def runjgsw(mesh_path, make_bool, projector):
"""
RUNJGSW: main call to JIGSAW to build the triangulation.
MESH-PATH should point to a user-defined mesh directory,
containing the COMPOSE.py template.
Firstly, MESH-PATH/COMPOSE.py is called to build
user-defined geometry, initial conditions, mesh spacing
and mesh configuration information.
The boolean flags MAKE-BOOL control whether mesh
information is built from scratch, or if an exitsing an
existing file is to be used. For example, setting
MAKE-BOOL.SPAC = FALSE relies on an existing spacing
pattern be available in MESH-PATH/tmp/.
This information is written to MESH-PATH/tmp/ to be
accessed by subsequent calls to JIGSAW.
Finally, JIGSAW is run to build the triangular mesh,
calling either the multi-level (TETRIS) or single-level
(JIGSAW) algorithms. Cells are assigned ID-tags via
the polygon/regions defined in GEOM.BOUNDS.
Returns full-dimensional and 2d-projected msh_t objects.
"""
# Authors: Darren Engwirda
mesh = jigsawpy.jigsaw_msh_t()
mprj = jigsawpy.jigsaw_msh_t()
gprj = jigsawpy.jigsaw_msh_t()
#------------------------------------ setup via user COMPOSE
base = \
mesh_path.replace(os.path.sep, ".")
if (make_bool.geom):
geom = getattr(import_module(
base + ".compose"), "setgeom")()
if (make_bool.spac):
spac = getattr(import_module(
base + ".compose"), "setspac")()
if (make_bool.init):
init = getattr(import_module(
base + ".compose"), "setinit")()
if (make_bool.opts):
opts = getattr(import_module(
base + ".compose"), "setopts")()
#------------------------------------ setup files for JIGSAW
opts.geom_file = os.path.join(
mesh_path, "tmp", "geom.msh")
opts.jcfg_file = os.path.join(
mesh_path, "tmp", "opts.jig")
opts.init_file = os.path.join(
mesh_path, "tmp", "init.msh")
opts.hfun_file = os.path.join(
mesh_path, "tmp", "spac.msh")
opts.mesh_file = os.path.join(
mesh_path, "tmp", "mesh.msh")
opts.hfun_tags = "precision = 9" # less float prec.
jigsawpy.savemsh(opts.geom_file, geom,
opts.geom_tags)
jigsawpy.savemsh(opts.hfun_file, spac,
opts.hfun_tags)
jigsawpy.savemsh(opts.init_file, init,
opts.init_tags)
#------------------------------------ make mesh using JIGSAW
if (not hasattr(opts, "bisection")):
opts.bisection = +0
if (opts.bisection < +0): # bisect heuristic
rbar = np.mean(geom.radii)
hbar = np.mean(spac.value)
nlev = round(math.log2(
rbar / math.sin(.4 * math.pi) / hbar)
)
nlev = nlev - 1
ttic = time.time()
jigsawpy.cmd.tetris(opts, nlev - 0, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
print("BISECT =", +nlev)
elif (opts.bisection > +0): # bisect specified
nlev = opts.bisection
ttic = time.time()
jigsawpy.cmd.tetris(opts, nlev - 0, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
print("BISECT =", +nlev)
else: # do non-recursive
ttic = time.time()
jigsawpy.cmd.jigsaw(opts, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
#------------------------------------ form local projections
gprj = copy.deepcopy(geom) # local 2d objects
mprj = copy.deepcopy(mesh)
if (mesh.vert3.size > +0):
project(geom, mesh, gprj, mprj, projector)
#------------------------------------ assign IDtag's to cell
if (geom.bound is not None and
geom.bound.size > +0): # tags per polygon
imin = np.amin(geom.bound["IDtag"])
imax = np.amax(geom.bound["IDtag"])
for itag in range(
imin + 0, imax + 1):
tagcell(geom, mesh, gprj, mprj, itag)
#------------------------------------ check mesh for quality
cost = jigsawpy.triscr2( # quality metrics!
mesh.point["coord"],
mesh.tria3["index"])
print("TRISCR =", np.min(cost), np.mean(cost))
cost = jigsawpy.pwrscr2(
mesh.point["coord"],
mesh.power,
mesh.tria3["index"])
print("PWRSCR =", np.min(cost), np.mean(cost))
tbad = jigsawpy.centre2(
mesh.point["coord"],
mesh.power,
mesh.tria3["index"])
print("OBTUSE =",
+np.count_nonzero(np.logical_not(tbad)))
ndeg = jigsawpy.trideg2(
mesh.point["coord"],
mesh.tria3["index"])
print("TOPOL. =",
+np.count_nonzero(ndeg==+6) / ndeg.size)
#------------------------------------ save mesh for Paraview
jigsawpy.savevtk(os.path.join(
mesh_path, "out", "geom.vtk"), geom)
jigsawpy.savevtk(os.path.join(
mesh_path, "out", "spac.vtk"), spac)
jigsawpy.savevtk(os.path.join(
mesh_path, "out", "init.vtk"), init)
jigsawpy.savevtk(os.path.join(
mesh_path, "out", "mesh.vtk"), mesh)
jigsawpy.savevtk(os.path.join(
mesh_path, "out", "geom_prj.vtk"), gprj)
jigsawpy.savevtk(os.path.join(
mesh_path, "out", "mesh_prj.vtk"), mprj)
return geom, gprj, mesh, mprj
def case_6_(src_path, dst_path):
# DEMO-6: generate a 2-dim. grid for the Australian coastal
# region, using scaled ocean-depth as a mesh-resolution
# heuristic. A local stereographic projection is employed.
opts = jigsawpy.jigsaw_jig_t()
topo = jigsawpy.jigsaw_msh_t()
geom = jigsawpy.jigsaw_msh_t()
mesh = jigsawpy.jigsaw_msh_t()
hmat = jigsawpy.jigsaw_msh_t()
proj = jigsawpy.jigsaw_prj_t()
#------------------------------------ setup files for JIGSAW
opts.geom_file = \
os.path.join(dst_path, "geom.msh")
opts.jcfg_file = \
os.path.join(dst_path, "aust.jig")
opts.mesh_file = \
os.path.join(dst_path, "mesh.msh")
opts.hfun_file = \
os.path.join(dst_path, "spac.msh")
#------------------------------------ define JIGSAW geometry
jigsawpy.loadmsh(os.path.join(src_path, "aust.msh"), geom)
jigsawpy.loadmsh(os.path.join(src_path, "topo.msh"), topo)
xmin = np.min(geom.point["coord"][:, 0])
ymin = np.min(geom.point["coord"][:, 1])
xmax = np.max(geom.point["coord"][:, 0])
ymax = np.max(geom.point["coord"][:, 1])
zlev = topo.value
xmsk = np.logical_and(topo.xgrid > xmin, topo.xgrid < xmax)
ymsk = np.logical_and(topo.ygrid > ymin, topo.ygrid < ymax)
zlev = zlev[:, xmsk]
zlev = zlev[ymsk, :]
#------------------------------------ define spacing pattern
hmat.mshID = "ellipsoid-grid"
hmat.radii = np.full(+3, +6371.0, dtype=jigsawpy.jigsaw_msh_t.REALS_t)
hmat.xgrid = \
topo.xgrid[xmsk] * np.pi / 180.
hmat.ygrid = \
topo.ygrid[ymsk] * np.pi / 180.
hmin = +1.0E+01
hmax = +1.0E+02
hmat.value = \
np.sqrt(np.maximum(-zlev, 0.)) / 0.5
hmat.value = \
np.maximum(hmat.value, hmin)
hmat.value = \
np.minimum(hmat.value, hmax)
hmat.slope = np.full(hmat.value.shape,
+0.1500,
dtype=jigsawpy.jigsaw_msh_t.REALS_t)
#------------------------------------ do stereographic proj.
geom.point["coord"][:, :] *= np.pi / 180.
proj.prjID = 'stereographic'
proj.radii = +6.371E+003
proj.xbase = \
+0.500 * (xmin + xmax) * np.pi / 180.
proj.ybase = \
+0.500 * (ymin + ymax) * np.pi / 180.
jigsawpy.project(geom, proj, "fwd")
jigsawpy.project(hmat, proj, "fwd")
jigsawpy.savemsh(opts.geom_file, geom)
jigsawpy.savemsh(opts.hfun_file, hmat)
#------------------------------------ set HFUN grad.-limiter
jigsawpy.cmd.marche(opts, hmat)
#------------------------------------ make mesh using JIGSAW
opts.hfun_scal = "absolute"
opts.hfun_hmax = float("inf") # null HFUN limits
opts.hfun_hmin = float(+0.00)
opts.mesh_dims = +2 # 2-dim. simplexes
opts.mesh_eps1 = +1.
ttic = time.time()
jigsawpy.cmd.jigsaw(opts, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
cost = jigsawpy.triscr2( # quality metrics!
mesh.point["coord"], mesh.tria3["index"])
print("TRISCR =", np.min(cost), np.mean(cost))
cost = jigsawpy.pwrscr2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("PWRSCR =", np.min(cost), np.mean(cost))
tbad = jigsawpy.centre2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("OBTUSE =", +np.count_nonzero(np.logical_not(tbad)))
#------------------------------------ save mesh for Paraview
print("Saving to ../cache/case_6a.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_6a.vtk"), mesh)
print("Saving to ../cache/case_6b.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_6b.vtk"), hmat)
return
def case_2_(src_path, dst_path):
# DEMO-2: generate a regionally-refined global grid with a
# high-resolution 37.5km patch embedded in a uniform 150km
# background grid.
opts = jigsawpy.jigsaw_jig_t()
topo = jigsawpy.jigsaw_msh_t()
geom = jigsawpy.jigsaw_msh_t()
hfun = jigsawpy.jigsaw_msh_t()
mesh = jigsawpy.jigsaw_msh_t()
#------------------------------------ setup files for JIGSAW
opts.geom_file = \
os.path.join(dst_path, "geom.msh")
opts.jcfg_file = \
os.path.join(dst_path, "opts.jig")
opts.mesh_file = \
os.path.join(dst_path, "mesh.msh")
opts.hfun_file = \
os.path.join(dst_path, "spac.msh")
#------------------------------------ define JIGSAW geometry
geom.mshID = "ellipsoid-mesh"
geom.radii = np.full(3, 6.371E+003, dtype=geom.REALS_t)
jigsawpy.savemsh(opts.geom_file, geom)
#------------------------------------ define spacing pattern
hfun.mshID = "ellipsoid-grid"
hfun.radii = geom.radii
hfun.xgrid = np.linspace(-1. * np.pi, +1. * np.pi, 360)
hfun.ygrid = np.linspace(-.5 * np.pi, +.5 * np.pi, 180)
xmat, ymat = \
np.meshgrid(hfun.xgrid, hfun.ygrid)
hfun.value = +150. - 112.5 * np.exp(-(+1.5 * (xmat + 1.0)**2 + +1.5 *
(ymat - 0.5)**2)**4)
jigsawpy.savemsh(opts.hfun_file, hfun)
#------------------------------------ make mesh using JIGSAW
opts.hfun_scal = "absolute"
opts.hfun_hmax = float("inf") # null HFUN limits
opts.hfun_hmin = float(+0.00)
opts.mesh_dims = +2 # 2-dim. simplexes
opts.optm_qlim = +9.5E-01 # tighter opt. tol
opts.optm_iter = +32
opts.optm_qtol = +1.0E-05
# opts.optm_kern = "cvt+dqdx"
rbar = np.mean(geom.radii) # bisect heuristic
hbar = np.mean(hfun.value)
nlev = round(math.log2(rbar / math.sin(.4 * math.pi) / hbar))
ttic = time.time()
jigsawpy.cmd.tetris(opts, nlev - 1, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
print("BISECT =", +nlev)
cost = jigsawpy.triscr2( # quality metrics!
mesh.point["coord"], mesh.tria3["index"])
print("TRISCR =", np.min(cost), np.mean(cost))
cost = jigsawpy.pwrscr2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("PWRSCR =", np.min(cost), np.mean(cost))
tbad = jigsawpy.centre2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("OBTUSE =", +np.count_nonzero(np.logical_not(tbad)))
ndeg = jigsawpy.trideg2(mesh.point["coord"], mesh.tria3["index"])
print("TOPOL. =", +np.count_nonzero(ndeg == +6) / ndeg.size)
#------------------------------------ save mesh for Paraview
jigsawpy.loadmsh(os.path.join(src_path, "topo.msh"), topo)
#------------------------------------ a very rough land mask
apos = jigsawpy.R3toS2(geom.radii, mesh.point["coord"][:])
apos = apos * 180. / np.pi
zfun = interpolate.RectBivariateSpline(topo.ygrid, topo.xgrid, topo.value)
mesh.value = zfun(apos[:, 1], apos[:, 0], grid=False)
cell = mesh.tria3["index"]
zmsk = \
mesh.value[cell[:, 0]] + \
mesh.value[cell[:, 1]] + \
mesh.value[cell[:, 2]]
zmsk = zmsk / +3.0
mesh.tria3 = mesh.tria3[zmsk < +0.]
print("Saving to ../cache/case_2a.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_2a.vtk"), mesh)
print("Saving to ../cache/case_2b.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_2b.vtk"), hfun)
return
def case_7_(src_path, dst_path):
# DEMO-7: generate a multi-part mesh of the (contiguous) USA
# using state boundaries to partition the mesh. A local
# stereographic projection is employed. The domain is meshed
# using uniform resolution.
opts = jigsawpy.jigsaw_jig_t()
geom = jigsawpy.jigsaw_msh_t()
mesh = jigsawpy.jigsaw_msh_t()
proj = jigsawpy.jigsaw_prj_t()
#------------------------------------ setup files for JIGSAW
opts.geom_file = \
os.path.join(dst_path, "geom.msh")
opts.jcfg_file = \
os.path.join(dst_path, "us48.jig")
opts.mesh_file = \
os.path.join(dst_path, "mesh.msh")
#------------------------------------ define JIGSAW geometry
jigsawpy.loadmsh(os.path.join(src_path, "us48.msh"), geom)
xmin = np.min(geom.point["coord"][:, 0])
ymin = np.min(geom.point["coord"][:, 1])
xmax = np.max(geom.point["coord"][:, 0])
ymax = np.max(geom.point["coord"][:, 1])
geom.point["coord"][:, :] *= np.pi / 180.
proj.prjID = 'stereographic'
proj.radii = +6.371E+003
proj.xbase = \
+0.500 * (xmin + xmax) * np.pi / 180.
proj.ybase = \
+0.500 * (ymin + ymax) * np.pi / 180.
jigsawpy.project(geom, proj, "fwd")
jigsawpy.savemsh(opts.geom_file, geom)
#------------------------------------ make mesh using JIGSAW
opts.hfun_hmax = .005
opts.mesh_dims = +2 # 2-dim. simplexes
opts.mesh_eps1 = +1 / 6.
ttic = time.time()
jigsawpy.cmd.jigsaw(opts, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
cost = jigsawpy.triscr2( # quality metrics!
mesh.point["coord"], mesh.tria3["index"])
print("TRISCR =", np.min(cost), np.mean(cost))
cost = jigsawpy.pwrscr2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("PWRSCR =", np.min(cost), np.mean(cost))
tbad = jigsawpy.centre2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("OBTUSE =", +np.count_nonzero(np.logical_not(tbad)))
#------------------------------------ save mesh for Paraview
print("Saving to ../cache/case_7a.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_7a.vtk"), mesh)
return
def case_4_(src_path, dst_path):
# DEMO-4: generate a multi-resolution mesh, via local refin-
# ement along coastlines and shallow ridges. Global grid
# resolution is 150KM, background resolution is 67KM and the
# min. adaptive resolution is 33KM.
opts = jigsawpy.jigsaw_jig_t()
topo = jigsawpy.jigsaw_msh_t()
geom = jigsawpy.jigsaw_msh_t()
mesh = jigsawpy.jigsaw_msh_t()
hmat = jigsawpy.jigsaw_msh_t()
#------------------------------------ setup files for JIGSAW
opts.geom_file = \
os.path.join(dst_path, "geom.msh")
opts.jcfg_file = \
os.path.join(dst_path, "opts.jig")
opts.mesh_file = \
os.path.join(dst_path, "mesh.msh")
opts.hfun_file = \
os.path.join(dst_path, "spac.msh")
#------------------------------------ define JIGSAW geometry
geom.mshID = "ellipsoid-mesh"
geom.radii = np.full(3, 6.371E+003, dtype=geom.REALS_t)
jigsawpy.savemsh(opts.geom_file, geom)
#------------------------------------ define spacing pattern
jigsawpy.loadmsh(os.path.join(src_path, "topo.msh"), topo)
hmat.mshID = "ellipsoid-grid"
hmat.radii = geom.radii
hmat.xgrid = topo.xgrid * np.pi / 180.
hmat.ygrid = topo.ygrid * np.pi / 180.
hfn0 = +150. # global spacing
hfn2 = +33. # adapt. spacing
hfn3 = +67. # arctic spacing
hmat.value = np.sqrt(np.maximum(-topo.value, 0.0))
hmat.value = \
np.maximum(hmat.value, hfn2)
hmat.value = \
np.minimum(hmat.value, hfn3)
mask = hmat.ygrid < 40. * np.pi / 180.
hmat.value[mask] = hfn0
#------------------------------------ set HFUN grad.-limiter
hmat.slope = np.full( # |dH/dx| limits
topo.value.shape, +0.050, dtype=hmat.REALS_t)
jigsawpy.savemsh(opts.hfun_file, hmat)
jigsawpy.cmd.marche(opts, hmat)
#------------------------------------ make mesh using JIGSAW
opts.hfun_scal = "absolute"
opts.hfun_hmax = float("inf") # null HFUN limits
opts.hfun_hmin = float(+0.00)
opts.mesh_dims = +2 # 2-dim. simplexes
opts.optm_qlim = +9.5E-01 # tighter opt. tol
opts.optm_iter = +32
opts.optm_qtol = +1.0E-05
# opts.optm_kern = "cvt+dqdx"
rbar = np.mean(geom.radii) # bisect heuristic
hbar = np.mean(hmat.value)
nlev = round(math.log2(rbar / math.sin(.4 * math.pi) / hbar))
ttic = time.time()
jigsawpy.cmd.tetris(opts, nlev - 1, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
print("BISECT =", +nlev)
cost = jigsawpy.triscr2( # quality metrics!
mesh.point["coord"], mesh.tria3["index"])
print("TRISCR =", np.min(cost), np.mean(cost))
cost = jigsawpy.pwrscr2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("PWRSCR =", np.min(cost), np.mean(cost))
tbad = jigsawpy.centre2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("OBTUSE =", +np.count_nonzero(np.logical_not(tbad)))
ndeg = jigsawpy.trideg2(mesh.point["coord"], mesh.tria3["index"])
print("TOPOL. =", +np.count_nonzero(ndeg == +6) / ndeg.size)
#------------------------------------ save mesh for Paraview
apos = jigsawpy.R3toS2(geom.radii, mesh.point["coord"][:])
apos = apos * 180. / np.pi
zfun = interpolate.RectBivariateSpline(topo.ygrid, topo.xgrid, topo.value)
mesh.value = zfun(apos[:, 1], apos[:, 0], grid=False)
cell = mesh.tria3["index"]
zmsk = \
mesh.value[cell[:, 0]] + \
mesh.value[cell[:, 1]] + \
mesh.value[cell[:, 2]]
zmsk = zmsk / +3.0
mesh.tria3 = mesh.tria3[zmsk < +0.]
print("Saving to ../cache/case_4a.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_4a.vtk"), mesh)
print("Saving to ../cache/case_4b.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_4b.vtk"), hmat)
return
def case_1_(src_path, dst_path):
# DEMO-1: generate a uniform resolution (150KM) global grid.
opts = jigsawpy.jigsaw_jig_t()
topo = jigsawpy.jigsaw_msh_t()
geom = jigsawpy.jigsaw_msh_t()
mesh = jigsawpy.jigsaw_msh_t()
#------------------------------------ setup files for JIGSAW
opts.geom_file = \
os.path.join(dst_path, "geom.msh")
opts.jcfg_file = \
os.path.join(dst_path, "opts.jig")
opts.mesh_file = \
os.path.join(dst_path, "mesh.msh")
#------------------------------------ define JIGSAW geometry
geom.mshID = "ellipsoid-mesh"
geom.radii = np.full(3, 6.371E+003, dtype=geom.REALS_t)
jigsawpy.savemsh(opts.geom_file, geom)
#------------------------------------ make mesh using JIGSAW
opts.hfun_scal = "absolute"
opts.hfun_hmax = +150. # uniform at 150km
opts.mesh_dims = +2 # 2-dim. simplexes
opts.optm_qlim = +9.5E-01 # tighter opt. tol
opts.optm_iter = +32
opts.optm_qtol = +1.0E-05
# opts.optm_kern = "cvt+dqdx"
rbar = np.mean(geom.radii) # bisect heuristic
nlev = round(math.log2(rbar / math.sin(.4 * math.pi) / opts.hfun_hmax))
ttic = time.time()
jigsawpy.cmd.tetris(opts, nlev - 1, mesh)
ttoc = time.time()
print("CPUSEC =", (ttoc - ttic))
print("BISECT =", +nlev)
cost = jigsawpy.triscr2( # quality metrics!
mesh.point["coord"], mesh.tria3["index"])
print("TRISCR =", np.min(cost), np.mean(cost))
cost = jigsawpy.pwrscr2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("PWRSCR =", np.min(cost), np.mean(cost))
tbad = jigsawpy.centre2(mesh.point["coord"], mesh.power,
mesh.tria3["index"])
print("OBTUSE =", +np.count_nonzero(np.logical_not(tbad)))
ndeg = jigsawpy.trideg2(mesh.point["coord"], mesh.tria3["index"])
print("TOPOL. =", +np.count_nonzero(ndeg == +6) / ndeg.size)
#------------------------------------ save mesh for Paraview
jigsawpy.loadmsh(os.path.join(src_path, "topo.msh"), topo)
#------------------------------------ a very rough land mask
apos = jigsawpy.R3toS2(geom.radii, mesh.point["coord"][:])
apos = apos * 180. / np.pi
zfun = interpolate.RectBivariateSpline(topo.ygrid, topo.xgrid, topo.value)
mesh.value = zfun(apos[:, 1], apos[:, 0], grid=False)
cell = mesh.tria3["index"]
zmsk = \
mesh.value[cell[:, 0]] + \
mesh.value[cell[:, 1]] + \
mesh.value[cell[:, 2]]
zmsk = zmsk / +3.0
mesh.tria3 = mesh.tria3[zmsk < +0.]
print("Saving to ../cache/case_1a.vtk")
jigsawpy.savevtk(os.path.join(dst_path, "case_1a.vtk"), mesh)
return