def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-o',
'',
metavar='filename',
action='store',
dest='filename',
default=None,
help=helps['filename'])
parser.add_option('-d',
'--dims',
metavar='dims',
action='store',
dest='dims',
default='[1.0, 1.0, 1.0]',
help=helps['dims'])
parser.add_option('-c',
'--centre',
metavar='centre',
action='store',
dest='centre',
default='[0.0, 0.0, 0.0]',
help=helps['centre'])
parser.add_option('-s',
'--shape',
metavar='shape',
action='store',
dest='shape',
default='[5, 5, 5]',
help=helps['shape'])
parser.add_option('',
'--degrees',
metavar='degrees',
action='store',
dest='degrees',
default='[2, 2, 2]',
help=helps['degrees'])
parser.add_option('',
'--continuity',
metavar='continuity',
action='store',
dest='continuity',
default=None,
help=helps['continuity'])
parser.add_option('-2',
'--2d',
action='store_true',
dest='is_2d',
default=False,
help=helps['2d'])
parser.add_option('-p',
'--plot',
action='store_true',
dest='plot',
default=False,
help=helps['plot'])
parser.add_option('-l',
'--label',
action='store_true',
dest='label',
default=False,
help=helps['label'])
(options, args) = parser.parse_args()
dim = 2 if options.is_2d else 3
filename = options.filename
if filename is None:
filename = 'block%dd.iga' % dim
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
degrees = nm.array(eval(options.degrees), dtype=nm.int32)[:dim]
if options.continuity is None:
continuity = degrees - 1
else:
continuity = nm.array(eval(options.continuity), dtype=nm.int32)[:dim]
output('dimensions:', dims)
output('centre: ', centre)
output('shape: ', shape)
output('degrees: ', degrees)
output('continuity:', continuity)
output('-> :', filename)
dd = centre - 0.5 * dims
block = cad.grid(shape - 1, degree=degrees, continuity=continuity)
for ia in xrange(dim):
block.scale(dims[ia], ia)
for ia in xrange(dim):
block.translate(dd[ia], ia)
# Force uniform control points. This prevents coarser resolution inside the
# block.
shape = nm.asarray(block.points.shape[:-1])
n_nod = nm.prod(shape)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
coors.shape = shape.tolist() + [dim]
block.array[..., :dim] = coors
# Compute Bezier extraction data.
cs = iga.compute_bezier_extraction(block.knots, block.degree)
n_els = [len(ii) for ii in cs]
conn, bconn = iga.create_connectivity(n_els, block.knots, block.degree)
ccs = iga.combine_bezier_extraction(cs)
cps = block.points[..., :dim].copy()
cps = cps.reshape((-1, dim))
bcps, bweights = iga.compute_bezier_control(cps, block.weights.ravel(),
ccs, conn, bconn)
regions = iga.get_patch_box_regions(n_els, block.degree)
io.write_iga_data(filename, block.knots, block.degree, cps,
block.weights.ravel(), cs, conn, bcps, bweights, bconn,
regions)
if options.plot:
pn.plt.rcParams['lines.linewidth'] = 2
ax = pn.plot_parametric_mesh(None, block.knots)
ax.set_title('parametric mesh')
ax.axis('equal')
points = block.points[..., :dim]
ax = pn.plot_control_mesh(None, points, label=options.label)
ax = pn.plot_iso_lines(ax, block)
ax.set_title('control mesh and iso lines (blue)'
' in Greville abscissae coordinates')
ax.axis('equal')
points = bcps
ax = pn.plot_bezier_mesh(None,
points,
bconn,
block.degree,
label=options.label)
ax = pn.plot_iso_lines(ax, block)
ax.set_title('Bezier mesh and iso lines (blue)'
' in Greville abscissae coordinates')
ax.axis('equal')
pn.plt.rcParams['lines.linewidth'] = 3
line = block.extract(0, 0)
if dim == 3:
line = line.extract(0, 0)
ax = pn.plot_nurbs_basis_1d(None,
line,
n_points=1000,
legend=options.label)
ax.set_xlabel('last parametric coordinate')
ax.set_title('1D NURBS basis')
ax = pn.plot_nurbs_basis_1d(None,
line,
n_points=1000,
x_axis=dim - 1,
legend=options.label)
ax.set_xlabel('last physical coordinate')
ax.set_title('1D NURBS basis')
pn.plt.show()
def gen_patch_block_domain(dims, shape, centre, degrees, continuity=None,
cp_mode='greville', name='block', verbose=True):
"""
Generate a single IGA patch block in 2D or 3D of given degrees and
continuity using igakit.
Parameters
----------
dims : array of D floats
Dimensions of the block.
shape : array of D ints
Numbers of unique knot values along each axis.
centre : array of D floats
Centre of the block.
degrees : array of D floats
NURBS degrees along each axis.
continuity : array of D ints, optional
NURBS continuity along each axis. If None, `degrees-1` is used.
cp_mode : 'greville' or 'uniform'
The control points mode. The default 'greville' results in a uniform
Bezier mesh, while the 'uniform' mode results in a uniform grid of
control points a finer Bezier mesh inside the block and a coarser
Bezier mesh near the block boundary.
name : string
Domain name.
verbose : bool
If True, report progress of the domain generation.
Returns
-------
nurbs : NurbsPatch instance
The NURBS data. The igakit NURBS object is stored as `nurbs` attribute.
bmesh : Struct instance
The Bezier mesh data.
regions : dict
The patch surface regions.
"""
import igakit.cad as cad
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
degrees = nm.asarray(degrees, dtype=nm.int32)
assert_(cp_mode in ['greville', 'uniform'],
"cp_mode has to be 'greville' or 'uniform'")
if continuity is None:
continuity = degrees - 1
else:
continuity = nm.asarray(continuity, dtype=nm.int32)
dim = len(shape)
output('generating NURBS...', verbose=verbose)
dd = centre - 0.5 * dims
block = cad.grid(shape - 1, degree=degrees, continuity=continuity)
for ia in range(dim):
block.scale(dims[ia], ia)
for ia in range(dim):
block.translate(dd[ia], ia)
if cp_mode == 'uniform':
# Force uniform control points. This prevents coarser resolution inside
# the block.
shape = nm.asarray(block.points.shape[:-1])
n_nod = nm.prod(shape)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
coors.shape = shape.tolist() + [dim]
block.array[..., :dim] = coors
output('...done', verbose=verbose)
nurbs, bmesh, regions = create_from_igakit(block, verbose=verbose)
return nurbs, bmesh, regions
def gen_patch_block_domain(dims, shape, centre, degrees, continuity=None,
name='block', verbose=True):
"""
Generate a single IGA patch block in 2D or 3D of given degrees and
continuity using igakit.
Parameters
----------
dims : array of D floats
Dimensions of the block.
shape : array of D ints
Numbers of unique knot values along each axis.
centre : array of D floats
Centre of the block.
degrees : array of D floats
NURBS degrees along each axis.
continuity : array of D ints, optional
NURBS continuity along each axis. If None, `degrees-1` is used.
name : string
Domain name.
verbose : bool
If True, report progress of the domain generation.
Returns
-------
nurbs : NurbsPatch instance
The NURBS data. The igakit NURBS object is stored as `nurbs` attribute.
bmesh : Struct instance
The Bezier mesh data.
regions : dict
The patch surface regions.
"""
import igakit.cad as cad
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
degrees = nm.asarray(degrees, dtype=nm.int32)
if continuity is None:
continuity = degrees - 1
else:
continuity = nm.asarray(continuity, dtype=nm.int32)
dim = len(shape)
output('generating NURBS...', verbose=verbose)
dd = centre - 0.5 * dims
block = cad.grid(shape - 1, degree=degrees, continuity=continuity)
for ia in xrange(dim):
block.scale(dims[ia], ia)
for ia in xrange(dim):
block.translate(dd[ia], ia)
# Force uniform control points. This prevents coarser resolution inside the
# block.
shape = nm.asarray(block.points.shape[:-1])
n_nod = nm.prod(shape)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
coors.shape = shape.tolist() + [dim]
block.array[..., :dim] = coors
output('...done', verbose=verbose)
# Compute Bezier extraction data.
output('computing Bezier mesh...', verbose=verbose)
cs = iga.compute_bezier_extraction(block.knots, block.degree)
n_els = [len(ii) for ii in cs]
conn, bconn = iga.create_connectivity(n_els, block.knots, block.degree)
ccs = iga.combine_bezier_extraction(cs)
cps = block.points[..., :dim].copy()
cps = cps.reshape((-1, dim))
bcps, bweights = iga.compute_bezier_control(cps, block.weights.ravel(), ccs,
conn, bconn)
nurbs = NurbsPatch(block.knots, degrees, cps, block.weights.ravel(), cs,
conn)
nurbs.nurbs = block
bmesh = Struct(name='bmesh', cps=bcps, weights=bweights, conn=bconn)
output('...done', verbose=verbose)
output('defining regions...', verbose=verbose)
regions = iga.get_patch_box_regions(n_els, block.degree)
output('...done', verbose=verbose)
return nurbs, bmesh, regions
def gen_patch_block_domain(dims,
shape,
centre,
degrees,
continuity=None,
cp_mode='greville',
name='block',
verbose=True):
"""
Generate a single IGA patch block in 2D or 3D of given degrees and
continuity using igakit.
Parameters
----------
dims : array of D floats
Dimensions of the block.
shape : array of D ints
Numbers of unique knot values along each axis.
centre : array of D floats
Centre of the block.
degrees : array of D floats
NURBS degrees along each axis.
continuity : array of D ints, optional
NURBS continuity along each axis. If None, `degrees-1` is used.
cp_mode : 'greville' or 'uniform'
The control points mode. The default 'greville' results in a uniform
Bezier mesh, while the 'uniform' mode results in a uniform grid of
control points a finer Bezier mesh inside the block and a coarser
Bezier mesh near the block boundary.
name : string
Domain name.
verbose : bool
If True, report progress of the domain generation.
Returns
-------
nurbs : NurbsPatch instance
The NURBS data. The igakit NURBS object is stored as `nurbs` attribute.
bmesh : Struct instance
The Bezier mesh data.
regions : dict
The patch surface regions.
"""
import igakit.cad as cad
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
degrees = nm.asarray(degrees, dtype=nm.int32)
assert_(cp_mode in ['greville', 'uniform'],
"cp_mode has to be 'greville' or 'uniform'")
if continuity is None:
continuity = degrees - 1
else:
continuity = nm.asarray(continuity, dtype=nm.int32)
dim = len(shape)
output('generating NURBS...', verbose=verbose)
dd = centre - 0.5 * dims
block = cad.grid(shape - 1, degree=degrees, continuity=continuity)
for ia in xrange(dim):
block.scale(dims[ia], ia)
for ia in xrange(dim):
block.translate(dd[ia], ia)
if cp_mode == 'uniform':
# Force uniform control points. This prevents coarser resolution inside
# the block.
shape = nm.asarray(block.points.shape[:-1])
n_nod = nm.prod(shape)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
coors.shape = shape.tolist() + [dim]
block.array[..., :dim] = coors
output('...done', verbose=verbose)
nurbs, bmesh, regions = create_from_igakit(block, verbose=verbose)
return nurbs, bmesh, regions
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-o', '', metavar='filename',
action='store', dest='filename',
default=None, help=helps['filename'])
parser.add_option('-d', '--dims', metavar='dims',
action='store', dest='dims',
default='[1.0, 1.0, 1.0]', help=helps['dims'])
parser.add_option('-c', '--centre', metavar='centre',
action='store', dest='centre',
default='[0.0, 0.0, 0.0]', help=helps['centre'])
parser.add_option('-s', '--shape', metavar='shape',
action='store', dest='shape',
default='[5, 5, 5]', help=helps['shape'])
parser.add_option('', '--degrees', metavar='degrees',
action='store', dest='degrees',
default='[2, 2, 2]', help=helps['degrees'])
parser.add_option('', '--continuity', metavar='continuity',
action='store', dest='continuity',
default=None, help=helps['continuity'])
parser.add_option('-2', '--2d',
action='store_true', dest='is_2d',
default=False, help=helps['2d'])
parser.add_option('-p', '--plot',
action='store_true', dest='plot',
default=False, help=helps['plot'])
parser.add_option('-l', '--label',
action='store_true', dest='label',
default=False, help=helps['label'])
(options, args) = parser.parse_args()
dim = 2 if options.is_2d else 3
filename = options.filename
if filename is None:
filename = 'block%dd.iga' % dim
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
degrees = nm.array(eval(options.degrees), dtype=nm.int32)[:dim]
if options.continuity is None:
continuity = degrees - 1
else:
continuity = nm.array(eval(options.continuity), dtype=nm.int32)[:dim]
output('dimensions:', dims)
output('centre: ', centre)
output('shape: ', shape)
output('degrees: ', degrees)
output('continuity:', continuity)
output('-> :', filename)
dd = centre - 0.5 * dims
block = cad.grid(shape - 1, degree=degrees, continuity=continuity)
for ia in xrange(dim):
block.scale(dims[ia], ia)
for ia in xrange(dim):
block.translate(dd[ia], ia)
# Force uniform control points. This prevents coarser resolution inside the
# block.
shape = nm.asarray(block.points.shape[:-1])
n_nod = nm.prod(shape)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
coors.shape = shape.tolist() + [dim]
block.array[..., :dim] = coors
# Compute Bezier extraction data.
cs = iga.compute_bezier_extraction(block.knots, block.degree)
n_els = [len(ii) for ii in cs]
conn, bconn = iga.create_connectivity(n_els, block.knots, block.degree)
ccs = iga.combine_bezier_extraction(cs)
cps = block.points[..., :dim].copy()
cps = cps.reshape((-1, dim))
bcps, bweights = iga.compute_bezier_control(cps, block.weights.ravel(), ccs,
conn, bconn)
regions = iga.get_patch_box_regions(n_els, block.degree)
io.write_iga_data(filename, block.knots, block.degree, cps,
block.weights.ravel(), cs, conn, bcps, bweights, bconn,
regions)
if options.plot:
pn.plt.rcParams['lines.linewidth'] = 2
ax = pn.plot_parametric_mesh(None, block.knots)
ax.set_title('parametric mesh')
ax.axis('equal')
points = block.points[..., :dim]
ax = pn.plot_control_mesh(None, points, label=options.label)
ax = pn.plot_iso_lines(ax, block)
ax.set_title('control mesh and iso lines (blue)'
' in Greville abscissae coordinates')
ax.axis('equal')
points = bcps
ax = pn.plot_bezier_mesh(None, points, bconn, block.degree,
label=options.label)
ax = pn.plot_iso_lines(ax, block)
ax.set_title('Bezier mesh and iso lines (blue)'
' in Greville abscissae coordinates')
ax.axis('equal')
pn.plt.rcParams['lines.linewidth'] = 3
line = block.extract(0, 0)
if dim == 3:
line = line.extract(0, 0)
ax = pn.plot_nurbs_basis_1d(None, line, n_points=1000,
legend=options.label)
ax.set_xlabel('last parametric coordinate')
ax.set_title('1D NURBS basis')
ax = pn.plot_nurbs_basis_1d(None, line, n_points=1000, x_axis=dim-1,
legend=options.label)
ax.set_xlabel('last physical coordinate')
ax.set_title('1D NURBS basis')
pn.plt.show()