/**
- * This class offers triangulations of some standard domains such as hypercubes,
- * hyperball and the like. Following is a list of domains that can be generated
- * by the functions of this class:
- * <ul>
- * <li> Hypercube:
- * the GridGenerator::hyper_cube function produces the unit line
- * segment, unit square, or unit cube:
- *
- * @image html hyper_cubes.png
- *
- * <li> Generalized L-shape domain:
- * using the GridGenerator::hyper_L (tria, a,b) function produces
- * the hypercube with the interval $[a,b]$ without the hypercube
- * made out of the interval $[(a+b)/2,b]$. Let, for example, be $a=-1$
- * and $b=1$, then the hpyer-L in two dimensions is the region
- * $[-1,1]^2 - [0,1]^2$. To create a hyper-L in one dimension results in
- * an error. The function is also implemented for three space dimensions
- * and produces the following domain (not completely to scale, the
- * cut-out part should have exactly half the edge length of the entire
- * cube):
- *
- * @image html hyper_l.png
- *
- * <li> Hyper ball:
- * You get the circle or ball (or generalized: hyperball) around
- * origin @p p and with radius @p r by calling
- * GridGenerator::hyper_ball (tria, p, r). 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 minimized in
- * some way. To create a hyperball in one dimension results in an
- * error.
- *
- * Do not forget to also attach a suitable boundary approximation object
- * to the triangulation object you passed to this function if you later want
- * the triangulation to be refined at the outer boundaries.
- *
- * <li> Half Hyper ball:
- * You get half of the circle or sphere generated by Hyper ball.
- * with center @p p and with radius @p r by calling
- * GridGenerator::half_hyper_ball (tria, p, r). The half-circle is
- * triangulated by four cells, while the half-sphere is triangulated by
- * six cells. The diameter of the center cell is
- * chosen to be the same as for the Hyper ball class.
- * To create a half-hyperball in one dimension results in
- * an error.
- *
- * Do not forget to also attach a suitable boundary approximation object
- * to the triangulation object you passed to this function if you later want
- * the triangulation to be refined at the outer boundaries. Both classes
- * HalfHyperBallBoundary and HyperBallBoundary will provide a valid
- * boundary object.
- *
- * <li> Hyper shell: A hyper shell is the region between two hyper
- * sphere with the same origin. Therefore, it is a ring in two
- * spatial dimensions. To triangulation it, call the function
- * GridGenerator::hyper_shell (tria, origin, inner_radius, outer_radius, N),
- * where the center of the spheres as well as
- * the inner and outer radius of the two spheres are given as
- * shown.
- *
- * The parameter @p N denotes how many cells are to be used for
- * this coarse triangulation. It defaults to zero, which tells
- * the function to chose the number itself; this, then, is done
- * such that the aspect ration of the resulting cells is as small
- * as possible. However, it should be mentioned that this
- * function does not work very well if the inner radius is much
- * smaller than the outer radius since only one layer of cells is
- * used in the radial direction.
- *
- * You need to attach a boundary object to the triangulation. A
- * suitable boundary class is provided as HyperSphereBoundary
- * in the library.
- *
- * <li> Half shells: This is a variant of the preceding domain,
- * where only one half of the shell is taken, defined by the first
- * coordinate having non-negative values. This class is useful in
- * computations with rotational symmetry, as then a 3d shell can be
- * modeled by a 2d half shell.
- *
- * <li> Slit domain: The slit domain is a variant of the hyper cube
- * domain. In two spatial dimensions, it is a square into which a
- * slit is sawed; if the initial square is though to be composed
- * of four smaller squares, then two of them are not connected
- * even though they are neighboring each other. Analogously, into
- * the cube in three spatial dimensions, a half-plane is sawed,
- * disconnecting four of the eight child-cubes from one of their
- * neighbors.
- *
- * <li> Hyper cube with cylindrical hole: This domain is a square on
- * the xy plane times the interval [0,L] with a cylindrical hole
- * in the middle. The parameters that can be set are the internal
- * radius, the external radius (inteded as the radius of the
- * biggest enclosed cylinder), the depth of the structure (used
- * only in three dimensions), and the number of repetitions along
- * the z direction.
- *
- * @image html cubes_hole.png
- *
- * </ul>
+ * This class provides a collection of functions for generating basic
+ * triangulations. Below, we try to provide some pictures in order to
+ * illustrate at least the more complex ones.
*
* Some of these functions receive a flag @p colorize. If this is
* set, parts of the boundary receive different boundary numbers,
* shell onto a grid of an airfoil, for example.
*
* @ingroup grid
- * @author Wolfgang Bangerth, Ralf Hartmann, Guido Kanschat, Stefan Nauber, Joerg Weimar, Yaqi Wang, 1998, 1999, 2000, 2001, 2002, 2003, 2006.
+ * @author Wolfgang Bangerth, Ralf Hartmann, Guido Kanschat, Stefan
+ * Nauber, Joerg Weimar, Yaqi Wang, 1998, 1999, 2000, 2001, 2002,
+ * 2003, 2006, 2007.
*/
class GridGenerator
{
* then producing the unit
* hypercube.
*
+ * @image html hyper_cubes.png
+ *
* See also
* subdivided_hyper_cube() for a
* coarse mesh consisting of
* Initialize the given
* triangulation with a
* hyperball, i.e. a circle or a
- * ball. See the general
- * documentation for a more
- * concise description. The
- * center of the hyperball
- * default to the origin, the
- * radius defaults to unity.
- *
- * The triangulation needs to be
- * void upon calling this
- * function.
+ * ball around <tt>center</tt>
+ * with given <tt>radius</tt>.
+ *
+ * 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
const Point<dim> ¢er = Point<dim>(),
const double radius = 1.);
+ /**
+ * This class produces a half
+ * hyper-ball around
+ * <tt>center</tt>, which
+ * contains four elements in 2d
+ * and 6 in 3d. The cut plane is
+ * perpendicular to the
+ * <i>x</i>-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>
+ static void half_hyper_ball (Triangulation<dim> &tria,
+ const Point<dim> ¢er = Point<dim>(),
+ const double radius = 1.);
+
/**
* Create a cylinder around the
* x-axis. The cylinder extends
* Initialize the given
* triangulation with a hyper-L
* consisting of exactly
- * <tt>2^dim-1</tt> cells. See the
- * general documentation for a
- * description of the
- * L-region. The limits default
- * to minus unity and unity.
+ * <tt>2^dim-1</tt> cells. It
+ * produces the hypercube with
+ * the interval [<i>left,right</i>] without
+ * the hypercube made out of the
+ * interval [<i>(a+b)/2,b</i>].
+ *
+ * @image html hyper_l.png
*
* The triangulation needs to be
* void upon calling this
/**
* Produce a 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. 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.
- *
- * The triangulation needs to be
- * void upon calling this
- * function.
+ * the region between two
+ * spheres around <tt>center</tt>,
+ * with given
+ * <tt>inner_radius</tt> and
+ * <tt>outer_radius</tt>.
+ *
+ * In 2D, the number
+ * <tt>n_cells</tt> 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 and 12 for the
+ * rhombic dodecahedron.
+ *
+ * @image html hypershell3d-6.png
+ * @image html hypershell3d-12.png
*
* This function is declared to
* exist for triangulations of
const double outer_radius,
const unsigned int n_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 @p
- * 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 @p
- * n_axial_cells.
- *
- * @note Although this function
- * is declared as a template, it
- * does not make sense in 1D and
- * 2D.
- *
- * @note The triangulation needs
- * to be void upon calling this
- * function.
- */
- template <int dim>
- static 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);
-
- /**
- * This class produces a half hyper-ball,
- * which contains four elements in 2d and
- * 6 in 3d. The orientation is such that
- * the cutting plane is the x=0.
- *
- * The triangulation needs to be
- * void upon calling this
- * function.
- *
- * 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>
- static void half_hyper_ball (Triangulation<dim> &tria,
- const Point<dim> ¢er = Point<dim>(),
- const double radius = 1.);
-
/**
* Produce a half hyper-shell,
* i.e. the space between two
* the resulting elements have
* the least aspect ratio.
*
- * The triangulation needs to be
- * void upon calling this
- * function.
- *
* At present, this function only
* exists in 2d.
*
const double outer_radius,
const unsigned int n_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 @p
+ * 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 @p
+ * n_axial_cells.
+ *
+ * @note Although this function
+ * is declared as a template, it
+ * does not make sense in 1D and
+ * 2D.
+ *
+ * @note The triangulation needs
+ * to be void upon calling this
+ * function.
+ */
+ template <int dim>
+ static 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);
+
/**
* This class produces a square
- * on the @p xy-plane with a
+ * on the <i>xy</i>-plane with a
* circular hole in the middle,
- * times the interval @p [0.L]
- * (only in 3d). It is
- * implemented in 2d and 3d, and
- * takes the following arguments:
+ * times the interval [0.L]
+ * (only in 3d).
+ *
+ * @image html cubes_hole.png
+ *
+ * It is implemented in 2d and
+ * 3d, and takes the following
+ * arguments:
*
- * - @p inner_radius: size of the
+ * @arg @p inner_radius: size of the
* internal hole
- * - @p outer_radius: size of the
+ * @arg @p outer_radius: size of the
* biggest enclosed cylinder
- * - @p L: extension on the @p z-direction
- * - @p repetitions: number of subdivisions
+ * @arg @p L: extension on the @p z-direction
+ * @arg @p repetitions: number of subdivisions
* along the @p z-direction
- * - @p colorize: wether to assign different
+ * @arg @p colorize: wether to assign different
* boundary indicators to different faces.
- * The colors are given in lexicografic
+ * 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).
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