The state \(y\) of an ode of 2nd order of the form \(M(x,v).a = F(x, v)\) with boundary conditions. More...

#include <OdeState.h>

Inheritance diagram for SurgSim::Math::OdeState:

Public Member Functions
	OdeState ()
	Default constructor.

virtual	~OdeState ()
	Destructor.

bool	operator== (const OdeState &state) const
	Comparison operator (equality test) More...

bool	operator!= (const OdeState &state) const
	Comparison operator (difference test) More...

virtual void	reset ()
	Resets the state. More...

virtual void	setNumDof (size_t numDofPerNode, size_t numNodes)
	Allocates the state for a given number of degrees of freedom. More...

size_t	getNumDof () const
	Retrieves the number of degrees of freedom. More...

size_t	getNumNodes () const
	Retrieves the number of nodes. More...

SurgSim::Math::Vector &	getPositions ()
	Retrieves all degrees of freedom's position (non-const version) More...

const SurgSim::Math::Vector &	getPositions () const
	Retrieves all degrees of freedom's position (const version) More...

const SurgSim::Math::Vector3d	getPosition (size_t nodeId) const
	Retrieves the position of a given node (const version) More...

SurgSim::Math::Vector &	getVelocities ()
	Retrieves all degrees of freedom's velocity (non-const version) More...

const SurgSim::Math::Vector &	getVelocities () const
	Retrieves all degrees of freedom's velocity (const version) More...

const SurgSim::Math::Vector3d	getVelocity (size_t nodeId) const
	Retrieves the velocity of a given node (const version) More...

void	addBoundaryCondition (size_t nodeId)
	Adds boundary conditions for a given node (fixes all the dof for this node) More...

void	addBoundaryCondition (size_t nodeId, size_t nodeDofId)
	Adds a boundary condition on a given dof of a given node (only 1 dof is fixed) More...

size_t	getNumBoundaryConditions () const
	Retrieves the number of boundary conditions. More...

const std::vector< size_t > &	getBoundaryConditions () const
	Retrieves all boundary conditions. More...

bool	isBoundaryCondition (size_t dof) const
	Queries if a specific dof is a boundary condition or not. More...

Vector *	applyBoundaryConditionsToVector (Vector *vector) const
	Apply boundary conditions to a given vector. More...

void	applyBoundaryConditionsToMatrix (Matrix *matrix, bool hasCompliance=true) const
	Apply boundary conditions to a given matrix. More...

void	applyBoundaryConditionsToMatrix (SparseMatrix *matrix, bool hasCompliance=true) const
	Apply boundary conditions to a given matrix. More...

void	addBoundaryConditionStaticDof (size_t nodeId, double value)
	Adds a boundary condition on the static dof of a given node (we consider here that each node has a single static dof) More...

size_t	getNumBoundaryConditionsStaticDof () const

const std::vector< std::pair< size_t, double > > &	getBoundaryConditionsStaticDof () const

void	setBoundaryConditionsStaticDof (const std::vector< std::pair< size_t, double >> &staticDof)
	Set all boundary conditions on static dofs. More...

void	changeBoundaryConditionStaticDof (size_t nodeId, double value)
	Set the value of an existing boundary condition on a static dof. More...

virtual bool	isValid () const
	Check if this state is numerically valid. More...

OdeState	interpolate (const OdeState &other, double t) const
	Returns the linear interpolated ODE state between this and other at parameter t. More...

Detailed Description

The state \(y\) of an ode of 2nd order of the form \(M(x,v).a = F(x, v)\) with boundary conditions.

This ode equation is solved as an ode of order 1 by defining the state vector \(y = \left(\begin{array}{c}x\\v\end{array}\right)\):

\[ y' = \left(\begin{array}{c} x' \\ v' \end{array}\right) = \left(\begin{array}{c} v \\ M(x, v)^{-1}.F(x, v) \end{array}\right) \]

Member Function Documentation

§ addBoundaryCondition() [1/2]

void SurgSim::Math::OdeState::addBoundaryCondition ( size_t nodeId )

Adds boundary conditions for a given node (fixes all the dof for this node)

Parameters

nodeId The node to set the boundary conditions on

§ addBoundaryCondition() [2/2]

void SurgSim::Math::OdeState::addBoundaryCondition	(	size_t	nodeId,
		size_t	nodeDofId
	)

Adds a boundary condition on a given dof of a given node (only 1 dof is fixed)

Parameters

nodeId	The node on which the boundary condition needs to be set
nodeDofId	The dof of the node to set as boundary condition

§ addBoundaryConditionStaticDof()

void SurgSim::Math::OdeState::addBoundaryConditionStaticDof	(	size_t	nodeId,
		double	value
	)

Adds a boundary condition on the static dof of a given node (we consider here that each node has a single static dof)

Parameters

nodeId	The node on which the boundary condition needs to be set
value	The boundary conidtion value that the static dof needs to be set on

Note: For example, this is fixing the twist angle of a Kircchoff model using a quasi-static update of the material frame.; i.e. the twist is not part of the dynamic DOF, but is still a static dof of the model.

§ applyBoundaryConditionsToMatrix() [1/2]

void SurgSim::Math::OdeState::applyBoundaryConditionsToMatrix	(	Matrix *	matrix,
		bool	hasCompliance = `true`
	)		const

Apply boundary conditions to a given matrix.

Parameters

matrix	The dense matrix to apply the boundary conditions on
hasCompliance	True if the fixed dofs should have a compliance of 1 with themselves in the matrix or not.

Note: hasCompliance is practical to remove all compliance, which is helpful when the compliance matrix is used; in an architecture of type LCP. It ensures that a separate constraint resolution will never violates the; boundary conditions.

§ applyBoundaryConditionsToMatrix() [2/2]

void SurgSim::Math::OdeState::applyBoundaryConditionsToMatrix	(	SparseMatrix *	matrix,
		bool	hasCompliance = `true`
	)		const

Apply boundary conditions to a given matrix.

Parameters

matrix	The sparse matrix to apply the boundary conditions on
hasCompliance	True if the fixed dofs should have a compliance of 1 with themselves in the matrix or not.

Note: hasCompliance is practical to remove all compliance, which is helpful when the compliance matrix is used; in an architecture of type LCP. It ensures that a separate constraint resolution will never violates the; boundary conditions.

§ applyBoundaryConditionsToVector()

Vector * SurgSim::Math::OdeState::applyBoundaryConditionsToVector ( Vector * vector ) const

Apply boundary conditions to a given vector.

Parameters

vector The vector to apply the boundary conditions on

Returns: The parameter vector. This enables chained use like \(U = K^1 * \text{applyBoundaryConditionsToVector}(x)\)

§ changeBoundaryConditionStaticDof()

void SurgSim::Math::OdeState::changeBoundaryConditionStaticDof	(	size_t	nodeId,
		double	value
	)

Set the value of an existing boundary condition on a static dof.

Parameters

nodeId	The node for which the static dof must be set
value	The value to set the static dof of the given node

Note: Does not do anything if the static dof boundary condition does not exists yet.

§ getBoundaryConditions()

const std::vector< size_t > & SurgSim::Math::OdeState::getBoundaryConditions ( ) const

Retrieves all boundary conditions.

Returns: All boundary conditions as a vector of dof ids

§ getBoundaryConditionsStaticDof()

const std::vector< std::pair< size_t, double > > & SurgSim::Math::OdeState::getBoundaryConditionsStaticDof ( ) const

Returns: All boundary conditions for statically defined Dof as a vector of dof ids

§ getNumBoundaryConditions()

size_t SurgSim::Math::OdeState::getNumBoundaryConditions ( ) const

Retrieves the number of boundary conditions.

Returns: The number of boundary conditions

§ getNumBoundaryConditionsStaticDof()

size_t SurgSim::Math::OdeState::getNumBoundaryConditionsStaticDof ( ) const

Returns: The number of boundary conditions for statically defined Dof

§ getNumDof()

size_t SurgSim::Math::OdeState::getNumDof ( ) const

Retrieves the number of degrees of freedom.

Returns: The number of DOF for this representation

§ getNumNodes()

size_t SurgSim::Math::OdeState::getNumNodes ( ) const

Retrieves the number of nodes.

Returns: The number of nodes for this representation

§ getPosition()

const SurgSim::Math::Vector3d SurgSim::Math::OdeState::getPosition ( size_t nodeId ) const

Retrieves the position of a given node (const version)

Parameters

nodeId The desired node id for which the position is requested (must be a valid id)

Returns: The position of the node nodeId

Note: Behavior undefined if the nodeId is not in the correct range [0 getNumNodes()-1]

§ getPositions() [1/2]

SurgSim::Math::Vector & SurgSim::Math::OdeState::getPositions ( )

Retrieves all degrees of freedom's position (non-const version)

Returns: Vector of collected DOF's position

§ getPositions() [2/2]

const SurgSim::Math::Vector & SurgSim::Math::OdeState::getPositions ( ) const

Retrieves all degrees of freedom's position (const version)

Returns: Vector of collected DOF's position

§ getVelocities() [1/2]

SurgSim::Math::Vector & SurgSim::Math::OdeState::getVelocities ( )

Retrieves all degrees of freedom's velocity (non-const version)

Returns: Vector of collected DOF's velocity

§ getVelocities() [2/2]

const SurgSim::Math::Vector & SurgSim::Math::OdeState::getVelocities ( ) const

Retrieves all degrees of freedom's velocity (const version)

Returns: Vector of collected DOF's velocity

§ getVelocity()

const SurgSim::Math::Vector3d SurgSim::Math::OdeState::getVelocity ( size_t nodeId ) const

Retrieves the velocity of a given node (const version)

Parameters

nodeId The desired node id for which the velocity is requested (must be a valid id)

Returns: The velocity of the node nodeId

Note: Behavior undefined if the nodeId is not in the correct range [0 getNumNodes()-1]

§ interpolate()

OdeState SurgSim::Math::OdeState::interpolate	(	const OdeState &	other,
		double	t
	)		const

Returns the linear interpolated ODE state between this and other at parameter t.

Parameters

other	the end point for the linear interpolation
t	the interpolation time

Returns: the interpolated state = this + (other - this) * t;

Note: All dof are independently linearly interpolated (This will not work correctly on rotation vectors where a slerp will be required.)

§ isBoundaryCondition()

bool SurgSim::Math::OdeState::isBoundaryCondition ( size_t dof ) const

Queries if a specific dof is a boundary condition or not.

Parameters

dof	The requested dof

Returns: True if dof is a boundary condition, False otherwise

Note: The behavior is undefined when dof is out of range [0 getNumBoundaryConditions()-1]

§ isValid()

bool SurgSim::Math::OdeState::isValid ( ) const

virtual

Check if this state is numerically valid.

Returns: True if all positions and velocities are valid numerical values, False otherwise

http://steve.hollasch.net/cgindex/coding/ieeefloat.html We use the IEEE754 standard stipulating that any arithmetic operation with a NaN operand will produce NaN and any sum of +-INF with a finite number or +-INF will produce +-INF. Therefore, testing if a vector contains only finite numbers can be achieve easily by summing all the values and testing if the result is a finite number or not.

§ operator!=()

bool SurgSim::Math::OdeState::operator!= ( const OdeState & state ) const

Comparison operator (difference test)

Parameters

state The state to compare it to

Returns: False if the 2 states are equal, True otherwise

§ operator==()

bool SurgSim::Math::OdeState::operator== ( const OdeState & state ) const

Comparison operator (equality test)

Parameters

state The state to compare it to

Returns: True if the 2 states are equal, False otherwise

§ reset()

void SurgSim::Math::OdeState::reset ( )

virtual

Resets the state.

Note: Simply set all positions/velocities to 0 and remove all boundary conditions

§ setBoundaryConditionsStaticDof()

void SurgSim::Math::OdeState::setBoundaryConditionsStaticDof ( const std::vector< std::pair< size_t, double >> & staticDof )

Set all boundary conditions on static dofs.

Parameters

staticDof The vector of static dof that must be set

Exceptions

SurgSim::Framework::AssertionFailure if a an item in staticDof does not have a valid nodeId (entry.first)

§ setNumDof()

void SurgSim::Math::OdeState::setNumDof	(	size_t	numDofPerNode,
		size_t	numNodes
	)

virtual

Allocates the state for a given number of degrees of freedom.

Parameters

numDofPerNode	The number of degrees of freedom per node to account for
numNodes	The number of nodes to account for

Note: This method clears all the data structures and remove all existing boundary conditions

The documentation for this class was generated from the following files:

SurgSim/Math/OdeState.h
SurgSim/Math/OdeState.cpp

Public Member Functions

Detailed Description

Member Function Documentation

§ addBoundaryCondition() [1/2]

§ addBoundaryCondition() [2/2]

§ addBoundaryConditionStaticDof()

§ applyBoundaryConditionsToMatrix() [1/2]

§ applyBoundaryConditionsToMatrix() [2/2]

§ applyBoundaryConditionsToVector()

§ changeBoundaryConditionStaticDof()

§ getBoundaryConditions()

§ getBoundaryConditionsStaticDof()

§ getNumBoundaryConditions()

§ getNumBoundaryConditionsStaticDof()

§ getNumDof()

§ getNumNodes()

§ getPosition()

§ getPositions() [1/2]

§ getPositions() [2/2]

§ getVelocities() [1/2]

§ getVelocities() [2/2]

§ getVelocity()

§ interpolate()

§ isBoundaryCondition()

§ isValid()

§ operator!=()

§ operator==()

§ reset()

§ setBoundaryConditionsStaticDof()

§ setNumDof()