def Volume(self):
(n1, n2, n3, n4, n5, n6) = self.nodePositions()
A1 = Area(n3 - n1, n2 - n1)
A2 = Area(n6 - n4, n5 - n4)
c1 = (n1 + n2 + n3) / 3.
c2 = (n4 + n5 + n6) / 3.
V = (A1 + A2) / 2. * (c1 - c2)
return abs(V)
def getFaceNodesAndArea(self, nid, nidOpposite):
nids = self.nodeIDs()[:6]
indx1 = nids.index(nid)
indx2 = nids.index(nidOpposite)
## offset so it's easier to map the nodes with the QRG
pack = [indx1 + 1, indx2 + 1]
pack.sort()
mapper = { # reverse points away from the element
[1, 2]: [1, 2, 3], # close
[2, 3]: [1, 2, 3],
[1, 3]: [1, 2, 3],
[4, 5]: [4, 5, 6], # far-reverse
[5, 6]: [4, 5, 6],
[4, 6]: [4, 5, 6],
[1, 5]: [1, 2, 5, 4], # bottom
[2, 4]: [1, 2, 5, 4],
[1, 6]: [1, 3, 6, 4], # left-reverse
[3, 4]: [1, 3, 6, 4],
[2, 6]: [2, 5, 6, 3], # right
[3, 5]: [2, 3, 6, 5],
}
pack2 = mapper[pack]
if len(pack2) == 3:
(n1, n2, n3) = pack2
faceNodeIDs = [n1, n2, n3]
n1i = nids.index(n1 - 1)
n2i = nids.index(n2 - 1)
n3i = nids.index(n3 - 1)
p1 = self.nodes[n1i].Position()
p2 = self.nodes[n2i].Position()
p3 = self.nodes[n3i].Position()
a = p1 - p2
b = p1 - p3
A = Area(a, b)
else:
(n1, n2, n3, n4) = pack2
n1i = nids.index(n1 - 1)
n2i = nids.index(n2 - 1)
n3i = nids.index(n3 - 1)
n4i = nids.index(n4 - 1)
faceNodeIDs = [n1, n2, n3, n4]
p1 = self.nodes[n1i].Position()
p2 = self.nodes[n2i].Position()
p3 = self.nodes[n3i].Position()
p4 = self.nodes[n4i].Position()
a = p1 - p3
b = p2 - p4
A = Area(a, b)
return [faceNodeIDs, A]
def areaCentroid(self, n1, n2, n3, n4):
a = n1 - n2
b = n2 - n4
area1 = Area(a, b)
c1 = (n1 + n2 + n4) / 3.
a = n2 - n4
b = n2 - n3
area2 = Area(a, b)
c2 = (n2 + n3 + n4) / 3.
area = area1 + area2
centroid = (c1 * area1 + c2 * area2) / area
return(area, centroid)
def Area(self):
r"""
\f[ A = \frac{1}{2} \lvert (n_1-n_3) \times (n_2-n_4) \rvert \f]
where a and b are the quad's cross node point vectors
"""
(n1, n2, n3, n4) = self.nodePositions()
a = n1 - n3
b = n2 - n4
area = Area(a, b)
return area
def Area(self):
r"""
returns the normal vector
\f[ \large A = \frac{1}{2} (n_0-n_1) times (n_0-n_2) \f]
"""
(n1, n2, n3, n4, n5, n6) = self.nodePositions()
a = n1 - n3
b = n1 - n5
area = Area(a, b)
return area
def Area(self):
r"""
returns the normal vector
\f[ \large A = \frac{1}{2} (n_0-n_1) \times (n_0-n_2) \f]
"""
(n0, n1, n2) = self.nodePositions()
a = n0 - n1
b = n0 - n2
area = Area(a, b)
return area
def AreaCentroid(self, debug=False):
"""
@code
1-----2
| /|
| A1/ |
| / |
|/ A2 |
4-----3
centroid
c = sum(ci*Ai)/sum(A)
where:
c=centroid
A=area
@endcode
"""
#if debug:
# print("nodes = %s" %(self.nodes))
(n1, n2, n3, n4) = self.nodePositions()
a = n1 - n2
b = n2 - n4
area1 = Area(a, b)
c1 = self.CentroidTriangle(n1, n2, n4)
a = n2 - n4
b = n2 - n3
area2 = Area(a, b)
c2 = self.CentroidTriangle(n2, n3, n4)
area = area1 + area2
centroid = (c1 * area1 + c2 * area2) / area
if debug:
print("c1=%s \n c2=%s \n a1=%s a2=%s" % (c1, c2, area1, area2))
print("type(centroid=%s centroid=%s \n" %
(type(centroid), centroid))
return (area, centroid)