Files
file	GraphicsHSet3D.cpp

file	GraphicsTripleSet.cpp

file	HSet2D.cpp

file	HSet3D.cpp

file	HSetMD.cpp

file	HSetND.cpp

file	TripleSet.cpp

file	GraphicsHSet3D.h

file	GraphicsTripleSet.h

file	GridSet.h

file	GridSets.h

file	HSet3D.h

file	HSetMD.hpp

file	HSetND.h

file	HSetND.hpp

Namespaces
	capd

Classes
class	capd::covrel::HSet< VectorT, IVectorT >
	this is an abstract class for h-sets - from paper by Gidea-Zgliczynski 'Covering relations ...' http://www.im.uj.edu.pl/~zgliczyn More...

class	capd::covrel::HSet2D< MatrixT, IMatrixT >
	This class provides a h-set in R^2 with one unstable and one stable direction. More...

struct	capd::covrel::CheckCoveringRelation2DParameters

class	capd::covrel::HSetMD< MatrixT, IMatrixT >
	This class provides a h-set in an arbitrary dimension. More...

class	capd::covrel::HSetWithCones< HSetT, QFormT >

class	capd::covrel::QuadraticForm< MatrixT >

class	capd::covrel::TripleSet
	TripleSet - a planar h-set with one unstable direction Authors: Implementation of derived classes and functions: Jaroslaw Dulak and Daniel Wilczak. More...

Enumerations
enum	capd::covrel::Side { capd::covrel::leftSide = -1, capd::covrel::bothSides = 0, capd::covrel::rightSide = 1 }

Functions
template<typename MatrixType >
bool	capd::covrel::isPositiveDefined (const MatrixType &A)

template<typename Map , typename HSet2D , typename QuadraticForm >
bool	capd::covrel::checkConesCondition (Map &f, const HSet2D &N1, const HSet2D &N2, const QuadraticForm &Q1, const QuadraticForm &Q2)
	Function checks cones condition. More...

template<typename Map , typename HSetWithCones >
bool	capd::covrel::checkConesCondition (Map &f, const HSetWithCones &N1, const HSetWithCones &N2, const capd::covrel::CheckCoveringRelation2DParameters &param=capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1))
	Function checks cones condition. More...

template<typename C0SetType , typename Map , typename DynSys , typename HSetWithCones >
bool	capd::covrel::checkCoveringRelationAndConesCondition (Map &f, DynSys &ds, const HSetWithCones &N1, const HSetWithCones &N2, const capd::covrel::CheckCoveringRelation2DParameters &param=capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1))
	Checks covering relation $N_1 \Rightarrow N_2$ and corresponding cones condition. More...

template<typename C0SetType , typename Map , typename DynSys , typename HSetWithCones >
bool	capd::covrel::checkCoveringRelationAndConesCondition (Map &f, const HSetWithCones &N1, const HSetWithCones &N2, const capd::covrel::CheckCoveringRelation2DParameters &param=capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1))
	Checks covering relation $N_1 \Rightarrow N_2$ and corresponding cones condition. More...

template<typename HSetType , typename SetType >
bool	capd::covrel::outside (const HSetType &hset, const SetType &set)
	verifies if `set` does not intersect the support of h-set More...

template<typename HSetType , typename SetType >
bool	capd::covrel::inside (const HSetType &hset, const SetType &set)
	verifies if `set` is inside the support of h-set More...

template<typename HSetType , typename SetType >
bool	capd::covrel::across (const HSetType &hset, const SetType &set)
	verifies if `set` does not intersect N^+ More...

template<typename HSetType , typename SetType >
bool	capd::covrel::mapaway (const HSetType &hset, const SetType &set)

template<typename HSetType , typename SetType >
bool	capd::covrel::onLeft (const HSetType &hset, const SetType &set)
	Checks if `set` in on the left side of the `hset` (works only in 2D) More...

template<typename HSetType , typename SetType >
bool	capd::covrel::onRight (const HSetType &hset, const SetType &set)
	Checks if `set` in on the right side of the `hset` (works only in 2D) More...

template<typename MatrixType , typename VectorType >
MatrixType	capd::covrel::convertColumnsTo (const VectorType &column1, const VectorType &column2)
	Converts two column vectors to given MatrixType. More...

template<typename C0SetType , typename DynSysT , typename MatrixT , typename IMatrixT >
bool	capd::covrel::checkCoveringRelation2D (DynSysT &dynsys, const capd::covrel::HSet2D< MatrixT, IMatrixT > &N1, const capd::covrel::HSet2D< MatrixT, IMatrixT > &N2, const CheckCoveringRelation2DParameters &param=CheckCoveringRelation2DParameters(1, 1, 1, 1))

template<typename Vector1 , typename Vector2 >
void	capd::covrel::embedVector (const Vector1 &v1, Vector2 &v2, const std::vector< typename Vector1::size_type > &d)

template<typename Vector1 , typename Vector2 >
void	capd::covrel::embedVector (const Vector1 &vector, Vector2 &result, size_t fullDimension, const std::vector< typename Vector1::size_type > &d)
	it embeds `vector` into a space of fullDimension in d[i] we pass coordiante where to put i-th coordinate of given vector other coordinates are set to 0. More...

template<typename Matrix1 , typename Matrix2 >
void	capd::covrel::embedMatrix (const Matrix1 &m1, Matrix2 &m2, const std::vector< typename Matrix1::size_type > &d)

template<typename IVector >
bool	capd::covrel::InSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	capd::covrel::InSide (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	capd::covrel::OutSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	capd::covrel::OutSide (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	capd::covrel::Across (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	capd::covrel::Across (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	capd::covrel::MapAway (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	capd::covrel::MapAway (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	capd::covrel::LeftSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	capd::covrel::LeftSide (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	capd::covrel::RightSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	capd::covrel::RightSide (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::HSet2D< MatrixT, IMatrixT >::gridLeftEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::HSet2D< MatrixT, IMatrixT >::gridRightEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::HSet2D< MatrixT, IMatrixT >::gridBottomEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::HSet2D< MatrixT, IMatrixT >::gridTopEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::HSet2D< MatrixT, IMatrixT >::gridSet (GridSet< IMatrix > &G, size_type grid1, size_type grid2, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::HSetMD< MatrixT, IMatrixT >::gridSet (GridSet< IMatrix > &G, const std::vector< size_type > &grid, const std::vector< size_type > &d, size_type totalDimension) const
	this procedure creates a grid of the whole h-set in the following form: G.center[i] + G.C * G.r d is a vector of indices of coordinates if the set is embeded in higher dimension More...

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::HSetMD< MatrixT, IMatrixT >::gridFace (GridSet< IMatrix > &grid, const std::vector< size_type > &gridSizes, const std::vector< size_type > &dimensions, size_type totalDimension, size_type coordinateToFix, Side side=bothSides) const
	in the `grid` it returns uniform grid of the given face More...

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::TripleSet::gridLeftEdge (GridSet< IMatrix > &G, size_type grid, size_type d1=0, size_type d2=1) const
	in the G it returns uniform grid of the left edge More...

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::TripleSet::gridRightEdge (GridSet< IMatrix > &G, size_type grid, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::TripleSet::gridBottomEdge (GridSet< IMatrix > &G, size_type grid, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::TripleSet::gridTopEdge (GridSet< IMatrix > &G, size_type grid, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	capd::covrel::TripleSet::gridSet (GridSet< IMatrix > &G, size_type grid1, size_type grid2, size_type d1=0, size_type d2=1) const

Detailed Description

Enumeration Type Documentation

◆ Side

enum capd::covrel::Side

Enumerator
leftSide
bothSides
rightSide

Function Documentation

◆ across()

template<typename HSetType , typename SetType >

bool capd::covrel::across	(	const HSetType &	hset,
		const SetType &	set
	)

inline

verifies if set does not intersect N^+

◆ Across() [1/2]

template<typename IVector >

bool capd::covrel::Across	(	const TripleSet &	S,
		const IVector &	IV,
		typename IVector::size_type	d1,
		typename IVector::size_type	d2
	)

◆ Across() [2/2]

bool capd::covrel::Across	(	const TripleSet &	S,
		const TripleSet::IntervalVector &	v
	)

inline

◆ checkConesCondition() [1/2]

template<typename Map , typename HSet2D , typename QuadraticForm >

bool capd::covrel::checkConesCondition	(	Map &	f,
		const HSet2D &	N1,
		const HSet2D &	N2,
		const QuadraticForm &	Q1,
		const QuadraticForm &	Q2
	)

Function checks cones condition.

Definition of cones condition: $\forall x,y\in |N1| Q2(f_c(x),f_c(y)) > Q1(x,y)$ , where f_c is map f expressed in coordinates of N1 and N2 Cones condition is satisfied if matrix $ V = Df_c^T * Q2 * Df_c - Q1 $ is positive defined.

Parameters

f	map R^n -> R^n
N1	first h-set
N2	second h-set
Q1	quadratic for associated with N1
Q2	quadratic for associated with N2

◆ checkConesCondition() [2/2]

template<typename Map , typename HSetWithCones >

bool capd::covrel::checkConesCondition	(	Map &	f,
		const HSetWithCones &	N1,
		const HSetWithCones &	N2,
		const capd::covrel::CheckCoveringRelation2DParameters &	param = `capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1)`
	)

Function checks cones condition.

Definition of cones condition: $\forall x,y\in |N1| Q2(f_c(x),f_c(y)) > Q1(x,y)$ , where f_c is map f expressed in coordinates of N1 and N2 Cones condition is satisfied if matrix $ V = Df_c^T * Q2 * Df_c - Q1 $ is positive defined.

Parameters

f	map R^n -> R^n
N1	first h-set with connes
N2	second h-set with connes
param	parameters of the computation

◆ checkCoveringRelation2D()

template<typename C0SetType , typename DynSysT , typename MatrixT , typename IMatrixT >

bool capd::covrel::checkCoveringRelation2D	(	DynSysT &	dynsys,
		const capd::covrel::HSet2D< MatrixT, IMatrixT > &	N1,
		const capd::covrel::HSet2D< MatrixT, IMatrixT > &	N2,
		const CheckCoveringRelation2DParameters &	param = `CheckCoveringRelation2DParameters(1, 1, 1, 1)`
	)

◆ checkCoveringRelationAndConesCondition() [1/2]

template<typename C0SetType , typename Map , typename DynSys , typename HSetWithCones >

bool capd::covrel::checkCoveringRelationAndConesCondition	(	Map &	f,
		const HSetWithCones &	N1,
		const HSetWithCones &	N2,
		const capd::covrel::CheckCoveringRelation2DParameters &	param = `capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1)`
	)

Checks covering relation $N_1 \Rightarrow N_2$ and corresponding cones condition.

See also: checkConesCondition

Parameters

f	map R^n -> R^n used to check cones condition
N1	first h-set with cones
N2	second h-set with cones

◆ checkCoveringRelationAndConesCondition() [2/2]

template<typename C0SetType , typename Map , typename DynSys , typename HSetWithCones >

bool capd::covrel::checkCoveringRelationAndConesCondition	(	Map &	f,
		DynSys &	ds,
		const HSetWithCones &	N1,
		const HSetWithCones &	N2,
		const capd::covrel::CheckCoveringRelation2DParameters &	param = `capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1)`
	)

Checks covering relation $N_1 \Rightarrow N_2$ and corresponding cones condition.

See also: checkConesCondition

Parameters

f	map R^n -> R^n used to check cones condition
ds	dynamical system used to move set in checking covering relation
N1	first h-set with cones
N2	second h-set with cones

◆ convertColumnsTo()

template<typename MatrixType , typename VectorType >

MatrixType capd::covrel::convertColumnsTo	(	const VectorType &	column1,
		const VectorType &	column2
	)

Converts two column vectors to given MatrixType.

Example: convertColumnsTo<DMatrix>( v1, v2);

◆ embedMatrix()

template<typename Matrix1 , typename Matrix2 >

void capd::covrel::embedMatrix	(	const Matrix1 &	m1,
		Matrix2 &	m2,
		const std::vector< typename Matrix1::size_type > &	d
	)

◆ embedVector() [1/2]

template<typename Vector1 , typename Vector2 >

void capd::covrel::embedVector	(	const Vector1 &	v1,
		Vector2 &	v2,
		const std::vector< typename Vector1::size_type > &	d
	)

◆ embedVector() [2/2]

template<typename Vector1 , typename Vector2 >

void capd::covrel::embedVector	(	const Vector1 &	vector,
		Vector2 &	result,
		size_t	fullDimension,
		const std::vector< typename Vector1::size_type > &	d
	)

it embeds vector into a space of fullDimension in d[i] we pass coordiante where to put i-th coordinate of given vector other coordinates are set to 0.

it resizes result vector (if needed).

◆ gridBottomEdge() [1/2]

template<typename IMatrix >

GridSet< IMatrix > & capd::covrel::TripleSet::gridBottomEdge	(	GridSet< IMatrix > &	G,
		size_type	grid,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

◆ gridBottomEdge() [2/2]

template<typename MatrixT , typename IMatrixT >

template<typename IMatrix >

template capd::covrel::GridSet< capd::IMatrix > & capd::covrel::HSet2D< MatrixT, IMatrixT >::gridBottomEdge< capd::IMatrix >	(	GridSet< IMatrix > &	G,
		size_type	gridSize,
		size_type	totalDimension = `2`,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

inline

◆ gridFace()

template<typename MatrixType , typename IMatrixType >

template<typename IMatrix >

GridSet< IMatrix > & capd::covrel::HSetMD< MatrixType, IMatrixType >::gridFace	(	GridSet< IMatrix > &	grid,
		const std::vector< size_type > &	gridSizes,
		const std::vector< size_type > &	dimensions,
		size_type	totalDimension,
		size_type	coordinateToFix,
		Side	side = `bothSides`
	)		const

in the grid it returns uniform grid of the given face

Parameters

gridSizes	number of pieces in the grid
coordinateToFix	which wall should be grided
side	which side of given coordinate should be grided : both, left or right
totalDimension	dimension of the space (can be bigger than 2 if we embed the set)
dimensions	if hset is embedded in higher dimension then we put first coordinate in dimensions[0] coordinate, second in dimensions[1], ... and the rest set to 0.

◆ gridLeftEdge() [1/2]

template<typename IMatrix >

GridSet< IMatrix > & capd::covrel::TripleSet::gridLeftEdge	(	GridSet< IMatrix > &	G,
		size_type	grid,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

in the G it returns uniform grid of the left edge

Parameters

grid	number of pieces in the grid
d1,d2	if hset is embeded in higher dimension than we put first coordinate in d1, second in d2 the rest sets to 0.

◆ gridLeftEdge() [2/2]

template<typename MatrixT , typename IMatrixT >

template<typename IMatrix >

template capd::covrel::GridSet< capd::IMatrix > & capd::covrel::HSet2D< MatrixT, IMatrixT >::gridLeftEdge< capd::IMatrix >	(	GridSet< IMatrix > &	G,
		size_type	gridSize,
		size_type	totalDimension = `2`,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

inline

◆ gridRightEdge() [1/2]

template<typename IMatrix >

GridSet< IMatrix > & capd::covrel::TripleSet::gridRightEdge	(	GridSet< IMatrix > &	G,
		size_type	grid,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

◆ gridRightEdge() [2/2]

template<typename MatrixT , typename IMatrixT >

template<typename IMatrix >

template capd::covrel::GridSet< capd::IMatrix > & capd::covrel::HSet2D< MatrixT, IMatrixT >::gridRightEdge< capd::IMatrix >	(	GridSet< IMatrix > &	G,
		size_type	gridSize,
		size_type	totalDimension = `2`,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

inline

◆ gridSet() [1/3]

template<typename MatrixType , typename IMatrixType >

template<typename IMatrix >

GridSet< IMatrix > & capd::covrel::HSetMD< MatrixType, IMatrixType >::gridSet	(	GridSet< IMatrix > &	G,
		const std::vector< size_type > &	grid,
		const std::vector< size_type > &	d,
		size_type	totalDimension
	)		const

this procedure creates a grid of the whole h-set in the following form: G.center[i] + G.C * G.r d is a vector of indices of coordinates if the set is embeded in higher dimension

◆ gridSet() [2/3]

template<typename IMatrix >

GridSet< IMatrix > & capd::covrel::TripleSet::gridSet	(	GridSet< IMatrix > &	G,
		size_type	grid1,
		size_type	grid2,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

◆ gridSet() [3/3]

template<typename MatrixT , typename IMatrixT >

template<typename IMatrix >

template capd::covrel::GridSet< capd::IMatrix > & capd::covrel::HSet2D< MatrixT, IMatrixT >::gridSet< capd::IMatrix >	(	GridSet< IMatrix > &	G,
		size_type	grid1,
		size_type	grid2,
		size_type	totalDimension = `2`,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

inline

◆ gridTopEdge() [1/2]

template<typename IMatrix >

GridSet< IMatrix > & capd::covrel::TripleSet::gridTopEdge	(	GridSet< IMatrix > &	G,
		size_type	grid,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

◆ gridTopEdge() [2/2]

template<typename MatrixT , typename IMatrixT >

template<typename IMatrix >

template capd::covrel::GridSet< capd::IMatrix > & capd::covrel::HSet2D< MatrixT, IMatrixT >::gridTopEdge< capd::IMatrix >	(	GridSet< IMatrix > &	G,
		size_type	gridSize,
		size_type	totalDimension = `2`,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

inline

◆ inside()

template<typename HSetType , typename SetType >

bool capd::covrel::inside	(	const HSetType &	hset,
		const SetType &	set
	)

inline

verifies if set is inside the support of h-set

◆ InSide() [1/2]

template<typename IVector >

bool capd::covrel::InSide	(	const TripleSet &	S,
		const IVector &	IV,
		typename IVector::size_type	d1,
		typename IVector::size_type	d2
	)

◆ InSide() [2/2]

bool capd::covrel::InSide	(	const TripleSet &	S,
		const TripleSet::IntervalVector &	v
	)

inline

◆ isPositiveDefined()

template<typename MatrixType >

bool capd::covrel::isPositiveDefined ( const MatrixType & A )

◆ LeftSide() [1/2]

template<typename IVector >

bool capd::covrel::LeftSide	(	const TripleSet &	S,
		const IVector &	IV,
		typename IVector::size_type	d1,
		typename IVector::size_type	d2
	)

◆ LeftSide() [2/2]

bool capd::covrel::LeftSide	(	const TripleSet &	S,
		const TripleSet::IntervalVector &	v
	)

inline

◆ mapaway()

template<typename HSetType , typename SetType >

bool capd::covrel::mapaway	(	const HSetType &	hset,
		const SetType &	set
	)

inline

◆ MapAway() [1/2]

template<typename IVector >

bool capd::covrel::MapAway	(	const TripleSet &	S,
		const IVector &	IV,
		typename IVector::size_type	d1,
		typename IVector::size_type	d2
	)

◆ MapAway() [2/2]

bool capd::covrel::MapAway	(	const TripleSet &	S,
		const TripleSet::IntervalVector &	v
	)

inline

◆ onLeft()

template<typename HSetType , typename SetType >

bool capd::covrel::onLeft	(	const HSetType &	hset,
		const SetType &	set
	)

inline

Checks if set in on the left side of the hset (works only in 2D)

◆ onRight()

template<typename HSetType , typename SetType >

bool capd::covrel::onRight	(	const HSetType &	hset,
		const SetType &	set
	)

inline

Checks if set in on the right side of the hset (works only in 2D)

◆ outside()

template<typename HSetType , typename SetType >

bool capd::covrel::outside	(	const HSetType &	hset,
		const SetType &	set
	)

inline

verifies if set does not intersect the support of h-set

◆ OutSide() [1/2]

template<typename IVector >

bool capd::covrel::OutSide	(	const TripleSet &	S,
		const IVector &	IV,
		typename IVector::size_type	d1,
		typename IVector::size_type	d2
	)

◆ OutSide() [2/2]

bool capd::covrel::OutSide	(	const TripleSet &	S,
		const TripleSet::IntervalVector &	v
	)

inline

◆ RightSide() [1/2]

template<typename IVector >

bool capd::covrel::RightSide	(	const TripleSet &	S,
		const IVector &	IV,
		typename IVector::size_type	d1,
		typename IVector::size_type	d2
	)

◆ RightSide() [2/2]

bool capd::covrel::RightSide	(	const TripleSet &	S,
		const TripleSet::IntervalVector &	v
	)

inline

Files

Namespaces

Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ Side

Function Documentation

◆ across()

◆ Across() [1/2]

◆ Across() [2/2]

◆ checkConesCondition() [1/2]

◆ checkConesCondition() [2/2]

◆ checkCoveringRelation2D()

◆ checkCoveringRelationAndConesCondition() [1/2]

◆ checkCoveringRelationAndConesCondition() [2/2]

◆ convertColumnsTo()

◆ embedMatrix()

◆ embedVector() [1/2]

◆ embedVector() [2/2]

◆ gridBottomEdge() [1/2]

◆ gridBottomEdge() [2/2]

◆ gridFace()

◆ gridLeftEdge() [1/2]

◆ gridLeftEdge() [2/2]

◆ gridRightEdge() [1/2]

◆ gridRightEdge() [2/2]

◆ gridSet() [1/3]

◆ gridSet() [2/3]

◆ gridSet() [3/3]

◆ gridTopEdge() [1/2]

◆ gridTopEdge() [2/2]

◆ inside()

◆ InSide() [1/2]

◆ InSide() [2/2]

◆ isPositiveDefined()

◆ LeftSide() [1/2]

◆ LeftSide() [2/2]

◆ mapaway()

◆ MapAway() [1/2]

◆ MapAway() [2/2]

◆ onLeft()

◆ onRight()

◆ outside()

◆ OutSide() [1/2]

◆ OutSide() [2/2]

◆ RightSide() [1/2]

◆ RightSide() [2/2]