def cubedsphere(opts, nlev, mesh):
"""
CUBEDSPHERE Nth-level cubedsphere mesh of the ellipsoid.
"""
if (not isinstance(opts, jigsaw_jig_t)):
raise Exception("Incorrect type: OPTS.")
if (not isinstance(mesh, jigsaw_msh_t)):
raise Exception("Incorrect type: MESH.")
geom = jigsaw_msh_t()
loadmsh(opts.geom_file, geom)
#-------------------------------- setup cubedsphere geometry
aval = math.atan(
+math.sqrt(+2.0) / +2.0)
mesh.mshID = "euclidean-mesh"
apos = np.array([
(+0.25 * np.pi, -aval),
(+0.75 * np.pi, -aval),
(-0.75 * np.pi, -aval),
(-0.25 * np.pi, -aval),
(+0.25 * np.pi, +aval),
(+0.75 * np.pi, +aval),
(-0.75 * np.pi, +aval),
(-0.25 * np.pi, +aval)])
mesh.vert3 = np.zeros(+ 8, dtype=mesh.VERT3_t)
mesh.vert3["coord"] = S2toR3(geom.radii, apos)
mesh.vert3["IDtag"] = - 1 # fix "corners"
#-------------------------------- setup cubedsphere topology
mesh.quad4 = np.array([
((0, 1, 2, 3), 0), # noqa
((0, 1, 5, 4), 1), # noqa
((1, 2, 6, 5), 2), # noqa
((2, 3, 7, 6), 3), # noqa
((3, 0, 4, 7), 4), # noqa
((4, 5, 6, 7), 5)], # noqa
dtype=mesh.QUAD4_t)
if (nlev <= +0): return
opts.init_file = opts.mesh_file
savemsh(opts.init_file, mesh)
refine(opts, nlev, mesh)
return
def refine(opts, nlev, mesh=None):
"""
REFINE generate a mesh using an inc. bisection strategy.
"""
if (not isinstance(opts, jigsaw_jig_t)):
raise Exception("Incorrect type: OPTS.")
if (mesh is not None and not
isinstance(mesh, jigsaw_msh_t)):
raise Exception("Incorrect type: MESH.")
#---------------------------- call JIGSAW via inc. bisection
opts.mesh_iter = +0
opts.optm_div_ = False
opts.optm_zip_ = False
for ilev in reversed(range(nlev + 1)):
if (opts.optm_dual is not None):
#------------------------ create/write current DUAL data
opts.optm_dual = ilev == 0
#------------------------ call JIGSAW kernel at this lev
jigsaw(opts, mesh)
if (ilev <= +0): break
if (opts.mesh_file is not None):
#------------------------ create/write current INIT data
path = Path(opts.mesh_file).parent
name = Path(opts.mesh_file).stem
fext = Path(opts.mesh_file).suffix
name = str(name)
fext = str(fext)
name = name + "-ITER" + fext
opts.init_file = str(path / name)
bisect(mesh)
attach(mesh)
savemsh(opts.init_file, mesh,
opts.mesh_tags)
return
def icosahedron(opts, nlev, mesh):
"""
ICOSAHEDRON Nth-level icosahedral mesh of the ellipsoid.
"""
if (not isinstance(opts, jigsaw_jig_t)):
raise Exception("Incorrect type: OPTS.")
if (not isinstance(mesh, jigsaw_msh_t)):
raise Exception("Incorrect type: MESH.")
geom = jigsaw_msh_t()
loadmsh(opts.geom_file, geom)
#-------------------------------- setup icosahedron geometry
la = math.atan(0.5)
lo = 2.0 / 10.0 * np.pi
PI = np.pi
mesh.mshID = "euclidean-mesh"
apos = np.array([(+0.0 * PI, -0.5 * PI), (+0.0 * PI, +0.5 * PI),
(+0.0 * lo, +1.0 * la), (+1.0 * lo, -1.0 * la),
(+2.0 * lo, +1.0 * la), (+3.0 * lo, -1.0 * la),
(+4.0 * lo, +1.0 * la), (+5.0 * lo, -1.0 * la),
(+6.0 * lo, +1.0 * la), (+7.0 * lo, -1.0 * la),
(+8.0 * lo, +1.0 * la), (+9.0 * lo, -1.0 * la)])
mesh.vert3 = np.zeros(+12, dtype=mesh.VERT3_t)
mesh.vert3["coord"] = S2toR3(geom.radii, apos)
mesh.vert3["IDtag"] = -1 # fix "corners"
#-------------------------------- setup icosahedron topology
mesh.tria3 = np.array(
[
((0, 3, 5), 0), # noqa
((0, 5, 7), 1), # noqa
((0, 7, 9), 2), # noqa
((0, 9, 11), 3), # noqa
((0, 11, 3), 4), # noqa
((1, 2, 4), 5), # noqa
((1, 4, 6), 6), # noqa
((1, 6, 8), 7), # noqa
((1, 8, 10), 8), # noqa
((1, 10, 2), 9), # noqa
((3, 2, 4), 10), # noqa
((5, 4, 6), 11), # noqa
((7, 6, 8), 12), # noqa
((9, 8, 10), 13), # noqa
((11, 10, 2), 14), # noqa
((4, 3, 5), 15), # noqa
((6, 5, 7), 16), # noqa
((8, 7, 9), 17), # noqa
((10, 9, 11), 18), # noqa
((2, 11, 3), 19)
], # noqa
dtype=mesh.TRIA3_t)
if (nlev <= +0): return
opts.init_file = opts.mesh_file
savemsh(opts.init_file, mesh)
refine(opts, nlev, mesh)
return
def tetris(opts, nlev, mesh=None):
"""
TETRIS generate a mesh using an inc. bisection strategy.
"""
if (not isinstance(opts, jigsaw_jig_t)):
raise Exception("Incorrect type: OPTS.")
if (mesh is not None and not isinstance(mesh, jigsaw_msh_t)):
raise Exception("Incorrect type: MESH.")
#---------------------------- call JIGSAW via inc. bisection
SCAL = +2.**nlev
OPTS = copy.deepcopy(opts)
flag = +1
while (nlev >= +0):
if (opts.optm_qlim is not None):
#------------------------ create/write current QLIM data
scal = min(2.0, (nlev + 1)**(1. / 4.))
QLIM = opts.optm_qlim
OPTS.optm_qlim = QLIM / scal
else:
scal = min(2.0, (nlev + 1)**(1. / 4.))
QLIM = 0.93750
OPTS.optm_qlim = QLIM / scal
if (opts.optm_dual is not None):
#------------------------ create/write current DUAL data
OPTS.optm_dual = nlev == 0
if (opts.hfun_hmax is not None):
#------------------------ create/write current HMAX data
OPTS.hfun_hmax = \
opts.hfun_hmax * SCAL
if (opts.hfun_hmin is not None):
#------------------------ create/write current HMIN data
OPTS.hfun_hmin = \
opts.hfun_hmin * SCAL
if (opts.hfun_file is not None):
#------------------------ create/write current HFUN data
path = Path(opts.hfun_file).parent
name = Path(opts.hfun_file).stem
fext = Path(opts.hfun_file).suffix
name = str(name)
fext = str(fext)
name = name + "-ITER" + fext
OPTS.hfun_file = str(path / name)
HFUN = jigsaw_msh_t()
loadmsh(opts.hfun_file, HFUN)
HFUN.value = HFUN.value * SCAL
savemsh(OPTS.hfun_file, HFUN, OPTS.hfun_tags)
if (nlev <= 1 or flag == 0):
#------------------------ call JIGSAW kernel at this lev
ninc = min(64, nlev**2)
flag = +1
jitter(OPTS, 2 + ninc, 3, mesh)
else:
ninc = min(64, nlev**2)
flag = +0
jitter(OPTS, 2 + ninc, 2, mesh)
nlev = nlev - 1
SCAL = SCAL / 2.
if (nlev < +0): break
if (opts.init_file is not None):
#------------------------ create/write current INIT data
path = Path(opts.init_file).parent
name = Path(opts.init_file).stem
fext = Path(opts.init_file).suffix
name = str(name)
fext = str(fext)
name = name + "-ITER" + fext
OPTS.init_file = str(path / name)
bisect(mesh)
attach(mesh)
savemsh(OPTS.init_file, mesh, OPTS.init_tags)
else:
#------------------------ create/write current INIT data
path = Path(opts.mesh_file).parent
name = Path(opts.mesh_file).stem
fext = Path(opts.mesh_file).suffix
name = str(name)
fext = str(fext)
name = name + "-ITER" + fext
OPTS.init_file = str(path / name)
bisect(mesh)
attach(mesh)
savemsh(OPTS.init_file, mesh, OPTS.mesh_tags)
return
def jitter(opts, imax, ibad, mesh=None):
"""
JITTER call JIGSAW iteratively; try to improve topology.
"""
if (not isinstance(opts, jigsaw_jig_t)):
raise Exception("Incorrect type: OPTS.")
if (mesh is not None and not isinstance(mesh, jigsaw_msh_t)):
raise Exception("Incorrect type: MESH.")
if (mesh is None): mesh = jigsaw_msh_t()
#--------- call JIGSAW iteratively; try to improve topology.
OPTS = copy.deepcopy(opts)
best = metric(mesh)
next = mesh
done = False
for iter in range(imax):
if (next.point is not None and next.point.size != +0):
nvrt = next.point.size
keep = np.full((nvrt), True, dtype=bool)
#------------------------------ setup initial conditions
path = Path(opts.mesh_file).parent
name = Path(opts.mesh_file).stem
fext = Path(opts.mesh_file).suffix
name = str(name)
fext = str(fext)
name = name + "-INIT" + fext
OPTS.init_file = str(path / name)
if (next.tria3 is not None and next.tria3.size != +0):
#------------------------------ mark any irregular nodes
vdeg = trideg2(next.point["coord"], next.tria3["index"])
ierr = np.abs(vdeg - 6) # err in topo. deg.
ierr[vdeg > 6] = ierr[vdeg > 6] * 2
ierr = ierr[next.tria3["index"]]
M = np.sum(ierr, axis=1) >= ibad
keep[next.tria3["index"][M, :]] = False
if (next.edge2 is not None and next.edge2.size != +0):
keep[next.edge2["index"][:, :]] = False
if (np.count_nonzero(keep) <= +8):
#------------------------------ don't delete everything!
keep = np.full((nvrt), True, dtype=bool)
done = np.all(keep)
#------------------------------ keep nodes far from seam
init = jigsaw_msh_t()
init.point = next.point[keep]
savemsh(OPTS.init_file, init, OPTS.mesh_tags)
#------------------------------ call JIGSAW with new ICs
jigsaw(OPTS, next) # noqa
cost = metric(next)
if (cost > best):
#------------------------------ keep "best" mesh so far!
mesh = copy.deepcopy(next)
best = cost
if (done): return
return
def tetris(opts, nlev, mesh=None):
"""
TETRIS generate a mesh using an inc. bisection strategy.
"""
if (not isinstance(opts, jigsaw_jig_t)):
raise Exception("Incorrect type: OPTS.")
if (mesh is not None and not
isinstance(mesh, jigsaw_msh_t)):
raise Exception("Incorrect type: MESH.")
#---------------------------- call JIGSAW via inc. bisection
SCAL = +2. ** nlev
OPTS = copy.copy(opts)
while (nlev >= +0):
if (opts.optm_dual is not None):
#------------------------ create/write current DUAL data
OPTS.optm_dual = nlev == 0
if (opts.hfun_hmax is not None):
#------------------------ create/write current HMAX data
OPTS.hfun_hmax = \
opts.hfun_hmax * SCAL
if (opts.hfun_hmin is not None):
#------------------------ create/write current HMIN data
OPTS.hfun_hmin = \
opts.hfun_hmin * SCAL
if (opts.hfun_file is not None):
#------------------------ create/write current HFUN data
path = Path(opts.hfun_file).parent
name = Path(opts.hfun_file).stem
fext = Path(opts.hfun_file).suffix
name = str(name)
fext = str(fext)
name = name + "-ITER" + fext
OPTS.hfun_file = str(path / name)
HFUN = jigsaw_msh_t()
loadmsh(opts.hfun_file, HFUN)
HFUN.value = HFUN.value * SCAL
savemsh(OPTS.hfun_file, HFUN)
#------------------------ call JIGSAW kernel at this lev
if (nlev >= +1):
njit = round(
3 * (nlev + 1) ** (+5. / 4.))
jitter(OPTS, njit, +1, mesh)
else:
njit = round(
3 * (nlev + 1) ** (+5. / 4.))
jitter(OPTS, njit, +1, mesh)
nlev = nlev - 1
SCAL = SCAL / 2.
if (nlev < +0): break
if (opts.init_file is not None):
#------------------------ create/write current INIT data
path = Path(opts.init_file).parent
name = Path(opts.init_file).stem
fext = Path(opts.init_file).suffix
name = str(name)
fext = str(fext)
name = name + "-ITER" + fext
OPTS.init_file = str(path / name)
bisect(mesh)
attach(mesh)
savemsh(OPTS.init_file, mesh)
else:
#------------------------ create/write current INIT data
path = Path(opts.mesh_file).parent
name = Path(opts.mesh_file).stem
fext = Path(opts.mesh_file).suffix
name = str(name)
fext = str(fext)
name = name + "-ITER" + fext
OPTS.init_file = str(path / name)
bisect(mesh)
attach(mesh)
savemsh(OPTS.init_file, mesh)
return