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Stephan Hilb
SemiSmoothNewton.jl
Commits
65804157
Commit
65804157
authored
Aug 22, 2021
by
Stephan Hilb
Browse files
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Plain Diff
get refinement working somewhat
parent
6d2a2f59
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Changes
3
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3 changed files
scripts/run.jl
+85
-65
85 additions, 65 deletions
scripts/run.jl
src/function.jl
+1
-1
1 addition, 1 deletion
src/function.jl
src/mesh.jl
+21
-3
21 additions, 3 deletions
src/mesh.jl
with
107 additions
and
69 deletions
scripts/run.jl
+
85
−
65
View file @
65804157
...
@@ -9,7 +9,8 @@ using OpticalFlowUtils
...
@@ -9,7 +9,8 @@ using OpticalFlowUtils
using
WriteVTK
:
paraview_collection
using
WriteVTK
:
paraview_collection
using
SemiSmoothNewton
using
SemiSmoothNewton
using
SemiSmoothNewton
:
project_img!
,
project!
using
SemiSmoothNewton
:
HMesh
,
ncells
,
refine
using
SemiSmoothNewton
:
project_img!
,
project_img2!
,
project!
using
SemiSmoothNewton
:
vtk_mesh
,
vtk_append!
,
vtk_save
using
SemiSmoothNewton
:
vtk_mesh
,
vtk_append!
,
vtk_save
include
(
"util.jl"
)
include
(
"util.jl"
)
...
@@ -63,8 +64,6 @@ struct L1L2TVContext{M, Ttype, Stype}
...
@@ -63,8 +64,6 @@ struct L1L2TVContext{M, Ttype, Stype}
du
::
FeFunction
du
::
FeFunction
dp1
::
FeFunction
dp1
::
FeFunction
dp2
::
FeFunction
dp2
::
FeFunction
nablau
nabladu
end
end
function
L1L2TVContext
(
name
,
mesh
,
m
;
T
,
tdata
,
S
,
function
L1L2TVContext
(
name
,
mesh
,
m
;
T
,
tdata
,
S
,
...
@@ -82,11 +81,9 @@ function L1L2TVContext(name, mesh, m; T, tdata, S,
...
@@ -82,11 +81,9 @@ function L1L2TVContext(name, mesh, m; T, tdata, S,
u
=
FeFunction
(
Vu
,
name
=
"u"
)
u
=
FeFunction
(
Vu
,
name
=
"u"
)
p1
=
FeFunction
(
Vp1
,
name
=
"p1"
)
p1
=
FeFunction
(
Vp1
,
name
=
"p1"
)
p2
=
FeFunction
(
Vp2
,
name
=
"p2"
)
p2
=
FeFunction
(
Vp2
,
name
=
"p2"
)
du
=
FeFunction
(
Vu
)
du
=
FeFunction
(
Vu
;
name
=
"du"
)
dp1
=
FeFunction
(
Vp1
)
dp1
=
FeFunction
(
Vp1
;
name
=
"dp1"
)
dp2
=
FeFunction
(
Vp2
)
dp2
=
FeFunction
(
Vp2
;
name
=
"dp2"
)
nablau
=
nabla
(
u
)
nabladu
=
nabla
(
du
)
est
.
data
.=
0
est
.
data
.=
0
g
.
data
.=
0
g
.
data
.=
0
...
@@ -99,7 +96,7 @@ function L1L2TVContext(name, mesh, m; T, tdata, S,
...
@@ -99,7 +96,7 @@ function L1L2TVContext(name, mesh, m; T, tdata, S,
return
L1L2TVContext
(
name
,
mesh
,
d
,
m
,
T
,
tdata
,
S
,
return
L1L2TVContext
(
name
,
mesh
,
d
,
m
,
T
,
tdata
,
S
,
alpha1
,
alpha2
,
beta
,
lambda
,
gamma1
,
gamma2
,
alpha1
,
alpha2
,
beta
,
lambda
,
gamma1
,
gamma2
,
est
,
g
,
u
,
p1
,
p2
,
du
,
dp1
,
dp2
,
nablau
,
nabladu
)
est
,
g
,
u
,
p1
,
p2
,
du
,
dp1
,
dp2
)
end
end
function
p1_project!
(
p1
,
alpha1
)
function
p1_project!
(
p1
,
alpha1
)
...
@@ -166,7 +163,7 @@ function step!(ctx::L1L2TVContext)
...
@@ -166,7 +163,7 @@ function step!(ctx::L1L2TVContext)
# solve du
# solve du
print
(
"assemble ... "
)
print
(
"assemble ... "
)
A
,
b
=
assemble
(
ctx
.
du
.
space
,
du_a
,
du_l
;
A
,
b
=
assemble
(
ctx
.
du
.
space
,
du_a
,
du_l
;
ctx
.
g
,
ctx
.
u
,
ctx
.
nablau
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
tdata
)
ctx
.
g
,
ctx
.
u
,
nablau
=
nabla
(
ctx
.
u
)
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
tdata
)
print
(
"solve ... "
)
print
(
"solve ... "
)
ctx
.
du
.
data
.=
A
\
b
ctx
.
du
.
data
.=
A
\
b
...
@@ -191,7 +188,7 @@ function step!(ctx::L1L2TVContext)
...
@@ -191,7 +188,7 @@ function step!(ctx::L1L2TVContext)
return
-
p2
+
lambda
/
m2
*
(
nablau
+
nabladu
)
-
cond
return
-
p2
+
lambda
/
m2
*
(
nablau
+
nabladu
)
-
cond
end
end
interpolate!
(
ctx
.
dp2
,
dp2_update
;
interpolate!
(
ctx
.
dp2
,
dp2_update
;
ctx
.
u
,
ctx
.
nablau
,
ctx
.
p2
,
ctx
.
du
,
ctx
.
nabladu
)
ctx
.
u
,
nablau
=
nabla
(
ctx
.
u
)
,
ctx
.
p2
,
ctx
.
du
,
nabladu
=
nabla
(
ctx
.
du
)
)
# newton update
# newton update
theta
=
1.
theta
=
1.
...
@@ -388,46 +385,49 @@ function estimate!(ctx::L1L2TVContext)
...
@@ -388,46 +385,49 @@ function estimate!(ctx::L1L2TVContext)
end
end
w
=
FeFunction
(
ctx
.
u
.
space
)
w
=
FeFunction
(
ctx
.
u
.
space
)
nablaw
=
nabla
(
w
)
solve_primal!
(
w
,
ctx
)
solve_primal!
(
w
,
ctx
)
project!
(
ctx
.
est
,
estf
;
ctx
.
g
,
ctx
.
u
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
nablau
,
w
,
nablaw
,
ctx
.
tdata
)
project!
(
ctx
.
est
,
estf
;
ctx
.
g
,
ctx
.
u
,
ctx
.
p1
,
ctx
.
p2
,
end
nablau
=
nabla
(
ctx
.
u
),
w
,
nablaw
=
nabla
(
w
),
ctx
.
tdata
)
end
function
refine
(
ctx
::
L1L2TVContext
,
marked_cells
;
fs_
...
)
fs
=
NamedTuple
(
fs_
)
# TODO: deprecate in favor of refine(mesh, marked_cells; fs...)
#function refine(ctx::L1L2TVContext, marked_cells; fs_...)
hmesh
=
HMesh
(
ctx
.
mesh
)
# fs = NamedTuple(fs_)
refined_functions
=
refine!
(
hmesh
,
Set
(
marked_cells
);
#
ctx
.
est
,
ctx
.
g
,
ctx
.
u
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
du
,
ctx
.
dp1
,
ctx
.
dp2
,
# hmesh = HMesh(ctx.mesh)
fs
...
)
# refined_functions = refine!(hmesh, Set(marked_cells);
new_mesh
=
refined_functions
.
u
.
space
.
mesh
# ctx.est, ctx.g, ctx.u, ctx.p1, ctx.p2, ctx.du, ctx.dp1, ctx.dp2,
# fs...)
new_ctx
=
L1L2TVContext
(
ctx
.
name
,
new_mesh
,
ctx
.
m
;
ctx
.
T
,
ctx
.
tdata
,
ctx
.
S
,
# new_mesh = refined_functions.u.space.mesh
ctx
.
alpha1
,
ctx
.
alpha2
,
ctx
.
beta
,
ctx
.
lambda
,
ctx
.
gamma1
,
ctx
.
gamma2
)
#
# # TODO: tdata needs to be recreated for refinement
fs_new
=
NamedTuple
(
x
[
1
]
=>
refined_functions
[
x
[
1
]]
for
x
in
pairs
(
fs
))
# new_ctx = L1L2TVContext(ctx.name, new_mesh, ctx.m; ctx.T, ctx.tdata, ctx.S,
# ctx.alpha1, ctx.alpha2, ctx.beta, ctx.lambda, ctx.gamma1, ctx.gamma2)
@assert
(
new_ctx
.
est
.
space
.
dofmap
==
refined_functions
.
est
.
space
.
dofmap
)
#
@assert
(
new_ctx
.
g
.
space
.
dofmap
==
refined_functions
.
g
.
space
.
dofmap
)
# fs_new = NamedTuple(x[1] => refined_functions[x[1]] for x in pairs(fs))
@assert
(
new_ctx
.
u
.
space
.
dofmap
==
refined_functions
.
u
.
space
.
dofmap
)
#
@assert
(
new_ctx
.
p1
.
space
.
dofmap
==
refined_functions
.
p1
.
space
.
dofmap
)
# @assert(new_ctx.est.space.dofmap == refined_functions.est.space.dofmap)
@assert
(
new_ctx
.
p2
.
space
.
dofmap
==
refined_functions
.
p2
.
space
.
dofmap
)
# @assert(new_ctx.g.space.dofmap == refined_functions.g.space.dofmap)
@assert
(
new_ctx
.
du
.
space
.
dofmap
==
refined_functions
.
du
.
space
.
dofmap
)
# @assert(new_ctx.u.space.dofmap == refined_functions.u.space.dofmap)
@assert
(
new_ctx
.
dp1
.
space
.
dofmap
==
refined_functions
.
dp1
.
space
.
dofmap
)
# @assert(new_ctx.p1.space.dofmap == refined_functions.p1.space.dofmap)
@assert
(
new_ctx
.
dp2
.
space
.
dofmap
==
refined_functions
.
dp2
.
space
.
dofmap
)
# @assert(new_ctx.p2.space.dofmap == refined_functions.p2.space.dofmap)
# @assert(new_ctx.du.space.dofmap == refined_functions.du.space.dofmap)
new_ctx
.
est
.
data
.=
refined_functions
.
est
.
data
# @assert(new_ctx.dp1.space.dofmap == refined_functions.dp1.space.dofmap)
new_ctx
.
g
.
data
.=
refined_functions
.
g
.
data
# @assert(new_ctx.dp2.space.dofmap == refined_functions.dp2.space.dofmap)
new_ctx
.
u
.
data
.=
refined_functions
.
u
.
data
#
new_ctx
.
p1
.
data
.=
refined_functions
.
p1
.
data
# new_ctx.est.data .= refined_functions.est.data
new_ctx
.
p2
.
data
.=
refined_functions
.
p2
.
data
# new_ctx.g.data .= refined_functions.g.data
new_ctx
.
du
.
data
.=
refined_functions
.
du
.
data
# new_ctx.u.data .= refined_functions.u.data
new_ctx
.
dp1
.
data
.=
refined_functions
.
dp1
.
data
# new_ctx.p1.data .= refined_functions.p1.data
new_ctx
.
dp2
.
data
.=
refined_functions
.
dp2
.
data
# new_ctx.p2.data .= refined_functions.p2.data
# new_ctx.du.data .= refined_functions.du.data
return
new_ctx
,
fs_new
# new_ctx.dp1.data .= refined_functions.dp1.data
end
# new_ctx.dp2.data .= refined_functions.dp2.data
#
# return new_ctx, fs_new
#end
# minimal Dörfler marking
function
mark
(
ctx
::
L1L2TVContext
;
theta
=
0.5
)
function
mark
(
ctx
::
L1L2TVContext
;
theta
=
0.5
)
n
=
ncells
(
ctx
.
mesh
)
n
=
ncells
(
ctx
.
mesh
)
esttotal
=
sum
(
ctx
.
est
.
data
)
esttotal
=
sum
(
ctx
.
est
.
data
)
...
@@ -461,7 +461,8 @@ function primal_energy(ctx::L1L2TVContext)
...
@@ -461,7 +461,8 @@ function primal_energy(ctx::L1L2TVContext)
ctx
.
beta
/
2
*
norm
(
ctx
.
S
(
u
,
nablau
))
^
2
+
ctx
.
beta
/
2
*
norm
(
ctx
.
S
(
u
,
nablau
))
^
2
+
ctx
.
lambda
*
huber
(
norm
(
nablau
),
ctx
.
gamma2
)
ctx
.
lambda
*
huber
(
norm
(
nablau
),
ctx
.
gamma2
)
end
end
return
integrate
(
ctx
.
mesh
,
integrand
;
ctx
.
g
,
ctx
.
u
,
ctx
.
nablau
,
ctx
.
tdata
)
return
integrate
(
ctx
.
mesh
,
integrand
;
ctx
.
g
,
ctx
.
u
,
nablau
=
nabla
(
ctx
.
u
),
ctx
.
tdata
)
end
end
norm_l2
(
f
)
=
sqrt
(
integrate
(
f
.
space
.
mesh
,
(
x
;
f
)
->
dot
(
f
,
f
);
f
))
norm_l2
(
f
)
=
sqrt
(
integrate
(
f
.
space
.
mesh
,
(
x
;
f
)
->
dot
(
f
,
f
);
f
))
...
@@ -482,7 +483,8 @@ function norm_residual(ctx::L1L2TVContext)
...
@@ -482,7 +483,8 @@ function norm_residual(ctx::L1L2TVContext)
ctx
.
lambda
*
nablau
ctx
.
lambda
*
nablau
return
norm
(
p1part
)
^
2
+
norm
(
p2part
)
^
2
return
norm
(
p1part
)
^
2
+
norm
(
p2part
)
^
2
end
end
ppart2
=
integrate
(
ctx
.
mesh
,
integrand
;
ctx
.
g
,
ctx
.
u
,
ctx
.
nablau
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
tdata
)
ppart2
=
integrate
(
ctx
.
mesh
,
integrand
;
ctx
.
g
,
ctx
.
u
,
nablau
=
nabla
(
ctx
.
u
),
ctx
.
p1
,
ctx
.
p2
,
ctx
.
tdata
)
return
sqrt
(
upart2
+
ppart2
)
return
sqrt
(
upart2
+
ppart2
)
end
end
...
@@ -694,7 +696,7 @@ function optflow(ctx)
...
@@ -694,7 +696,7 @@ function optflow(ctx)
m
=
2
m
=
2
#mesh = init_grid(imgf0; type=:vertex)
#mesh = init_grid(imgf0; type=:vertex)
mesh
=
init_grid
(
imgf0
,
20
,
20
)
mesh
=
init_grid
(
imgf0
,
1
,
1
)
#mesh = init_grid(imgf0)
#mesh = init_grid(imgf0)
# optflow specific stuff
# optflow specific stuff
...
@@ -702,12 +704,12 @@ function optflow(ctx)
...
@@ -702,12 +704,12 @@ function optflow(ctx)
f0
=
FeFunction
(
Vg
,
name
=
"f0"
)
f0
=
FeFunction
(
Vg
,
name
=
"f0"
)
f1
=
FeFunction
(
Vg
,
name
=
"f1"
)
f1
=
FeFunction
(
Vg
,
name
=
"f1"
)
fw
=
FeFunction
(
Vg
,
name
=
"fw"
)
fw
=
FeFunction
(
Vg
,
name
=
"fw"
)
nablafw
=
nabla
(
fw
)
T
(
tdata
,
u
)
=
tdata
*
u
# tdata = nablafw
T
(
tdata
,
u
)
=
tdata
*
u
# tdata = nablafw
S
(
u
,
nablau
)
=
nablau
#S(u, nablau) = nablau
S
(
u
,
nablau
)
=
u
st
=
L1L2TVContext
(
"run"
,
mesh
,
m
;
T
,
tdata
=
nablafw
,
S
,
st
=
L1L2TVContext
(
"run"
,
mesh
,
m
;
T
,
tdata
=
nabla
(
fw
)
,
S
,
ctx
.
params
.
alpha1
,
ctx
.
params
.
alpha2
,
ctx
.
params
.
lambda
,
ctx
.
params
.
beta
,
ctx
.
params
.
alpha1
,
ctx
.
params
.
alpha2
,
ctx
.
params
.
lambda
,
ctx
.
params
.
beta
,
ctx
.
params
.
gamma1
,
ctx
.
params
.
gamma2
)
ctx
.
params
.
gamma1
,
ctx
.
params
.
gamma2
)
...
@@ -720,7 +722,7 @@ function optflow(ctx)
...
@@ -720,7 +722,7 @@ function optflow(ctx)
g_optflow
(
x
;
u
,
f0
,
fw
,
nablafw
)
=
g_optflow
(
x
;
u
,
f0
,
fw
,
nablafw
)
=
nablafw
*
u
-
(
fw
-
f0
)
nablafw
*
u
-
(
fw
-
f0
)
interpolate!
(
st
.
g
,
g_optflow
;
st
.
u
,
f0
,
fw
,
nablafw
)
interpolate!
(
st
.
g
,
g_optflow
;
st
.
u
,
f0
,
fw
,
nablafw
=
nabla
(
fw
)
)
end
end
reproject!
()
reproject!
()
...
@@ -728,15 +730,33 @@ function optflow(ctx)
...
@@ -728,15 +730,33 @@ function optflow(ctx)
output
(
st
,
joinpath
(
ctx
.
outdir
,
"output_
$
(lpad(i, 5, '0')).vtu"
),
output
(
st
,
joinpath
(
ctx
.
outdir
,
"output_
$
(lpad(i, 5, '0')).vtu"
),
st
.
g
,
st
.
u
,
st
.
p1
,
st
.
p2
,
st
.
est
,
f0
,
f1
,
fw
)
st
.
g
,
st
.
u
,
st
.
p1
,
st
.
p2
,
st
.
est
,
f0
,
f1
,
fw
)
pvd
=
paraview_collection
(
joinpath
(
ctx
.
outdir
,
"output.pvd"
))
i
=
0
pvd
[
0
]
=
save_step
(
0
)
pvd
=
paraview_collection
(
joinpath
(
ctx
.
outdir
,
"output.pvd"
))
do
pvd
for
i
in
1
:
10
pvd
[
i
]
=
save_step
(
i
)
while
true
for
k
in
1
:
10
i
+=
1
step!
(
st
)
step!
(
st
)
estimate!
(
st
)
estimate!
(
st
)
pvd
[
i
]
=
save_step
(
i
)
pvd
[
i
]
=
save_step
(
i
)
println
()
println
()
end
end
vtk_save
(
pvd
)
marked_cells
=
mark
(
st
;
theta
=
0.5
)
println
(
"refining ..."
)
mesh
,
fs
=
refine
(
mesh
,
marked_cells
;
st
.
est
,
st
.
g
,
st
.
u
,
st
.
p1
,
st
.
p2
,
st
.
du
,
st
.
dp1
,
st
.
dp2
,
f0
,
f1
,
fw
)
st
=
L1L2TVContext
(
"run"
,
mesh
,
st
.
d
,
st
.
m
,
T
,
nabla
(
fs
.
fw
),
S
,
st
.
alpha1
,
st
.
alpha2
,
st
.
beta
,
st
.
lambda
,
st
.
gamma1
,
st
.
gamma2
,
fs
.
est
,
fs
.
g
,
fs
.
u
,
fs
.
p1
,
fs
.
p2
,
fs
.
du
,
fs
.
dp1
,
fs
.
dp2
)
f0
,
f1
,
fw
=
(
fs
.
f0
,
fs
.
f1
,
fs
.
fw
)
println
(
"reprojecting ..."
)
reproject!
()
end
end
display
(
plot
(
colorflow
(
to_img
(
sample
(
st
.
u
)))))
display
(
plot
(
colorflow
(
to_img
(
sample
(
st
.
u
)))))
#CSV.write(joinpath(ctx.outdir, "energies.csv"), df)
#CSV.write(joinpath(ctx.outdir, "energies.csv"), df)
...
...
This diff is collapsed.
Click to expand it.
src/function.jl
+
1
−
1
View file @
65804157
This diff is collapsed.
Click to expand it.
src/mesh.jl
+
21
−
3
View file @
65804157
export
init_grid
,
init_hgrid
,
save
,
refine!
,
cells
,
vertices
,
export
init_grid
,
init_hgrid
,
save
,
refine!
,
refine
,
cells
,
vertices
,
ndims_domain
,
ndims_space
ndims_domain
,
ndims_space
using
LinearAlgebra
:
norm
using
LinearAlgebra
:
norm
...
@@ -286,7 +286,7 @@ function refine!(hmesh::HMesh, marked_cells::Set; fs...)
...
@@ -286,7 +286,7 @@ function refine!(hmesh::HMesh, marked_cells::Set; fs...)
# extended functions onto newly created cells
# extended functions onto newly created cells
extended_fs
=
map
(
NamedTuple
(
fs
))
do
f
extended_fs
=
map
(
NamedTuple
(
fs
))
do
f
space
=
FeSpace
(
extended_mesh
,
f
.
space
.
element
,
f
.
space
.
size
)
space
=
FeSpace
(
extended_mesh
,
f
.
space
.
element
,
f
.
space
.
size
)
return
FeFunction
(
space
)
return
FeFunction
(
space
;
f
.
name
)
end
end
# copy over previous data for unmodified cells
# copy over previous data for unmodified cells
for
(
f
,
extended_f
)
in
zip
(
NamedTuple
(
fs
),
extended_fs
)
for
(
f
,
extended_f
)
in
zip
(
NamedTuple
(
fs
),
extended_fs
)
...
@@ -302,7 +302,7 @@ function refine!(hmesh::HMesh, marked_cells::Set; fs...)
...
@@ -302,7 +302,7 @@ function refine!(hmesh::HMesh, marked_cells::Set; fs...)
# retain only non-refined cells
# retain only non-refined cells
new_fs
=
map
(
NamedTuple
(
extended_fs
))
do
f
new_fs
=
map
(
NamedTuple
(
extended_fs
))
do
f
space
=
FeSpace
(
new_mesh
,
f
.
space
.
element
,
f
.
space
.
size
)
space
=
FeSpace
(
new_mesh
,
f
.
space
.
element
,
f
.
space
.
size
)
return
FeFunction
(
space
)
return
FeFunction
(
space
;
f
.
name
)
end
end
retained_cells
=
setdiff
(
cells
(
extended_mesh
),
removed_cells
)
retained_cells
=
setdiff
(
cells
(
extended_mesh
),
removed_cells
)
@assert
(
retained_cells
==
cells
(
hmesh
))
@assert
(
retained_cells
==
cells
(
hmesh
))
...
@@ -316,6 +316,24 @@ function refine!(hmesh::HMesh, marked_cells::Set; fs...)
...
@@ -316,6 +316,24 @@ function refine!(hmesh::HMesh, marked_cells::Set; fs...)
return
new_fs
return
new_fs
end
end
"refine by creating temporary hierarchical mesh on the fly"
function
refine
(
mesh
::
Mesh
,
marked_cells
;
fs
...
)
hmesh
=
HMesh
(
mesh
)
fs_new
=
refine!
(
hmesh
,
Set
(
marked_cells
);
fs
...
)
mesh_new
=
sub_mesh
(
hmesh
)
return
mesh_new
,
fs_new
end
function
geo_tolocal
(
A
,
v
)
J
=
jacobian
(
x
->
A
*
[
1
-
x
[
1
]
-
x
[
2
],
x
[
1
],
x
[
2
]],
[
0.
,
0.
])
return
J
\
(
v
-
A
[
:
,
1
])
end
function
geo_contains
(
A
,
v
)
J
=
jacobian
(
x
->
A
*
[
1
-
x
[
1
]
-
x
[
2
],
x
[
1
],
x
[
2
]],
[
0.
,
0.
])
λ
=
J
\
(
v
-
A
[
:
,
1
])
return
all
(
λ
.>=
0
)
&&
sum
(
λ
)
<=
1
end
#function cell_contains(mesh, cell, v)
#function cell_contains(mesh, cell, v)
# geo = mesh.vertices[:, mesh.cells[:, cell]]
# geo = mesh.vertices[:, mesh.cells[:, cell]]
...
...
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