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concepts::Hexahedron3d Class Reference
Geometry

A 3D cell: hexahedron. More...

#include <cell3D.hh>

Inheritance diagram for concepts::Hexahedron3d:
concepts::Cell3 concepts::Cell concepts::OutputOperator

Classes

struct  Index
 Subclass of Hexahedron3d representing its index. More...
 

Public Types

typedef uint index_type
 

Public Member Functions

Real3d center () const
 Returns the center of the cell. More...
 
Real3d chi (Real xi, Real eta, Real zeta) const
 The element map. More...
 
virtual Hexahedron3d * child (uint i)
 Returns a pointer to the ith child. More...
 
virtual const Hexahedron3d * child (uint i) const
 Returns a pointer to the ith child. More...
 
Hexahedron & connector () const
 Returns the connector. More...
 
virtual Real3d elemMap (const Real coord_local) const
 Element map from point local coordinates in 1D. More...
 
virtual Real3d elemMap (const Real2d &coord_local) const
 Element map from point local coordinates in 2D. More...
 
Real3d elemMap (const Real3d &coord_local) const
 Element map from point local coordinates in 3D. More...
 
MappingQuad3d * faceMap (uint face) const
 Returns the mapping of a face. More...
 
const Hex3dSubdivision * getStrategy () const
 Returns the subdivision strategy of this hexahedron. More...
 
bool hasChildren () const
 Returns true if there is a least one child. More...
 
MapReal3d hessian (const uint i, const concepts::Real3d &p) const
 
MapReal3d hessian (const uint i, const Real xi, const Real eta, const Real zeta) const
 
 Hexahedron3d (Hexahedron &cntr, const MappingHexahedron3d &map)
 Constructor. More...
 
MapReal3d jacobian (const concepts::Real3d &p) const
 
MapReal3d jacobian (const Real xi, const Real eta, const Real zeta) const
 Computes the Jacobian for xi, eta, zeta $\in [0,1]$. More...
 
Real jacobianDeterminant (const Real xi, const Real eta, const Real zeta) const
 Returns the determinant of the Jacobian for xi, eta, zeta $\in [0,1]$. More...
 
MapReal3d jacobianInverse (const Real xi, const Real eta, const Real zeta) const
 Returns the inverse of the Jacobian for xi, eta, zeta $\in [0,1]$. More...
 
const Level< 3 > & level () const
 Returns the level of the cell. More...
 
const MappingHexahedron3d * map () const
 Returns the element map. More...
 
void setStrategy (const Hex3dSubdivision *strategy=0) throw (StrategyChange)
 Sets the subdivision strategy of this hexahedron. More...
 
Real3d vertex (uint i) const
 Returns the coordinates of the ith vertex. More...
 
virtual ~Hexahedron3d ()
 

Static Public Attributes

static uint MAX_LEVEL
 

Protected Member Functions

virtual std::ostream & info (std::ostream &os) const
 Returns information in an output stream. More...
 

Private Member Functions

 Hexahedron3d (Hexahedron &cntr, MappingHexahedron3d *map, const Index &idx)
 Private constructor. More...
 

Private Attributes

Hexahedron3d * chld_
 Pointer to the first child. More...
 
Hexahedron & cntr_
 Reference to the hexahedron connector (topology) More...
 
Index idx_
 Index of this element. More...
 
Hexahedron3d * lnk_
 Pointer to a sibling. More...
 
MappingHexahedron3d * map_
 Pointer to the element map. More...
 
const Hex3dSubdivision * subdivStrategy_
 Subdivision strategy for the hexahedron. More...
 

Friends

class Hex3dSubdiv2x
 
class Hex3dSubdiv2y
 
class Hex3dSubdiv2z
 
class Hex3dSubdiv4x
 
class Hex3dSubdiv4y
 
class Hex3dSubdiv4z
 
class Hex3dSubdiv8
 
class Hex3dSubdivision
 
std::ostream & operator<< (std::ostream &os, const Hexahedron3d::Index &i)
 

Detailed Description

A 3D cell: hexahedron.

This cell contains a reference to the topological information of the hexahedron in cntr_. If a hexahedron is subdivided, two, four or eight new hexahedra are created. This happens automatically, if a child is requested, depending on the strategy that has been set.

The faces of the hexahedron have the following local coordinates in the element:

  • face 0 (bottom): z = 0
  • face 1 (front): y = 0
  • face 2 (right): x = 1
  • face 3 (back): y = 1
  • face 4 (left): x = 0
  • face 5 (top): z = 1
Examples
meshes.cc.

Definition at line 317 of file cell3D.hh.

Member Typedef Documentation

◆ index_type

typedef uint concepts::Hexahedron3d::index_type

Definition at line 333 of file cell3D.hh.

Constructor & Destructor Documentation

◆ Hexahedron3d() [1/2]

concepts::Hexahedron3d::Hexahedron3d ( Hexahedron &  cntr,
const MappingHexahedron3d &  map 
)

Constructor.

Takes the connector cntr and the element map map and creates a cell.

Parameters
cntrTopological information of the hexadron
mapElement map of the hexahedron

◆ ~Hexahedron3d()

virtual concepts::Hexahedron3d::~Hexahedron3d ( )
virtual

◆ Hexahedron3d() [2/2]

concepts::Hexahedron3d::Hexahedron3d ( Hexahedron &  cntr,
MappingHexahedron3d *  map,
const Index &  idx 
)
private

Private constructor.

Member Function Documentation

◆ center()

Real3d concepts::Hexahedron3d::center ( ) const
inlinevirtual

Returns the center of the cell.

Implements concepts::Cell3.

Definition at line 456 of file cell3D.hh.

◆ chi()

Real3d concepts::Hexahedron3d::chi ( Real  xi,
Real  eta,
Real  zeta 
) const

The element map.

Maps a point from the unit cube $[0,1]^3$ onto the element.

Returns
Point in 3D in physical coordinates.
Parameters
xi$\in [0,1]$
eta$\in [0,1]$
zeta$\in [0,1]$

◆ child() [1/2]

virtual Hexahedron3d* concepts::Hexahedron3d::child ( uint  i)
virtual

Returns a pointer to the ith child.

Children are created if they do not already exist.

Implements concepts::Cell3.

◆ child() [2/2]

virtual const Hexahedron3d* concepts::Hexahedron3d::child ( uint  i) const
virtual

Returns a pointer to the ith child.

Children are not created if they do not already exist, instead 0 is returned.

Implements concepts::Cell3.

◆ connector()

Hexahedron& concepts::Hexahedron3d::connector ( ) const
inlinevirtual

Returns the connector.

Implements concepts::Cell3.

Definition at line 382 of file cell3D.hh.

◆ elemMap() [1/3]

virtual Real3d concepts::Cell::elemMap ( const Real  coord_local) const
virtualinherited

Element map from point local coordinates in 1D.

Reimplemented in concepts::Edge2d, concepts::Edge1d, concepts::Sphere3d, and concepts::SphericalSurface3d.

◆ elemMap() [2/3]

virtual Real3d concepts::Cell::elemMap ( const Real2d &  coord_local) const
virtualinherited

Element map from point local coordinates in 2D.

Reimplemented in concepts::Edge2d, concepts::Edge1d, concepts::Sphere3d, concepts::SphericalSurface3d, concepts::Cell2, concepts::Quad3d, concepts::Triangle3d, concepts::InfiniteRect2d, concepts::Quad2d, and concepts::Triangle2d.

◆ elemMap() [3/3]

Real3d concepts::Hexahedron3d::elemMap ( const Real3d &  coord_local) const
inlinevirtual

Element map from point local coordinates in 3D.

Reimplemented from concepts::Cell.

Definition at line 394 of file cell3D.hh.

◆ faceMap()

MappingQuad3d* concepts::Hexahedron3d::faceMap ( uint  face) const

Returns the mapping of a face.

Constructs a cell for a face of this Hexahedron.

◆ getStrategy()

const Hex3dSubdivision* concepts::Hexahedron3d::getStrategy ( ) const
inline

Returns the subdivision strategy of this hexahedron.

If you want to find check against another strategy use 

hex.getStrategy() == Hex3dSubdiv4x::instance()

Definition at line 486 of file cell3D.hh.

◆ hasChildren()

bool concepts::Cell::hasChildren ( ) const
inlineinherited

Returns true if there is a least one child.

Definition at line 50 of file cell.hh.

◆ hessian() [1/2]

MapReal3d concepts::Hexahedron3d::hessian ( const uint  i,
const concepts::Real3d &  p 
) const

◆ hessian() [2/2]

MapReal3d concepts::Hexahedron3d::hessian ( const uint  i,
const Real  xi,
const Real  eta,
const Real  zeta 
) const

◆ info()

virtual std::ostream& concepts::Hexahedron3d::info ( std::ostream &  os) const
protectedvirtual

Returns information in an output stream.

Implements concepts::Cell.

◆ jacobian() [1/2]

MapReal3d concepts::Hexahedron3d::jacobian ( const concepts::Real3d &  p) const

◆ jacobian() [2/2]

MapReal3d concepts::Hexahedron3d::jacobian ( const Real  xi,
const Real  eta,
const Real  zeta 
) const

Computes the Jacobian for xi, eta, zeta $\in [0,1]$.

The Jacobian of a cell in the initial mesh is computed by the element map. The Jacobian of a subdivided cell is computed as follows. Let $H : \hat K \rightarrow \hat K'$ be the subdivision map in the reference coordinates (0,1)3 and $F_K : \hat K \rightarrow K$, $F_{K'} : \hat K \rightarrow K'$ the element maps of K and K' respectively. Then,

\[F_K : \hat K' \rightarrow K' \quad \text{and} \quad F_K \circ H = F_{K'}. \]

The subdivision map H in reference coordinates is

\[H : \vec\xi \mapsto \begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix} \vec \xi \]

where $a = 2^{-l_0}$, $b = 2^{-l_1}$, $c = 2^{-l_2}$ $\vec l = (l_0, l_1, l_2)$ is the level of the cell with respect to the cell in the initial mesh. The derivative of H is $dH = \begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix}$.

Then, the Jacobian of $F_{K'}$ is

\[dF_{K'} = dF_K \circ H \cdot dH. \]

The part $dF_K \circ H$ (without H) is computed by the element map and the part $\cdot dH$ is computed in jacobian().

◆ jacobianDeterminant()

Real concepts::Hexahedron3d::jacobianDeterminant ( const Real  xi,
const Real  eta,
const Real  zeta 
) const
inline

Returns the determinant of the Jacobian for xi, eta, zeta $\in [0,1]$.

Definition at line 447 of file cell3D.hh.

◆ jacobianInverse()

MapReal3d concepts::Hexahedron3d::jacobianInverse ( const Real  xi,
const Real  eta,
const Real  zeta 
) const
inline

Returns the inverse of the Jacobian for xi, eta, zeta $\in [0,1]$.

Definition at line 439 of file cell3D.hh.

◆ level()

const Level<3>& concepts::Hexahedron3d::level ( ) const
inline

Returns the level of the cell.

Definition at line 453 of file cell3D.hh.

◆ map()

const MappingHexahedron3d* concepts::Hexahedron3d::map ( ) const
inline

Returns the element map.

Definition at line 459 of file cell3D.hh.

◆ setStrategy()

void concepts::Hexahedron3d::setStrategy ( const Hex3dSubdivision *  strategy = 0)
throw (StrategyChange
)

Sets the subdivision strategy of this hexahedron.

If the parameter is set to 0 (or if the method is called without parameter) the strategy is set to the default (if not already set). The default subdivision strategy is subdivision into 8 children. 

  @param strategy Pointer to an instance of a subdivision strategy.
Exceptions
StrategyChangeif the change is not allowed (the change is not allowed if there are children present or the topological strategy is set).

◆ vertex()

Real3d concepts::Hexahedron3d::vertex ( uint  i) const
virtual

Returns the coordinates of the ith vertex.

Implements concepts::Cell3.

Friends And Related Function Documentation

◆ Hex3dSubdiv2x

friend class Hex3dSubdiv2x
friend

Definition at line 320 of file cell3D.hh.

◆ Hex3dSubdiv2y

friend class Hex3dSubdiv2y
friend

Definition at line 321 of file cell3D.hh.

◆ Hex3dSubdiv2z

friend class Hex3dSubdiv2z
friend

Definition at line 322 of file cell3D.hh.

◆ Hex3dSubdiv4x

friend class Hex3dSubdiv4x
friend

Definition at line 323 of file cell3D.hh.

◆ Hex3dSubdiv4y

friend class Hex3dSubdiv4y
friend

Definition at line 324 of file cell3D.hh.

◆ Hex3dSubdiv4z

friend class Hex3dSubdiv4z
friend

Definition at line 325 of file cell3D.hh.

◆ Hex3dSubdiv8

friend class Hex3dSubdiv8
friend

Definition at line 319 of file cell3D.hh.

◆ Hex3dSubdivision

friend class Hex3dSubdivision
friend

Definition at line 318 of file cell3D.hh.

◆ operator<<

std::ostream& operator<< ( std::ostream &  os,
const Hexahedron3d::Index &  i 
)
friend

Member Data Documentation

◆ chld_

Hexahedron3d* concepts::Hexahedron3d::chld_
private

Pointer to the first child.

The children are stored in a linked list.

Definition at line 502 of file cell3D.hh.

◆ cntr_

Hexahedron& concepts::Hexahedron3d::cntr_
private

Reference to the hexahedron connector (topology)

Definition at line 494 of file cell3D.hh.

◆ idx_

Index concepts::Hexahedron3d::idx_
private

Index of this element.

Definition at line 491 of file cell3D.hh.

◆ lnk_

Hexahedron3d* concepts::Hexahedron3d::lnk_
private

Pointer to a sibling.

Definition at line 497 of file cell3D.hh.

◆ map_

MappingHexahedron3d* concepts::Hexahedron3d::map_
private

Pointer to the element map.

Definition at line 505 of file cell3D.hh.

◆ MAX_LEVEL

uint concepts::Hexahedron3d::MAX_LEVEL
static

Definition at line 337 of file cell3D.hh.

◆ subdivStrategy_

const Hex3dSubdivision* concepts::Hexahedron3d::subdivStrategy_
private

Subdivision strategy for the hexahedron.

Definition at line 508 of file cell3D.hh.

The documentation for this class was generated from the following file:
Page URL: http://wiki.math.ethz.ch/bin/view/Concepts/WebHome
21 August 2020
© 2020 Eidgenössische Technische Hochschule Zürich