def voronoi(centres):
vor = Voronoi(centres)
vor.ridge_vertices = np.array(list(
zip(*vor.ridge_vertices))).T # simple np.array call is too slow..
# edges are not consistently oriented so we fix this
_correct_orientation(vor)
return vor
def finite_voronoi(vor, scale=1):
"""
finite_voronoi(vor, scale=1)
Construct finite boundaries for Voronoi diagram.
Parameters
----------
points : ndarray of floats, shape (npoints, 2)
Coordinates of points to construct a convex hull from
scale : float, optional
Scale of extension lines. Some points may be outside their associated
region if scale < 1
Attributes
----------
points : ndarray of double, shape (npoints, 2)
Coordinates of input points.
vertices : ndarray of double, shape (nvertices, 2)
Coordinates of the Voronoi vertices.
ridge_points : ndarray of ints, shape (nridges, 2)
Indices of the points between which each Voronoi ridge lies.
ridge_vertices : list of list of ints, shape (nridges, *)
Indices of the Voronoi vertices forming each Voronoi ridge.
regions : list of list of ints, shape (nregions, *)
Indices of the Voronoi vertices forming each Voronoi region.
point_region : list of ints, shape (npoints)
Index of the Voronoi region for each input point.
"""
vor = Voronoi(points)
# Calculate size of extension lines
ptp_bound = vor.points.ptp(axis=0).max() * scale
# Count number of new vertices required
nv_existing = len(vor.vertices)
nv_required = len([v for v in vor.ridge_vertices if v[0] < 0])
new_vertices = list(range(nv_existing, nv_existing + nv_required))
outer_vertices = []
center = vor.points.mean(axis=0)
for idx, pointidx, simplex in zip(range(len(vor.ridge_points)),
vor.ridge_points, vor.ridge_vertices):
simplex = np.asarray(simplex)
if np.any(simplex < 0):
# Find finite end Voronoi vertex
i = simplex[simplex >= 0][0]
# Calculate tangent and normal
t = vor.points[pointidx[1]] - vor.points[pointidx[0]]
t /= np.linalg.norm(t)
n = np.array([-t[1], t[0]])
# Draw line
midpoint = vor.points[pointidx].mean(axis=0)
direction = np.sign(np.dot(midpoint - center, n)) * n
far_point = vor.vertices[i] + direction * ptp_bound
outer_vertices.append(list(pointidx))
# Add start point to ridge vertices
vor.ridge_vertices[idx][0] = len(vor.vertices)
vor.vertices = np.vstack([vor.vertices, far_point])
# Assign points to outer vertices
outer_points = list(
set([item for sublist in outer_vertices for item in sublist]))
for op in outer_points:
p = [nv for nv, ov in zip(new_vertices, outer_vertices) if op in ov]
vor.ridge_vertices = np.vstack([vor.ridge_vertices, p])
vor.ridge_points = np.vstack([vor.ridge_points, [op, -1]])
# Cycle through points
for point_idx in range(len(vor.points)):
region_idx = vor.point_region[point_idx]
segs = vor.ridge_vertices[(vor.ridge_points == point_idx).any(axis=1)]
# Remove first point from segment, to force correct direction
segs[0, 0] = segs[0, 1]
# Put segments in correct order
for i in range(1, len(segs)):
idx = np.where([np.any(np.in1d(segs[i - 1], s))
for s in segs[i:]])[0][-1]
segs[i:] = np.roll(segs[i:], -idx, axis=0)
# Extract vertices from segments
pts = segs.flatten()
_, i = np.unique(pts, return_index=True)
vor.regions[region_idx] = pts[np.sort(i)]
return vor