dot(midpoint - center, n)) * n
far_point = vor.vertices[v2] + direction * radius
new_region.append(len(new_vertices))
new_vertices.append(far_point.tolist())
# sort region counterclockwise
vs = np.asarray([new_vertices[v] for v in new_region])
c = vs.mean(axis=0)
angles = np.arctan2(vs[:, 1] - c[1], vs[:, 0] - c[0])
new_region = np.array(new_region)[np.argsort(angles)]
# finish
new_regions.append(new_region.tolist())
return new_regions, np.asarray(new_vertices)
def plot_vor(x, ax, L, c_types, colors, plot_scatter, line_width, tri=False):
"""
Plot the Voronoi.
Takes in a set of cell locs (x), tiles these 9-fold, plots the full voronoi, then crops to the field-of-view
:param x: Cell locations (nc x 2)
:param ax: matplotlib axis
:param L: Domain size (width, height)
:param c_types: Cell types/categories
:param colors: Color for each cell type
"""
# TODO: need to explain what's being done here...
grid_x, grid_y = np.mgrid[-1:2, -1:2]
grid_x[0, 0], grid_x[1, 1] = grid_x[1, 1], grid_x[0, 0]
grid_y[0, 0], grid_y[1, 1] = grid_y[1, 1], grid_y[0, 0]
y = np.vstack([x + np.array([i*L[0], j*L[1]]) for i, j in np.array([grid_x.ravel(), grid_y.ravel()]).T])
# ...the following in particular is spaghetti:
c_types_print = np.tile(c_types, 9)
bleed = 0.1 # TODO: no undocumented magic!
c_types_print = c_types_print[(y<L*(1+bleed)).all(axis=1) + (y>-L*bleed).all(axis=1)]
y = y[(y<L*(1+bleed)).all(axis=1) + (y>-L*bleed).all(axis=1)]
regions, vertices = _voronoi_finite_polygons_2d(Voronoi(y))
aspect_ratio = 1.0 # NOTE: this is wrt. given xlim, ylim - so we want 1.0 always
ax.set(aspect=aspect_ratio, xlim=(0,L[0]), ylim=(0,L[1]))
if type(c_types) is list:
# ax.scatter(x[:, 0], x[:, 1],color="grey",zorder=1000)
for region in regions:
polygon = vertices[region]
plt.fill(*zip(*polygon), alpha=0.4, color="grey")
else:
if plot_scatter is True:
for j,i in enumerate(np.unique(c_types)):
ax.scatter(x[c_types==i, 0], x[c_types==i, 1], color=colors[i], zorder=1000)
patches = []
for i, region in enumerate(regions):
patches.append( Polygon(vertices[region], True, \
facecolor=colors[c_types_print[i]], \
edgecolor=(1,1,1,1), linewidth=line_width) )
p = PatchCollection(patches, match_original=True)
# p.set_array(c_types_print)
ax.add_collection(p)
if tri is not False:
for TRI in tri:
for j in range(3):
a, b = TRI[j], TRI[np.mod(j + 1, 3)]
if (a >= 0) and (b >= 0):
X = np.stack((x[a], x[b])).T
ax.plot(X[0], X[1], color="black")
def plot_vor_boundary(x, ax, L, c_types, colors, plot_scatter, line_width, tri=False):
"""
Plot the Voronoi.
Takes in a set of cell locs (x), tiles these 9-fold, plots the full voronoi, then crops to the field-of-view
:param x: Cell locations (nc x 2)
:param ax: matplotlib axis
:param tri: Is either a (n_v x 3) np.ndarray of dtype **np.int64** defining the triangulation.
Or **False** where the triangulation is not plotted
"""
n_C = np.size(c_types) # number of actual cells (= excl. boundary particles)
x = x[~np.isnan(x[:,0])]
c_types_print = np.ones(x.shape[0],dtype=np.int32)*-1
c_types_print[:n_C] = c_types
regions, vertices = _voronoi_finite_polygons_2d(Voronoi(x))
ax.set(aspect=1, xlim=(0,L[0]), ylim=(0,L[1]))
if type(c_types) is list:
# ax.scatter(x[:, 0], x[:, 1],color="grey",zorder=1000)
for region in regions:
polygon = vertices[region]
plt.fill(*zip(*polygon), alpha=0.4, color="grey")
else:
patches = []
if plot_scatter is True:
ax.scatter(x[:n_C, 0], x[:n_C, 1], color="black", zorder=1000)
ax.scatter(x[n_C:, 0], x[n_C:, 1], color="grey", zorder=1000)
for i, region in enumerate(regions):
patches.append( Polygon(vertices[region], True, \
facecolor=colors[c_types_print[i]], \
edgecolor="white", alpha=0.5, linewidth=line_width) )
p = PatchCollection(patches, match_original=True)
# p.set_array(c_types_print)
ax.add_collection(p)
if tri is not False:
for TRI in tri:
for j in range(3):
a, b = TRI[j], TRI[np.mod(j + 1, 3)]
if (a >= 0) and (b >= 0):
X = np.stack((x[a], x[b])).T
ax.plot(X[0], X[1], color="black")
def check_forces(data, iter, F, dir_name="plots"):
"""
Plot the forces (quiver) on each cell (voronoi)
To be used as a quick check.
:param x: Cell coordinates (nc x 2)
:param F: Forces on each cell (nc x 2)
"""
x = data
Vor = Voronoi(x)
fig, ax = plt.subplots()
ax.set(aspect=1)
voronoi_plot_2d(Vor, ax=ax)
# ax.scatter(x[:, 0], x[:, 1])
ax.quiver(x[:, 0], x[:, 1], F[:, 0], F[:, 1])
fig.savefig("%s/%d.png" %(dir_name, iter), bbox_inches='tight', pad_inches=0, dpi=200)
plt.close(fig)
def plot_step(data, iter, domain_size, c_types, colors, plot_scatter, tri_save, \
dir_name="plots", an_type="periodic", line_width=1.0, tri=False):
"""
Writes the given simulation stage into a .png file.
TODO: Add optional force plotting. See animate() in voronoi_model_periodic.py
:param data: Simulation stage.
:param iter: Current iteration.
:param dir_name: Directory name to save simulation within
:param an_type: Animation-type -- either "periodic" or "boundary"
"""
if an_type == "periodic":
plot_fn = plot_vor
if an_type == "boundary":
plot_fn = plot_vor_boundary
if not os.path.exists(dir_name):
os.makedirs(dir_name)
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
ax1.cla()
ax1.axis('off')
if tri is True:
plot_fn(data, ax1, domain_size, c_types, colors, plot_scatter, line_width, tri=tri_save)
else:
plot_fn(data, ax1, domain_size, c_types, colors, plot_scatter, line_width, tri=False)
# if self.plot_forces is True:
# x = self.x_save[skip*i]
# mask = ~np.isnan(self.x_save[skip*i,:,0]) * ~np.isnan(self.x_save[skip*i+1,:,0])
# x = x[mask]
# F = self.x_save[skip*i+1,mask] - self.x_save[skip*i,mask]
# ax1.quiver(x[:,0],x[:,1],F[:,0],F[:,1])
ax1.set(aspect=1, xlim=(0, domain_size[0]), ylim=(0, domain_size[1]))
fig.savefig("%s/%s.png" %(dir_name, iter), bbox_inches='tight', pad_inches=0, dpi=300)
plt.close(fig)