This page was generated from unit-4.2-csg/csg.ipynb.

4.2 Constructive Solid Geometry (CSG)

These geometries are bases on primitives (e.g. sphere, cylinder, plane) which are used to build solids by performing boolean operations. Netgen offers the following primitives

primitive	csg syntax	meaning
half-space	Plane(Pnt a,Vec n)	point p in plane, normal vector
sphere	Sphere(Pnt c,float r)	sphere with center c and radius r
cylinder	Cylinder(Pnt a, Pnt b, float r)	points a and b define the axes of a infinite cylinder of radius r
brick	OrthoBrick (Pnt a, Pnt b)	axes parallel brick with minimal coordinates a and maximal coordinates b

and the boolean operators

operator	set operation
\(*\)	intersection
\(+\)	union
\(-\)	intersection with complement

import netgen.gui
from ngsolve import Draw, Redraw # just for visualization

Using these primitives and operations, we can easily construct a cube. First we import the netgen.csg module, create 6 plane and intersect them to get the solid cube.

from netgen.csg import *

left  = Plane (Pnt(0,0,0), Vec(-1,0,0) )
right = Plane (Pnt(1,1,1), Vec( 1,0,0) )
front = Plane (Pnt(0,0,0), Vec(0,-1,0) )
back  = Plane (Pnt(1,1,1), Vec(0, 1,0) )
bot   = Plane (Pnt(0,0,0), Vec(0,0,-1) )
top   = Plane (Pnt(1,1,1), Vec(0,0, 1) )

cube = left * right * front * back * bot * top

Then we create a CSGeometry object and add the solid.

geo = CSGeometry()
geo.Add (cube)

mesh = geo.GenerateMesh(maxh=0.25)
Redraw()
# mesh.Save("cube.vol")

 Start Findpoints
 main-solids: 1
 Found points 8
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 CalcLocalH: 44 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Surface 1 / 6
 load internal triangle rules
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 36 elements, 55 points
 Surface 2 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 38 elements, 67 points
 Surface 3 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 36 elements, 78 points
 Surface 4 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 34 elements, 88 points
 Surface 5 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 36 elements, 99 points
 Surface 6 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 42 elements, 113 points
 SplitSeparateFaces
 Check subdomain 1 / 1

 Meshing subdomain 1 of 1
 Use internal rules
 Delaunay meshing
 number of points: 108
 blockfill local h
 number of points: 161
 Points: 161
 Elements: 872
 Tree data entries per element: 1.6055
 Tree nodes per element: 0.0309633
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 161 points, 612 elements
 start tetmeshing
 Use internal rules
 Success !
 161 points, 612 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

from netgen.csg import *

cube = OrthoBrick( Pnt(0,0,0), Pnt(1,1,1) )
hole = Cylinder ( Pnt(0.5, 0.5, 0), Pnt(0.5, 0.5, 1), 0.2)

geo = CSGeometry()
geo.Add (cube-hole.maxh(0.05))
mesh = geo.GenerateMesh(maxh=0.1)
Redraw()

 Start Findpoints
 main-solids: 1
 Found points 16
 Analyze spec points
 Find edges
 14 edges found
 Check intersecting edges
 CalcLocalH: 166 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 14 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 14 edges found
 Check intersecting edges
 Surface 1 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 285 elements, 276 points
 Surface 2 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 234 elements, 374 points
 Surface 3 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 246 elements, 478 points
 Surface 4 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 248 elements, 583 points
 Surface 5 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 289 elements, 695 points
 Surface 6 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 252 elements, 802 points
 Surface 7 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 1148 elements, 1351 points
 SplitSeparateFaces
 Check subdomain 1 / 1

 Meshing subdomain 1 of 1
 Use internal rules
 Delaunay meshing
 number of points: 1342
 blockfill local h
 number of points: 3009
 Points: 3009
 Elements: 20511
 Tree data entries per element: 1.51626
 Tree nodes per element: 0.0302764
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 1 degenerated elements removed
 Remove intersecting
 Remove outer
 3005 points, 14997 elements
 start tetmeshing
 Use internal rules
 Success !
 3019 points, 15129 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

Setting properties of solids

A solid has members which we can set to define the desired properties.

sphere = Sphere(Pnt(0,0,0),1)

Now we can set a boundary name and a maximal mesh size on the surface of this sphere

sphere.bc("sphere").maxh(0.25)

<netgen.libngpy._csg.Solid at 0x7faeb4e1eeb0>

and define a material for the volume

sphere.mat("iron")

<netgen.libngpy._csg.Solid at 0x7faeb4e1eeb0>

In case we want to visualize the geometry we can define the color (using rgb values) and transparency of the solid.

sphere.col([1,0,0])#.transp()

<netgen.libngpy._csg.Solid at 0x7faeb4e1eeb0>

geo = CSGeometry()
geo.Add(sphere)
geo.Draw()

 Calc Triangle Approximation
 Object 0 has 882 triangles

ngmesh = geo.GenerateMesh()
print(type(ngmesh))
Redraw()

 Start Findpoints
 main-solids: 1
 Found points 0
 Analyze spec points
 Find edges
 0 edges found
 Check intersecting edges
 CalcLocalH: 2 Points 0 Elements 0 Surface Elements
 Start Findpoints
 main-solids: 1
 Found points 0
 Analyze spec points
 Find edges
 0 edges found
 Check intersecting edges
 Start Findpoints
 main-solids: 1
 Found points 0
 Analyze spec points
 Find edges
 0 edges found
 Check intersecting edges
 Surface 1 / 1
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 414 elements, 209 points
 SplitSeparateFaces
 Check subdomain 1 / 1

 Meshing subdomain 1 of 1
 Use internal rules
 Delaunay meshing
 number of points: 209
 blockfill local h
 number of points: 240
 Points: 240
 Elements: 1211
 Tree data entries per element: 1.56895
 Tree nodes per element: 0.0305533
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 240 points, 737 elements
 start tetmeshing
 Use internal rules
 Success !
 240 points, 737 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
<class 'netgen.libngpy._meshing.Mesh'>

To improve the approximation of curved geometries it is possible to use curved elements. This can be done within NGSolve. Thus we have to convert the Netgen mesh to a NGSolve mesh before curving it.

from ngsolve.comp import Mesh
mesh = Mesh(ngmesh)
print(type(mesh))
Redraw()

 Update mesh topology
<class 'ngsolve.comp.Mesh'>
 Update clusters

mesh.Curve(3)
Draw(mesh)

 Curve elements, order = 3
 Update clusters
 Curving edges
 Curving faces

Setting the mesh size

There are the following options to set the mesh size:

• globally as argument maxh of GenerateMesh

• to the surface of one solid (maxh property as above mentioned)

• for the volume of a solid as optional argument when adding it to the geometry Add(...,bc)

• restrict the mesh size for one point using RestrictH

• use CloseSurfaces to generate anisotropic meshes

Global mesh size

The global mesh size can be set with the named argument maxh. The following two versions are equivalent since all arguments of the of the GenerateMesh function are parsed to the MeshingParameters if no named argument mp is given.

unit_cube.GenerateMesh(maxh=0.4)

 Start Findpoints
 main-solids: 1
 Found points 8
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 CalcLocalH: 32 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Surface 1 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 36 points
 Surface 2 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 40 points
 Surface 3 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 44 points
 Surface 4 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 48 points
 Surface 5 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 52 points
 Surface 6 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 56 points
 SplitSeparateFaces
 Check subdomain 1 / 1

 Meshing subdomain 1 of 1
 Use internal rules
 Delaunay meshing
 number of points: 52
 blockfill local h
 number of points: 61
 Points: 61
 Elements: 302
 Tree data entries per element: 1.3245
 Tree nodes per element: 0.0231788
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 61 points, 166 elements
 start tetmeshing
 Use internal rules
 Success !
 61 points, 166 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

<netgen.libngpy._meshing.Mesh at 0x7faeb60ea870>

from netgen.meshing import MeshingParameters
mp = MeshingParameters(maxh=0.4)
unit_cube.GenerateMesh(mp = mp)

 Start Findpoints
 main-solids: 1
 Found points 8
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 CalcLocalH: 32 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Surface 1 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 36 points
 Surface 2 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 40 points
 Surface 3 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 44 points
 Surface 4 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 48 points
 Surface 5 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 52 points
 Surface 6 / 6
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 18 elements, 56 points
 SplitSeparateFaces
 Check subdomain 1 / 1

 Meshing subdomain 1 of 1
 Use internal rules
 Delaunay meshing
 number of points: 52
 blockfill local h
 number of points: 61
 Points: 61
 Elements: 302
 Tree data entries per element: 1.3245
 Tree nodes per element: 0.0231788
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 61 points, 166 elements
 start tetmeshing
 Use internal rules
 Success !
 61 points, 166 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

<netgen.libngpy._meshing.Mesh at 0x7faeb4e303b0>

Mesh size for one solid

To set the mesh size for one domain of the mesh we have to add the desired maxh as argument when adding the solid to the geometry

geo = CSGeometry()

brick = OrthoBrick(Pnt(-2,-2,-2),Pnt(2,2,2))
sphere = Sphere(Pnt(0,0,0),1)

geo.Add(brick-sphere)
geo.Add(sphere,maxh=0.1)
ngmesh = geo.GenerateMesh(maxh=0.4)

 Start Findpoints
 main-solids: 2
 Found points 8
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 CalcLocalH: 118 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Surface 1 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 226 elements, 212 points
 Surface 2 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 244 elements, 315 points
 Surface 3 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 236 elements, 414 points
 Surface 4 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 248 elements, 519 points
 Surface 5 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 242 elements, 621 points
 Surface 6 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 248 elements, 726 points
 Surface 7 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 2722 elements, 2087 points
 SplitSeparateFaces
 Check subdomain 1 / 2
 Check subdomain 2 / 2

 Meshing subdomain 1 of 2
 Use internal rules
 Delaunay meshing
 number of points: 2066
 blockfill local h
 number of points: 5722
 Points: 5722
 Elements: 35074
 Tree data entries per element: 1.51679
 Tree nodes per element: 0.0303074
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 9 degenerated elements removed
 Remove intersecting
 Remove outer
 5652 points, 29391 elements
 start tetmeshing
 Use internal rules
 Success !
 5750 points, 30496 elements

 Meshing subdomain 2 of 2
 Use internal rules
 Delaunay meshing
 number of points: 5750
 blockfill local h
 number of points: 9755
 Points: 5363
 Elements: 31246
 Tree data entries per element: 1.5682
 Tree nodes per element: 0.031332
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 9749 points, 58739 elements
 start tetmeshing
 Use internal rules
 Success !
 9749 points, 58739 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

Mesh size on a surface

If we want to refine just on a surface we define it as property of the solid.

geo = CSGeometry()

brick = OrthoBrick(Pnt(-2,-2,-2),Pnt(2,2,2))
sphere = Sphere(Pnt(0,0,0),1)

geo.Add(brick-sphere)
geo.Add(sphere.maxh(0.1))
ngmesh = geo.GenerateMesh()

 Start Findpoints
 main-solids: 2
 Found points 8
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 CalcLocalH: 10 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Surface 1 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 13 elements, 30 points
 Surface 2 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 19 elements, 36 points
 Surface 3 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 13 elements, 39 points
 Surface 4 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 16 elements, 43 points
 Surface 5 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 28 elements, 52 points
 Surface 6 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 13 elements, 55 points
 Surface 7 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 2722 elements, 1416 points
 SplitSeparateFaces
 Check subdomain 1 / 2
 Check subdomain 2 / 2

 Meshing subdomain 1 of 2
 Use internal rules
 Delaunay meshing
 number of points: 1408
 blockfill local h
 number of points: 4971
 Points: 4971
 Elements: 30900
 Tree data entries per element: 1.54045
 Tree nodes per element: 0.0307767
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 10 degenerated elements removed
 Remove intersecting
 Remove outer
 4897 points, 26492 elements
 start tetmeshing
 Use internal rules
 Success !
 4983 points, 27661 elements

 Meshing subdomain 2 of 2
 Use internal rules
 Delaunay meshing
 number of points: 4983
 blockfill local h
 number of points: 6425
 Points: 2800
 Elements: 16601
 Tree data entries per element: 1.53003
 Tree nodes per element: 0.0305403
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 3 degenerated elements removed
 Remove intersecting
 Remove outer
 6407 points, 40950 elements
 start tetmeshing
 Use internal rules
 ImproveMesh
 CombineImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 Call remove problem
 Elements before Remove: 34914
 Elements after Remove: 34820
 start tetmeshing
 Use internal rules
 Success !
 5595 points, 34927 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

Mesh size in points

This can be done with the MeshingParameters. Using RestrictH we can define the mesh size in an arbitrary point.

geo = CSGeometry()

brick = OrthoBrick(Pnt(-2,-2,-2),Pnt(2,2,2))
sphere = Sphere(Pnt(0,0,0),1)

mp = MeshingParameters(maxh=0.4)
mp.RestrictH (x=0, y=0, z=1, h=0.025)

geo.Add(brick-sphere)
geo.Add(sphere)
ngmesh = geo.GenerateMesh(mp = mp)

 Start Findpoints
 main-solids: 2
 Found points 8
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 CalcLocalH: 118 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 12 edges found
 Check intersecting edges
 Surface 1 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 226 elements, 212 points
 Surface 2 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 244 elements, 315 points
 Surface 3 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 236 elements, 414 points
 Surface 4 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 248 elements, 519 points
 Surface 5 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 242 elements, 621 points
 Surface 6 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 248 elements, 726 points
 Surface 7 / 7
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 296 elements, 874 points
 SplitSeparateFaces
 Check subdomain 1 / 2
 Check subdomain 2 / 2

 Meshing subdomain 1 of 2
 Use internal rules
 Delaunay meshing
 number of points: 857
 blockfill local h
 number of points: 1533
 Points: 1533
 Elements: 8608
 Tree data entries per element: 1.85874
 Tree nodes per element: 0.0370586
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 1533 points, 6796 elements
 start tetmeshing
 Use internal rules
 Success !
 1533 points, 6796 elements

 Meshing subdomain 2 of 2
 Use internal rules
 Delaunay meshing
 number of points: 1533
 blockfill local h
 number of points: 1622
 Points: 238
 Elements: 1279
 Tree data entries per element: 1.48554
 Tree nodes per element: 0.0289289
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 1 degenerated elements removed
 Remove intersecting
 Remove outer
 1618 points, 7590 elements
 start tetmeshing
 Use internal rules
 Success !
 1649 points, 7871 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

Anisotropic meshes

If the geometry contains thin layers we can use CloseSurfaces to avoid elements with small angles.

from netgen.csg import *

geo = CSGeometry()

box = OrthoBrick(Pnt(0,0,0),Pnt(1,1,1))
top = Plane(Pnt(0,0,0.52),Vec(0,0,1))
bot = Plane(Pnt(0,0,0.48),Vec(0,0,-1))
plate = box * top * bot

geo.Add((box-top).mat("air"))
geo.Add(plate.mat("plate"))
geo.Add((box-bot).mat("air"))

slices = [2**(-i) for i in reversed(range(1,6))]
# define the close surfaces
geo.CloseSurfaces(bot,top)#,slices)
nmesh = geo.GenerateMesh(maxh=0.3)
# refine the mesh between the close surfaces
# ZRefinement(nmesh,geo)

surface ids1 = 0: 21

surface ids2 = 0: 13

 Start Findpoints
 main-solids: 3
 Found points 16
 Analyze spec points
 Find edges
 28 edges found
 Find Identifications
 Check intersecting edges
 CalcLocalH: 56 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 28 edges found
 Find Identifications
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 28 edges found
 Find Identifications
 Check intersecting edges
 Surface 1 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 14 elements, 70 points
 Surface 2 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 14 elements, 72 points
 Surface 3 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 11 elements, 73 points
 Surface 4 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 9 elements, 73 points
 Surface 5 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 22 elements, 79 points
 Surface 6 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 13 elements, 81 points
 Surface 7 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 13 elements, 83 points
 Surface 8 / 16
 insert quad layer of 4 elements at face 8
 Surface meshing done
 0 illegal triangles
 4 elements, 83 points
 Surface 9 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 24 elements, 88 points
 Surface 10 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 14 elements, 90 points
 Surface 12 / 16
 insert quad layer of 4 elements at face 12
 Surface meshing done
 0 illegal triangles
 4 elements, 90 points
 Surface 13 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 14 elements, 92 points
 Surface 14 / 16
 insert quad layer of 4 elements at face 14
 Surface meshing done
 0 illegal triangles
 4 elements, 92 points
 Surface 15 / 16
 insert quad layer of 4 elements at face 15
 Surface meshing done
 0 illegal triangles
 4 elements, 92 points
 Surface 16 / 16
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 30 elements, 100 points
 Surface 11
 22 elements, 102 points
 SplitSeparateFaces
 Check subdomain 1 / 3
 Check subdomain 2 / 3
 Check subdomain 3 / 3

 Meshing subdomain 1 of 3
 Use internal rules
 Delaunay meshing
 number of points: 102
 blockfill local h
 number of points: 102
 Points: 56
 Elements: 252
 Tree data entries per element: 1.5873
 Tree nodes per element: 0.0277778
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 102 points, 108 elements
 start tetmeshing
 Use internal rules
 Success !
 102 points, 108 elements

 Meshing subdomain 2 of 3
 Use internal rules
 102 points, 130 elements

 Meshing subdomain 3 of 3
 Use internal rules
 Delaunay meshing
 number of points: 102
 blockfill local h
 number of points: 104
 Points: 48
 Elements: 224
 Tree data entries per element: 1.33929
 Tree nodes per element: 0.0223214
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 104 points, 232 elements
 start tetmeshing
 Use internal rules
 Success !
 104 points, 232 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

Setting boundary conditions

Boundary condition on the surface of a solid

Setting a boundary condition on the whole surface of solid can be achieved by adding it as property to the solid.

brick = OrthoBrick(Pnt(-2,-2,-2),Pnt(2,2,2)).bc('outer')
sphere = Sphere(Pnt(0,0,0),1).bc('sphere')

Modify boundary between two solids

This can be done by adding the named argument bcmod when adding the solid to the geometry. Here we change the boundary condition on the surface between the halfsphere and the already added box.

halfsphere = sphere * Plane(Pnt(0,0,0),Vec(1,0,0)).bc('plane')
box = brick-sphere
geo = CSGeometry()
geo.Add(box.col([1,0,0]).transp())
geo.Add(halfsphere.col([0,0,1]),bcmod=[(box,"halfsphere")])
geo.Draw()

 Calc Triangle Approximation
 Object 0 has 1842 triangles
 Object 1 has 1473 triangles

ngmesh = geo.GenerateMesh()
mesh = Mesh(ngmesh)
mesh.GetBoundaries()

 Start Findpoints
 main-solids: 2
 Found points 12
 Analyze spec points
 Find edges
 13 edges found
 Check intersecting edges
 CalcLocalH: 21 Points 0 Elements 0 Surface Elements
 Start Findpoints
 Analyze spec points
 Find edges
 13 edges found
 Check intersecting edges
 Start Findpoints
 Analyze spec points
 Find edges
 13 edges found
 Check intersecting edges
 Surface 1 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 22 elements, 51 points
 Surface 2 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 22 elements, 57 points
 Surface 3 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 24 elements, 64 points
 Surface 4 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 20 elements, 69 points
 Surface 5 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 24 elements, 76 points
 Surface 6 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 22 elements, 82 points
 Surface 7 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 59 elements, 106 points
 Surface 8 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 69 elements, 135 points
 Surface 9 / 9
 Surface meshing done
 0 illegal triangles
 Optimize Surface
 Edgeswapping, topological
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 Edgeswapping, metric
 Smoothing
 Combine improve
 Smoothing
 27 elements, 143 points
 SplitSeparateFaces
 Check subdomain 1 / 2
 Check subdomain 2 / 2

 Meshing subdomain 1 of 2
 Use internal rules
 Delaunay meshing
 number of points: 140
 blockfill local h
 number of points: 166
 Points: 158
 Elements: 849
 Tree data entries per element: 1.649
 Tree nodes per element: 0.0318021
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 166 points, 565 elements
 start tetmeshing
 Use internal rules
 Success !
 166 points, 565 elements

 Meshing subdomain 2 of 2
 Use internal rules
 Delaunay meshing
 number of points: 166
 blockfill local h
 number of points: 167
 Points: 51
 Elements: 237
 Tree data entries per element: 1.26582
 Tree nodes per element: 0.021097
 SwapImprove
 SwapImprove
 SwapImprove
 SwapImprove
 0 degenerated elements removed
 Remove intersecting
 Remove outer
 167 points, 674 elements
 start tetmeshing
 Use internal rules
 Success !
 167 points, 674 elements
 Remove Illegal Elements
 Volume Optimization
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh
 CombineImprove
 ImproveMesh
 SplitImprove
 ImproveMesh
 SwapImprove
 SwapImprove2
 ImproveMesh

('outer',
 'outer',
 'outer',
 'outer',
 'outer',
 'outer',
 'sphere',
 'halfsphere',
 'plane')

 Update mesh topology
 Update clusters