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 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)
plt.cpoint(crv_diapir)
plt.cwire(crv_diapir)
plt.plot(crv_diapir)
ax = plt.backend.gca()
ax.set_xlim((-3,3))
ax.set_ylim((0,6))
plt.show()
#%%
c_bot = [[-1.5,0],
[0,0],
[1.5,0]]
U = [0,0,0,1,1,1]
cr_bot = NURBS([U], c_bot)
#%%
diapir = ruled(crv_diapir, cr_bot)
plt.figure()
#plt.cpoint(diapir)
plt.cwire(diapir)
plt.plot(diapir, resolution=100)
plt.kpoint(diapir)
ax = plt.backend.gca()
ax.set_xlim((-3,3))
ax.set_ylim((0,6))
plt.show()
#%%
C_1 = [[-1.5, 0],
[-1, 0.5],
[-1, 1],
[-1.2, 2],
[-1, 3],
import sys, numpy as np from igakit.nurbs import NURBS from igakit.cad import circle, line, join, revolve, ruled from igakit.plot import plt from math import pi as Pi from igakit.io import PetIGA from numpy import linspace #Geometry R = 1.0 c1 = circle(0.005 * R, (0, 0, 1)) c2 = circle(R, (0, 0, 1)) #c1 = circle(radius=R) #c2 = circle(radius=20*R) S = ruled(c1, c2).transpose().elevate(0, 1) #refine along X to_insertX = np.setdiff1d(linspace(0, 0.25, 11)[1:-1], S.knots[0]) S.refine(0, to_insertX) #to_insertX = np.setdiff1d(linspace(0.25,1.0,5)[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.refine(1, to_insertY) #S.elevate (1,1); #periodicity S.unclamp(1, continuity=1)
def create_patch(R1, R2, C1, C2, order=2, viewpatch=False):
"""
Create a single 2d NURBS-patch of the area between two coplanar nested
circles using igakit.
Parameters
----------
R1 : float
Radius of the inner circle.
R2 : float
Radius of the outer circle.
C1 : list of two floats
Coordinates of the center of the inner circle given as [x1, y1].
C2 : list of two floats
Coordinates of the center of the outer circle given as [x2, y2].
order : int, optional
Degree of the NURBS basis functions. The default is 2.
viewpatch : bool, optional
When set to True, display the NURBS patch. The default is False.
Returns
-------
None.
"""
from sfepy.discrete.iga.domain_generators import create_from_igakit
import sfepy.discrete.iga.io as io
from igakit.cad import circle, ruled
from igakit.plot import plt as iplt
from numpy import pi
# Assert the inner circle is inside the outer one
inter_centers = nm.sqrt((C2[0] - C1[0])**2 + (C2[1] - C1[1])**2)
assert R2 > R1, "Outer circle should have a larger radius than the inner one"
assert inter_centers < R2 - R1, "Circles are not nested"
# Geometry Creation
centers_direction = [C2[0] - C1[0], C2[1] - C1[1]]
if centers_direction[0] == 0 and centers_direction[1] == 0:
start_angle = 0.0
else:
start_angle = nm.arctan2(centers_direction[1], centers_direction[0])
c1 = circle(radius=R1,
center=C1,
angle=(start_angle, start_angle + 2 * pi))
c2 = circle(radius=R2,
center=C2,
angle=(start_angle, start_angle + 2 * pi))
srf = ruled(c1, c2).transpose() # make the radial direction first
# Refinement
insert_U = insert_uniformly(srf.knots[0], 6)
insert_V = insert_uniformly(srf.knots[1], 6)
srf.refine(0, insert_U).refine(1, insert_V)
# Setting the NURBS-surface degree
srf.elevate(0, order - srf.degree[0] if order - srf.degree[0] > 0 else 0)
srf.elevate(1, order - srf.degree[1] if order - srf.degree[1] > 0 else 0)
# Sfepy .iga file creation
nurbs, bmesh, regions = create_from_igakit(srf, verbose=True)
# Save .iga file in sfepy/meshes/iga
filename_domain = data_dir + '/meshes/iga/concentric_circles.iga'
io.write_iga_data(filename_domain, None, nurbs.knots, nurbs.degrees,
nurbs.cps, nurbs.weights, nurbs.cs, nurbs.conn,
bmesh.cps, bmesh.weights, bmesh.conn, regions)
if viewpatch:
try:
iplt.use('mayavi')
iplt.figure()
iplt.plot(srf)
iplt.show()
except ImportError:
iplt.use('matplotlib')
iplt.figure()
iplt.plot(srf)
iplt.show()
conf_srf = srf.copy()
conf_srf.control[:,:,0] = U[:shift].reshape((conf_srf.shape[0],conf_srf.shape[1]),order='f')
conf_srf.control[:,:,1] = U[shift:].reshape((conf_srf.shape[0],conf_srf.shape[1]),order='f')
return conf_srf
if __name__ == "__main__":
# generates two random curves
cp = np.outer([0,0.3,0.5,0.6,1.0],[1,1])
cp[:,1] = np.random.rand(5)
c1 = NURBS([[0,0,0,0,0.5,1,1,1,1]],cp)
cp[:,0] += 0.3
cp[:,1] = 1.+np.random.rand(5)
c2 = NURBS([[0,0,0,0,0.5,1,1,1,1]],cp)
# create a surface by linearly blending curves, then refine
srf = ruled(c1,c2)
srf.elevate(1,1)
srf.refine(0,np.linspace(0,0.5,6)[1:-1])
srf.refine(0,np.linspace(0.5,1.0,6)[1:-1])
srf.refine(1,np.linspace(0,1,11)[1:-1])
# make the projection
err0 = ConformalProjectionError(srf)
srf = QuasiConformalProjection(srf)
print "Relative error: %.6e" % (ConformalProjectionError(srf)/err0)
from igakit.io import VTK
VTK().write("conformal.vtk", srf)