class Component2(object):
""" Base class for Wing, Body, and Junction components. """
def __init__(self):
self.Ps = []
self.Ks = []
self.oml0 = []
def createSurfaces(self, Ks, nu, nv, du, dv, d):
Ps = []
for j in range(len(nv)):
for i in range(len(nu)):
u1 = (sum(nu[:i]) - i) / (sum(nu) - len(nu))
u2 = (sum(nu[: i + 1]) - i - 1) / (sum(nu) - len(nu))
v1 = (sum(nv[:j]) - j) / (sum(nv) - len(nv))
v2 = (sum(nv[: j + 1]) - j - 1) / (sum(nv) - len(nv))
P = PAMlib.createsurfaces(nu[i], nv[j], du, dv, d, u1, u2, v1, v2)
Ps.append(P)
K = numpy.zeros((len(nu), len(nv)), int)
counter = 0
if len(Ks) > 0:
counter = numpy.max(Ks[-1]) + 1
for j in range(len(nv)):
for i in range(len(nu)):
K[i, j] = counter
counter += 1
return Ps, K
def createInterface(self, n, edge1, edge2, swap=False):
P = PAMlib.createinterface(n, edge1.shape[0], edge1, edge2)
if swap:
P = numpy.swapaxes(P, 0, 1)
return P
def translatePoints(self, dx, dy, dz):
for k in range(len(self.Ps)):
self.Ps[k][:, :, 0] += dx
self.Ps[k][:, :, 1] += dy
self.Ps[k][:, :, 2] += dz
def updateQs(self):
Qs = self.Qs
Ns = self.Ns
oml0 = self.oml0
for f in range(len(Ns)):
PAMlib.updateqs(oml0.nQ, Ns[f].shape[0], Ns[f].shape[1], Ns[f], Qs[f], oml0.Q)
def initializeDOFs(self):
oml0 = self.oml0
Ks = self.Ks
Qs = []
Ns = []
for f in range(len(Ks)):
ni = self.getni(f, 0)
nj = self.getni(f, 1)
Qs.append(numpy.zeros((sum(ni) + 1, sum(nj) + 1, 3), complex))
Ns.append(numpy.zeros((sum(ni) + 1, sum(nj) + 1, 5), int))
Ns[f][:, :, :] = -1
for j in range(Ks[f].shape[1]):
for i in range(Ks[f].shape[0]):
surf = Ks[f][i, j]
if surf != -1:
for v in range(nj[j] + 1):
jj = sum(nj[:j]) + v
for u in range(ni[i] + 1):
ii = sum(ni[:i]) + u
uType = self.classifyC(u, ii, ni[i] + 1, Ns[f].shape[0])
vType = self.classifyC(v, jj, nj[j] + 1, Ns[f].shape[1])
isInteriorDOF = uType == 2 and vType == 2
if isInteriorDOF or self.isExteriorDOF(f, uType, vType, i, j):
Ns[f][ii, jj, 0] = oml0.getIndex(surf, u, v, 2)
Ns[f][ii, jj, 1] = i
Ns[f][ii, jj, 2] = u
Ns[f][ii, jj, 3] = j
Ns[f][ii, jj, 4] = v
self.Qs = Qs
self.Ns = Ns
def classifyC(self, u, i, lenu, leni):
if i == 0:
return 0
elif i == leni - 1:
return -1
elif u == 0:
return 1
elif u == lenu - 1:
return 1
else:
return 2
def computeDims(self, aircraft):
ndims = int(numpy.max(abs(self.faces)))
oml0 = self.oml0
Ks = self.Ks
dims = []
for d in range(ndims):
dims.append([])
for f in range(self.faces.shape[0]):
for k in range(2):
d = abs(self.faces[f, k]) - 1
dims[d] = numpy.zeros(Ks[f].shape[k], int)
for f in range(self.faces.shape[0]):
for i in range(Ks[f].shape[0]):
for j in range(Ks[f].shape[1]):
surf = Ks[f][i, j]
if not surf == -1:
for k in range(2):
edge = oml0.surf_edge[surf, k, 0]
group = oml0.edge_group[abs(edge) - 1] - 1
m = oml0.group_m[group] - 1
d = abs(self.faces[f, k]) - 1
if k == 0:
index = i
else:
index = j
if self.faces[f, k] > 0:
dims[d][index] = int(m)
else:
dims[d][-index - 1] = int(m)
self.dims = dims
def getni(self, f, a):
d = abs(self.faces[f, a]) - 1
if self.faces[f, a] > 0:
return self.dims[d]
else:
return self.dims[d][::-1]
def setC1(self, t, f, i=None, j=None, u=None, v=None, d=None, val=True):
""" Set C1 continuity
t: {string} surface or edge C1
f: face index
i,j: surface index
both given: only consider [i,j] surface
one given: loop through and apply to all of the other index
none given: apply to all surfaces
u,v: edge/vert index (for surfC1)
both given: only consider [u,v] corner/side
one given: loop through and apply to all of the other index
none given: apply to all corners/sides
u,v,d: side index (for edgeC1)
"""
if t == "surf":
func = self.setSurfC1
elif t == "edge":
func = self.setEdgeC1
if (not i == None) and (not j == None):
func(f, i, j, u, v, d, val)
elif not i == None:
for j in range(self.Ks[f].shape[1]):
func(f, i, j, u, v, d, val)
elif not j == None:
for i in range(self.Ks[f].shape[0]):
func(f, i, j, u, v, d, val)
else:
for j in range(self.Ks[f].shape[1]):
for i in range(self.Ks[f].shape[0]):
func(f, i, j, u, v, d, val)
def setSurfC1(self, f, i, j, u, v, d, val):
oml0 = self.oml0
surf = self.Ks[f][i, j]
if not surf == -1:
if u == None and v == None:
oml0.surf_c1[surf, :, :] = val
elif u == None:
oml0.surf_c1[surf, :, v] = val
elif v == None:
oml0.surf_c1[surf, u, :] = val
else:
oml0.surf_c1[surf, u, v] = val
def setEdgeC1(self, f, i, j, u, v, d, val):
oml0 = self.oml0
surf = self.Ks[f][i, j]
if not surf == -1:
if u == None:
edge = oml0.surf_edge[surf, 0, v]
else:
edge = oml0.surf_edge[surf, 1, u]
if d == None:
oml0.edge_c1[abs(edge) - 1, :] = val
elif edge > 0:
oml0.edge_c1[abs(edge) - 1, d] = val
else:
oml0.edge_c1[abs(edge) - 1, 1 - abs(d)] = val
def setCornerC1(self, f, i=0, j=0, val=True):
self.setC1("edge", f, i=i, j=j, u=i, d=j, val=val)
self.setC1("edge", f, i=i, j=j, v=j, d=i, val=val)
def check(self, uType, vType, u=None, v=None):
if u == None:
uVal = uType == 2
else:
uVal = uType == u
if v == None:
vVal = vType == 2
else:
vVal = vType == v
return uVal and vVal
def computeMs(self):
oml0 = self.oml0
Ks = self.Ks
Ms = []
for f in range(len(Ks)):
ni = self.getni(f, 0)
nj = self.getni(f, 1)
Ms.append(numpy.zeros((sum(ni) + 1, sum(nj) + 1), int))
Ms[f][:, :] = -1
for j in range(Ks[f].shape[1]):
for i in range(Ks[f].shape[0]):
surf = Ks[f][i, j]
if surf != -1:
for v in range(nj[j] + 1):
jj = sum(nj[:j]) + v
for u in range(ni[i] + 1):
ii = sum(ni[:i]) + u
Ms[f][ii, jj] = oml0.getIndex(surf, u, v, 1)
self.Ms = Ms
def findJunctions(self):
oml0 = self.oml0
Ks = self.Ks
Js = []
for f in range(len(Ks)):
ni = self.getni(f, 0)
nj = self.getni(f, 1)
k0 = Ks[f].shape[0]
k1 = Ks[f].shape[1]
SPs = []
EPs = []
for j in range(k1):
for i in range(k0):
if Ks[f][i, j] == -1:
SPs.append([i, j])
EPs.append([i, j])
if (i > 0 and Ks[f][i - 1, j] == -1) or (j > 0 and Ks[f][i, j - 1] == -1):
SPs.pop()
if (i < k0 - 1 and Ks[f][i + 1, j] == -1) or (j < k1 - 1 and Ks[f][i, j + 1] == -1):
EPs.pop()
J = numpy.zeros((len(SPs), 4), int)
for s in range(len(SPs)):
SP = SPs[s]
for e in range(len(EPs)):
EP = EPs[e]
if SP[0] <= EP[0] and SP[1] <= EP[1]:
if numpy.linalg.norm(1 + Ks[f][SP[0] : EP[0] + 1, SP[1] : EP[1] + 1]) < 1e-14:
J[s, :] = [sum(ni[: SP[0]]), sum(nj[: SP[1]]), sum(ni[: EP[0] + 1]), sum(nj[: EP[1] + 1])]
Js.append(J)
self.Js = Js
def flattenGeometry(self):
oml0 = self.oml0
Ms = self.Ms
for f in range(len(Ms)):
ni = Ms[f].shape[0]
nj = Ms[f].shape[1]
for i in range(ni):
for j in range(nj):
oml0.C[Ms[f][i, j], :] = self.getFlattenedC(f, i, j, ni, nj)
oml0.computePointsC()
def initializeLayout(self):
def getv(r, v1, v2):
return numpy.array(v1) * (1 - r) + numpy.array(v2) * r
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
edges = []
edges.append([0, 0, 0, 1])
edges.append([0, 0, 1, 0])
edges.append([0, 1, 1, 1])
edges.append([1, 0, 1, 1])
skinIndices = self.getSkinIndices()
for s in range(len(skinIndices)):
for f in skinIndices[s]:
for k in range(Js[f].shape[0]):
C11 = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C12 = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C21 = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C22 = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
edges.append([C11[0], C11[1], C12[0], C12[1]])
edges.append([C11[0], C11[1], C21[0], C21[1]])
edges.append([C12[0], C12[1], C22[0], C22[1]])
edges.append([C21[0], C21[1], C22[0], C22[1]])
for m in self.keys:
member = self.members[m]
for i in range(member.nmem):
if member.nmem == 1:
ii = 0
else:
ii = i / (member.nmem - 1)
A = getv(ii, member.A1, member.A2)
B = getv(ii, member.B1, member.B2)
C = getv(ii, member.C1, member.C2)
D = getv(ii, member.D1, member.D2)
for j in range(member.ndiv):
if (B[2] == 0 and C[2] == 0) or (B[2] == 1 and C[2] == 1):
V0 = getv(j / member.ndiv, B, C)
V1 = getv((j + 1) / member.ndiv, B, C)
edges.append([V0[0], V0[1], V1[0], V1[1]])
if (A[2] == 0 and D[2] == 0) or (A[2] == 1 and D[2] == 1):
V0 = getv(j / member.ndiv, A, D)
V1 = getv((j + 1) / member.ndiv, A, D)
edges.append([V0[0], V0[1], V1[0], V1[1]])
self.layout = Layout(6, self.getAR(), 1, numpy.array(edges))
def findJunctionQuadsAndEdges(self):
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
C = numpy.zeros((4, 2))
ctd = numpy.zeros(2)
nquad = self.layout.nquad
nedge = self.layout.nedge
edges = self.layout.edges
verts = self.layout.verts
poly_vert = self.layout.poly_vert
skinIndices = self.getSkinIndices()
JQs = []
JEs = []
quad_indices = []
for s in range(len(skinIndices)):
JQ = []
for f in skinIndices[s]:
for q in range(nquad):
ctd[:] = 0
for k in range(4):
ctd[:] += 0.25 * verts[poly_vert[q, k] - 1, :]
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
if (
min(C[:, 0]) < ctd[0]
and ctd[0] < max(C[:, 0])
and min(C[:, 1]) < ctd[1]
and ctd[1] < max(C[:, 1])
):
JQ.append(q + 1)
if JQ == []:
JQ.append(-1)
JQs.append(JQ)
JE = []
for f in skinIndices[s]:
for e in range(nedge):
ctd[:] = 0
for k in range(2):
ctd[:] += 0.5 * verts[edges[e, k] - 1, :]
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
if (
min(C[:, 0]) < ctd[0]
and ctd[0] < max(C[:, 0])
and min(C[:, 1]) < ctd[1]
and ctd[1] < max(C[:, 1])
):
JEs.append(e + 1)
JEs.append(JE)
quad_indices.append(self.layout.getQuadIndices(JQ))
if len(quad_indices) == 1:
quad_indices.append(quad_indices[0])
self.JQs = JQs
self.JEs = JEs
self.quad_indices = numpy.array(quad_indices, order="F").T
def projectSkins(self):
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
skinIndices = self.getSkinIndices()
C = numpy.zeros((4, 2), order="F")
Bs = []
Ss = []
quad_indices = []
for s in range(len(skinIndices)):
Ps = []
P, S = self.layout.extractFlattened(self.JQs[s], max(self.quad_indices[:, s]))
Ps.append(P)
Ss.append(S)
for f in skinIndices[s]:
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
P = self.layout.extractEdges(self.JQs[s], min(C[:, 0]), max(C[:, 0]), min(C[:, 1]), max(C[:, 1]))
Ps.append(P)
P = numpy.vstack(Ps)
surfindices = []
for f in skinIndices[s]:
surfindices.append(self.Ks[f].flatten())
surfs = numpy.unique(numpy.hstack(surfindices))
if surfs[0] == -1:
surfs = numpy.delete(surfs, 0)
Q = numpy.zeros((P.shape[0], 3))
Q[:, 2] = 1.0
ss, u, v = oml0.computeProjection(P, surfs=surfs, Q=Q)
Bs.append(oml0.computeBases(ss, u, v))
B = oml0.vstackSparse(Bs)
BM = B.dot(oml0.M)
P = BM.dot(oml0.Q)
As, S = self.computeStructure(P)
Ss.append(S)
A = oml0.vstackSparse(As)
ABM = A.dot(BM)
S = numpy.vstack(Ss)
self.strABM = ABM
self.strS = S
def computeStructure(self, P):
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
layout = self.layout
skinIndices = self.getSkinIndices()
C = numpy.zeros((4, 2), order="F")
As = []
Jns = []
Jus = []
col = 0
for s in range(len(skinIndices)):
n = max(self.quad_indices[:, s]) * self.layout.n ** 2
Aa = numpy.ones(n)
Ai = numpy.linspace(0, n - 1, n)
Aj = numpy.linspace(0, n - 1, n) + col
As.append(scipy.sparse.csr_matrix((Aa, (Ai, Aj)), shape=(n, P.shape[0])))
Jn = []
Ju = []
col += n
for f in skinIndices[s]:
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
nu1, nu2, nv1, nv2 = layout.countJunctionEdges(
self.JQs[s], min(C[:, 0]), max(C[:, 0]), min(C[:, 1]), max(C[:, 1])
)
Jn.append([nu1, nu2, nv1, nv2])
Ju.append([min(C[:, 0]), max(C[:, 0]), min(C[:, 1]), max(C[:, 1])])
nP = layout.n * (nu1 + nu2 + nv1 + nv2)
col += nP
if Jn == []:
Jn.append([-1, -1, -1, -1])
Ju.append([-1, -1, -1, -1])
Jns.append(numpy.array(Jn, int, order="F"))
Jus.append(numpy.array(Ju, order="F"))
nM = len(self.keys)
members = numpy.zeros((nM, 34), order="F")
for i in range(nM):
member = self.members[self.keys[i]]
members[i, :4] = [member.domain, member.shape, member.nmem, member.ndiv]
members[i, 4:16] = member.A1 + member.B1 + member.C1 + member.D1
members[i, 16:28] = member.A2 + member.B2 + member.C2 + member.D2
members[i, 28:] = [member.tx, member.ty, member.rx, member.ry, member.n1, member.n2]
nP, nS = PAMlib.countinternalnodes(self.layout.n, nM, members)
P2, M, S = PAMlib.computeinternalnodes(nP, nS, self.layout.n, nM, members)
nA = PAMlib.countannz(nP, layout.nvert, layout.nquad, layout.verts, layout.poly_vert, self.quad_indices, P2, M)
if len(skinIndices) == 1:
Aa, Ai, Aj = PAMlib.assembleamtx(
nA,
self.layout.n,
nP,
Jns[0].shape[0],
Jns[0].shape[0],
self.layout.nvert,
self.layout.nquad,
Jns[0],
Jns[0],
Jus[0],
Jus[0],
self.quad_indices,
self.layout.verts,
self.layout.poly_vert,
P2,
M,
)
else:
Aa, Ai, Aj = PAMlib.assembleamtx(
nA,
self.layout.n,
nP,
Jns[0].shape[0],
Jns[1].shape[0],
self.layout.nvert,
self.layout.nquad,
Jns[0],
Jns[1],
Jus[0],
Jus[1],
self.quad_indices,
self.layout.verts,
self.layout.poly_vert,
P2,
M,
)
As.append(scipy.sparse.csr_matrix((Aa, (Ai, Aj)), shape=(max(Ai) + 1, P.shape[0])))
return As, S
def buildStructure(self):
self.computeMs()
self.findJunctions()
self.flattenGeometry()
self.initializeLayout()
self.findJunctionQuadsAndEdges()
self.projectSkins()
def addMembers(
self,
name,
domain,
shape,
nmem,
ndiv,
A1=None,
B1=None,
C1=None,
D1=None,
A2=None,
B2=None,
C2=None,
D2=None,
tx=0.5,
ty=0.5,
rx=1.0,
ry=1.0,
n1=5,
n2=5,
):
if A2 == None:
A2 = [-1, -1, -1]
B2 = [-1, -1, -1]
C2 = [-1, -1, -1]
D2 = [-1, -1, -1]
if B1 == None:
B1 = [-1, -1, -1]
B1[:2] = A1[:2]
B1[2] = C1[2]
if D1 == None:
D1 = [-1, -1, -1]
D1[:2] = C1[:2]
D1[2] = A1[2]
if B2 == None:
B2 = [-1, -1, -1]
B2[:2] = A2[:2]
B2[2] = C2[2]
if D2 == None:
D2 = [-1, -1, -1]
D2[:2] = C2[:2]
D2[2] = A2[2]
self.members[name] = Member(domain, shape, nmem, ndiv, A1, B1, C1, D1, A2, B2, C2, D2, tx, ty, rx, ry, n1, n2)
self.keys.append(name)
class Component2(object):
""" Base class for Wing, Body, and Junction components. """
def __init__(self):
self.Ps = []
self.Ks = []
self.oml0 = []
def createSurfaces(self, Ks, nu, nv, du, dv, d):
Ps = []
for j in range(len(nv)):
for i in range(len(nu)):
u1 = (sum(nu[:i]) - i) / (sum(nu) - len(nu))
u2 = (sum(nu[:i + 1]) - i - 1) / (sum(nu) - len(nu))
v1 = (sum(nv[:j]) - j) / (sum(nv) - len(nv))
v2 = (sum(nv[:j + 1]) - j - 1) / (sum(nv) - len(nv))
P = PAMlib.createsurfaces(nu[i], nv[j], du, dv, d, u1, u2, v1,
v2)
Ps.append(P)
K = numpy.zeros((len(nu), len(nv)), int)
counter = 0
if len(Ks) > 0:
counter = numpy.max(Ks[-1]) + 1
for j in range(len(nv)):
for i in range(len(nu)):
K[i, j] = counter
counter += 1
return Ps, K
def createInterface(self, n, edge1, edge2, swap=False):
P = PAMlib.createinterface(n, edge1.shape[0], edge1, edge2)
if swap:
P = numpy.swapaxes(P, 0, 1)
return P
def translatePoints(self, dx, dy, dz):
for k in range(len(self.Ps)):
self.Ps[k][:, :, 0] += dx
self.Ps[k][:, :, 1] += dy
self.Ps[k][:, :, 2] += dz
def updateQs(self):
Qs = self.Qs
Ns = self.Ns
oml0 = self.oml0
for f in range(len(Ns)):
PAMlib.updateqs(oml0.nQ, Ns[f].shape[0], Ns[f].shape[1], Ns[f],
Qs[f], oml0.Q)
def initializeDOFs(self):
oml0 = self.oml0
Ks = self.Ks
Qs = []
Ns = []
for f in range(len(Ks)):
ni = self.getni(f, 0)
nj = self.getni(f, 1)
Qs.append(numpy.zeros((sum(ni) + 1, sum(nj) + 1, 3), complex))
Ns.append(numpy.zeros((sum(ni) + 1, sum(nj) + 1, 5), int))
Ns[f][:, :, :] = -1
for j in range(Ks[f].shape[1]):
for i in range(Ks[f].shape[0]):
surf = Ks[f][i, j]
if surf != -1:
for v in range(nj[j] + 1):
jj = sum(nj[:j]) + v
for u in range(ni[i] + 1):
ii = sum(ni[:i]) + u
uType = self.classifyC(u, ii, ni[i] + 1,
Ns[f].shape[0])
vType = self.classifyC(v, jj, nj[j] + 1,
Ns[f].shape[1])
isInteriorDOF = (uType == 2 and vType == 2)
if isInteriorDOF or self.isExteriorDOF(
f, uType, vType, i, j):
Ns[f][ii, jj,
0] = oml0.getIndex(surf, u, v, 2)
Ns[f][ii, jj, 1] = i
Ns[f][ii, jj, 2] = u
Ns[f][ii, jj, 3] = j
Ns[f][ii, jj, 4] = v
self.Qs = Qs
self.Ns = Ns
def classifyC(self, u, i, lenu, leni):
if i == 0:
return 0
elif i == leni - 1:
return -1
elif u == 0:
return 1
elif u == lenu - 1:
return 1
else:
return 2
def computeDims(self, aircraft):
ndims = int(numpy.max(abs(self.faces)))
oml0 = self.oml0
Ks = self.Ks
dims = []
for d in range(ndims):
dims.append([])
for f in range(self.faces.shape[0]):
for k in range(2):
d = abs(self.faces[f, k]) - 1
dims[d] = numpy.zeros(Ks[f].shape[k], int)
for f in range(self.faces.shape[0]):
for i in range(Ks[f].shape[0]):
for j in range(Ks[f].shape[1]):
surf = Ks[f][i, j]
if not surf == -1:
for k in range(2):
edge = oml0.surf_edge[surf, k, 0]
group = oml0.edge_group[abs(edge) - 1] - 1
m = oml0.group_m[group] - 1
d = abs(self.faces[f, k]) - 1
if k == 0:
index = i
else:
index = j
if self.faces[f, k] > 0:
dims[d][index] = int(m)
else:
dims[d][-index - 1] = int(m)
self.dims = dims
def getni(self, f, a):
d = abs(self.faces[f, a]) - 1
if self.faces[f, a] > 0:
return self.dims[d]
else:
return self.dims[d][::-1]
def setC1(self, t, f, i=None, j=None, u=None, v=None, d=None, val=True):
""" Set C1 continuity
t: {string} surface or edge C1
f: face index
i,j: surface index
both given: only consider [i,j] surface
one given: loop through and apply to all of the other index
none given: apply to all surfaces
u,v: edge/vert index (for surfC1)
both given: only consider [u,v] corner/side
one given: loop through and apply to all of the other index
none given: apply to all corners/sides
u,v,d: side index (for edgeC1)
"""
if t == 'surf':
func = self.setSurfC1
elif t == 'edge':
func = self.setEdgeC1
if (not i == None) and (not j == None):
func(f, i, j, u, v, d, val)
elif not i == None:
for j in range(self.Ks[f].shape[1]):
func(f, i, j, u, v, d, val)
elif not j == None:
for i in range(self.Ks[f].shape[0]):
func(f, i, j, u, v, d, val)
else:
for j in range(self.Ks[f].shape[1]):
for i in range(self.Ks[f].shape[0]):
func(f, i, j, u, v, d, val)
def setSurfC1(self, f, i, j, u, v, d, val):
oml0 = self.oml0
surf = self.Ks[f][i, j]
if not surf == -1:
if u == None and v == None:
oml0.surf_c1[surf, :, :] = val
elif u == None:
oml0.surf_c1[surf, :, v] = val
elif v == None:
oml0.surf_c1[surf, u, :] = val
else:
oml0.surf_c1[surf, u, v] = val
def setEdgeC1(self, f, i, j, u, v, d, val):
oml0 = self.oml0
surf = self.Ks[f][i, j]
if not surf == -1:
if u == None:
edge = oml0.surf_edge[surf, 0, v]
else:
edge = oml0.surf_edge[surf, 1, u]
if d == None:
oml0.edge_c1[abs(edge) - 1, :] = val
elif edge > 0:
oml0.edge_c1[abs(edge) - 1, d] = val
else:
oml0.edge_c1[abs(edge) - 1, 1 - abs(d)] = val
def setCornerC1(self, f, i=0, j=0, val=True):
self.setC1('edge', f, i=i, j=j, u=i, d=j, val=val)
self.setC1('edge', f, i=i, j=j, v=j, d=i, val=val)
def check(self, uType, vType, u=None, v=None):
if u == None:
uVal = uType == 2
else:
uVal = uType == u
if v == None:
vVal = vType == 2
else:
vVal = vType == v
return uVal and vVal
def computeMs(self):
oml0 = self.oml0
Ks = self.Ks
Ms = []
for f in range(len(Ks)):
ni = self.getni(f, 0)
nj = self.getni(f, 1)
Ms.append(numpy.zeros((sum(ni) + 1, sum(nj) + 1), int))
Ms[f][:, :] = -1
for j in range(Ks[f].shape[1]):
for i in range(Ks[f].shape[0]):
surf = Ks[f][i, j]
if surf != -1:
for v in range(nj[j] + 1):
jj = sum(nj[:j]) + v
for u in range(ni[i] + 1):
ii = sum(ni[:i]) + u
Ms[f][ii, jj] = oml0.getIndex(surf, u, v, 1)
self.Ms = Ms
def findJunctions(self):
oml0 = self.oml0
Ks = self.Ks
Js = []
for f in range(len(Ks)):
ni = self.getni(f, 0)
nj = self.getni(f, 1)
k0 = Ks[f].shape[0]
k1 = Ks[f].shape[1]
SPs = []
EPs = []
for j in range(k1):
for i in range(k0):
if Ks[f][i, j] == -1:
SPs.append([i, j])
EPs.append([i, j])
if (i > 0 and Ks[f][i - 1, j]
== -1) or (j > 0 and Ks[f][i, j - 1] == -1):
SPs.pop()
if (i < k0 - 1 and Ks[f][i + 1, j] == -1) or (
j < k1 - 1 and Ks[f][i, j + 1] == -1):
EPs.pop()
J = numpy.zeros((len(SPs), 4), int)
for s in range(len(SPs)):
SP = SPs[s]
for e in range(len(EPs)):
EP = EPs[e]
if SP[0] <= EP[0] and SP[1] <= EP[1]:
if numpy.linalg.norm(1 +
Ks[f][SP[0]:EP[0] + 1,
SP[1]:EP[1] + 1]) < 1e-14:
J[s, :] = [
sum(ni[:SP[0]]),
sum(nj[:SP[1]]),
sum(ni[:EP[0] + 1]),
sum(nj[:EP[1] + 1])
]
Js.append(J)
self.Js = Js
def flattenGeometry(self):
oml0 = self.oml0
Ms = self.Ms
for f in range(len(Ms)):
ni = Ms[f].shape[0]
nj = Ms[f].shape[1]
for i in range(ni):
for j in range(nj):
oml0.C[Ms[f][i,
j], :] = self.getFlattenedC(f, i, j, ni, nj)
oml0.computePointsC()
def initializeLayout(self):
def getv(r, v1, v2):
return numpy.array(v1) * (1 - r) + numpy.array(v2) * r
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
edges = []
edges.append([0, 0, 0, 1])
edges.append([0, 0, 1, 0])
edges.append([0, 1, 1, 1])
edges.append([1, 0, 1, 1])
skinIndices = self.getSkinIndices()
for s in range(len(skinIndices)):
for f in skinIndices[s]:
for k in range(Js[f].shape[0]):
C11 = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C12 = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C21 = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C22 = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
edges.append([C11[0], C11[1], C12[0], C12[1]])
edges.append([C11[0], C11[1], C21[0], C21[1]])
edges.append([C12[0], C12[1], C22[0], C22[1]])
edges.append([C21[0], C21[1], C22[0], C22[1]])
for m in self.keys:
member = self.members[m]
for i in range(member.nmem):
if member.nmem == 1:
ii = 0
else:
ii = i / (member.nmem - 1)
A = getv(ii, member.A1, member.A2)
B = getv(ii, member.B1, member.B2)
C = getv(ii, member.C1, member.C2)
D = getv(ii, member.D1, member.D2)
for j in range(member.ndiv):
if (B[2] == 0 and C[2] == 0) or (B[2] == 1 and C[2] == 1):
V0 = getv(j / member.ndiv, B, C)
V1 = getv((j + 1) / member.ndiv, B, C)
edges.append([V0[0], V0[1], V1[0], V1[1]])
if (A[2] == 0 and D[2] == 0) or (A[2] == 1 and D[2] == 1):
V0 = getv(j / member.ndiv, A, D)
V1 = getv((j + 1) / member.ndiv, A, D)
edges.append([V0[0], V0[1], V1[0], V1[1]])
self.layout = Layout(6, self.getAR(), 1, numpy.array(edges))
def findJunctionQuadsAndEdges(self):
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
C = numpy.zeros((4, 2))
ctd = numpy.zeros(2)
nquad = self.layout.nquad
nedge = self.layout.nedge
edges = self.layout.edges
verts = self.layout.verts
poly_vert = self.layout.poly_vert
skinIndices = self.getSkinIndices()
JQs = []
JEs = []
quad_indices = []
for s in range(len(skinIndices)):
JQ = []
for f in skinIndices[s]:
for q in range(nquad):
ctd[:] = 0
for k in range(4):
ctd[:] += 0.25 * verts[poly_vert[q, k] - 1, :]
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
if min(C[:, 0]) < ctd[0] and ctd[0] < max(
C[:, 0]) and min(
C[:, 1]) < ctd[1] and ctd[1] < max(C[:,
1]):
JQ.append(q + 1)
if JQ == []:
JQ.append(-1)
JQs.append(JQ)
JE = []
for f in skinIndices[s]:
for e in range(nedge):
ctd[:] = 0
for k in range(2):
ctd[:] += 0.5 * verts[edges[e, k] - 1, :]
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
if min(C[:, 0]) < ctd[0] and ctd[0] < max(
C[:, 0]) and min(
C[:, 1]) < ctd[1] and ctd[1] < max(C[:,
1]):
JEs.append(e + 1)
JEs.append(JE)
quad_indices.append(self.layout.getQuadIndices(JQ))
if len(quad_indices) == 1:
quad_indices.append(quad_indices[0])
self.JQs = JQs
self.JEs = JEs
self.quad_indices = numpy.array(quad_indices, order='F').T
def projectSkins(self):
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
skinIndices = self.getSkinIndices()
C = numpy.zeros((4, 2), order='F')
Bs = []
Ss = []
quad_indices = []
for s in range(len(skinIndices)):
Ps = []
P, S = self.layout.extractFlattened(self.JQs[s],
max(self.quad_indices[:, s]))
Ps.append(P)
Ss.append(S)
for f in skinIndices[s]:
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
P = self.layout.extractEdges(self.JQs[s], min(C[:, 0]),
max(C[:, 0]), min(C[:, 1]),
max(C[:, 1]))
Ps.append(P)
P = numpy.vstack(Ps)
surfindices = []
for f in skinIndices[s]:
surfindices.append(self.Ks[f].flatten())
surfs = numpy.unique(numpy.hstack(surfindices))
if surfs[0] == -1:
surfs = numpy.delete(surfs, 0)
Q = numpy.zeros((P.shape[0], 3))
Q[:, 2] = 1.0
ss, u, v = oml0.computeProjection(P, surfs=surfs, Q=Q)
Bs.append(oml0.computeBases(ss, u, v))
B = oml0.vstackSparse(Bs)
BM = B.dot(oml0.M)
P = BM.dot(oml0.Q)
As, S = self.computeStructure(P)
Ss.append(S)
A = oml0.vstackSparse(As)
ABM = A.dot(BM)
S = numpy.vstack(Ss)
self.strABM = ABM
self.strS = S
def computeStructure(self, P):
oml0 = self.oml0
Ms = self.Ms
Js = self.Js
layout = self.layout
skinIndices = self.getSkinIndices()
C = numpy.zeros((4, 2), order='F')
As = []
Jns = []
Jus = []
col = 0
for s in range(len(skinIndices)):
n = max(self.quad_indices[:, s]) * self.layout.n**2
Aa = numpy.ones(n)
Ai = numpy.linspace(0, n - 1, n)
Aj = numpy.linspace(0, n - 1, n) + col
As.append(
scipy.sparse.csr_matrix((Aa, (Ai, Aj)), shape=(n, P.shape[0])))
Jn = []
Ju = []
col += n
for f in skinIndices[s]:
for k in range(Js[f].shape[0]):
C[0, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 1]], :2]
C[1, :] = oml0.C[Ms[f][Js[f][k, 0], Js[f][k, 3]], :2]
C[2, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 1]], :2]
C[3, :] = oml0.C[Ms[f][Js[f][k, 2], Js[f][k, 3]], :2]
nu1, nu2, nv1, nv2 = layout.countJunctionEdges(
self.JQs[s], min(C[:, 0]), max(C[:, 0]), min(C[:, 1]),
max(C[:, 1]))
Jn.append([nu1, nu2, nv1, nv2])
Ju.append([
min(C[:, 0]),
max(C[:, 0]),
min(C[:, 1]),
max(C[:, 1])
])
nP = layout.n * (nu1 + nu2 + nv1 + nv2)
col += nP
if Jn == []:
Jn.append([-1, -1, -1, -1])
Ju.append([-1, -1, -1, -1])
Jns.append(numpy.array(Jn, int, order='F'))
Jus.append(numpy.array(Ju, order='F'))
nM = len(self.keys)
members = numpy.zeros((nM, 34), order='F')
for i in range(nM):
member = self.members[self.keys[i]]
members[i, :4] = [
member.domain, member.shape, member.nmem, member.ndiv
]
members[i, 4:16] = member.A1 + member.B1 + member.C1 + member.D1
members[i, 16:28] = member.A2 + member.B2 + member.C2 + member.D2
members[i, 28:] = [
member.tx, member.ty, member.rx, member.ry, member.n1,
member.n2
]
nP, nS = PAMlib.countinternalnodes(self.layout.n, nM, members)
P2, M, S = PAMlib.computeinternalnodes(nP, nS, self.layout.n, nM,
members)
nA = PAMlib.countannz(nP, layout.nvert, layout.nquad, layout.verts,
layout.poly_vert, self.quad_indices, P2, M)
if len(skinIndices) == 1:
Aa, Ai, Aj = PAMlib.assembleamtx(
nA, self.layout.n, nP, Jns[0].shape[0], Jns[0].shape[0],
self.layout.nvert, self.layout.nquad, Jns[0], Jns[0], Jus[0],
Jus[0], self.quad_indices, self.layout.verts,
self.layout.poly_vert, P2, M)
else:
Aa, Ai, Aj = PAMlib.assembleamtx(
nA, self.layout.n, nP, Jns[0].shape[0], Jns[1].shape[0],
self.layout.nvert, self.layout.nquad, Jns[0], Jns[1], Jus[0],
Jus[1], self.quad_indices, self.layout.verts,
self.layout.poly_vert, P2, M)
As.append(
scipy.sparse.csr_matrix((Aa, (Ai, Aj)),
shape=(max(Ai) + 1, P.shape[0])))
return As, S
def buildStructure(self):
self.computeMs()
self.findJunctions()
self.flattenGeometry()
self.initializeLayout()
self.findJunctionQuadsAndEdges()
self.projectSkins()
def addMembers(self,
name,
domain,
shape,
nmem,
ndiv,
A1=None,
B1=None,
C1=None,
D1=None,
A2=None,
B2=None,
C2=None,
D2=None,
tx=0.5,
ty=0.5,
rx=1.0,
ry=1.0,
n1=5,
n2=5):
if A2 == None:
A2 = [-1, -1, -1]
B2 = [-1, -1, -1]
C2 = [-1, -1, -1]
D2 = [-1, -1, -1]
if B1 == None:
B1 = [-1, -1, -1]
B1[:2] = A1[:2]
B1[2] = C1[2]
if D1 == None:
D1 = [-1, -1, -1]
D1[:2] = C1[:2]
D1[2] = A1[2]
if B2 == None:
B2 = [-1, -1, -1]
B2[:2] = A2[:2]
B2[2] = C2[2]
if D2 == None:
D2 = [-1, -1, -1]
D2[:2] = C2[:2]
D2[2] = A2[2]
self.members[name] = Member(domain, shape, nmem, ndiv, A1, B1, C1, D1,
A2, B2, C2, D2, tx, ty, rx, ry, n1, n2)
self.keys.append(name)
