A 3D element map for a hexahedron. More...

#include <elementMaps3D.hh>

Inheritance diagram for concepts::MapHexahedron3d:

Collaboration diagram for concepts::MapHexahedron3d:

Public Member Functions
MapHexahedron3d *	clone () const
	Returns a copy of the map.
std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
MapReal3d	jacobian (const Real x, const Real y, const Real z) const
	Returns the jacobian of the element map $\left(\frac{\partial F_K}{\partial\vec\xi}\right) = \left\{\frac{\partial x^i}{\partial \xi_j}\right\}_{i,j=1}^3$ .
Real	jacobianDeterminant (const Real x, const Real y, const Real z) const
	Returns the determinant of the Jacobian.
MapReal3d	jacobianInverse (const Real x, const Real y, const Real z) const
	Computes the inverse of the jacobian: $\left(\frac{\partial F_K}{\partial\vec\xi}\right)^{-1} = \left\{\frac{\partial \xi_i}{\partial x^j}\right\}_{i,j=1}^3$ .
	MapHexahedron3d (const MapHexahedron3d &map)
	Copy constructor.
	MapHexahedron3d (const Real3d &vtx0, const Real3d &vtx1, const Real3d &vtx2, const Real3d &vtx3, const Real3d &vtx4, const Real3d &vtx5, const Real3d &vtx6, const Real3d &vtx7)
	Constructor.
	MapHexahedron3d (char *map, Real scX, Real scY, Real scZ)
	Constructor.
Real3d	operator() (Real x, Real y, Real z) const
	Returns a point in 3D mapped from the unit cube onto the element in the original mesh.
	~MapHexahedron3d ()
Private Member Functions
void	operator= (const MapHexahedron3d &)
	Private assignement operator.
Private Attributes
Real3d *	comp_
	Computed map.
uchar *	map_
	Parsed formula for the map.
Real	scx_
	Right border of the x parameter domain.
Real	scy_
	Right border of the y parameter domain.
Real	scz_
	Right border of the z parameter domain.
uint	sz_
	Length of the parsed formula.

Detailed Description

A 3D element map for a hexahedron.

The reference element is the unit cube.

There are two ways to fix the map of the hexahedron: give the mapping explicitly or give the eight corners and the map is computed internally.

When giving the eight corners of the hexahedron, they must be given in the correct order, ie. first the corners of the floor (in right screwed orientation pointing into the hexahedron) and then the corners of the ceiling (in right screwed orientation pointing out of the hexahedron).

The application operator maps a point from the unit square onto the physical domain taking into account the parameter domain given in the constructor.

Examples:: meshes.cc.

Definition at line 176 of file elementMaps3D.hh.

Constructor & Destructor Documentation

concepts::MapHexahedron3d::MapHexahedron3d	(	char *	map,
		Real	scX,
		Real	scY,
		Real	scZ
	)

Constructor.

The values of scX, scY and scZ are only for the map, they are not needed by the user for mapping a point from the reference element onto the Real element.

Parameters:

map	The element map for this triangle as a string, x, y and z are the allowed variables, the component are separated by a comma.
scX	The range of x is [0, scX].
scY	The range of y is [0, scY].
scZ	The range of z is [0, scZ].

concepts::MapHexahedron3d::MapHexahedron3d	(	const Real3d &	vtx0,
		const Real3d &	vtx1,
		const Real3d &	vtx2,
		const Real3d &	vtx3,
		const Real3d &	vtx4,
		const Real3d &	vtx5,
		const Real3d &	vtx6,
		const Real3d &	vtx7
	)

Constructor.

Takes the four physical corners of the hexahedron and computes the element map: $F_K : S \rightarrow K$ with $\vec x = F_K(\xi) = B \cdot \vec \xi + \vec b$ , where $\vec b = \mbox{vtx0}$ and $B = [ (\mbox{vtx1} - \vec b) (\mbox{vtx2} - \vec b) (\mbox{vtx3} - \vec b) ]$ .