def vol(self):
"""
Construct cell volumes of the 3D model as 1d array
"""
if getattr(self, '_vol', None) is None:
if self.dim == 2:
A, B, C, D = utils.indexCube('ABCD', self.vnC+1)
normal, area = utils.faceInfo(np.c_[self.gridN, np.zeros(
(self.nN, 1))], A, B, C, D)
self._vol = area
elif self.dim == 3:
# Each polyhedron can be decomposed into 5 tetrahedrons
# However, this presents a choice so we may as well divide in
# two ways and average.
A, B, C, D, E, F, G, H = utils.indexCube('ABCDEFGH', self.vnC +
1)
vol1 = (utils.volTetra(self.gridN, A, B, D, E) + # cutted edge top
utils.volTetra(self.gridN, B, E, F, G) + # cutted edge top
utils.volTetra(self.gridN, B, D, E, G) + # middle
utils.volTetra(self.gridN, B, C, D, G) + # cutted edge bottom
utils.volTetra(self.gridN, D, E, G, H)) # cutted edge bottom
vol2 = (utils.volTetra(self.gridN, A, F, B, C) + # cutted edge top
utils.volTetra(self.gridN, A, E, F, H) + # cutted edge top
utils.volTetra(self.gridN, A, H, F, C) + # middle
utils.volTetra(self.gridN, C, H, D, A) + # cutted edge bottom
utils.volTetra(self.gridN, C, G, H, F)) # cutted edge bottom
self._vol = (vol1 + vol2)/2
return self._vol
def area(self):
if (getattr(self, '_area', None) is None or
getattr(self, '_normals', None) is None):
# Compute areas of cell faces
if(self.dim == 2):
xy = self.gridN
A, B = utils.indexCube('AB', self.vnC+1, np.array([self.nNx,
self.nCy]))
edge1 = xy[B, :] - xy[A, :]
normal1 = np.c_[edge1[:, 1], -edge1[:, 0]]
area1 = length2D(edge1)
A, D = utils.indexCube('AD', self.vnC+1, np.array([self.nCx,
self.nNy]))
# Note that we are doing A-D to make sure the normal points the
# right way.
# Think about it. Look at the picture. Normal points towards C
# iff you do this.
edge2 = xy[A, :] - xy[D, :]
normal2 = np.c_[edge2[:, 1], -edge2[:, 0]]
area2 = length2D(edge2)
self._area = np.r_[utils.mkvc(area1), utils.mkvc(area2)]
self._normals = [normalize2D(normal1), normalize2D(normal2)]
elif(self.dim == 3):
A, E, F, B = utils.indexCube('AEFB', self.vnC+1, np.array(
[self.nNx, self.nCy, self.nCz]))
normal1, area1 = utils.faceInfo(self.gridN, A, E, F, B,
average=False,
normalizeNormals=False)
A, D, H, E = utils.indexCube('ADHE', self.vnC+1, np.array(
[self.nCx, self.nNy, self.nCz]))
normal2, area2 = utils.faceInfo(self.gridN, A, D, H, E,
average=False,
normalizeNormals=False)
A, B, C, D = utils.indexCube('ABCD', self.vnC+1, np.array(
[self.nCx, self.nCy, self.nNz]))
normal3, area3 = utils.faceInfo(self.gridN, A, B, C, D,
average=False,
normalizeNormals=False)
self._area = np.r_[utils.mkvc(area1), utils.mkvc(area2),
utils.mkvc(area3)]
self._normals = [normal1, normal2, normal3]
return self._area