def __compute_dual_volume(self, s, parent, pts, bpts, signs, dim):
## s: simplex whose dual volume is desired (NumPy array)
## parent: simplex initiating this call whose face is s (NumPy
## array)
## pts: circumcenters at all dimensions (NumPy array)
## bpts: circumcenters at all dimensions in barycentric
## coordinates (Python list)
## Remark: Sign s is determined by location of cicumcenter
## with respect to a face of a simplex and the opposite vertex
## of the face in the simplex. It is +1 if the circumcenter
## and the opposite vertex lie on the same side with respect
## to the halfplane generated by the face. It is -1 if they
## lie on opposite sides of this halfplane. Consequently, sign
## can be determined as the sign of that component of the
## barycentric coordiante of the circumcenter which
## corresponds to the opposite vertex.
data = self[dim]
index = data.simplex_to_index[s]
pts[dim] = data.circumcenter[index]
bpts[dim] = data.bary_circumcenter[index]
sgn = 1
if parent is not None:
opposite_vertex = list(set(parent) - set(s))[0]
ov_index = list(parent).index(opposite_vertex)
signs[dim] = copysign(1, bpts[-1][ov_index])
for i in range(dim, self.complex_dimension()):
sgn *= signs[i]
data.dual_volume[index] += sgn * unsigned_volume(pts[dim:,:])
if dim > 0:
for bs in s.boundary():
self.__compute_dual_volume(bs, s, pts, bpts, signs, dim-1)
def __compute_dual_volume(self,s,pts,dim):
data = self[dim]
index = data.simplex_to_index[s]
pts[dim] = data.circumcenter[index]
data.dual_volume[index] += unsigned_volume(pts[dim:,:])
if dim > 0:
for bs in s.boundary():
self.__compute_dual_volume(bs,pts,dim-1)
def compute_primal_volume(self,dim):
"""Compute the volume of all simplices for a given dimension
If the top simplex is of the same dimension as its embedding,
the signed volume is computed.
"""
data = self[dim]
data.primal_volume = zeros((data.num_simplices,))
if dim == self.embedding_dimension():
for i,s in enumerate(self.simplices):
pts = self.vertices[s,:]
data.primal_volume[i] = signed_volume(pts)
else:
for i,s in enumerate(data.simplices):
pts = self.vertices[s,:]
data.primal_volume[i] = unsigned_volume(pts)
