def tetrahedralize(self,
psc=0,
refine=0,
quality=1,
nobisect=True,
coarsen=0,
metric=0,
weighted=0,
brio_hilbert=1,
incrflip=0,
flipinsert=0,
varvolume=0,
fixedvolume=0,
noexact=0,
nostaticfilter=0,
insertaddpoints=0,
regionattrib=0,
cdtrefine=0,
diagnose=0,
convex=0,
zeroindex=0,
facesout=0,
edgesout=0,
neighout=0,
voroout=0,
meditview=0,
vtkview=0,
nobound=0,
nonodewritten=1,
noelewritten=1,
nofacewritten=1,
noiterationnum=0,
nomergefacet=0,
nomergevertex=0,
nojettison=0,
docheck=0,
quiet=0,
verbose=0,
vertexperblock=4092,
tetrahedraperblock=8188,
shellfaceperblock=4092,
nobisect_nomerge=1,
supsteiner_level=2,
addsteiner_algo=1,
coarsen_param=0,
weighted_param=0,
fliplinklevel=-1,
flipstarsize=-1,
fliplinklevelinc=1,
reflevel=3,
optscheme=7,
optlevel=2,
delmaxfliplevel=1,
order=2,
reversetetori=0,
steinerleft=10000,
no_sort=0,
hilbert_order=52,
hilbert_limit=8,
brio_threshold=64,
brio_ratio=0.125,
facet_separate_ang_tol=179.9,
facet_overlap_ang_tol=0.001,
facet_small_ang_tol=15.0,
maxvolume=-1.0,
minratio=2.0,
mindihedral=0.0,
optmaxdihedral=165.0,
optminsmtdihed=179.0,
optminslidihed=179.0,
epsilon=1.0e-8,
coarsen_percent=1.0,
switches=None):
"""Generates tetrahedrals interior to the surface mesh
described by the vertex and face arrays already loaded.
Returns nodes and elements belonging to the all tetrahedral
mesh.
The tetrahedral generator uses the C++ library TetGen and can
be configured by either using a string of ``switches`` or by
changing the underlying behavior using optional inputs.
Should the user desire more control over the mesh
tetrahedralization or wish to control the tetrahedralization
in a more pythonic manner, use the optional inputs rather than
inputting switches.
Parameters
----------
facet_overlap_ang_tol : double, optional
Threshold angle at which TetGen will consider to faces
overlapping. Raising this will require a higher quality
mesh input and may cause tetrahedralize to fail. Default
0.001.
quality : bool, optional
Enables/disables mesh improvement. Enabled by default.
Disable this to speed up mesh generation while sacrificing
quality. Default True.
minratio : double, optional.
Maximum allowable radius-edge ratio. Must be greater than
1.0 the closer to 1.0, the higher the quality of the mesh.
Be sure to raise steinerleft to allow for the addition of
points to improve the quality of the mesh. Avoid overly
restrictive requirements, otherwise, meshing will appear
to hang. Default 2.0
Testing has showed that 1.1 is a reasonable input for a
high quality mesh.
mindihedral : double, optional
Minimum allowable dihedral angle. The larger this number,
the higher the quality of the resulting mesh. Be sure to
raise steinerleft to allow for the addition of points to
improve the quality of the mesh. Avoid overly restrictive
requirements, otherwise, meshing will appear to hang.
Default 0.0
Testing has shown that 10 is a reasonable input
verbose : int, optional
Controls the underlying TetGen library to output text to
console. Users using iPython will not see this output.
Setting to 1 enables some information about the mesh
generation while setting verbose to 2 enables more debug
output. Default 0, or no output.
nobisect : bool, optional
Controls if Steiner points are added to the input surface
mesh. When enabled, the surface mesh will be modified.
Default False.
Testing has shown that if your input surface mesh is
already well shaped, disabling this setting will improve
meshing speed and mesh quality.
steinerleft : int, optional
Steiner points are points added to the original surface
mesh to create a valid tetrahedral mesh. Settings this to
-1 will allow tetgen to create an unlimited number of
steiner points, but the program will likely hang if this
is used in combination with narrow quality requirements.
Default 100000.
The first type of Steiner points are used in creating an
initial tetrahedralization of PLC. These Steiner points
are mandatory in order to create a valid
tetrahedralization
The second type of Steiner points are used in creating
quality tetra- hedral meshes of PLCs. These Steiner points
are optional, while they may be necessary in order to
improve the mesh quality or to conform the size of mesh
elements.
double : optmaxdihedral, optional
Setting unreachable using switches. Controls the optimial
maximum dihedral. Settings closer, but not exceeding, 180
degrees results in a lower quality mesh. Should be
between 135 and 180 degrees. Default 165.0
order : int optional
Controls whether TetGen creates linear tetrahedrals or
quadradic tetrahedrals. Set order to 2 to output
quadradic tetrahedrals. Default 2.
Examples
--------
The following switches "pq1.1/10Y" would be:
>>> node, elem = tgen.tetrahedralize(nobisect=True, quality=True,
minratio=1.1, mindihedral=10)
Using the switches option:
>>> node, elem = tgen.tetrahedralize(switches="pq1.1/10Y")
Notes
-----
There are many other options and the TetGen documentation
contains descritpions only for the switches of the original
C++ program. This is the relationship between tetgen switches
and python optinal inputs:
- ``psc`` --> ``'-s'``
- ``refine`` --> ``'-r'``
- ``quality`` --> ``'-q'``
- ``nobisect`` --> ``'-Y'``
- ``coarsen`` --> ``'-R'``
- ``weighted`` --> ``'-w'``
- ``brio_hilbert`` --> ``'-b'``
- ``incrflip`` --> ``'-l'``
- ``flipinsert`` --> ``'-L'``
- ``metric`` --> ``'-m'``
- ``varvolume`` --> ``'-a'``
- ``fixedvolume`` --> ``'-a'``
- ``regionattrib`` --> ``'-A'``
- ``cdtrefine`` --> ``'-D'``
- ``insertaddpoints`` --> ``'-i'``
- ``diagnose`` --> ``'-d'``
- ``convex`` --> ``'-c'``
- ``nomergefacet`` --> ``'-M'``
- ``nomergevertex`` --> ``'-M'``
- ``noexact`` --> ``'-X'``
- ``nostaticfilter`` --> ``'-X'``
- ``zeroindex`` --> ``'-z'``
- ``voroout`` --> ``'-v'``
- ``meditview`` --> ``'-g'``
- ``vtkview`` --> ``'-k'``
- ``nobound`` --> ``'-B'``
- ``noiterationnum`` --> ``'-I'``
- ``nojettison`` --> ``'-J'``
- ``docheck`` --> ``'-C'``
- ``quiet`` --> ``'-Q'``
- ``verbose`` --> ``'-V'``
- ``vertexperblock`` --> ``'-x', 4092.``
- ``tetrahedraperblock`` --> ``'-x', 8188.``
- ``shellfaceperblock`` --> ``'-x', 2044.``
- ``nobisect_nomerge`` --> ``'-Y', 1.``
- ``supsteiner_level`` --> ``'-Y/', 2.``
- ``addsteiner_algo`` --> ``'-Y//', 1.``
- ``coarsen_param`` --> ``'-R', 0.``
- ``weighted_param`` --> ``'-w', 0.``
- ``reflevel`` --> ``'-D', 3.``
- ``optlevel`` --> ``'-O', 2.``
- ``optscheme`` --> ``'-O', 7.``
- ``order`` --> ``'-o', 1.``
- ``reversetetori`` --> ``'-o/', 0.``
- ``steinerleft`` --> ``'-S', 0.``
- ``hilbert_order`` --> ``'-b///', 52.``
- ``hilbert_limit`` --> ``'-b//' 8.``
- ``brio_threshold`` --> ``'-b' 64.``
- ``brio_ratio`` --> ``'-b/' 0.125.``
- ``facet_separate_ang_tol`` --> ``'-p', 179.9.``
- ``facet_overlap_ang_tol`` --> ``'-p/', 0.1.``
- ``facet_small_ang_tol`` --> ``'-p//', 15.0.``
- ``maxvolume`` --> ``'-a', -1.0.``
- ``minratio`` --> ``'-q', 0.0.``
- ``mindihedral`` --> ``'-q', 5.0.``
- ``optmaxdihedral`` --> ``165.0.``
- ``optminsmtdihed`` --> ``179.0.``
- ``optminslidihed`` --> ``179.0.``
- ``epsilon`` --> ``'-T', 1.0e-8.``
- ``coarsen_percent`` --> ``-R1/#, 1.0.``
"""
# format switches
if switches is None:
switches_str = b''
else:
switches_str = bytes(switches, 'utf-8')
# check verbose switch
if verbose == 0:
quiet = 1
# Call libary
plc = True # always true
try:
meshdata = _tetgen.Tetrahedralize(self.v,
self.f,
switches_str,
plc,
psc,
refine,
quality,
nobisect,
coarsen,
metric,
weighted,
brio_hilbert,
incrflip,
flipinsert,
varvolume,
fixedvolume,
noexact,
nostaticfilter,
insertaddpoints,
regionattrib,
cdtrefine,
diagnose,
convex,
zeroindex,
facesout,
edgesout,
neighout,
voroout,
meditview,
vtkview,
nobound,
nonodewritten,
noelewritten,
nofacewritten,
noiterationnum,
nomergefacet,
nomergevertex,
nojettison,
docheck,
quiet,
verbose,
vertexperblock,
tetrahedraperblock,
shellfaceperblock,
nobisect_nomerge,
supsteiner_level,
addsteiner_algo,
coarsen_param,
weighted_param,
fliplinklevel,
flipstarsize,
fliplinklevelinc,
reflevel,
optscheme,
optlevel,
delmaxfliplevel,
order,
reversetetori,
steinerleft,
no_sort,
hilbert_order,
hilbert_limit,
brio_threshold,
brio_ratio,
facet_separate_ang_tol,
facet_overlap_ang_tol,
facet_small_ang_tol,
maxvolume,
minratio,
mindihedral,
optmaxdihedral,
optminsmtdihed,
optminslidihed,
epsilon,
coarsen_percent)
if regionattrib:
self.node, self.elem, self.elemattr = meshdata
else:
self.node, self.elem = meshdata
except RuntimeError as e:
raise RuntimeError('Failed to tetrahedralize.\n' +
'May need to repair surface by making it manifold:\n' +
str(e))
# check if a mesh was generated
if not np.any(self.node):
raise RuntimeError('Failed to tetrahedralize.\n' +
'May need to repair surface by making it manifold')
# Return nodes and elements
LOG.info('Generated mesh with %d nodes and %d elements', self.node.shape[0],
self.elem.shape[0])
self._updated = True
if regionattrib:
return self.node, self.elem, self.elemattr
else:
return self.node, self.elem
def tetrahedralize(self,
switches='',
plc=1,
psc=0,
refine=0,
quality=1,
nobisect=True,
coarsen=0,
metric=0,
weighted=0,
brio_hilbert=1,
incrflip=0,
flipinsert=0,
varvolume=0,
fixedvolume=0,
noexact=0,
nostaticfilter=0,
insertaddpoints=0,
regionattrib=0,
cdtrefine=0,
diagnose=0,
convex=0,
zeroindex=0,
facesout=0,
edgesout=0,
neighout=0,
voroout=0,
meditview=0,
vtkview=0,
nobound=0,
nonodewritten=1,
noelewritten=1,
nofacewritten=1,
noiterationnum=0,
nomergefacet=0,
nomergevertex=0,
nojettison=0,
docheck=0,
quiet=0,
verbose=0,
vertexperblock=4092,
tetrahedraperblock=8188,
shellfaceperblock=4092,
nobisect_nomerge=1,
supsteiner_level=2,
addsteiner_algo=1,
coarsen_param=0,
weighted_param=0,
fliplinklevel=-1,
flipstarsize=-1,
fliplinklevelinc=1,
reflevel=3,
optscheme=7,
optlevel=2,
delmaxfliplevel=1,
order=2,
reversetetori=0,
steinerleft=10000,
no_sort=0,
hilbert_order=52,
hilbert_limit=8,
brio_threshold=64,
brio_ratio=0.125,
facet_separate_ang_tol=179.9,
facet_overlap_ang_tol=0.001,
facet_small_ang_tol=15.0,
maxvolume=-1.0,
minratio=2.0,
mindihedral=0.0,
optmaxdihedral=165.0,
optminsmtdihed=179.0,
optminslidihed=179.0,
epsilon=1.0e-8,
coarsen_percent=1.0):
"""
Generates tetrahedrals interior to the surface mesh described by the
vertex and face arrays already loaded. Returns nodes and elements
belonging to the all tetrahedral mesh.
The tetrehedral generator uses the C++ library TetGen and can be
configured by either using a string of 'switches' or by changing the
underlying behavior using optional inputs.
Should the user desire more control over the mesh tetrahedralization or
wish to control the tetrahedralization in a more pythonic manner, use
the optional inputs rather than inputting switches.
Parameters
----------
switches : string, optional
String containing the same switches as in the C++ standalone
implementation:
-p Tetrahedralizes a piecewise linear complex (PLC).
-Y Preserves the input surface mesh (does not modify it).
-q Refines mesh (to improve mesh quality).
-R Mesh coarsening (to reduce the mesh elements).
-A Assigns attributes to tetrahedra in different regions.
-a Applies a maximum tetrahedron volume constraint.
-m Applies a mesh sizing function.
-O Specifies the level of mesh optimization.
-S Specifies maximum number of added points.
-T Sets a tolerance for coplanar test (default 1E-8)
-X Suppresses use of exact arithmetic.
-M No merge of coplanar facets or very close vertices.
-w Generates weighted Delaunay (regular) triangulation.
-c Retains the convex hull of the PLC.
-d Detects self-intersections of facets of the PLC.
-z Numbers all output items starting from zero.
-f Outputs all faces to .face file.
-e Outputs all edges to .edge file.
-n Outputs tetrahedra neighbors to .neigh file.
-v Outputs Voronoi diagram to files.
-g Outputs mesh to .mesh file for viewing by Medit.
-k Outputs mesh to .vtk file for viewing by Paraview.
-J No jettison of unused vertices from output .node file.
-B Suppresses output of boundary information.
-N Suppresses output of .node file.
-E Suppresses output of .ele file.
-F Suppresses output of .face and .edge file.
-I Suppresses mesh iteration numbers.
-C Checks the consistency of the final mesh.
-Q Quiet: No terminal output except errors.
-V Verbose: Detailed information, more terminal output.
-h Help: A brief instruction for using TetGen.
plc : bool, optional
Enables/disables tetrahedral generation. Default True.
facet_overlap_ang_tol : double, optional
Threshold angle at which TetGen will consider to faces overlapping.
Raising this will require a higher quality mesh input and may cause
tetrahedralize to fail. Default 0.001.
quality : bool, optional
Enables/disables mesh improvement. Enabled by default. Disable
this to speed up mesh generation while sacrificing quality.
Default True.
minratio : double, optional.
Maximum allowable radius-edge ratio. Must be greater than 1.0
the closer to 1.0, the higher the quality of the mesh. Be sure
to raise steinerleft to allow for the addition of points to improve
the quality of the mesh. Avoid overly restrictive requirements,
otherwise, meshing will appear to hang. Default 2.0
Testing has showed that 1.1 is a reasonable input for a high quality
mesh.
mindihedral : double, optional
Minimum allowable dihedral angle. The larger this number, the
higher the quality of the resulting mesh. Be sure to raise
steinerleft to allow for the addition of points to improve
the quality of the mesh. Avoid overly restrictive requirements,
otherwise, meshing will appear to hang. Default 0.0
Testing has shown that 10 is a reasonable input
verbose : int, optional
Controls the underlying TetGen library to output text to console.
Users using iPython will not see this output. Setting to 1 enables
some information about the mesh generation while setting verbose to
2 enables more debug output. Default 0, or no output.
nobisect : bool, optional
Controls if Steiner points are added to the input surface
mesh. When enabled, the surface mesh will be modified. Default False.
Testing has shown that if your input surface mesh is already well
shaped, disabling this setting will improve meshing speed and
mesh quality.
steinerleft : int, optional
Steiner points are points added to the original surface mesh to
create a valid tetrahedral mesh. Settings this to -1 will allow
tetgen to create an unlimited number of steiner points, but the
program will likely hang if this is used in combination with narrow
quality requirements. Default 100000.
The first type of Steiner points are used in creating an initial
tetrahedralization of PLC. These Steiner points are mandatory in
order to create a valid tetrahedralization
The second type of Steiner points are used in creating quality tetra-
hedral meshes of PLCs. These Steiner points are optional, while they
may be necessary in order to improve the mesh quality or to conform
the size of mesh elements.
double : optmaxdihedral, optional
Setting unreachable using switches. Controls the optimial maximum
dihedral. Settings closer, but not exceeding, 180 degrees results
in a lower quality mesh. Should be between 135 and 180 degrees.
Default 165.0
order : int optional
Controls whether TetGen creates linear tetrahedrals or quadradic
tetrahedrals. Set order to 2 to output quadradic tetrahedrals.
Default 2.
Examples
--------
>>> node, elem = Tetrahedralize(switches='pq1.1/10Y')
>>> node, elem = Tetrahedralize(plc=1, nobisect=True, quality=True,
minratio=1.1, mindihedral=10)
Notes
-----
There are many other options and the TetGen documentation contains
descritpions only for the switches of the original C++ program. This
is the relationship between tetgen switches and python optinal inputs:
PYTHON OPTION TETGEN SWITCH
int plc; // -p
int psc; // -s
int refine; // -r
int quality; // -q
int nobisect; // -Y
int coarsen; // -R
int weighted; // -w
int brio_hilbert; // -b
int incrflip; // -l
int flipinsert; // -L
int metric; // -m
int varvolume; // -a
int fixedvolume; // -a
int regionattrib; // -A
int cdtrefine; // -D
int insertaddpoints; // -i
int diagnose; // -d
int convex; // -c
int nomergefacet; // -M
int nomergevertex; // -M
int noexact; // -X
int nostaticfilter; // -X
int zeroindex; // -z
int facesout; // -f
int edgesout; // -e
int neighout; // -n
int voroout; // -v
int meditview; // -g
int vtkview; // -k
int nobound; // -B
int nonodewritten; // -N
int noelewritten; // -E
int nofacewritten; // -F
int noiterationnum; // -I
int nojettison; // -J
int docheck; // -C
int quiet; // -Q
int verbose; // -V
PYTHON OPTION TETGEN SWITCH
int vertexperblock; // '-x', 4092.
int tetrahedraperblock; // '-x', 8188.
int shellfaceperblock; // '-x', 2044.
int nobisect_nomerge; // '-Y', 1.
int supsteiner_level; // '-Y/', 2.
int addsteiner_algo; // '-Y//', 1.
int coarsen_param; // '-R', 0.
int weighted_param; // '-w', 0.
int fliplinklevel; // -1.
int flipstarsize; // -1.
int fliplinklevelinc; // 1.
int reflevel; // '-D', 3.
int optlevel; // '-O', 2.
int optscheme; // '-O', 7.
int delmaxfliplevel; // 1.
int order; // '-o', 1.
int reversetetori; // '-o/', 0.
int steinerleft; // '-S', 0.
int no_sort; // 0.
int hilbert_order; // '-b///', 52.
int hilbert_limit; // '-b//' 8.
int brio_threshold; // '-b' 64.
REAL brio_ratio; // '-b/' 0.125.
REAL facet_separate_ang_tol; // '-p', 179.9.
REAL facet_overlap_ang_tol; // '-p/', 0.1.
REAL facet_small_ang_tol; // '-p//', 15.0.
REAL maxvolume; // '-a', -1.0.
REAL minratio; // '-q', 0.0.
REAL mindihedral; // '-q', 5.0.
REAL optmaxdihedral; // 165.0.
REAL optminsmtdihed; // 179.0.
REAL optminslidihed; // 179.0.
REAL epsilon; // '-T', 1.0e-8.
REAL coarsen_percent; // -R1/#, 1.0.
"""
# python 2/3 compatability
if not isinstance(switches, bytes):
switches = switches.encode()
# check verbose switch
if verbose == 0:
quiet = 1
# Call libary
try:
self.node, self.elem = _tetgen.Tetrahedralize(
self.v, self.f, switches, plc, psc, refine, quality, nobisect,
coarsen, metric, weighted, brio_hilbert, incrflip, flipinsert,
varvolume, fixedvolume, noexact, nostaticfilter,
insertaddpoints, regionattrib, cdtrefine, diagnose, convex,
zeroindex, facesout, edgesout, neighout, voroout, meditview,
vtkview, nobound, nonodewritten, noelewritten, nofacewritten,
noiterationnum, nomergefacet, nomergevertex, nojettison,
docheck, quiet, verbose, vertexperblock, tetrahedraperblock,
shellfaceperblock, nobisect_nomerge, supsteiner_level,
addsteiner_algo, coarsen_param, weighted_param, fliplinklevel,
flipstarsize, fliplinklevelinc, reflevel, optscheme, optlevel,
delmaxfliplevel, order, reversetetori, steinerleft, no_sort,
hilbert_order, hilbert_limit, brio_threshold, brio_ratio,
facet_separate_ang_tol, facet_overlap_ang_tol,
facet_small_ang_tol, maxvolume, minratio, mindihedral,
optmaxdihedral, optminsmtdihed, optminslidihed, epsilon,
coarsen_percent)
except RuntimeError:
raise Exception('Failed to tetrahedralize.\n' +
'May need to repair surface by making it manifold')
# check if a mesh was generated
if not np.any(self.node):
raise Exception('Failed to tetrahedralize.\n' +
'May need to repair surface by making it manifold')
# Return nodes and elements
info = (self.node.shape[0], self.elem.shape[0])
log.info('Generated mesh with %d nodes and %d elements' % info)
self._updated = True
return self.node, self.elem
def tetrahedralize(self,
plc=True,
psc=0.,
refine=0.,
quality=True,
nobisect=False,
cdt=0.,
cdtrefine=7.,
coarsen=0.,
weighted=0.,
brio_hilbert=1.,
flipinsert=0.,
metric=0.,
varvolume=0.,
fixedvolume=0.,
regionattrib=0.,
insertaddpoints=0.,
diagnose=0.,
convex=0.,
nomergefacet=0.,
nomergevertex=0.,
noexact=0.,
nostaticfilter=0.,
zeroindex=0.,
facesout=0.,
edgesout=0.,
neighout=0.,
voroout=0.,
meditview=0.,
vtkview=0.,
vtksurfview=0.,
nobound=0.,
nonodewritten=0.,
noelewritten=0.,
nofacewritten=0.,
noiterationnum=0.,
nojettison=0.,
docheck=0.,
quiet=0.,
nowarning=0.,
verbose=0.,
vertexperblock=4092.,
tetrahedraperblock=8188.,
shellfaceperblock=2044.,
supsteiner_level=2.,
addsteiner_algo=1.,
coarsen_param=0.,
weighted_param=0.,
fliplinklevel=-1.,
flipstarsize=-1.,
fliplinklevelinc=1.,
opt_max_flip_level=3.,
opt_scheme=7.,
opt_iterations=3.,
smooth_cirterion=1.,
smooth_maxiter=7.,
delmaxfliplevel=1.,
order=1.,
reversetetori=0.,
steinerleft=100000.,
unflip_queue_limit=1000.,
no_sort=0.,
hilbert_order=52.,
hilbert_limit=8.,
brio_threshold=64.,
brio_ratio=0.125,
epsilon=1.0e-8,
facet_separate_ang_tol=179.9,
collinear_ang_tol=179.9,
facet_small_ang_tol=15.0,
maxvolume=-1.0,
maxvolume_length=-1.0,
minratio=2.0,
opt_max_asp_ratio=1000.0,
opt_max_edge_ratio=100.0,
mindihedral=0.0,
optmaxdihedral=177.0,
metric_scale=1.0,
smooth_alpha=0.3,
coarsen_percent=1.0,
elem_growth_ratio=0.0,
refine_progress_ratio=0.333,
switches=None):
"""Generates tetrahedrals interior to the surface mesh
described by the vertex and face arrays already loaded.
Returns nodes and elements belonging to the all tetrahedral
mesh.
The tetrahedral generator uses the C++ library TetGen and can
be configured by either using a string of ``switches`` or by
changing the underlying behavior using optional inputs.
Should the user desire more control over the mesh
tetrahedralization or wish to control the tetrahedralization
in a more pythonic manner, use the optional inputs rather than
inputting switches.
Parameters
----------
quality : bool, optional
Enables/disables mesh improvement. Enabled by default.
Disable this to speed up mesh generation while sacrificing
quality. Default True.
minratio : double, optional.
Maximum allowable radius-edge ratio. Must be greater than
1.0 the closer to 1.0, the higher the quality of the mesh.
Be sure to raise ``steinerleft`` to allow for the addition of
points to improve the quality of the mesh. Avoid overly
restrictive requirements, otherwise, meshing will appear
to hang. Default 2.0
Testing has showed that 1.1 is a reasonable input for a
high quality mesh.
mindihedral : double, optional
Minimum allowable dihedral angle. The larger this number,
the higher the quality of the resulting mesh. Be sure to
raise ``steinerleft`` to allow for the addition of points to
improve the quality of the mesh. Avoid overly restrictive
requirements, otherwise, meshing will appear to hang.
Default 0.0
Testing has shown that 10 is a reasonable input
verbose : int, optional
Controls the underlying TetGen library to output text to
console. Users using iPython will not see this output.
Setting to 1 enables some information about the mesh
generation while setting verbose to 2 enables more debug
output. Default 0, or no output.
nobisect : bool, optional
Controls if Steiner points are added to the input surface
mesh. When enabled, the surface mesh will be modified.
Default False.
Testing has shown that if your input surface mesh is
already well shaped, disabling this setting will improve
meshing speed and mesh quality.
steinerleft : int, optional
Steiner points are points added to the original surface
mesh to create a valid tetrahedral mesh. Settings this to
-1 will allow tetgen to create an unlimited number of
steiner points, but the program will likely hang if this
is used in combination with narrow quality requirements.
Default 100000.
The first type of Steiner points are used in creating an
initial tetrahedralization of PLC. These Steiner points
are mandatory in order to create a valid
tetrahedralization
The second type of Steiner points are used in creating
quality tetra- hedral meshes of PLCs. These Steiner points
are optional, while they may be necessary in order to
improve the mesh quality or to conform the size of mesh
elements.
order : int optional
Controls whether TetGen creates linear tetrahedrals or
quadradic tetrahedrals. Set order to 2 to output
quadradic tetrahedrals. Default 2.
Examples
--------
The following switches "pq1.1/10Y" would be:
>>> node, elem = tgen.tetrahedralize(nobisect=True, quality=True,
minratio=1.1, mindihedral=10)
Using the switches option:
>>> node, elem = tgen.tetrahedralize(switches="pq1.1/10Y")
Notes
-----
There are many other options and the TetGen documentation
contains descriptions only for the switches of the original
C++ program. This is the relationship between tetgen switches
and python optional inputs:
Switches of TetGen.
+---------------------------+---------------+---------+
| Option | Switch | Default |
+---------------------------+---------------+---------+
| plc | ``'-p'`` | 0. |
+---------------------------+---------------+---------+
| psc | ``'-s'`` | 0. |
+---------------------------+---------------+---------+
| refine | ``'-r'`` | 0. |
+---------------------------+---------------+---------+
| quality | ``'-q'`` | 0. |
+---------------------------+---------------+---------+
| nobisect | ``'-Y'`` | 0. |
+---------------------------+---------------+---------+
| cdt | ``'-D'`` | 0. |
+---------------------------+---------------+---------+
| cdtrefine | ``'-D#'`` | 7. |
+---------------------------+---------------+---------+
| coarsen | ``'-R'`` | 0. |
+---------------------------+---------------+---------+
| weighted | ``'-w'`` | 0. |
+---------------------------+---------------+---------+
| brio_hilbert | ``'-b'`` | 1. |
+---------------------------+---------------+---------+
| flipinsert | ``'-L'`` | 0. |
+---------------------------+---------------+---------+
| metric | ``'-m'`` | 0. |
+---------------------------+---------------+---------+
| varvolume | ``'-a'`` | 0. |
+---------------------------+---------------+---------+
| fixedvolume | ``'-a'`` | 0. |
+---------------------------+---------------+---------+
| regionattrib | ``'-A'`` | 0. |
+---------------------------+---------------+---------+
| insertaddpoints | ``'-i'`` | 0. |
+---------------------------+---------------+---------+
| diagnose | ``'-d'`` | 0. |
+---------------------------+---------------+---------+
| convex | ``'-c'`` | 0. |
+---------------------------+---------------+---------+
| nomergefacet | ``'-M'`` | 0. |
+---------------------------+---------------+---------+
| nomergevertex | ``'-M'`` | 0. |
+---------------------------+---------------+---------+
| noexact | ``'-X'`` | 0. |
+---------------------------+---------------+---------+
| nostaticfilter | ``'-X'`` | 0. |
+---------------------------+---------------+---------+
| zeroindex | ``'-z'`` | 0. |
+---------------------------+---------------+---------+
| facesout | ``'-f'`` | 0. |
+---------------------------+---------------+---------+
| edgesout | ``'-e'`` | 0. |
+---------------------------+---------------+---------+
| neighout | ``'-n'`` | 0. |
+---------------------------+---------------+---------+
| voroout | ``'-v'`` | 0. |
+---------------------------+---------------+---------+
| meditview | ``'-g'`` | 0. |
+---------------------------+---------------+---------+
| vtkview | ``'-k'`` | 0. |
+---------------------------+---------------+---------+
| vtksurfview | ``'-k'`` | 0. |
+---------------------------+---------------+---------+
| nobound | ``'-B'`` | 0. |
+---------------------------+---------------+---------+
| nonodewritten | ``'-N'`` | 0. |
+---------------------------+---------------+---------+
| noelewritten | ``'-E'`` | 0. |
+---------------------------+---------------+---------+
| nofacewritten | ``'-F'`` | 0. |
+---------------------------+---------------+---------+
| noiterationnum | ``'-I'`` | 0. |
+---------------------------+---------------+---------+
| nojettison | ``'-J'`` | 0. |
+---------------------------+---------------+---------+
| docheck | ``'-C'`` | 0. |
+---------------------------+---------------+---------+
| quiet | ``'-Q'`` | 0. |
+---------------------------+---------------+---------+
| nowarning | ``'-W'`` | 0. |
+---------------------------+---------------+---------+
| verbose | ``'-V'`` | 0. |
+---------------------------+---------------+---------+
Parameters of TetGen.
+---------------------------+---------------+---------+
| Option | Switch | Default |
+---------------------------+---------------+---------+
| vertexperblock | ``'-x'`` | 4092. |
+---------------------------+---------------+---------+
| tetrahedraperblock | ``'-x'`` | 8188. |
+---------------------------+---------------+---------+
| shellfaceperblock | ``'-x'`` | 2044. |
+---------------------------+---------------+---------+
| supsteiner_level | ``'-Y/'`` | 2. |
+---------------------------+---------------+---------+
| addsteiner_algo | ``'-Y//'`` | 1. |
+---------------------------+---------------+---------+
| coarsen_param | ``'-R'`` | 0. |
+---------------------------+---------------+---------+
| weighted_param | ``'-w'`` | 0. |
+---------------------------+---------------+---------+
| opt_max_flip_level | ``'-O'`` | 3. |
+---------------------------+---------------+---------+
| opt_scheme | ``'-O/#'`` | 7. |
+---------------------------+---------------+---------+
| opt_iterations | ``'-O//#'`` | 3. |
+---------------------------+---------------+---------+
| smooth_cirterion | ``'-s'`` | 1. |
+---------------------------+---------------+---------+
| smooth_maxiter | ``'-s'`` | 7. |
+---------------------------+---------------+---------+
| order | ``'-o'`` | 1. |
+---------------------------+---------------+---------+
| reversetetori | ``'-o/'`` | 0. |
+---------------------------+---------------+---------+
| steinerleft | ``'-S'`` | 0. |
+---------------------------+---------------+---------+
| unflip_queue_limit | ``'-U#'`` | 1000. |
+---------------------------+---------------+---------+
| hilbert_order | ``'-b///'`` | 52. |
+---------------------------+---------------+---------+
| hilbert_limit | ``'-b//'`` | 8. |
+---------------------------+---------------+---------+
| brio_threshold | ``'-b'`` | 64. |
+---------------------------+---------------+---------+
| brio_ratio | ``'-b/'`` |0.125. |
+---------------------------+---------------+---------+
| epsilon | ``'-T'`` | 1.0e-8. |
+---------------------------+---------------+---------+
| facet_separate_ang_tol | ``'-p'`` | 179.9. |
+---------------------------+---------------+---------+
| collinear_ang_tol | ``'-p/'`` | 179.9. |
+---------------------------+---------------+---------+
| facet_small_ang_tol | ``'-p//'`` | 15.0. |
+---------------------------+---------------+---------+
| maxvolume | ``'-a'`` | -1.0. |
+---------------------------+---------------+---------+
| maxvolume_length | ``'-a'`` | -1.0. |
+---------------------------+---------------+---------+
| minratio | ``'-q'`` | 0.0. |
+---------------------------+---------------+---------+
| mindihedral | ``'-q'`` | 5.0. |
+---------------------------+---------------+---------+
| optmaxdihedral | ``'-o/#'`` | 177.0. |
+---------------------------+---------------+---------+
| metric_scale | ``'-m#'`` | 1.0. |
+---------------------------+---------------+---------+
| smooth_alpha | ``'-s'`` | 0.3. |
+---------------------------+---------------+---------+
| coarsen_percent | ``'-R1/#'`` | 1.0. |
+---------------------------+---------------+---------+
| elem_growth_ratio | ``'-r#'`` | 0.0. |
+---------------------------+---------------+---------+
| refine_progress_ratio | ``'-r/#'`` | 0.333. |
+---------------------------+---------------+---------+
"""
# format switches
if switches is None:
switches_str = b''
else:
switches_str = bytes(switches, 'utf-8')
# check verbose switch
if verbose == 0:
quiet = 1
# Call library
plc = True # always true
try:
self.node, self.elem = _tetgen.Tetrahedralize(
self.v,
self.f,
switches_str,
plc,
psc,
refine,
quality,
nobisect,
cdt,
cdtrefine,
coarsen,
weighted,
brio_hilbert,
flipinsert,
metric,
varvolume,
fixedvolume,
regionattrib,
insertaddpoints,
diagnose,
convex,
nomergefacet,
nomergevertex,
noexact,
nostaticfilter,
zeroindex,
facesout,
edgesout,
neighout,
voroout,
meditview,
vtkview,
vtksurfview,
nobound,
nonodewritten,
noelewritten,
nofacewritten,
noiterationnum,
nojettison,
docheck,
quiet,
nowarning,
verbose,
vertexperblock,
tetrahedraperblock,
shellfaceperblock,
supsteiner_level,
addsteiner_algo,
coarsen_param,
weighted_param,
fliplinklevel,
flipstarsize,
fliplinklevelinc,
opt_max_flip_level,
opt_scheme,
opt_iterations,
smooth_cirterion,
smooth_maxiter,
delmaxfliplevel,
order,
reversetetori,
steinerleft,
unflip_queue_limit,
no_sort,
hilbert_order,
hilbert_limit,
brio_threshold,
brio_ratio,
epsilon,
facet_separate_ang_tol,
collinear_ang_tol,
facet_small_ang_tol,
maxvolume,
maxvolume_length,
minratio,
opt_max_asp_ratio,
opt_max_edge_ratio,
mindihedral,
optmaxdihedral,
metric_scale,
smooth_alpha,
coarsen_percent,
elem_growth_ratio,
refine_progress_ratio,
)
except RuntimeError as e:
raise RuntimeError(
'Failed to tetrahedralize.\n' +
'May need to repair surface by making it manifold:\n' + str(e))
# check if a mesh was generated
if not np.any(self.node):
raise RuntimeError(
'Failed to tetrahedralize.\n' +
'May need to repair surface by making it manifold')
# Return nodes and elements
LOG.info('Generated mesh with %d nodes and %d elements',
self.node.shape[0], self.elem.shape[0])
self._updated = True
return self.node, self.elem