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 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()
# 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)
# Output in PetIGA format
if (mpirank == 0):
PetIGA().write("out.dat", ikNURBS)
MPI.barrier(worldcomm)
####### Preprocessing #######
if (mpirank == 0):
print("Generating extraction...")
# Read in the generated geometry to create a control mesh.
splineMesh = NURBSControlMesh("out.dat", useRect=True)
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()
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()
C = np.zeros((2, 3, 4))
val = np.sqrt(2) * 0.5
C[0, 0, :] = [0, -100, 0, 1]
C[1, 0, :] = [100, -100, 0, 1]
C[0, 1, :] = [0, -100, 100, 1]
C[1, 1, :] = [100, -100, 100, 1]
C[0, 2, :] = [0, 0, 100, 1]
C[1, 2, :] = [100, 0, 100, 1]
C[:, 1, :] *= val
geom = NURBS([U, V], C)
geom.elevate(0, max(p - 1, 0)).elevate(1, max(p - 2, 0))
h = 1. / N
insert = np.linspace(h, 1. - h, N - 1)
geom.refine(0, insert).refine(1, insert)
if True:
from igakit.io import PetIGA
PetIGA().write("ClassicalShell.dat", geom, nsd=3)
if False:
from igakit.plot import plt
plt.figure()
plt.cpoint(geom)
plt.cwire(geom)
plt.kwire(geom)
plt.surface(geom)
plt.show()
if False:
