def __init__(self, control=None, fields=None, weights=None):
if control is not None:
shape = control.shape
degree = shape[:-1]
knots = []
for p in degree:
u = [-1.0] * p + [1.0] * p
knots.append(u)
NURBS.__init__(self, knots, control)
def __init__(self, control=None, fields=None, weights=None):
if control is not None:
shape = control.shape
degree = shape[:-1]
knots = []
for p in degree:
u = [-1.] * p + [1.] * p
knots.append(u)
NURBS.__init__(self, knots, control)
def test_srf_ki(PLOT=0):
p = 2
q = 1
U = np.asarray([0,0,0, 1,1,1], dtype=float)
V = np.asarray([0,0, 1,1], dtype=float)
n = len(U)-1-(p+1)
m = len(V)-1-(q+1)
Pw = np.zeros((n+1,m+1,4))
Pw[0,0,:] = [0.0, 0.5, 0.0, 1.0]
Pw[1,0,:] = [0.5, 0.5, 0.0, 1.0]
Pw[2,0,:] = [0.5, 0.0, 0.0, 1.0]
Pw[0,1,:] = [0.0, 1.0, 0.0, 1.0]
Pw[1,1,:] = [1.0, 1.0, 0.0, 1.0]
Pw[2,1,:] = [1.0, 0.0, 0.0, 1.0]
Pw[1,:,:] *= np.sqrt(2)/2
nurbs = NURBS([U,V],Pw)
X = np.asarray([])
Y = np.asarray([])
nrb = nurbs.copy().refine(0,X).refine(1,Y)
(Ubar, Vbar), Qw = nrb.knots, nrb.control
assert np.allclose(U, Ubar)
assert np.allclose(V, Vbar)
assert np.allclose(Pw, Qw)
X = np.asarray([.25, 0.5])#;X = np.asarray([])
Y = np.asarray([0.5, .75])#;Y = np.asarray([])
nrb = nurbs.refine(0,X).refine(1,Y)
(Ubar, Vbar), Qw = nrb.knots, nrb.control
u = np.linspace(Ubar[0], Ubar[-1], 31)
v = np.linspace(Vbar[0], Vbar[-1], 10)
Cw = bsp.Evaluate2(p,Ubar,q,Vbar,Qw,u,v)
Q = Qw[:,:,:2] / Qw[:,:,3,None]
C = Cw[:,:,:2] / Cw[:,:,3,None]
if not PLOT: return
plt.figure()
plt.title("Surface - Knot Insertion")
x = Q[:,:,0]
y = Q[:,:,1]
plt.plot(x,y,'sr')
x = C[:,:,0]
y = C[:,:,1]
plt.plot(x,y,'.b')
t = np.linspace(0,np.pi/2,100)
a = np.cos(t)
b = np.sin(t)
plt.plot(1.0*a,1.0*b,'-k')
plt.plot(0.5*a,0.5*b,'-k')
plt.axis("equal")
def VolumifyInterior(nrb):
"""
Creates volumes from closed surfaces.
Given a tube-like, closed surface, return a nurbs volume of the
interior. Actually returns 5 volumes, one of the core and 4 which
connect the core to the outer hull. Assumes that the
circumferential direction is 1st direction
..note: Lisandro, for now I am just making this work for the pipe
example, but several things will need to be made more general.
"""
assert nrb.dim == 2
"""
Step 1: extract 4 C0 surfaces from the single input surface. I
propose that we simple insert knots to extract at
[0.25,0.5,0.75]*U[-1]. Note that in this case, these knots are
already inserted and so I skip this part.
"""
"""
Step 2: locate the control point id's which corresponds to the C0
lines we just inserted. Create a trilinear solid which will form
the core of the returned volume. Degree elevate to make equal to
the 1st dim of the input surface.
"""
fct = 0.75
c0 = 0; c1 = 2; c2 = 4; c3 = 6; c4 = 8
C = np.zeros((2,2,nrb.shape[1],4))
C[0,0,:,:] = fct*nrb.control[c0,:,:] + (1.0-fct)*nrb.control[c2,:,:]
C[1,1,:,:] = (1.0-fct)*nrb.control[c0,:,:] + fct*nrb.control[c2,:,:]
C[1,0,:,:] = fct*nrb.control[c1,:,:] + (1.0-fct)*nrb.control[c3,:,:]
C[0,1,:,:] = (1.0-fct)*nrb.control[c1,:,:] + fct*nrb.control[c3,:,:]
core = NURBS(C,[[0,0,1,1],[0,0,1,1],nrb.knots[1]])
t=max(0,nrb.degree[0]-core.degree[0])
core.elevate(t,t,0)
"""
Step 3: create 4 volumes around the core.
"""
D1 = np.zeros((3,2,nrb.shape[1],4))
D1[:,0,:,:] = core.control[:,0,:,:]
D1[:,1,:,:] = nrb.control[c0:c1+1,:,:]
v1 = NURBS(D1,[[0,0,0,1,1,1],[0,0,1,1],nrb.knots[1]])
D2 = np.zeros((3,2,nrb.shape[1],4))
D2[:,0,:,:] = core.control[2,:,:,:]
D2[:,1,:,:] = nrb.control[c1:c2+1,:,:]
v2 = NURBS(D2,[[0,0,0,1,1,1],[0,0,1,1],nrb.knots[1]])
D3 = np.zeros((3,2,nrb.shape[1],4))
D3[:,0,:,:] = core.control[:,2,:,:]
D3[:,1,:,:] = CntRev(nrb.control[c2:c3+1,:,:],0)
v3 = NURBS(D3,[[0,0,0,1,1,1],[0,0,1,1],nrb.knots[1]])
D4 = np.zeros((3,2,nrb.shape[1],4))
D4[:,0,:,:] = core.control[0,:,:,:]
D4[:,1,:,:] = CntRev(nrb.control[c3:c4+1,:,:],0)
v4 = NURBS(D4,[[0,0,0,1,1,1],[0,0,1,1],nrb.knots[1]])
return core,v1,v2,v3,v4
def sweep(section, trajectory):
"""
Construct the translational sweep of a section
curve/surface along a trajectory curve.
S(u,v) = C(u) + T(v)
V(u,v,w) = S(u,v) + T(w)
Parameters
----------
section : NURBS
Section curve/surface
trajectory : NURBS
Trajectory curve
"""
assert 1 <= section.dim <= 2
assert trajectory.dim == 1
Cs, ws = section.points, section.weights
Ct, wt = trajectory.points, trajectory.weights
C = Cs[..., np.newaxis, :] + Ct
w = ws[..., np.newaxis] * wt
UVW = section.knots + trajectory.knots
return NURBS(UVW, (C, w))
def extrude(nrb, displ, axis=None):
"""
Construct a NURBS surface/volume by
extruding a NURBS curve/surface.
Parameters
----------
nrb : NURBS
displ : array_like or float
axis : array_like or int, optional
Example
-------
>>> crv = circle()
>>> srf = extrude(crv, displ=1, axis=2)
>>> srf = bilinear()
>>> vol = extrude(srf, displ=1, axis=2)
"""
assert nrb.dim <= 2
T = transform().translate(displ, axis)
Cw = np.empty(nrb.shape + (2, 4))
Cw[..., 0, :] = nrb.control
Cw[..., 1, :] = T(nrb.control)
UVW = nrb.knots + ([0, 0, 1, 1], )
return NURBS(UVW, Cw)
def trilinear(points=None):
"""
p[0,1,1] p[1,1,1]
o------------o
/| /|
/ | / | w
o------------o | ^ v
| p[0,0,1] | p[1,0,1] | /
| | | | |/
| o-------- | -o +----> u
| / p[0,1,0] | / p[1,1,0]
|/ |/
o------------o
p[0,0,0] p[1,0,0]
"""
if points is None:
s = slice(-0.5, +0.5, 2j)
x, y, z = np.ogrid[s, s, s]
points = np.zeros((2, 2, 2, 3), dtype='d')
points[..., 0] = x
points[..., 1] = y
points[..., 2] = z
else:
points = np.array(points, dtype='d')
assert points.shape[:-1] == (2, 2, 2)
knots = [0, 0, 1, 1]
return NURBS([knots] * 3, points)
def __init__(
self,
patch,
backend="matplotlib"
): # backend can be 'mayavi' or 'matplotlib' or "null" or "none"
self.backend = backend
plt.use(self.backend)
if patch.WorkingSpaceDimension() == 2:
U = patch.FESpace().KnotU
V = patch.FESpace().KnotV
C = patch.GridFunction(CONTROL_POINT).ControlGrid.ControlValues
self.nurbs = NURBS([V, U], C)
elif patch.WorkingSpaceDimension() == 3:
U = patch.FESpace().KnotU
V = patch.FESpace().KnotV
W = patch.FESpace().KnotW
C = patch.GridFunction(CONTROL_POINT).ControlGrid.ControlValues
self.nurbs = NURBS([W, V, U], C)
def line(p0=(0, 0), p1=(1, 0)):
"""
p0 p1
o-----------o
+--> u
"""
p0 = np.asarray(p0, dtype='d')
p1 = np.asarray(p1, dtype='d')
points = np.zeros((2, 3), dtype='d')
points[0, :p0.size] = p0
points[1, :p1.size] = p1
knots = [0, 0, 1, 1]
return NURBS([knots], points)
def make_srf():
C = np.zeros((3, 5, 5))
C[:, :, 0] = [
[0.0, 3.0, 5.0, 8.0, 10.0],
[0.0, 0.0, 0.0, 0.0, 0.0],
[2.0, 2.0, 7.0, 7.0, 8.0],
]
C[:, :, 1] = [
[0.0, 3.0, 5.0, 8.0, 10.0],
[3.0, 3.0, 3.0, 3.0, 3.0],
[0.0, 0.0, 5.0, 5.0, 7.0],
]
C[:, :, 2] = [
[0.0, 3.0, 5.0, 8.0, 10.0],
[5.0, 5.0, 5.0, 5.0, 5.0],
[0.0, 0.0, 5.0, 5.0, 7.0],
]
C[:, :, 3] = [
[0.0, 3.0, 5.0, 8.0, 10.0],
[8.0, 8.0, 8.0, 8.0, 8.0],
[5.0, 5.0, 8.0, 8.0, 10.0],
]
C[:, :, 4] = [
[0.0, 3.0, 5.0, 8.0, 10.0],
[10.0, 10.0, 10.0, 10.0, 10.0],
[5.0, 5.0, 8.0, 8.0, 10.0],
]
C = C.transpose()
U = [
0,
0,
0,
1 / 3.,
2 / 3.,
1,
1,
1,
]
V = [
0,
0,
0,
1 / 3.,
2 / 3.,
1,
1,
1,
]
nrb = NURBS([U, V], C)
return nrb
def coons(curves, tol=1.e-10):
"""
C[1,1]
o--------------o
| v |
| ^ |
C[0,0] | | | C[0,1]
| | |
| +------> u |
o--------------o
C[1,0]
"""
(C00, C01), (C10, C11) = curves
assert C00.dim == C01.dim == 1
assert C10.dim == C11.dim == 1
#
(C00, C01) = compat(C00, C01)
(C10, C11) = compat(C10, C11)
#
p, U = C10.degree[0], C10.knots[0]
u0, u1 = U[p], U[-p - 1]
P = np.zeros((2, 2, 3), dtype='d')
P[0, 0] = C10(u0)
P[1, 0] = C10(u1)
P[0, 1] = C11(u0)
P[1, 1] = C11(u1)
#
q, V = C00.degree[0], C00.knots[0]
v0, v1 = V[q], V[-q - 1]
Q = np.zeros((2, 2, 3), dtype='d')
Q[0, 0] = C00(v0)
Q[0, 1] = C00(v1)
Q[1, 0] = C01(v0)
Q[1, 1] = C01(v1)
#
# print "P[0,0] ", P[0,0] , " Q[0,0] ", Q[0,0]
# print "P[1,0] ", P[1,0] , " Q[1,0] ", Q[1,0]
# print "P[0,1] ", P[0,1] , " Q[0,1] ", Q[0,1]
# print "P[1,1] ", P[1,1] , " Q[1,1] ", Q[1,1]
assert np.allclose(P, Q, rtol=0, atol=tol)
#
R0 = ruled(C00, C01).transpose()
R1 = ruled(C10, C11)
B = bilinear(P)
R0, R1, B = compat(R0, R1, B)
control = R0.control + R1.control - B.control
knots = B.knots
return NURBS(knots, control)
def test_refinement_iga():
from igakit.nurbs import NURBS
points = np.array([
[0, 0, 0], # , 0],
[1, 1, 0], # 0],
[2, 0, 0], # 0],
# [1,0,0]
])
knot = np.array([0, 0, 0, 1, 1, 1]) # D1
resolution = 500
reso = np.linspace(0, 1, resolution)
weight = np.ones((points.shape[0], 1))
crv = NURBS([knot], points)
crv.refine(0, [0.5, 0.6])
fig1, ax1 = plt.subplots()
ax1.plot(crv(reso)[..., 0], crv(reso)[..., 1], 'b')
ax1.plot(crv.control[..., 0],
crv.control[..., 1],
color='red',
marker='s',
linestyle='None')
ax1.set_ylim(0, 1)
fig1.show()
def linear(points=None):
"""
p[0] p[1]
o------------o
+----> u
"""
if points is None:
points = np.zeros((2, 2), dtype='d')
points[0, 0] = -0.5
points[1, 0] = +0.5
else:
points = np.asarray(points, dtype='d')
assert points.shape[:-1] == (2, )
knots = [0, 0, 1, 1]
return NURBS([knots], points)
def test_srf_de(PLOT=0):
p = 2
q = 1
U = np.asarray([0,0,0, 1,1,1], dtype=float)
V = np.asarray([0,0, 1,1], dtype=float)
n = len(U)-1-(p+1)
m = len(V)-1-(q+1)
Pw = np.zeros((n+1,m+1,4))
Pw[0,0,:] = [0.0, 0.5, 0.0, 1.0]
Pw[1,0,:] = [0.5, 0.5, 0.0, 1.0]
Pw[2,0,:] = [0.5, 0.0, 0.0, 1.0]
Pw[0,1,:] = [0.0, 1.0, 0.0, 1.0]
Pw[1,1,:] = [1.0, 1.0, 0.0, 1.0]
Pw[2,1,:] = [1.0, 0.0, 0.0, 1.0]
Pw[1,:,:] *= np.sqrt(2)/2
nurbs = NURBS([U,V],Pw)
nrb = nurbs.copy().elevate(0,0).elevate(1,0)
(Uh, Vh), Qw = nrb.knots, nrb.control
nrb = nurbs.copy().elevate(0,1).elevate(1,0)
(Uh, Vh), Qw = nrb.knots, nrb.control
nrb = nurbs.copy().elevate(0,0).elevate(1,1)
(Uh, Vh), Qw = nrb.knots, nrb.control
r, s = 1, 2
nrb = nurbs.copy().elevate(0,r).elevate(1,s)
(Uh, Vh), Qw = nrb.knots, nrb.control
ph = p+r; qh = q+s;
u = np.linspace(Uh[0], Uh[-1], 31)
v = np.linspace(Vh[0], Vh[-1], 10)
Cw = bsp.Evaluate2(ph,Uh,qh,Vh,Qw,u,v)
Q = Qw[:,:,:2] / Qw[:,:,3, None]
C = Cw[:,:,:2] / Cw[:,:,3, None]
if not PLOT: return
plt.figure()
plt.title("Surface - Degree Elevation")
x = Q[:,:,0]
y = Q[:,:,1]
plt.plot(x,y,'sr')
x = C[:,:,0]
y = C[:,:,1]
plt.plot(x,y,'.b')
t = np.linspace(0,np.pi/2,100)
a = np.cos(t)
b = np.sin(t)
plt.plot(1.0*a,1.0*b,'-k')
plt.plot(0.5*a,0.5*b,'-k')
plt.axis("equal")
def make_vol():
C = np.zeros((3,2,3,4), dtype='d')
C[0,0,:,0:2] = [0.0, 0.5]
C[1,0,:,0:2] = [0.5, 0.5]
C[2,0,:,0:2] = [0.5, 0.0]
C[0,1,:,0:2] = [0.0, 1.0]
C[1,1,:,0:2] = [1.0, 1.0]
C[2,1,:,0:2] = [1.0, 0.0]
C[:,:,0,2] = 0.0
C[:,:,1,2] = 0.5
C[:,:,2,2] = 1.0
C[:,:,:,3] = 1.0
C[1,:,:,:] *= np.sqrt(2)/2
U = [0,0,0, 1,1,1]
V = [0,0, 1,1]
W = [0,0, 0.5, 1,1]
vol = NURBS([U,V,W], C)
return vol
def ruled(nrb1, nrb2):
"""
Construct a ruled surface/volume
between two NURBS curves/surfaces.
Parameters
----------
nrb1, nrb2 : NURBS
"""
assert nrb1.dim == nrb2.dim
assert nrb1.dim <= 2
assert nrb2.dim <= 2
nrb1, nrb2 = compat(nrb1, nrb2)
Cw = np.zeros(nrb1.shape + (2, 4), dtype='d')
Cw[..., 0, :] = nrb1.control
Cw[..., 1, :] = nrb2.control
UVW = nrb1.knots + ([0, 0, 1, 1], )
return NURBS(UVW, Cw)
def make_crv():
C = [[ 6.0, 0.0, 6.0],
[-5.5, 0.5, 5.5],
[-5.0, 1.0,-5.0],
[ 4.5, 1.5,-4.5],
[ 4.0, 2.0, 4.0],
[-3.5, 2.5, 3.5],
[-3.0, 3.0,-3.0],
[ 2.5, 3.5,-2.5],
[ 2.0, 4.0, 2.0],
[-1.5, 4.5, 1.5],
[-1.0, 5.0,-1.0],
[ 0.5, 5.5,-0.5],
[ 0.0, 6.0, 0.0],]
U = [0, 0, 0, 0,
.1, .2, .3, .4, .5, .6, .7, .8, .9,
1, 1, 1, 1,]
crv = NURBS([U], C)
return crv
def bilinear(points=None):
"""
p[0,1] p[1,1]
o------------o
| v |
| ^ |
| | |
| +----> u |
o------------o
p[0,0] p[1,0]
"""
if points is None:
s = slice(-0.5, +0.5, 2j)
x, y = np.ogrid[s, s]
points = np.zeros((2, 2, 2), dtype='d')
points[..., 0] = x
points[..., 1] = y
else:
points = np.array(points, dtype='d')
assert points.shape[:-1] == (2, 2)
knots = [0, 0, 1, 1]
return NURBS([knots] * 2, points)
def test_k_refinement():
try:
from igakit.nurbs import NURBS
active = True
except:
raise ImportError
points = np.array([
[0, 0], # , 0],
[1, 1], # 0],
[2, 0], # 0],
# [1,0,0]
])
knot = np.array([0, 0, 0, 1, 1, 1]) # D1
resolution = 500
reso = np.linspace(0, 1, resolution)
crv = NURBS([knot], points)
basis_fun, _ = gn.NURB_engine.basis_function_array_nurbs(
crv.knots[0], crv.degree[0], resolution, crv.weights)
_0 = crv.control
fig = make_plot(crv.control, basis_fun, reso, crv(reso))
print(crv.knots)
crv.insert(axis=0, value=0.3).insert(axis=0, value=0.5)
basis_fun1, _ = gn.NURB_engine.basis_function_array_nurbs(
crv.knots[0], crv.degree[0], resolution, crv.weights)
_1 = crv.control
fig1 = make_plot(crv.control, basis_fun1, reso, crv(reso))
print(crv.knots)
crv.elevate(axis=0, times=1)
basis_fun2, _ = gn.NURB_engine.basis_function_array_nurbs(
crv.knots[0], crv.degree[0], resolution, crv.weights)
_2 = crv.control
fig2 = make_plot(crv.control, basis_fun2, reso, crv(reso))
print(crv.knots)
save = False
if save or save_all:
fig.savefig(fig_folder + "k_refine_ori.pdf", **kwargs_savefig)
fig1.savefig(fig_folder + "k_refine_1.pdf", **kwargs_savefig)
fig2.savefig(fig_folder + "k_refine_2.pdf", **kwargs_savefig)
def test_refinement_order():
try:
from igakit.nurbs import NURBS
active = True
except:
_0 = np.asarray([[0., 0., 0., 1.], [1., 1., 0., 1.], [2., 0., 0., 1.]])
_1 = np.asarray([[
0.,
0.,
0.,
1.,
], [
0.66666667,
0.66666667,
0.,
1.,
], [
1.33333333,
0.66666667,
0.,
1.,
], [
2.,
0.,
0.,
1.,
]])
_2 = np.asarray([[0., 0., 0., 1.], [
0.5,
0.5,
0.,
1.,
], [
1.,
0.66666667,
0.,
1.,
], [
1.5,
0.5,
0.,
1.,
], [
2.,
0.,
0.,
1.,
]])
active = False
points = np.array([
[0, 0], # , 0],
[1, 1], # 0],
[2, 0], # 0],
# [1,0,0]
])
knot = np.array([0, 0, 0, 1, 1, 1]) # D1
resolution = 500
reso = np.linspace(0, 1, resolution)
if active:
crv = NURBS([knot], points)
basis_fun, _ = gn.NURB_engine.basis_function_array_nurbs(
crv.knots[0], crv.degree[0], resolution, crv.weights)
_0 = crv.control
fig = make_plot(crv.control, basis_fun, reso, crv(reso))
crv.elevate(axis=0, times=1)
basis_fun1, _ = gn.NURB_engine.basis_function_array_nurbs(
crv.knots[0], crv.degree[0], resolution, crv.weights)
_1 = crv.control
fig1 = make_plot(crv.control, basis_fun1, reso, crv(reso))
crv.elevate(axis=0, times=1)
basis_fun2, _ = gn.NURB_engine.basis_function_array_nurbs(
crv.knots[0], crv.degree[0], resolution, crv.weights)
_2 = crv.control
fig2 = make_plot(crv.control, basis_fun1, reso, crv(reso))
else:
x, y, z = gn.engine.NURB_construction([knot], _0, resolution, None)
basis_fun, _ = gn.NURB_engine.basis_function_array_nurbs(
knot, 2, resolution, None)
fig = make_plot(_0, basis_fun, reso, np.asarray([x, y]).T)
knot1 = np.asarray([0, 0, 0, 0, 1, 1, 1, 1])
x1, y1, z1 = gn.engine.NURB_construction([knot1], _1, resolution, None)
basis_fun1, _ = gn.NURB_engine.basis_function_array_nurbs(
knot1, 3, resolution, None)
fig1 = make_plot(_1, basis_fun1, reso, np.asarray([x1, y1]).T)
knot2 = np.asarray([0, 0, 0, 0, 0, 1, 1, 1, 1, 1])
x2, y2, z2 = gn.engine.NURB_construction([knot2], _2, resolution, None)
basis_fun2, _ = gn.NURB_engine.basis_function_array_nurbs(
knot2, 4, resolution, None)
fig2 = make_plot(_2, basis_fun2, reso, np.asarray([x2, y2]).T)
save = False
if save or save_all:
fig.savefig(fig_folder + "p_refine_2.pdf", **kwargs_savefig)
fig1.savefig(fig_folder + "p_refine_3.pdf", **kwargs_savefig)
fig2.savefig(fig_folder + "p_refine_4.pdf", **kwargs_savefig)
def create_model(self, engine=None):
if engine is None:
engine = self.engine
if engine == "c++":
try:
import gempyExplicit
except Exception:
traceback.print_exc()
if self.dim == 1:
self.model = gempyExplicit.NURBS_Curve(self.degree[0],
self.knots[0],
self.cpoints,
self.weight,
self.resolution,
engine="auto")
return self.dim
elif self.dim == 2:
self.model, self.triangles = gempyExplicit.NURBS_Surface(
self.degree[0],
self.degree[1],
self.knots[0],
self.knots[1],
self.cpoints,
self.weight,
self.resolution,
self.resolution,
engine="auto")
return self.dim
elif self.dim == 3:
self.model, self.triangles, self.surf_triangles = gempyExplicit.NURBS_Volume(
self.degree[0],
self.degree[1],
self.degree[2],
self.knots[0],
self.knots[1],
self.knots[2],
self.cpoints,
self.weight,
self.resolution,
self.resolution,
self.resolution,
engine="auto")
return self.dim
else:
print(self.dim)
return TypeError
elif engine == "python":
try:
from pygeoiga.engine import NURB_construction
except:
traceback.print_exc()
self.model = NURB_construction(list(self.knots), self.cpoints,
self.resolution, self.weight)
return self.dim
elif engine == "igakit":
try:
from igakit.nurbs import NURBS
except Exception:
traceback.print_exc()
self._NURB = NURBS(knots=list(self.knots),
control=self.B) #, weights=self.weight)
else:
print(self.engine, "Not available")
return TypeError
# Open knot vectors for a one-Bezier-element bi-unit square.
uKnots = [-1.0, -1.0, -1.0, 1.0, 1.0, 1.0]
vKnots = [-1.0, -1.0, -1.0, 1.0, 1.0, 1.0]
# Array of control points, for a bi-unit square with the interior
# parameterization distorted.
cpArray = array([[[-1.0, -1.0], [0.0, -1.0], [1.0, -1.0]],
[[-1.0, 0.0], [0.7, 0.3], [1.0, 0.0]],
[[-1.0, 1.0], [0.0, 1.0], [1.0, 1.0]]])
# NOTE: Polynomial degree is determined based on the number of knots and
# control points. In this case, the NURBS is quadratic.
# Create initial mesh
ikNURBS = NURBS_ik([uKnots, vKnots], cpArray)
# Refinement
numNewKnots = 1
for i in range(0, REF_LEVEL):
numNewKnots *= 2
h = 2.0 / float(numNewKnots)
numNewKnots -= 1
knotList = []
for i in range(0, numNewKnots):
knotList += [
float(i + 1) * h - 1.0,
]
newKnots = array(knotList)
ikNURBS.refine(0, newKnots)
ikNURBS.refine(1, newKnots)
U[degree + 1:-degree - 2] = vec_add
U = np.sort(U)
U[-degree - 1:] = 1
U[:degree + 1] = 0
return U
#%%
U = make_knot_vector(degree=2, len_cp=tot_U)
V = make_knot_vector(degree=2, len_cp=tot_V)
#%%%%
#to igakit
from igakit.plot import plt as plt_surf
surface = NURBS([U, V], control_points)
plt_surf.figure()
plt_surf.cpoint(surface)
plt_surf.cwire(surface)
plt_surf.curve(surface)
plt.show()
# %% anti-refinement
new_surf = surface.clone()
deviation = 10000000
for i in U:
new_surf = new_surf.remove(0, i, deviation=deviation)
for j in V:
new_surf = new_surf.remove(1, i, deviation=deviation)
plt_surf.figure()
from tIGAr import *
from tIGAr.NURBS import *
from igakit.nurbs import NURBS as NURBS_ik
from igakit.io import PetIGA
#from igakit.plot import plt
import matplotlib.pyplot as plt
import math
vKnots = [0.0,0.0,0.0,1.0,1.0,1.0]
uKnots = [0.0,0.0,1.0,1.0]
cpArray = array([[[1.0,0.0],[1.0,1.0],[0.0,1.0]],
[[2.0,0.0],[2.0,2.0],[0.0,2.0]]])
w = array([[[1.0],[sqrt(2)/2],[1.0]],[[1.0],[sqrt(2)/2],[1.0]]])
ikNURBS = NURBS_ik([uKnots,vKnots],cpArray)
ikNURBS.elevate(0,1)
print(ikNURBS.degree)
print(ikNURBS.knots)
numNewKnots = 1
for i in range(0,6):
numNewKnots *= 2
h = 1.0/float(numNewKnots)
numNewKnots -= 1
knotList = []
for i in range(0,numNewKnots):
knotList += [float(i+1)*h,]
newKnots = array(knotList)
ikNURBS.refine(0,newKnots)
ikNURBS.refine(1,newKnots)
t2 = transform().move(0, 2)
t3 = transform()
t3.scale([np.sqrt(2), 1, np.sqrt(2)])
t3.rotate(-np.pi/4, 1).move(-Rb, 2)
t4 = transform()
t4.rotate(-np.pi/2, 1).move([Rb, 0, -Rb])
bentpipe[:,0,:] = t0(circle)
bentpipe[:,1,:] = t1(circle)
bentpipe[:,2,:] = t2(circle)
bentpipe[:,3,:] = t3(circle)
bentpipe[:,4,:] = t4(circle)
Pw = bentpipe
U = [0,0,0, 1,1, 2,2, 3,3, 4,4,4]
W = [0,0,0, 1,1, 2,2,2]
nrb = NURBS(Pw, [U,W])
import sys
try:
backend = sys.argv[1]
plt.use(backend)
except IndexError:
pass
plt.figure()
plt.plot(nrb)
n1,n2,n3,n4,n5 = VolumifyInterior(nrb)
plt.figure()
for i in range(1,6):
# geo = patch(n=[nx,ny],p=[px,py])
geo_s = square(p=[2,2])
nrb = geo_s[0]
U,V = nrb.knots
#C = nrb.points
C = np.zeros_like(nrb.points)
s = 1./np.sqrt(2)
weights = np.ones((3,3))
weights[1,0] = s
weights[0,1] = s
weights[2,1] = s
weights[1,2] = s
srf = NURBS([U,V], C, weights=weights)
geo = cad_geometry()
geo.append(srf)
geo._internal_faces = geo_s._internal_faces
geo._external_faces = geo_s._external_faces
geo._connectivity = geo_s._connectivity
#
srf = geo[0]
dim = srf.dim
n = [nx,ny]
list_t = []
for axis in range(0,dim):
ub = srf.knots[axis][0]
ue = srf.knots[axis][-1]
list_t.append(np.linspace(ub,ue,n[axis]+2)[1:-1])
"""
Step 1: Create a quadratic curve between each line. The extra control
point is determined as the point where the lines intersect. This way
the construction is C1.
"""
P = np.zeros((3, 2))
C = []
C.append(L[0])
for i in range(len(L) - 1):
mid = seg_intersect(L[i].points[0, 0:2], L[i].points[1, 0:2],
L[i + 1].points[0, 0:2], L[i + 1].points[1, 0:2])
plt.plot(mid[0], mid[1], 'yo', markersize=ms)
P[0, :] = L[i].points[1, 0:2]
P[1, :] = mid[0:2]
P[2, :] = L[i + 1].points[0, 0:2]
C.append(NURBS(P, [[0, 0, 0, 1, 1, 1]]))
C.append(L[i + 1])
"""
Step 2-4: Degree elevate to make all curves p=2. Also compute each
curve's length and the total combined length.
"""
plt.subplot(313)
L = []
for c in C:
c.elevate(2 - c.degree[0])
L.append(curve_length(c))
L = np.asarray(L)
Lt = L.sum()
L /= Lt
"""
Step 5-6: Combine all curves into 1. This we do by juxtaposing each
P[6, 1, :] = [5.24524, 50.0859]
P[7, 1, :] = [42.1936, 50.0884]
P[8, 1, :] = [95.7095, 50.0937]
P[9, 1, :] = [128.203, 50.0974]
P[10, 1, :] = [183.546, 47.168]
P[11, 1, :] = [335.568, 38.9067]
P[12, 1, :] = [782.636, 12.9908]
P[13, 1, :] = [1120.1, -10.3521]
# Adjust control points such that the length scale is 1
delx = P[:, :, 0].max() - P[:, :, 0].min()
minx = P[:, :, 0].min()
P -= minx
P /= delx
tube = NURBS(P, [U, V])
tube.elevate(0, 1)
# Determine which knots to insert
res = 32
insert_U = InsertUniformly(U, 4 * res)
insert_V = InsertUniformly(V, res)
tube.refine(insert_U, insert_V)
plt.use('mayavi')
plt.figure()
plt.plot(tube)
plt.show()
data = {}
cwdir = os.getcwd()
geom = PetIGA().read('mesh.dat')
inc = 1
if (nPrjtnScalars + nPrjtnVectors > 0):
for filename1, filename2 in zip(glob.glob('outU*.dat'),
glob.glob('outE*.dat')):
if int(filename1.split(".")[0][4:]) >= bound:
filename2 = "outE" + filename1.split(".")[0][4:] + ".dat"
outname = "out" + filename1.split(".")[0][4:] + ".vtk"
sol2 = PetIGA().read_vec(filename1, geom)
sol1 = PetIGA().read_vec(filename2, geom)
if (sol1.ndim == dim):
sol1 = np.expand_dims(sol1, axis=dim)
if (sol2.ndim == dim):
sol2 = np.expand_dims(sol2, axis=dim)
sol = np.concatenate((sol1, sol2), axis=dim)
nrb = NURBS(geom.knots, (geom.points, geom.weights), sol)
VTK().write(outname, nrb, scalars=scalars, vectors=vectors)
else:
for filename in glob.glob('outU*.dat'):
if int(filename.split(".")[0][4:]) >= bound:
outname = "out" + filename.split(".")[0][4:] + ".vtk"
sol = PetIGA().read_vec(filename, geom)
nrb = NURBS(geom.knots, (geom.points, geom.weights), sol)
VTK().write(outname, nrb, scalars=scalars, vectors=vectors)
def join(nrb1, nrb2, axis):
"""
Join two curves/surfaces/volumes along a
specified parametric axis.
Parameters
----------
nrb1, nrb2 : NURBS
axis : int
Examples
--------
>>> C1 = circle(radius=0.5)
>>> C2 = circle(radius=1.0)
>>> annulus = ruled(C1, C2)
>>> pipe = extrude(annulus, displ=2, axis=2)
>>> elbow = revolve(annulus, point=(1.5,0,0),
... axis=(0,-1,0), angle=Pi/2)
>>> bentpipe = join(pipe.reverse(2), elbow, axis=2)
"""
dim = nrb1.dim
assert dim == nrb2.dim
assert 0 <= axis < dim
axes = list(range(dim))
del axes[axis]
nrb1, nrb2 = compat(nrb1, nrb2, axes=axes)
nrb1 = nrb1.clamp(axis, side=1)
nrb2 = nrb2.clamp(axis, side=0)
p1 = nrb1.degree[axis]
p2 = nrb2.degree[axis]
U1 = nrb1.knots[axis]
U2 = nrb2.knots[axis]
u = U1[-p1-1]
a = U2[p2]
b = U2[-p2-1]
nrb2.remap(axis, a+u, b+u)
p = max(p1, p2)
nrb1.elevate(axis, p-p1)
nrb2.elevate(axis, p-p2)
A1 = nrb1.array
A2 = nrb2.array
I1 = [slice(None)] * (dim+1)
I2 = [slice(None)] * (dim+1)
I1[axis] = slice(0,-1)
I2[axis] = slice(1,None)
Al = A1[I1]
Ar = A2[I2]
I1[axis] = -1
I2[axis] = +0
Ac = (A1[I1]+A2[I2])/2.0
Ic = [slice(None)] * (dim+1)
Ic[axis] = np.newaxis
Ac = Ac[Ic]
A = np.concatenate([Al, Ac, Ar], axis)
U1 = nrb1.knots[axis]
U2 = nrb2.knots[axis]
Ul = U1[:-p-1]
Ur = U2[p+1:]
Uc = [u]*p
U = np.concatenate([Ul, Uc, Ur])
knots = list(nrb1.knots)
knots[axis] = U
nrb = NURBS.__new__(type(nrb1))
nrb._array = np.ascontiguousarray(A)
nrb._knots = tuple(knots)
nrb.remove(axis, u, p-1)
return nrb
P[6,1,:] = [5.24524, 50.0859]
P[7,1,:] = [42.1936, 50.0884]
P[8,1,:] = [95.7095, 50.0937]
P[9,1,:] = [128.203, 50.0974]
P[10,1,:] = [183.546, 47.168]
P[11,1,:] = [335.568, 38.9067]
P[12,1,:] = [782.636, 12.9908]
P[13,1,:] = [1120.1, -10.3521]
# Adjust control points such that the length scale is 1
delx=P[:,:,0].max()-P[:,:,0].min()
minx=P[:,:,0].min()
P -= minx
P /= delx
tube = NURBS(P,[U,V])
tube.elevate(0,1)
# Determine which knots to insert
res = 32
insert_U=InsertUniformly(U,4*res)
insert_V=InsertUniformly(V,res)
tube.refine(insert_U,insert_V)
plt.use('mayavi')
plt.figure()
plt.plot(tube)
plt.show()
circleFileName='circle40.mat'; splineFileName='tubeFullWithBaseFor1R4Helix40.mat' outputFileName='tubeFullWithBaseFor1R4HelixH200.dat' C2Continuity=False; #Read from mat file mat = scipy.io.loadmat(splineFileName) order = np.array(mat['order']) order = order.tolist()[0][0]; knots = np.array(mat['knots']) knots = knots.tolist()[0]; C = np.transpose(np.array(mat['controlPoints'])) U=knots; Curve = NURBS([U],C) S = revolve(Curve, circleFileName, (0,0), 1) print S.knots[0]; print S.knots[1]; #refine along X #to_insertX = np.setdiff1d(linspace(0.25,0.5,11)[1:-1],S.knots[0]); #S.refine(0,to_insertX) #refine along Y #to_insertY = np.setdiff1d(linspace(0,1.0,21)[1:-1],S.knots[1]); #S.elevate(0,1); #S.elevate(1,1); #S.refine(1,kX); #S.refine(1,kX);
#%%
cpoints, knot1, knot2 = make_srf()
#%%
from igakit.nurbs import NURBS
from igakit.plot import plt
import matplotlib
matplotlib.use('Qt5Agg')
C1 = [[-1.5, 0],
[-1, 0.5],
[-1, 1]]
U = [0, 0, 0, 1, 1, 1]
crv = NURBS([U], C1)
plt.figure()
plt.cpoint(crv)
plt.cwire(crv)
plt.plot(crv)
plt.show()
#%%
C1 = [[-1, 1],
[-1.2, 2],
[-1, 3]]
U1 = [0, 0, 0, 1, 1, 1]
crv1 = NURBS([U1], C1)
plt.figure()
help='project while enforcing end conditions')
opts,args = parser.parse_args()
nelem = opts.nelem
p = opts.p
l2 = opts.L2
h1 = opts.H1
dbc = opts.dbc
k = opts.k
# setup function space
xmax = 1.0
xmin = -1.0
U = iga.iga.KnotVector(nelem,p,k,-1,1,0)
C = np.zeros((U.size-p-1,2))
crv = NURBS([U],C)
# plot exact solution
fh = 4.0
fig = plt.figure(figsize=(2.0*fh*1.62,fh))
u = np.linspace(-1.0,1.0,1000,endpoint=True)
x=[]
dx=[]
for i in range(len(u)):
x.append(f(u[i]))
dx.append(df(u[i]))
plt.subplot(121)
plt.plot(u,x,'r-',label='exact')
plt.subplot(122)
plt.plot(u,dx,'r-',label='exact')
