mutable struct BinnedPointList{T}

Binned point list structure allowing for fast check for already existing points.

This provides better performance for indendifying already inserted points than the naive linear search.

OTOH the implementation is still quite naive - it dynamically maintains a cuboid bining region with a fixed number of bins.

Probably tree based adaptive methods (a la octree) will be more efficient, however they will be harder to implement.

In an ideal world, we would maintain a dynamic Delaunay triangulation, which at once could be the starting point of mesh generation which will follow here anyway.

BinnedPointList(dim; kwargs...)

Create and initialize binned point list

BinnedPointList(
    ,
    dim;
    tol,
    number_of_directional_bins,
    binning_region_increase_factor,
    num_allowed_unbinned_points,
    max_unbinned_ratio
)
BinnedPointList(dim; kwargs...)

Create and initialize binned point list

mutable struct SimplexGridBuilder

Simplex grid builder: wrapper around array based mesh generator interface. It allows to build up the input data incrementally.

SimplexGridBuilder(; Generator=nothing,
                     tol=1.0e-12,
                     checkexisting=true)

Create a SimplexGridBuilder.

• Generator: module corresponding to mesh generator package. Valid choices are TetGen and Triangulate, corresponding to the respective Julia packages.
• checkexisting: whether to check for already existing points
• tol: two points below this tolerance will be merged if checkexisting is true

insert!(bpl, p)

If another point with distance less the tol from p is in pointlist, return its index. Otherwise, insert point into pointlist.

dim_space(builder)

Space dimension of builder.

function simplexgrid(Generator;
                     points=Array{Cdouble,2}(undef,0,0),
                     bfaces=Array{Cint,2}(undef,0,0),
                     bfaceregions=Array{Cint,1}(undef,0),
                     regionpoints=Array{Cdouble,2}(undef,0,0),
                     regionnumbers=Array{Cint,1}(undef,0),
                     regionvolumes=Array{Cdouble,1}(undef,0);
                     kwargs...
                  )

Create Grid from a number of input arrays. The 2D input arrays are transposed if necessary and converted to the proper data types for Triangulate or TetGen

This conversion is not performed if the data types are those indicated in the defaults and the leading dimension of 2D arrays corresponds to the space dimension.

See default_options for available kwargs.

simplexgrid(builder; kwargs...)

Build simplex grid from the current state of the builder. kwargs overwrite those set with the options! method. See default_options for available kwargs.

simplexgrid(
    ::Type{SimplexGridFactory.TetGenType},
    TetGen,
    input;
    kwargs...
) -> ExtendableGrids.ExtendableGrid

Create Grid from TetGen data.

See default_options for available kwargs.

simplexgrid(
    ::Type{SimplexGridFactory.TriangulateType},
    Triangulate,
    input;
    kwargs...
) -> ExtendableGrids.ExtendableGrid

Create Grid from Triangle input data.

See default_options for available kwargs.

bregions!(builder::SimplexGridBuilder,grid,regionlist;facetregions=nothing)

Add all boundary facets of grid with region numbers in region list to geometry description. The optional parameter facetregions allows to overwrite the numbers in regionlist.

bregions!(builder::SimplexGridBuilder,grid, pairs...)

Add boundary facets of grid with region numbers mentioned as first element in pairs with region number mentioned as second element of pairs to the geometry description.

Example:

bregions!(builder,grid, 1=>2, 3=>5)

builderplot(gb::SimplexGridBuilder; Plotter, kwargs...)

Two panel visualization of gridfactory with input and resulting grid See default_options for available kwargs.

cellregion!(builder,region)

Set the current cell region (acts on subsequent regionpoint() calls)

Cell regions can be used to distinguish cells of different materials etc. In the API they are characterized by

• region number set via cellregion!
• maximum cell volume set via maxvolume!
• region point set via regionpoint!. This is some point located within the respective region which must be surrounded by facets in a watertight manner.

checkexisting!(builder, b)

Whether to check for already existing points

circle!(builder, center, radius; n=20)

Add points and facets approximating a circle.

default_options()

Create dictionary of mesh generation options with default values. These at once describe the keyword arguments available to the methods of the package and are listed in the following table:

For mesh generation, these are turned into mesh generator control flags. This process can be completely ovewritten by specifying the flags parameter.

For the flags parameter in 2D see the short resp. long documentation of the Triangle control flags.

For the 3D case, see the corresponding TetGen flags

The unsuitable parameter should be a function, see triunsuitable .

facet!(builder,i1)
facet!(builder,i1,i2)
facet!(builder,i1,i2,i3,i4)
facet!(builder,vector_or_tuple)
facet!(builder, (x1,y1), (x2,y2))
facet!(builder, (x1,y1,z1), (x2,y2,z2),(x3,y3,z3))

Add a facet via the corresponding point indices returned by point!.

Facets of two points are solely used for 2D grids. Facets with more than two poins are used for 3D grids and must be planar.

facetregion!(builder,region)

Set the current facet region. Subsequent facets will be marked with this number. Facet regions can be used to mark different parts of the boundary, e.g. for distinguishing boundary conditions.

holepoint!(builder,x)
holepoint!(builder,x,y)
holepoint!(builder,x,y,z)
holepoint!(builder,vec_or_tuple)

Add a point marking a hole region. Hole regions need to be surrounded by facets in a watertight manner.

lineto!(builder, pt)

Generate a line from the current pen position to the target point pt, s moveto!(), (2D, 3D). pt is either an existing point index or a table of point coordinates. In the latter case, the point is added. It returns index of the target point.

Example 2D: draw a square with different facetregion numbers

 p = moveto!(b,[0,0])
 facetregion!(b,1);  lineto!(b,[1,0])
 facetregion!(b,2);  lineto!(b,[1,1])
 facetregion!(b,3);  lineto!(b,[0,1])
 facetregion!(b,4);  lineto!(b,p)

Example 3D: two planar facet with different facetregion numbers

 facetregion!(b,1);
 p1 = moveto!(b,[0,0,0])
 p2 = moveto!(b,[1,0,0])
 p3 = moveto!(b,[1,1,0])
 p4 = moveto!(b,[0,1,0])
 polyfacet!(b,[p1,p2,p3,p4])

 facetregion!(b,2);
 p1 = moveto!(b,[0,0,1])
 p2 = moveto!(b,[1,0,1])
 p3 = moveto!(b,[1,1,1])
 p4 = moveto!(b,[0,1,1])
 polyfacet!(b,[p1,p2,p3,p4])

maxvolume!(builder,vol)

Set the current cell volume resp. area (acts on subsequent regionpoint() calls). See cellregion!.

 maybewatertight(this::SimplexGridBuilder; bregions=nothing)

Check if facets belonging to boundare regions in bregions are watertight. This is based on a nuber of heuristics, only a negative answer is definitive.

  mesh3d!(builder, mesh; translate=(0,0,0), cellregion=0, hole=false)

Incorporate 3d model from mesh.

model3d!(builder, filename; translate=(0,0,0), cellregion=0, hole=false)

Load 3D model from file. File formats are those supported by MeshIO.jl.

moveto!(builder, pt)

Move the (virtual) pen to the target point pt (2D, 3D). pt is either an existing point index or a table of point coordinates. In the latter case, the point is added. It returns index of the target point.

options!(builder; kwargs...)

Set some mesh generation options, see default_options

point!(builder,x)
point!(builder,x,y)
point!(builder,x,y,z)
point!(builder,vec_or_tuple)

Add point or merge with already existing point. Returns its index which can be used to set up facets with facet!.

points(bpl)

Return the array of points in the point list.

polyfacet!(builder,vector_or_tuple)

Add a polygonal facet via the corresponding point indices returned by point!.

Facets with more than two poins are used for 3D grids and must be planar.

rect2d!(builder, sw, ne; facetregions=nothing)

Add points and facets describing a rectangle via points describing its south-west and north-east corners. On default, the corresponding facet regions are deduced from the current facetregion. Alternatively, a 4-vector of facetregions can be passed.

rect3d!(builder, bsw, tne; facetregions=nothing)

Add points and facets describing a qudrilateral via points describing its bottom south-west and top north-east corners. On default, the corresponding facet regions are deduced from the current facetregion. Alternatively, a 6-vector of facetregions can be passed (in the sequence s-e-n-w-b-t)

regionpoint!(builder,x)
regionpoint!(builder,x,y)
regionpoint!(builder,x,y,z)
regionpoint!(builder,vec_or_tuple)

Add a region point marking a region, using current cell volume an cell region See cellregion!.

sphere!(builder, center, radius; nref=3)

Add points and facets approximating a sphere. nref is a refinement level.

tetgenio(
    TetGen;
    points,
    bfaces,
    bfaceregions,
    regionpoints,
    regionnumbers,
    regionvolumes
) -> Any

Create a RawTetGenIO structure from a number of input arrays. The 2D input arrays are transposed if necessary and converted to the proper data types for TetGen.

This conversion is not performed if the data types are those indicated in the defaults and the leading dimension of 2D arrays corresponds to the space dimension.

tetgenio(this::SimplexGridBuilder) -> Any

Create tetgen input from the current state of the builder.

triangulateio(
    Triangulate;
    points,
    bfaces,
    bfaceregions,
    regionpoints,
    regionnumbers,
    regionvolumes
) -> Any

Create a TriangulateIO structure from a number of input arrays. The 2D input arrays are transposed if necessary and converted to the proper data types for Triangulate.

This conversion is not performed if the data types are those indicated in the defaults and the leading dimension of 2D arrays corresponds to the space dimension.

triangulateio(this::SimplexGridBuilder) -> Any

Create triangle input from the current state of the builder.