import numpy as nm
from sfepy import data_dir
from sfepy.mesh.splinebox import SplineBox, SplineRegion2D
from sfepy.mesh.bspline import BSpline
from sfepy.discrete.fem import Mesh
import sfepy.base.testing as tst
[docs]def tetravolume(cells, vertices):
vol = 0.0
c1 = nm.ones((4,4), dtype=nm.float64)
mul = 1.0 / 6.0
for ic in cells:
c1[:,:3] = vertices[ic,:]
vol += mul * nm.linalg.det(c1)
return -vol
tolerance = 1e-6
[docs]def test_spbox_3d():
"""
Check volume change of the mesh which is deformed using
the SplineBox functions.
"""
from sfepy.discrete.fem import Mesh
from sfepy.mesh.splinebox import SplineBox
mesh = Mesh.from_file(data_dir + '/meshes/3d/cylinder.vtk')
conn = mesh.get_conn('3_4')
vol0 = tetravolume(conn, mesh.coors)
bbox = nm.array(mesh.get_bounding_box()).T
spbox = SplineBox(bbox, mesh.coors)
cpoints0 = spbox.get_control_points(init=True)
for ii in range(4):
for jj in range(4):
spbox.move_control_point((0, ii, jj), [-0.02, 0, 0])
coors = spbox.evaluate()
vol1 = tetravolume(conn, coors)
mesh.coors[:] = coors
spbox.set_control_points(cpoints0)
coors = spbox.evaluate()
vol2 = tetravolume(conn, coors)
ok = True
actual_volumes = (vol0, vol1, vol2)
expected_volumes = (1.22460186e-4, 1.46950423e-4, 1.22460186e-4)
for ii in range(3):
relerr = abs(actual_volumes[ii] - expected_volumes[ii])\
/ expected_volumes[ii]
ok = ok and (relerr < tolerance)
if not ok:
tst.report('expected volumes:')
tst.report(expected_volumes)
tst.report('actual volumes:')
tst.report(actual_volumes)
assert ok
[docs]def test_spbox_2d():
"""
Check position of a given vertex in the deformed mesh.
"""
mesh = Mesh.from_file(data_dir + '/meshes/2d/square_tri1.mesh')
spb = SplineBox([[-1, 1], [-1, 0.6]], mesh.coors, nsg=[2,1])
spb.move_control_point(1, [0.1, -0.2])
spb.move_control_point(2, [0.2, -0.3])
spb.move_control_point(3, [0.0, -0.1])
pt0 = mesh.coors[175,:].copy()
mesh.cmesh.coors[:] = spb.evaluate()
pt1 = mesh.coors[175,:]
expected_distance = 0.165892726387
actual_distance = nm.linalg.norm(pt0 - pt1)
ok = nm.fabs(actual_distance - expected_distance)\
/ expected_distance < tolerance
if not ok:
tst.report('expected distance:')
tst.report(expected_distance)
tst.report('actual distance:')
tst.report(actual_distance)
assert ok
[docs]def test_spbox_field():
"""
'Field' vs. 'coors'.
"""
mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.mesh')
coors = mesh.coors.copy()
bbox = nm.vstack((nm.amin(coors, 0), nm.amax(coors, 0))).T
coors_1 = coors.copy()
alpha = coors[:, 0]
spbox = SplineBox(bbox, coors, nsg=[1, 2], field=alpha)
dv1 = spbox.evaluate_derivative(6, 1)
spbox.move_control_point(6, -0.2)
c1 = spbox.evaluate()
coors_1[:, 0] = c1[:, 0]
alpha = coors[:, 1]
spbox = SplineBox(bbox, coors, nsg=[1, 2], field=alpha)
dv2 = spbox.evaluate_derivative(6, 1)
spbox.move_control_point(6, 0.2)
c2 = spbox.evaluate()
coors_1[:, 1] = c2[:, 0]
spbox = SplineBox(bbox, coors, nsg=[1, 2])
dv = spbox.evaluate_derivative(6, [1, 1])
spbox.move_control_point(6, [-0.2, 0.2])
coors_2 = spbox.evaluate()
rel_coor_dist = nm.linalg.norm(coors_2 - coors_1)\
/ nm.linalg.norm(coors_2)
ok = rel_coor_dist < tolerance
rel_dvel_dist = nm.linalg.norm(dv - nm.hstack([dv1, dv2]))\
/ nm.linalg.norm(dv)
ok = ok and rel_dvel_dist < tolerance
if not ok:
tst.report('modified coordinates do not match, relative error:')
tst.report(rel_coor_dist)
tst.report('derivatives do not match, relative error:')
tst.report(rel_dvel_dist)
assert ok
[docs]def test_spregion2d():
"""
Check position of a given vertex in the deformed mesh.
"""
line_l = nm.array([[-1, 1], [-1, .5], [-1, 0], [-1, -.5]])
line_r = nm.array([[0, -.2], [.1, .2], [.3, .6], [.4, 1]])
sp_l = BSpline(3, is_cyclic=False)
sp_l.approximate(line_l, ncp=4)
kn_lr = sp_l.get_knot_vector()
sp_r = BSpline(3, is_cyclic=False)
sp_r.approximate(line_r, knots=kn_lr)
line_b = nm.array([[-1, -.5], [-.8, -.6], [-.5, -.4], [-.2, -.2],
[0, -.2]])
line_t = nm.array([[.4, 1], [0, 1], [-.2, 1], [-.6, 1], [-1, 1]])
sp_b = BSpline(3, is_cyclic=False)
sp_b.approximate(line_b, ncp=5)
kn_bt = sp_b.get_knot_vector()
sp_t = BSpline(3, is_cyclic=False)
sp_t.approximate(line_t, knots=kn_bt)
mesh = Mesh.from_file(data_dir + '/meshes/2d/square_tri1.mesh')
spb = SplineRegion2D([sp_b, sp_r, sp_t, sp_l], mesh.coors)
spb.move_control_point(5, [-.2, .1])
spb.move_control_point(10, [-.3, .2])
spb.move_control_point(15, [-.1, .2])
pt0 = mesh.coors[145,:].copy()
mesh.cmesh.coors[:] = spb.evaluate()
pt1 = mesh.coors[145,:]
expected_distance = 0.0908306614584
actual_distance = nm.linalg.norm(pt0 - pt1)
ok = nm.fabs(actual_distance - expected_distance)\
/ expected_distance < tolerance
if not ok:
tst.report('expected distance:')
tst.report(expected_distance)
tst.report('actual distance:')
tst.report(actual_distance)
assert ok