Topological description of polytope cells (polygons and polyhedrons) in terms of their subcells. More...

Classes
struct	shards::Node
	Topological traits: Dimension = 0, Vertices = 0, Nodes = 0. More...

struct	shards::Particle
	Topological traits: Dimension = 0, Vertices = 1, Nodes = 1. More...

struct	shards::Line< NodeCount >
	Topological traits: Dimension = 1, Vertices = 2, Nodes = 2 or 3. More...

struct	shards::Beam< NodeCount >
	Topological traits: Dimension = 2, Edges = 1, Vertices = 2, and Nodes = 2 or 3. More...

struct	shards::ShellLine< NodeCount >
	Topological traits: Dimension = 2, Edges = 2, Vertices = 2, and Nodes = 2 or 3. More...

struct	shards::Triangle< NodeCount >
	Topological traits: Dimension = 2, Edges = 3, Vertices = 3, and Nodes = 3 or 6. More...

struct	shards::ShellTriangle< NodeCount >
	Topological traits: Dimension = 3, Sides = 2, Edges = 3, Vertices = 3, and Nodes = 3 or 6. More...

struct	shards::Quadrilateral< NodeCount >
	Topological traits: Dimension = 2, Edges = 4, Vertices = 4, and Nodes = 4, 8, or 9. More...

struct	shards::ShellQuadrilateral< NodeCount >
	Topological traits: Dimension = 2, Sides = 2, Edges = 4, Vertices = 4, and Nodes = 4, 8, or 9. More...

struct	shards::Tetrahedron< NodeCount >
	Topological traits: Dimension = 3, Sides = 4, Edges = 6, Vertices = 4, and Nodes = 4 or 10. More...

struct	shards::Pyramid< NodeCount >
	Topological traits: Dimension = 3, Sides = 5, Edges = 8, Vertices = 5, and Nodes = 5, 13, or 14. More...

struct	shards::Wedge< NodeCount >
	Topological traits: Dimension = 3, Sides = 5, Edges = 9, Vertices = 6, and Nodes = 6, 15, or 18. More...

struct	shards::Hexahedron< NodeCount >
	Topological traits: Dimension = 3, Sides = 6, Edges = 12, Vertices = 8, and Nodes = 8, 20, or 27. More...

class	shards::CellTopology
	Provide input checked access (in debug mode) to cell topology data and a procedure to create custom cell topologies. More...

struct	CellTopologyData
	A simple 'C' struct of cell topology attributes. More...

struct	CellTopologyData_Subcell
	Subcell information. More...

struct	CellTopologyData_Permutation
	Array of node permutations. More...

struct	shards::CellTopologyTraits< Dimension, Number_Vertex, Number_Node, EdgeList, EdgeMaps, FaceList, FaceMaps, PermutationMaps, PermutationPolarity >
	Compile-time traits for a cell topology. More...

Typedefs
typedef struct CellTopologyData	CellTopologyData
	Self-typedef.

Enumerations
enum	shards::ECellType { ALL_CELLS = 0, STANDARD_CELL, NONSTANDARD_CELL }
	Enumeration of cell types in Shards.

enum	shards::ETopologyType { ALL_TOPOLOGIES, BASE_TOPOLOGY, EXTENDED_TOPOLOGY }
	Enumeration of topology types in Shards.

enum	{ CELL_PERMUTATION_POLARITY_IRRELEVANT = 0, CELL_PERMUTATION_POLARITY_POSITIVE = 1, CELL_PERMUTATION_POLARITY_NEGATIVE = 2 }
	Values for the CellTopologyData_Permutation polarity.

Functions
template<>
const CellTopologyData *	shards::getCellTopologyData< Node > ()
	Singleton for Node topology.

template<>
const CellTopologyData *	shards::getCellTopologyData< Particle > ()
	Singleton for Particle topology.

template<>
const CellTopologyData *	shards::getCellTopologyData< Line< 2 > > ()
	Singleton for line topology with two nodes.

template<>
const CellTopologyData *	shards::getCellTopologyData< Line< 3 > > ()
	Singleton for line topology with three nodes.

template<>
const CellTopologyData *	shards::getCellTopologyData< Beam< 2 > > ()
	Singleton for beam topology with two nodes.

template<>
const CellTopologyData *	shards::getCellTopologyData< Beam< 3 > > ()
	Singleton for beam topology with three nodes.

template<>
const CellTopologyData *	shards::getCellTopologyData< ShellLine< 2 > > ()
	Singleton for shell-line topology with two nodes.

template<>
const CellTopologyData *	shards::getCellTopologyData< ShellLine< 3 > > ()
	Singleton for shell-line topology with three nodes.

template<>
const CellTopologyData *	shards::getCellTopologyData< Triangle< 3 > > ()
	Return CellTopologyData singleton for the Triangle<3>

template<>
const CellTopologyData *	shards::getCellTopologyData< Triangle< 6 > > ()
	Return CellTopologyData singleton for the Triangle<6>

template<>
const CellTopologyData *	shards::getCellTopologyData< Triangle< 4 > > ()
	Return CellTopologyData singleton for the Triangle<4> (Face of Tet8)

template<>
const CellTopologyData *	shards::getCellTopologyData< ShellTriangle< 3 > > ()
	Return CellTopologyData singleton for the ShellTriangle<3>

template<>
const CellTopologyData *	shards::getCellTopologyData< ShellTriangle< 6 > > ()
	Return CellTopologyData singleton for the ShellTriangle<6>

template<>
const CellTopologyData *	shards::getCellTopologyData< Quadrilateral< 4 > > ()
	Return CellTopologyData singleton for the Quadrilateral<4>

template<>
const CellTopologyData *	shards::getCellTopologyData< Quadrilateral< 8 > > ()
	Return CellTopologyData singleton for the Quadrilateral<8>

template<>
const CellTopologyData *	shards::getCellTopologyData< Quadrilateral< 9 > > ()
	Return CellTopologyData singleton for the Quadrilateral<9>

template<>
const CellTopologyData *	shards::getCellTopologyData< ShellQuadrilateral< 4 > > ()
	Return CellTopologyData singleton for the ShellQuadrilateral<4>

template<>
const CellTopologyData *	shards::getCellTopologyData< ShellQuadrilateral< 8 > > ()
	Return CellTopologyData singleton for the ShellQuadrilateral<8>

template<>
const CellTopologyData *	shards::getCellTopologyData< ShellQuadrilateral< 9 > > ()
	Return CellTopologyData singleton for the ShellQuadrilateral<9>

template<>
const CellTopologyData *	shards::getCellTopologyData< Tetrahedron< 4 > > ()
	Return CellTopologyData singleton for the Tetrahedron<4>

template<>
const CellTopologyData *	shards::getCellTopologyData< Tetrahedron< 10 > > ()
	Return CellTopologyData singleton for the Tetrahedron<10>

template<>
const CellTopologyData *	shards::getCellTopologyData< Tetrahedron< 8 > > ()
	Return CellTopologyData singleton for the Tetrahedron<8>

template<>
const CellTopologyData *	shards::getCellTopologyData< Tetrahedron< 11 > > ()
	Return CellTopologyData singleton for the Tetrahedron<11>

template<>
const CellTopologyData *	shards::getCellTopologyData< Pyramid< 5 > > ()
	Return CellTopologyData singleton for the Pyramid<5>

template<>
const CellTopologyData *	shards::getCellTopologyData< Pyramid< 13 > > ()
	Return CellTopologyData singleton for the Pyramid<13>

template<>
const CellTopologyData *	shards::getCellTopologyData< Pyramid< 14 > > ()
	Return CellTopologyData singleton for the Pyramid<14>

template<>
const CellTopologyData *	shards::getCellTopologyData< Wedge< 6 > > ()
	Return CellTopologyData singleton for the Wedge<6>

template<>
const CellTopologyData *	shards::getCellTopologyData< Wedge< 15 > > ()
	Return CellTopologyData singleton for the Wedge<15>

template<>
const CellTopologyData *	shards::getCellTopologyData< Wedge< 18 > > ()
	Return CellTopologyData singleton for the Wedge<18>

template<>
const CellTopologyData *	shards::getCellTopologyData< Hexahedron< 8 > > ()
	Return CellTopologyData singleton for the Hexahedron<8>

template<>
const CellTopologyData *	shards::getCellTopologyData< Hexahedron< 20 > > ()
	Return CellTopologyData singleton for the Hexahedron<20>

template<>
const CellTopologyData *	shards::getCellTopologyData< Hexahedron< 27 > > ()
	Return CellTopologyData singleton for the Hexahedron<27>

std::ostream &	shards::operator<< (std::ostream &, const CellTopology &)
	Overloaded << operator for CellTopologyData objects. More...

std::string	shards::ECellTypeToString (ECellType cellType)

std::string	shards::ETopologyTypeToString (ETopologyType topologyType)

void	shards::getTopologies (std::vector< shards::CellTopology > &topologies, const unsigned cellDim=4, const ECellType cellType=ALL_CELLS, const ETopologyType topologyType=ALL_TOPOLOGIES)
	Returns an std::vector with all cell topologies that meet the specified selection flags. More...

int	shards::isPredefinedCell (const CellTopology &cell)
	Checks if the cell topology is predefined in shards. More...

template<typename id_type >
int	shards::findPermutation (const CellTopologyData &top, const id_type const expected_node, const id_type const actual_node)

template<typename id_type >
int	shards::findPermutation (const CellTopology &top, const id_type const expected_node, const id_type const actual_node)

void	shards::badCellTopologyKey (const unsigned dimension, const unsigned face_count, const unsigned edge_count, const unsigned vertex_count, const unsigned node_count)
	Generates detailed message if one or more input parameters are out of their admissible bounds. More...

unsigned	shards::cellTopologyKey (const unsigned dimension, const unsigned face_count, const unsigned edge_count, const unsigned vertex_count, const unsigned node_count)
	Generate integer key from topological dimensions. More...

bool	shards::operator== (const CellTopology &left, const CellTopology &right)

bool	shards::operator< (const CellTopology &left, const CellTopology &right)

bool	shards::operator!= (const CellTopology &left, const CellTopology &right)

int	mapCellFaceEdge (const CellTopologyData *cell_topology, unsigned face_ordinal, unsigned face_edge_ordinal)
	Map a cell->face->edge ordinal to the cell->edge ordinal. Return -1 for erroneous input.

template<class Traits >
const CellTopologyData *	shards::getCellTopologyData ()
	Return a CellTopology singleton for the given cell topology traits.

Detailed Description

Topological description of polytope cells (polygons and polyhedrons) in terms of their subcells.

Polytope (2D polygon or 3D polyhedron)

A cell topology defines a polytope in terms of its vertex, edge, and side connectivity. However, a cell topology does not define a geometric realization of that polytope - it does not associate spatial coordinates with any of the vertices.

Dimension (of the polytope)

The dimension of cell topology is the smallest spatial dimension in which that cell can be realized. For example, a tetrahedron or quadrilateral shell can only be realized in a 3D space.

Base and Extended Cell Topologies

The base cell topology of a polytope associates exactly one ${Cell}^{0}$ subcell with each vertex of the polytope. These vertices are given a canonical ordering from which vertex-ordinals are defined. For example, the vertex-ordinals for quadrilateral are defined counter-clockwise around the quadrilateral as (0,1,2,3). An extended cell topology is defined associating additional ${Cell}^{0}$ subcells with the polytope's edges, sides, or interior. These additional ${Cell}^{0}$ subcells are always ordered after the vertex subcells.

Node, Edge, Side, and Element Cells

A Node is a ${Cell}^{0}$ subcell
An Edge is a ${Cell}^{1}$ subcell of a parent ${Cell}^{D}$ , where
A Side is a ${Cell}^{D-1}$ subcell of a parent ${Cell}^{D}$ , where
An Element is a ${Cell}^{D}$ in an D-dimensional space

Subcell Orientation

A subcell ${Cell}^{d}$ of a parent ${Cell}^{D}$ , where $ 0 < d < D $ , has vertices that are associated with the parent cell's vertices. This association defines a map from the subcell's vertex-ordinals to the parent's vertex-ordinals. For example, the four edge subcells of a quadrilateral have a vertex-ordinal map of ( (0,1), (1,2), (2,3), (3,0) ).

Function Documentation

std::ostream& shards::operator<<	(	std::ostream &	,
		const CellTopology &
	)

Overloaded << operator for CellTopologyData objects.

Overloaded << operator for CellTopology objects.

void shards::getTopologies	(	std::vector< shards::CellTopology > &	topologies,
		const unsigned	cellDim = `4`,
		const ECellType	cellType = `ALL_CELLS`,
		const ETopologyType	topologyType = `ALL_TOPOLOGIES`
	)

Returns an std::vector with all cell topologies that meet the specified selection flags.

Parameters

topologies	[out] - vector with all topologies that
cellDim	[in] - cell dimension; 0, 1, 2, 3, or 4 (default = all dimensions)
cellType	[in] - cell type: default = ALL_CELLS
topologyType	[in] - topology type: default = ALL_TOPOLOGIES

int shards::isPredefinedCell ( const CellTopology & cell )

Checks if the cell topology is predefined in shards.

Parameters

cell	[in] - cell topology

Returns: 1 if the cell topology is defined in shards, 0 if it is a custom, user-defined cell-topology

void shards::badCellTopologyKey	(	const unsigned	dimension,
		const unsigned	face_count,
		const unsigned	edge_count,
		const unsigned	vertex_count,
		const unsigned	node_count
	)

Generates detailed message if one or more input parameters are out of their admissible bounds.

Parameters

dimension	[in] - maximum value = 7
face_count	[in] - maximum value = 63
edge_count	[in] - maximum value = 63
vertex_count	[in] - maximum value = 63
node_count	[in] - maximum value = 1023

unsigned shards::cellTopologyKey	(	const unsigned	dimension,
		const unsigned	face_count,
		const unsigned	edge_count,
		const unsigned	vertex_count,
		const unsigned	node_count
	)

inline

Generate integer key from topological dimensions.

Parameters

dimension	[in] - maximum value = 7 (3 bits)
face_count	[in] - maximum value = 63 (6 bits)
edge_count	[in] - maximum value = 63 (6 bits)
vertex_count	[in] - maximum value = 63 (6 bits)
node_count	[in] - maximum value = 1023 (10 bits) The key uses all but the first bit in a 32 bit unsigned.

Definition at line 649 of file Shards_CellTopology.hpp.

Classes

Typedefs

Enumerations

Functions

Detailed Description

Polytope (2D polygon or 3D polyhedron)

Dimension (of the polytope)

Base and Extended Cell Topologies

Node, Edge, Side, and Element Cells

Subcell Orientation

Function Documentation