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Functions
GridGenerator Namespace Reference

Functions

template<int dim, int spacedim>
void hyper_cube (Triangulation< dim, spacedim > &tria, const double left=0., const double right=1.)
 
template<int dim>
void subdivided_hyper_cube (Triangulation< dim > &tria, const unsigned int repetitions, const double left=0., const double right=1.)
 
template<int dim, int spacedim>
void hyper_rectangle (Triangulation< dim, spacedim > &tria, const Point< spacedim > &p1, const Point< spacedim > &p2, const bool colorize=false)
 
template<int dim>
void subdivided_hyper_rectangle (Triangulation< dim > &tria, const std::vector< unsigned int > &repetitions, const Point< dim > &p1, const Point< dim > &p2, const bool colorize=false)
 
template<int dim>
void subdivided_hyper_rectangle (Triangulation< dim > &tria, const std::vector< std::vector< double > > &step_sizes, const Point< dim > &p_1, const Point< dim > &p_2, const bool colorize)
 
template<int dim>
void subdivided_hyper_rectangle (Triangulation< dim > &tria, const std::vector< std::vector< double > > &spacing, const Point< dim > &p, const Table< dim, types::material_id > &material_id, const bool colorize=false)
 
template<int dim>
void parallelogram (Triangulation< dim > &tria, const Point< dim > corners[dim], const bool colorize=false)
 
template<int dim>
void parallelogram (Triangulation< dim > &tria, const Tensor< 2, dim > &corners, const bool colorize=false) DEAL_II_DEPRECATED
 
template<int dim>
void parallelepiped (Triangulation< dim > &tria, const Point< dim >(&corners)[dim], const bool colorize=false)
 
template<int dim>
void subdivided_parallelepiped (Triangulation< dim > &tria, const unsigned int n_subdivisions, const Point< dim >(&corners)[dim], const bool colorize=false)
 
template<int dim>
void subdivided_parallelepiped (Triangulation< dim > &tria, const unsigned int(n_subdivisions)[dim], const Point< dim >(&corners)[dim], const bool colorize=false)
 
template<int dim>
void enclosed_hyper_cube (Triangulation< dim > &tria, const double left=0., const double right=1., const double thickness=1., const bool colorize=false)
 
template<int dim>
void hyper_ball (Triangulation< dim > &tria, const Point< dim > &center=Point< dim >(), const double radius=1.)
 
template<int dim>
void half_hyper_ball (Triangulation< dim > &tria, const Point< dim > &center=Point< dim >(), const double radius=1.)
 
template<int dim>
void cylinder (Triangulation< dim > &tria, const double radius=1., const double half_length=1.)
 
template<int dim>
void truncated_cone (Triangulation< dim > &tria, const double radius_0=1.0, const double radius_1=0.5, const double half_length=1.0)
 
template<int dim>
void hyper_L (Triangulation< dim > &tria, const double left=-1., const double right=1.)
 
template<int dim>
void hyper_cube_slit (Triangulation< dim > &tria, const double left=0., const double right=1., const bool colorize=false)
 
template<int dim>
void hyper_shell (Triangulation< dim > &tria, const Point< dim > &center, const double inner_radius, const double outer_radius, const unsigned int n_cells=0, bool colorize=false)
 
template<int dim>
void half_hyper_shell (Triangulation< dim > &tria, const Point< dim > &center, const double inner_radius, const double outer_radius, const unsigned int n_cells=0, const bool colorize=false)
 
template<int dim>
void quarter_hyper_shell (Triangulation< dim > &tria, const Point< dim > &center, const double inner_radius, const double outer_radius, const unsigned int n_cells=0, const bool colorize=false)
 
template<int dim>
void cylinder_shell (Triangulation< dim > &tria, const double length, const double inner_radius, const double outer_radius, const unsigned int n_radial_cells=0, const unsigned int n_axial_cells=0)
 
void torus (Triangulation< 2, 3 > &tria, const double R, const double r)
 
template<int dim>
void hyper_cube_with_cylindrical_hole (Triangulation< dim > &triangulation, const double inner_radius=.25, const double outer_radius=.5, const double L=.5, const unsigned int repetition=1, const bool colorize=false)
 
void moebius (Triangulation< 3, 3 > &tria, const unsigned int n_cells, const unsigned int n_rotations, const double R, const double r)
 
template<int dim, int spacedim>
void merge_triangulations (const Triangulation< dim, spacedim > &triangulation_1, const Triangulation< dim, spacedim > &triangulation_2, Triangulation< dim, spacedim > &result)
 
void extrude_triangulation (const Triangulation< 2, 2 > &input, const unsigned int n_slices, const double height, Triangulation< 3, 3 > &result)
 
template<int dim>
void laplace_transformation (Triangulation< dim > &tria, const std::map< unsigned int, Point< dim > > &new_points) DEAL_II_DEPRECATED
 
 DeclException0 (ExcInvalidRadii)
 
 DeclException1 (ExcInvalidRepetitions, int,<< "The number of repetitions "<< arg1<< " must be >=1.")
 
 DeclException1 (ExcInvalidRepetitionsDimension, int,<< "The vector of repetitions must have "<< arg1<<" elements.")
 

Detailed Description

This namespace provides a collection of functions for generating triangulations for some basic geometries.

Some of these functions receive a flag colorize. If this is set, parts of the boundary receive different boundary indicators (GlossBoundaryIndicator), allowing them to be distinguished for the purpose of attaching geometry objects and evaluating different boundary conditions.

This namespace also provides a function GridGenerator::laplace_transformation that smoothly transforms a domain into another one. This can be used to transform basic geometries to more complicated ones, like a shell to a grid of an airfoil, for example.

Function Documentation

template<int dim, int spacedim>
void GridGenerator::hyper_cube ( Triangulation< dim, spacedim > &  tria,
const double  left = 0.,
const double  right = 1. 
)

Initialize the given triangulation with a hypercube (line in 1D, square in 2D, etc) consisting of exactly one cell. The hypercube volume is the tensor product interval [left,right]dim in the present number of dimensions, where the limits are given as arguments. They default to zero and unity, then producing the unit hypercube. All boundary indicators are set to zero ("not colorized") for 2d and 3d. In 1d the indicators are colorized, see hyper_rectangle().

hyper_cubes.png

See also subdivided_hyper_cube() for a coarse mesh consisting of several cells. See hyper_rectangle(), if different lengths in different ordinate directions are required.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::subdivided_hyper_cube ( Triangulation< dim > &  tria,
const unsigned int  repetitions,
const double  left = 0.,
const double  right = 1. 
)

Same as hyper_cube(), but with the difference that not only one cell is created but each coordinate direction is subdivided into repetitions cells. Thus, the number of cells filling the given volume is repetitionsdim.

If spacedim=dim+1 the same mesh as in the case spacedim=dim is created, but the vertices have an additional coordinate =0. So, if dim=1 one obtains line along the x axis in the xy plane, and if dim=3 one obtains a square in lying in the xy plane in 3d space.

Note
The triangulation needs to be void upon calling this function.
template<int dim, int spacedim>
void GridGenerator::hyper_rectangle ( Triangulation< dim, spacedim > &  tria,
const Point< spacedim > &  p1,
const Point< spacedim > &  p2,
const bool  colorize = false 
)

Create a coordinate-parallel brick from the two diagonally opposite corner points p1 and p2.

If the colorize flag is set, the boundary_indicators of the surfaces are assigned, such that the lower one in x-direction is 0, the upper one is 1. The indicators for the surfaces in y-direction are 2 and 3, the ones for z are 4 and 5. Additionally, material ids are assigned to the cells according to the octant their center is in: being in the right half plane for any coordinate direction xi adds 2i. For instance, the center point (1,-1,1) yields a material id 5.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::subdivided_hyper_rectangle ( Triangulation< dim > &  tria,
const std::vector< unsigned int > &  repetitions,
const Point< dim > &  p1,
const Point< dim > &  p2,
const bool  colorize = false 
)

Create a coordinate-parallel parallelepiped from the two diagonally opposite corner points p1 and p2. In dimension i, repetitions[i] cells are generated.

To get cells with an aspect ratio different from that of the domain, use different numbers of subdivisions in different coordinate directions. The minimum number of subdivisions in each direction is 1. repetitions is a list of integers denoting the number of subdivisions in each coordinate direction.

If the colorize flag is set, the boundary_indicators of the surfaces are assigned, such that the lower one in x-direction is 0, the upper one is 1 (the left and the right vertical face). The indicators for the surfaces in y-direction are 2 and 3, the ones for z are 4 and 5. Additionally, material ids are assigned to the cells according to the octant their center is in: being in the right half plane for any coordinate direction xi adds 2i. For instance, the center point (1,-1,1) yields a material id 5 (this means that in 2d only material ids 0,1,2,3 are assigned independent from the number of repetitions).

Note that the colorize flag is ignored in 1d and is assumed to always be true. That means the boundary indicator is 0 on the left and 1 on the right. See step-15 for details.

Note
The triangulation needs to be void upon calling this function.
For an example of the use of this function see the step-28 tutorial program.
template<int dim>
void GridGenerator::subdivided_hyper_rectangle ( Triangulation< dim > &  tria,
const std::vector< std::vector< double > > &  step_sizes,
const Point< dim > &  p_1,
const Point< dim > &  p_2,
const bool  colorize 
)

Like the previous function. However, here the second argument does not denote the number of subdivisions in each coordinate direction, but a sequence of step sizes for each coordinate direction. The domain will therefore be subdivided into step_sizes[i].size() cells in coordinate direction i, with widths step_sizes[i][j] for the jth cell.

This function is therefore the right one to generate graded meshes where cells are concentrated in certain areas, rather than a uniformly subdivided mesh as the previous function generates.

The step sizes have to add up to the dimensions of the hyper rectangle specified by the points p1 and p2.

template<int dim>
void GridGenerator::subdivided_hyper_rectangle ( Triangulation< dim > &  tria,
const std::vector< std::vector< double > > &  spacing,
const Point< dim > &  p,
const Table< dim, types::material_id > &  material_id,
const bool  colorize = false 
)

Like the previous function, but with the following twist: the material_id argument is a dim-dimensional array that, for each cell, indicates which material_id should be set. In addition, and this is the major new functionality, if the material_id of a cell is (unsigned char)(-1), then that cell is deleted from the triangulation, i.e. the domain will have a void there.

template<int dim>
void GridGenerator::parallelogram ( Triangulation< dim > &  tria,
const Point< dim >  corners[dim],
const bool  colorize = false 
)

A parallelogram. The first corner point is the origin. The dim adjacent points are the ones given in the second argument and the fourth point will be the sum of these two vectors. Colorizing is done in the same way as in hyper_rectangle().

Note
This function is implemented in 2d only.
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::parallelogram ( Triangulation< dim > &  tria,
const Tensor< 2, dim > &  corners,
const bool  colorize = false 
)
Deprecated:
Use the other function of same name.
template<int dim>
void GridGenerator::parallelepiped ( Triangulation< dim > &  tria,
const Point< dim >(&)  corners[dim],
const bool  colorize = false 
)

A parallelepiped. The first corner point is the origin. The dim adjacent points are vectors describing the edges of the parallelepiped with respect to the origin. Additional points are sums of these dim vectors. Colorizing is done according to hyper_rectangle().

Note
This function silently reorders the vertices on the cells to lexiographic ordering (see GridReordering::reorder_grid). In other words, if reodering of the vertices does occur, the ordering of vertices in the array of corners will no longer refer to the same triangulation.
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::subdivided_parallelepiped ( Triangulation< dim > &  tria,
const unsigned int  n_subdivisions,
const Point< dim >(&)  corners[dim],
const bool  colorize = false 
)

A subdivided parallelepiped. The first corner point is the origin. The dim adjacent points are vectors describing the edges of the parallelepiped with respect to the origin. Additional points are sums of these dim vectors. The variable n_subdivisions designates the number of subdivisions in each of the dim directions. Colorizing is done according to hyper_rectangle().

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::subdivided_parallelepiped ( Triangulation< dim > &  tria,
const unsigned   int(n_subdivisions)[dim],
const Point< dim >(&)  corners[dim],
const bool  colorize = false 
)

A subdivided parallelepiped, ie. the same as above, but where the number of subdivisions in each of the dim directions may vary. Colorizing is done according to hyper_rectangle().

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::enclosed_hyper_cube ( Triangulation< dim > &  tria,
const double  left = 0.,
const double  right = 1.,
const double  thickness = 1.,
const bool  colorize = false 
)

Hypercube with a layer of hypercubes around it. The first two parameters give the lower and upper bound of the inner hypercube in all coordinate directions. thickness marks the size of the layer cells.

If the flag colorize is set, the outer cells get material id's according to the following scheme: extending over the inner cube in (+/-) x-direction: 1/2. In y-direction 4/8, in z-direction 16/32. The cells at corners and edges (3d) get these values bitwise or'd.

Presently only available in 2d and 3d.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::hyper_ball ( Triangulation< dim > &  tria,
const Point< dim > &  center = Point< dim >(),
const double  radius = 1. 
)

Initialize the given triangulation with a hyperball, i.e. a circle or a ball around center with given radius.

In order to avoid degenerate cells at the boundaries, the circle is triangulated by five cells, the ball by seven cells. The diameter of the center cell is chosen so that the aspect ratio of the boundary cells after one refinement is optimized.

This function is declared to exist for triangulations of all space dimensions, but throws an error if called in 1d.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::half_hyper_ball ( Triangulation< dim > &  tria,
const Point< dim > &  center = Point< dim >(),
const double  radius = 1. 
)

This class produces a half hyper-ball around center, which contains four elements in 2d and 6 in 3d. The cut plane is perpendicular to the x-axis.

The boundary indicators for the final triangulation are 0 for the curved boundary and 1 for the cut plane.

The appropriate boundary class is HalfHyperBallBoundary, or HyperBallBoundary.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::cylinder ( Triangulation< dim > &  tria,
const double  radius = 1.,
const double  half_length = 1. 
)

Create a cylinder around the x-axis. The cylinder extends from x=-half_length to x=+half_length and its projection into the yz-plane is a circle of radius radius.

In two dimensions, the cylinder is a rectangle from x=-half_length to x=+half_length and from y=-radius to y=radius.

The boundaries are colored according to the following scheme: 0 for the hull of the cylinder, 1 for the left hand face and 2 for the right hand face.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::truncated_cone ( Triangulation< dim > &  tria,
const double  radius_0 = 1.0,
const double  radius_1 = 0.5,
const double  half_length = 1.0 
)

Create a cutted cone around the x-axis. The cone extends from x=-half_length to x=half_length and its projection into the yz-plane is a circle of radius radius_0 at x=-half_length and a circle of radius radius_1 at x=+half_length. In between the radius is linearly decreasing.

In two dimensions, the cone is a trapezoid from x=-half_length to x=+half_length and from y=-radius_0 to y=radius_0 at x=-half_length and from y=-radius_1 to y=radius_1 at x=+half_length. In between the range of y is linearly decreasing.

The boundaries are colored according to the following scheme: 0 for the hull of the cone, 1 for the left hand face and 2 for the right hand face.

An example of use can be found in the documentation of the ConeBoundary class, with which you probably want to associate boundary indicator 0 (the hull of the cone).

Note
The triangulation needs to be void upon calling this function.
Author
Markus Bürg, 2009
template<int dim>
void GridGenerator::hyper_L ( Triangulation< dim > &  tria,
const double  left = -1.,
const double  right = 1. 
)

Initialize the given triangulation with a hyper-L consisting of exactly 2^dim-1 cells. It produces the hypercube with the interval [left,right] without the hypercube made out of the interval [(a+b)/2,b].

hyper_l.png

The triangulation needs to be void upon calling this function.

This function is declared to exist for triangulations of all space dimensions, but throws an error if called in 1d.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::hyper_cube_slit ( Triangulation< dim > &  tria,
const double  left = 0.,
const double  right = 1.,
const bool  colorize = false 
)

Initialize the given Triangulation with a hypercube with a slit. In each coordinate direction, the hypercube extends from left to right.

In 2d, the split goes in vertical direction from x=(left+right)/2, y=left to the center of the square at x=y=(left+right)/2.

In 3d, the 2d domain is just extended in the z-direction, such that a plane cuts the lower half of a rectangle in two.

This function is declared to exist for triangulations of all space dimensions, but throws an error if called in 1d.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::hyper_shell ( Triangulation< dim > &  tria,
const Point< dim > &  center,
const double  inner_radius,
const double  outer_radius,
const unsigned int  n_cells = 0,
bool  colorize = false 
)

Produce a hyper-shell, the region between two spheres around center, with given inner_radius and outer_radius. The number n_cells indicates the number of cells of the resulting triangulation, i.e., how many cells form the ring (in 2d) or the shell (in 3d).

If the flag colorize is true, then the outer boundary will have the indicator 1, while the inner boundary has id zero. If the flag is false, both have indicator zero.

In 2D, the number n_cells of elements for this initial triangulation can be chosen arbitrarily. If the number of initial cells is zero (as is the default), then it is computed adaptively such that the resulting elements have the least aspect ratio.

In 3D, only two different numbers are meaningful, 6 for a surface based on a hexahedron (i.e. 6 panels on the inner sphere extruded in radial direction to form 6 cells) and 12 for the rhombic dodecahedron. These give rise to the following meshes upon one refinement:

hypershell3d-6.png
hypershell3d-12.png

Neither of these meshes is particularly good since one ends up with poorly shaped cells at the inner edge upon refinement. For example, this is the middle plane of the mesh for the n_cells=6:

hyper_shell_6_cross_plane.png

The mesh generated with n_cells=6 is better but still not good. As a consequence, you may also specify n_cells=96 as a third option. The mesh generated in this way is based on a once refined version of the one with n_cells=12, where all internal nodes are re-placed along a shell somewhere between the inner and outer boundary of the domain. The following two images compare half of the hyper shell for n_cells=12 and n_cells=96 (note that the doubled radial lines on the cross section are artifacts of the visualization):

hyper_shell_12_cut.png
hyper_shell_96_cut.png
Note
This function is declared to exist for triangulations of all space dimensions, but throws an error if called in 1d.
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::half_hyper_shell ( Triangulation< dim > &  tria,
const Point< dim > &  center,
const double  inner_radius,
const double  outer_radius,
const unsigned int  n_cells = 0,
const bool  colorize = false 
)

Produce a half hyper-shell, i.e. the space between two circles in two space dimensions and the region between two spheres in 3d, with given inner and outer radius and a given number of elements for this initial triangulation. However, opposed to the previous function, it does not produce a whole shell, but only one half of it, namely that part for which the first component is restricted to non-negative values. The purpose of this class is to enable computations for solutions which have rotational symmetry, in which case the half shell in 2d represents a shell in 3d.

If the number of initial cells is zero (as is the default), then it is computed adaptively such that the resulting elements have the least aspect ratio.

If colorize is set to true, the inner, outer, left, and right boundary get indicator 0, 1, 2, and 3, respectively. Otherwise all indicators are set to 0.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::quarter_hyper_shell ( Triangulation< dim > &  tria,
const Point< dim > &  center,
const double  inner_radius,
const double  outer_radius,
const unsigned int  n_cells = 0,
const bool  colorize = false 
)

Produce a domain that is the intersection between a hyper-shell with given inner and outer radius, i.e. the space between two circles in two space dimensions and the region between two spheres in 3d, and the positive quadrant (in 2d) or octant (in 3d). In 2d, this is indeed a quarter of the full annulus, while the function is a misnomer in 3d because there the domain is not a quarter but one eighth of the full shell.

If the number of initial cells is zero (as is the default), then it is computed adaptively such that the resulting elements have the least aspect ratio in 2d.

If colorize is set to true, the inner, outer, left, and right boundary get indicator 0, 1, 2, and 3 in 2d, respectively. Otherwise all indicators are set to 0. In 3d indicator 2 is at the face x=0, 3 at y=0, 4 at z=0.

Note
The triangulation needs to be void upon calling this function.
template<int dim>
void GridGenerator::cylinder_shell ( Triangulation< dim > &  tria,
const double  length,
const double  inner_radius,
const double  outer_radius,
const unsigned int  n_radial_cells = 0,
const unsigned int  n_axial_cells = 0 
)

Produce a domain that is the space between two cylinders in 3d, with given length, inner and outer radius and a given number of elements for this initial triangulation. If n_radial_cells is zero (as is the default), then it is computed adaptively such that the resulting elements have the least aspect ratio. The same holds for n_axial_cells.

Note
Although this function is declared as a template, it does not make sense in 1D and 2D.
The triangulation needs to be void upon calling this function.
void GridGenerator::torus ( Triangulation< 2, 3 > &  tria,
const double  R,
const double  r 
)

Produce the surface meshing of the torus. The axis of the torus is the $y$-axis while the plane of the torus is the $x$- $z$ plane. The boundary of this object can be described by the TorusBoundary class.

Parameters
triaThe triangulation to be filled.
RThe radius of the circle, which forms the middle line of the torus containing the loop of cells. Must be greater than r.
rThe inner radius of the torus.
template<int dim>
void GridGenerator::hyper_cube_with_cylindrical_hole ( Triangulation< dim > &  triangulation,
const double  inner_radius = .25,
const double  outer_radius = .5,
const double  L = .5,
const unsigned int  repetition = 1,
const bool  colorize = false 
)

This class produces a square on the xy-plane with a circular hole in the middle. Square and circle are centered at the origin. In 3d, this geometry is extruded in $z$ direction to the interval $[0,L]$.

cubes_hole.png

It is implemented in 2d and 3d, and takes the following arguments:

  • inner_radius: radius of the internal hole
  • outer_radius: half of the edge length of the square
  • L: extension in z-direction (only used in 3d)
  • repetitions: number of subdivisions along the z-direction
  • colorize: whether to assign different boundary indicators to different faces. The colors are given in lexicographic ordering for the flat faces (0 to 3 in 2d, 0 to 5 in 3d) plus the curved hole (4 in 2d, and 6 in 3d). If colorize is set to false, then flat faces get the number 0 and the hole gets number 1.
void GridGenerator::moebius ( Triangulation< 3, 3 > &  tria,
const unsigned int  n_cells,
const unsigned int  n_rotations,
const double  R,
const double  r 
)

Produce a ring of cells in 3D that is cut open, twisted and glued together again. This results in a kind of moebius-loop.

Parameters
triaThe triangulation to be worked on.
n_cellsThe number of cells in the loop. Must be greater than 4.
n_rotationsThe number of rotations (Pi/2 each) to be performed before glueing the loop together.
RThe radius of the circle, which forms the middle line of the torus containing the loop of cells. Must be greater than r.
rThe radius of the cylinder bend together as loop.
template<int dim, int spacedim>
void GridGenerator::merge_triangulations ( const Triangulation< dim, spacedim > &  triangulation_1,
const Triangulation< dim, spacedim > &  triangulation_2,
Triangulation< dim, spacedim > &  result 
)

Given the two triangulations specified as the first two arguments, create the triangulation that contains the cells of both triangulation and store it in the third parameter. Previous content of result will be deleted.

This function is most often used to compose meshes for more complicated geometries if the geometry can be composed of simpler parts for which functions exist to generate coarse meshes. For example, the channel mesh used in step-35 could in principle be created using a mesh created by the GridGenerator::hyper_cube_with_cylindrical_hole function and several rectangles, and merging them using the current function. The rectangles will have to be translated to the right for this, a task that can be done using the GridTools::shift function (other tools to transform individual mesh building blocks are GridTools::transform, GridTools::rotate, and GridTools::scale).

Note
The two input triangulations must be coarse meshes that have no refined cells.
The function copies the material ids of the cells of the two input triangulations into the output triangulation but it currently makes no attempt to do the same for boundary ids. In other words, if the two coarse meshes have anything but the default boundary indicators, then you will currently have to set boundary indicators again by hand in the output triangulation.
For a related operation on refined meshes when both meshes are derived from the same coarse mesh, see GridTools::create_union_triangulation .
void GridGenerator::extrude_triangulation ( const Triangulation< 2, 2 > &  input,
const unsigned int  n_slices,
const double  height,
Triangulation< 3, 3 > &  result 
)

Take a 2d Triangulation that is being extruded in z direction by the total height of height using n_slices slices (minimum is 2). The boundary indicators of the faces of input are going to be assigned to the corresponding side walls in z direction. The bottom and top get the next two free boundary indicators.

template<int dim>
void GridGenerator::laplace_transformation ( Triangulation< dim > &  tria,
const std::map< unsigned int, Point< dim > > &  new_points 
)

This function transformes the Triangulation tria smoothly to a domain that is described by the boundary points in the map new_points. This map maps the point indices to the boundary points in the transformed domain.

Note, that the Triangulation is changed in-place, therefore you don't need to keep two triangulations, but the given triangulation is changed (overwritten).

In 1d, this function is not currently implemented.

Deprecated:
This function has been moved to GridTools::laplace_transform
GridGenerator::DeclException0 ( ExcInvalidRadii  )

Exception

GridGenerator::DeclException1 ( ExcInvalidRepetitions  ,
int  ,
<< "The number of repetitions "<< arg1<< " must be >=1."   
)

Exception

GridGenerator::DeclException1 ( ExcInvalidRepetitionsDimension  ,
int  ,
<< "The vector of repetitions must have "<< arg1<<" elements."   
)

Exception