Encapsulates the geometrical properties of a finite element in its local coordinate system. More...

Inheritance diagram for jive::geom::StdShape:

Public Types
typedef jem::String	String
	A string type. More...

typedef util::Vector	Vector
	A vector type. More...

typedef util::Matrix	Matrix
	A matrix type. More...

typedef util::Cubix	Cubix
	A three-dimensional array of doubles. More...

Public Member Functions
virtual String	name () const =0
	Returns the name of this shape. More...

virtual int	rank () const =0
	Returns the rank of this shape. More...

virtual int	nodeCount () const =0
	Returns the number of nodes attached to this shape. More...

virtual Matrix	getNodeCoords () const =0
	Returns the local node coordinates. More...

virtual bool	containsPoint (const Vector &u) const =0
	Tests whether a point is located within this shape. More...

virtual void	evalShapeFunctions (const Vector &h, const Vector &u) const =0
	Computes the shape functions in a given point. More...

virtual void	evalShapeFunctions (const Matrix &h, const Matrix &u) const
	Computes the shape functions in multiple points within this shape. More...

virtual void	evalShapeGradients (const Matrix &g, const Vector &u) const =0
	Computes the gradients of the shape functions in a specific point within this shape. More...

virtual void	evalShapeGradients (const Cubix &g, const Matrix &u) const
	Computes the gradients of the shape functions in multiple points within this shape. More...

Static Public Member Functions
static void	registerShape (StdShape *shape)
	Registers a standard shape. More...

static StdShape *	findShape (const String &name)
	Searches for a standard shape with a given name. More...

static void	encodeShape (jem::io::DataOutput &out, StdShape *shape)
	Writes a standard shape to a data output stream. More...

static StdShape *	decodeShape (jem::io::DataInput &in)
	Reads a standard shape from a data input stream. More...

Protected Member Functions
	StdShape ()
	Constructs an empty shape object. More...

virtual	~StdShape ()
	Protected destructor to invalidate delete expressions. More...

Detailed Description

#include <jive/geom/StdShape.h>

The abstract base class StdShape encapsulates the properties of a finite element in its local coordinate system. It can be used to get the local node coordinates of an element; to evaluate the shape functions of an element; and to evaluate the gradients of the shape functions in the local coordinate system.

In addition to a set of nodes and shape functions, a StdShape object has a name and a rank. The former is a string that may have any value as long as it is unique for each StdShape object. The latter is an integer number that equals the number of dimensions of the local coordinate system.

The StdShape class implements the Singleton pattern. This means that there exists only one StdShape object for each type of element. For instance, there is one StdShape object that captures the local geometrical properties of a triangle element with linear shape functions. This particular object can be obtained by calling the static member function getShape of the class StdLinearTriangle. The shape object representing other element types can be obtained in a similar way. You can use the helper class StdShapeInstance to create a single instance of a class derived from the StdShape class in a thread-safe way.

Since the number of StdShape objects in a program is limited to the number of element types that are used, there is no need to destroy and deallocate StdShape objects when they are no longer needed. In fact, they can not be destroyed because the destructor of the StdShape class is a protected member. This design eliminates the possibility that a program accidentaly accesses an invalid pointer to a StdShape object.

The StdShape class encapsulates a static table containing pointers to the StdShape objects that are used in a program. Access to this table is provided by the static member functions findShape() and registerShape(). The the first function returns a pointer to a shape object given its name, while the second function registers a standard shape object by inserting it into the table. You can use the helper class StdShapeRegisterAgent to automate the registration of shape objects.

The static shape table is used – among others – by the serialization functions encodeShape() and decodeShape(). The first writes the name of a StdShape object to a data output stream. The second reads the name of a StdShape object from a data input stream and then calls the function findShape() to obtain a pointer to that shape object.

See also: StdShapeInstance, StdShapeRegisterAgent, Shape

Member Typedef Documentation

typedef jem::String jive::geom::StdShape::String

The String type encapsulates the name of a StdShape object. It is just a convenient alias for jem::String.

typedef util::Vector jive::geom::StdShape::Vector

The Vector type represents a one-dimensional array of doubles. It is just a convenient alias for jive::util::Vector.

typedef util::Matrix jive::geom::StdShape::Matrix

The Matrix type represents a two-dimensional array of double. It is just an alias for jive::util::Matrix.

typedef util::Cubix jive::geom::StdShape::Cubix

The Cubix type is a three-dimensional array of doubles. It is simply an alias for jive::util::Cubix.

Constructor & Destructor Documentation

jive::geom::StdShape::StdShape ( )

protected

The default constructor does nothing; it simply creates an empty StdShape object.

virtual jive::geom::StdShape::~StdShape ( )

protectedvirtual

The destructor of the StdShape class is a protected member to ensure that a StdShape object can not be created on the stack and that a StdShape object can not be deleted. All classes derived from the StdShape class should also declare their destructor protected.

The destructor of the StdShape class does nothing.

Member Function Documentation

virtual String jive::geom::StdShape::name ( ) const

pure virtual

Returns the name of this StdShape object. The name can be any string as long as it is unique for each StdShape object. To avoid name conflicts, it is strongly recommended that the name of a StdShape is similar to the name of the element type represented by that shape object. For instance, if this shape object represents a triangle element with linear shape functions, then this function should return the string "LinearTriangle", or something similar.

Returns: The name of this shape.

virtual int jive::geom::StdShape::rank ( ) const

pure virtual

Returns the rank (number of dimensions) of the local coordinate system of this shape.

Returns: The rank of this shape.

Implemented in jive::geom::StdBezierShape, jive::geom::StdBoundary, jive::geom::StdPrism, jive::geom::StdPumShape, jive::geom::StdHyperCube, jive::geom::StdCube, jive::geom::StdLine, jive::geom::StdSquare, jive::geom::StdTetrahedron, jive::geom::StdTriangle, and jive::geom::StdWedge.

virtual int jive::geom::StdShape::nodeCount ( ) const

pure virtual

Returns the number of nodes attached to this shape.

Returns: The number of nodes.

virtual Matrix jive::geom::StdShape::getNodeCoords ( ) const

pure virtual

Returns a matrix containing the local coordinates of the nodes attached to this shape. If c denotes the returned matrix, then c(i,j) equals the i-th coordinate of the j-th node.

Returns: The local node coordinates.

virtual bool jive::geom::StdShape::containsPoint ( const Vector & u ) const

pure virtual

Returns true if the point specified by the local coordinate vector u lies within this shape, and false otherwise.

Parameters

u	- a local coordinate vector.

Precondition: u.size() == this->rank()

Returns: true if the specified point lies within this shape, and false otherwise.

Implemented in jive::geom::StdBezierShape, jive::geom::StdBoundary, jive::geom::StdPrism, jive::geom::StdPumShape, jive::geom::StdHyperCube, jive::geom::StdCube, jive::geom::StdLine, jive::geom::StdSquare, jive::geom::StdTetrahedron, jive::geom::StdTriangle, and jive::geom::StdWedge.

virtual void jive::geom::StdShape::evalShapeFunctions	(	const Vector &	h,
		const Vector &	u
	)		const

pure virtual

Fills the vector h with the values of the shape functions in a specific point within this shape: h[i] is set to the i-th shape function in that point. The vector u should contain the local coordinates of the point: u[i] should be equal to the i-th local coordinate.

Parameters

h	- a vector that will be filled with the values of the shape functions in a specific point within this shape.
u	- a vector containing the local coordinates of the specified point.

Precondition: h.size() == this->nodeCount() && u.size() == this->rank() && this->containsPoint ( u )

virtual void jive::geom::StdShape::evalShapeFunctions	(	const Matrix &	h,
		const Matrix &	u
	)		const

virtual

Fills the matrix h with the values of the shape functions in a set of points within this shape: h(i,j) is set to the i-th shape function in the j-th point. The matrix u should contain the local coordinates of the points: u(i,j) should be equal to the i-th local coordinate of the j-th point.

The implementation of this function provided by the StdShape class simply executes:

int j;
for ( j = 0; j < u.size(1); j++ ) {
  evalShapeFunctions ( h( slice(ALL), j ), u( slice(ALL), j ) );
}

Parameters

h	- a matrix that will be filled with the values of the shape functions in a specific set of points within this shape.
u	- a matrix containing the local coordinates of the specified points.

Precondition: h.size(0) == this->nodeCount() && u.size(0) == this->rank() && h.size(1) == u.size(1)

virtual void jive::geom::StdShape::evalShapeGradients	(	const Matrix &	g,
		const Vector &	u
	)		const

pure virtual

Fills the matrix g with the spatial derivatives of the shape functions in a specific point in this shape: g(i,j) is set to the i-th derivative of the j-th shape function in that point. The vector u should contain the local coordinates of that point: u[i] should be equal to the i-th local coordinate.

Note that the derivatives are computed in the local coordinate system.

Parameters

g	- a matrix that will be filled with the gradients of the shape functions.
u	- a local coordinate vector.

Precondition: g.size(0) == this->rank() && g.size(1) == this->nodeCount() && u.size() == this->rank()

virtual void jive::geom::StdShape::evalShapeGradients	(	const Cubix &	g,
		const Matrix &	u
	)		const

virtual

Fills the three-dimensional array g with the spatial derivatives of the shape functions in a specified set of points in this shape: g(i,j,k) is set to the i-th derivative of the j-th shape function in the k-th point. The matrix u should contain the local coordinates of the points: u(i,k) should be equal to the i-th local coordinate of the k-th point.

Note that the derivatives are computed in the local coordinate system.

The implementation of this function provided by the StdShape class basically executes the following code:

int k;
for ( k = 0; k < u.size(1); k++ ) {
  evalShapeGradients ( g( slice(ALL), slice(ALL), k ),
                       u( slice(ALL), k ) );
}

Parameters

g	- a three-dimensional array that will be filled with the gradients of the shape functions in a specific set of points.
u	- a matrix containing the local coordinates of the specified points.

Precondition: g.size(0) == this->rank() && g.size(1) == this->nodeCount() && u.size(0) == this->rank() && u.size(1) == g.size(2)

static void jive::geom::StdShape::registerShape ( StdShape * shape )

static

Registers the standard shape shape by inserting it into the static shape table that is encapsulated by the StdShape class. If the table already contains a shape with the same name as shape, then shape replaces the current object in the table. You can use the helper class StdShapeRegisterAgent to automate the registration of standard shapes.

This function is thread safe.

Parameters

shape - a pointer to a StdShape object.

Precondition: shape != NULL

Postcondition: findShape( shape->name() ) == shape

static StdShape* jive::geom::StdShape::findShape ( const String & name )

static

Returns a pointer to the shape object with name name. If no shape with that name has been registered – with the registerShape() function – then NULL is returned.

This function is thread safe.

Parameters

name	- the name of a standard shape.

Returns: A pointer to StdShape object with name name, or NULL if there is no shape with that name.

static void jive::geom::StdShape::encodeShape	(	jem::io::DataOutput &	out,
		StdShape *	shape
	)

static

Writes the name of the StdShape object shape to the data output stream out. The member function decodeShape() can be used to reverse this procedure.

Parameters

out	- a data output stream.
shape	- a pointer to a `StdShape` object.

Precondition: shape != NULL

Exceptions

jem::io::IOException - if an I/O error occurs.

static StdShape* jive::geom::StdShape::decodeShape ( jem::io::DataInput & in )

static

Reads the name of a standard shape from the input stream in, and returns a pointer to the StdShape object with that name.

Parameters

in	- a data input stream.

Exceptions

jem::io::SerializationException - if there is no StdShape object with the extracted name.

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation