def VORONOI2(points, Amat=np.zeros((0, 2)), bvec=np.zeros(0)):
"""
get the voronoi partition of the set { x : A x \leq b } (assume closed),
generated by points
"""
# Approach: per point, just get all equations in play...
# then, do edge enumeration!
# [DN] get Delaunay neighbors graph
# [DN.1] triangulate
tri = spatial.Delaunay(points)
graph = nx.Graph()
# [DN.2] find the edges in the triangulation
indices, seq = tri.vertex_neighbor_vertices
for i, pt in enumerate(tri.points):
for j in seq[indices[i] : indices[i + 1]]:
graph.add_edge(i, j)
def Abij(i, j):
# gets the jth row of Ai, bi, describing ith voronoi cell
xi = np.array(tri.points[i])
xj = np.array(tri.points[j])
aij = 2.0 * (xj - xi)
bij = np.sum(np.power(xj, 2.0)) - np.sum(np.power(xi, 2.0))
return aij, bij
def Abi(i):
# gets (A,b) of the ith voronoi cell
rows = [Abij(i, j) for j in graph.neighbors_iter(i)]
AA = np.vstack([a for a, b in rows])
bb = np.array([b for a, b in rows])
AA = np.vstack([AA, Amat]) # augment with bbox
bb = np.hstack([bb, bvec])
return celim.eliminate_redundant_constraints(AA, bb)
res = [None for i in xrange(len(points))]
for i in graph.nodes_iter():
Ai, bi = Abi(i)
res[i] = geom2.poly2_topology(*sys)
return res
def VORONOI2(points, Amat=np.zeros((0, 2)), bvec=np.zeros(0)):
"""
get the voronoi partition of the set { x : A x \leq b } (assume closed),
generated by points
"""
# Approach: per point, just get all equations in play...
# then, do edge enumeration!
# [DN] get Delaunay neighbors graph
# [DN.1] triangulate
tri = spatial.Delaunay(points)
graph = nx.Graph()
# [DN.2] find the edges in the triangulation
indices, seq = tri.vertex_neighbor_vertices
for i, pt in enumerate(tri.points):
for j in seq[indices[i]:indices[i + 1]]:
graph.add_edge(i, j)
def Abij(i, j):
# gets the jth row of Ai, bi, describing ith voronoi cell
xi = np.array(tri.points[i])
xj = np.array(tri.points[j])
aij = 2. * (xj - xi)
bij = np.sum(np.power(xj, 2.)) - np.sum(np.power(xi, 2.))
return aij, bij
def Abi(i):
# gets (A,b) of the ith voronoi cell
rows = [Abij(i, j) for j in graph.neighbors_iter(i)]
AA = np.vstack([a for a, b in rows])
bb = np.array([b for a, b in rows])
AA = np.vstack([AA, Amat]) # augment with bbox
bb = np.hstack([bb, bvec])
return celim.eliminate_redundant_constraints(AA, bb)
res = [None for i in xrange(len(points))]
for i in graph.nodes_iter():
Ai, bi = Abi(i)
res[i] = geom2.poly2_topology(*sys)
return res
if __name__ == "__main__":
import matplotlib.pyplot as plt
plt.close("all")
import geom2
# generators
points = [np.random.rand(2) for i in xrange(10)]
# bounding box
A, b = geom2.box2()
# voronoi cell ineq. representations
sys = VORONOI(points, A, b)
# topologies
TOPO = [geom2.poly2_topology(A, b) for A, b in sys]
plt.figure()
X, Y = geom2.get_xy(points)
plt.scatter(X, Y, marker="x")
for topo in TOPO:
pos = {}
for u, data in topo.nodes_iter(data=True):
pos[u] = data.get("pos")
nx.draw(topo, pos=pos)
ax = plt.gca()
ax.set_aspect("equal")
plt.show()
if __name__ == '__main__':
import matplotlib.pyplot as plt
plt.close('all')
import geom2
# generators
points = [np.random.rand(2) for i in xrange(10)]
# bounding box
A, b = geom2.box2()
# voronoi cell ineq. representations
sys = VORONOI(points, A, b)
# topologies
TOPO = [geom2.poly2_topology(A, b) for A, b in sys]
plt.figure()
X, Y = geom2.get_xy(points)
plt.scatter(X, Y, marker='x')
for topo in TOPO:
pos = {}
for u, data in topo.nodes_iter(data=True):
pos[u] = data.get('pos')
nx.draw(topo, pos=pos)
ax = plt.gca()
ax.set_aspect('equal')
plt.show()