All Frameworks Class Hierarchy This Framework Indexes Previous Next

AdvancedMathematics CATMathIntervalND

Usage: you must use this class as is. You should never derive it.

public class CATMathIntervalND

Class representing a closed bounded interval of R^N.

A CATMathIntervalND is the set of the points whose each coordinate x_i ,i=0,..,N-1 is lying between two real bounds Low_i and High_i: Low_i <= x_i <= High_i. If there exists one coordinate for which Low_i > High_i, the interval is empty.

Constructor and Destructor Index

o CATMathIntervalND(): Constructs a CATMathIntervalND of dimension N=0, only containing 0.
o CATMathIntervalND(CATLONG32): Allocates a CATMathInterval of a given dimension.
o CATMathIntervalND(CATLONG32,double*): Constructs a CATMathIntervalND of a given dimension from the array of the boundaries of each coordinates.
o CATMathIntervalND(CATMathIntervalND&): Copy constructor.
o ~CATMathIntervalND(): Destructor.

Method Index

o Center(double*): Returns the center point of this CATMathIntervalND.
o ContainsPoint(double*): Tests whether this CATMathIntervalND contains a given point (of dimension N).
o ContainsPoint(double*,double&): Tests whether a point is inside this CATMathIntervalND at a given tolerance.
o GetCoords()
o GetCoords(): Returns the limitations of this CATMathIntervalND in an array.
o GetDimension()
o GetDimension(): Returns the dimension of this CATMathIntervalND.
o GetInterval(CATLONG32): Returns the CATMathInterval associated with a coordinate of this CATMathIntervalND.
o GetMax(CATLONG32): Returns the high limitation of a coordinate of this CATMathIntervalND.
o GetMin(CATLONG32): Returns the low limitation of a coordinate of this CATMathIntervalND.
o Intersection(double*,double*,double&,CATLONG32&): Intersects this CATMathIntervalND with a segment.
o IsEmpty(): Tests whether this CATMathIntervalND is empty.
o MinSquareDistance(double*,double*): Projects a given point onto this CATMathIntervalND.
o SetCoords(double*): Sets the limitations of this CATMathIntervalND with an array.
o SetInterval(CATLONG32,CATMathInterval&): Modifies the limitations associated with a coordinate of this CATMathIntervalND.
o SetMax(CATLONG32,double): Modifies the high limitation of a coordinate of this CATMathIntervalND.
o SetMin(CATLONG32,double): Modifies the low limitation of a coordinate of this CATMathIntervalND.
o Width(): Returns the sum of the interval width of each coordinate of this CATMathIntervalND.
o operator =(CATMathIntervalND&): Assignement operator.

Constructor and Destructor

o CATMathIntervalND

public CATMathIntervalND(

)

Constructs a CATMathIntervalND of dimension N=0, only containing 0.

o CATMathIntervalND

public CATMathIntervalND( const iN)

Allocates a CATMathInterval of a given dimension.
Note that this does not initialize the Low_i and High_i boundaries of each coordinates.

Parameters:

iN: The dimension of the interval.

o CATMathIntervalND

public CATMathIntervalND(	const	`iN`,
	const	`iMinMax`)

Constructs a CATMathIntervalND of a given dimension from the array of the boundaries of each coordinates.

Parameters:

iN: The dimension of the interval.
iMinMax: The array [2,iN] of the boundaries.
The domain is then [iMinMax[0], iMinMax[1]] X ... X [iMinMax[2iN-2], iMinMax[2iN-1]]

o CATMathIntervalND

public CATMathIntervalND( const iDomainToCopy)

Copy constructor.

o ~CATMathIntervalND

public virtual ~CATMathIntervalND(

)

Destructor.

Methods

o Center

public Center( ioCenter)

Returns the center point of this CATMathIntervalND.

Parameters:

oCenter: The array (already allocated) of the coordinates of the interval center.

o ContainsPoint

public virtual ContainsPoint( const iPoint)

Tests whether this CATMathIntervalND contains a given point (of dimension N).

Parameters:

iPoint: The array [N] of the coordinates of the point.

Returns:

The result of the test.
Legal values:

TRUE: if the point is inside the CATMathIntervalND.
FALSE: otherwise.

o ContainsPoint

public virtual ContainsPoint(	const	`iPoint`,
	const	`iTol`)

Tests whether a point is inside this CATMathIntervalND at a given tolerance.

Parameters:

iPoint: The array [N] of the coordinates of the point.

Returns:

The result of the test.
Legal values:

TRUE: if the point is inside the CATMathIntervalND defined by iTol.
FALSE: otherwise.

o GetCoords

public GetCoords(

)

o GetCoords

public GetCoords(

)

Returns the limitations of this CATMathIntervalND in an array.

Returns:: The array [2,N] of the limitations. The domain is then [iTab[0], iTab[1]] X ... X [iTab[2N-2], iTab[2N-1]].
As part of the class, the array must not be deleted.

o GetDimension

public GetDimension(

)

o GetDimension

public GetDimension(

)

Returns the dimension of this CATMathIntervalND.

Returns:: The dimension.

o GetInterval

public GetInterval( const iCoordIndex)

Returns the CATMathInterval associated with a coordinate of this CATMathIntervalND.

Parameters:

iCoordIndex: The index (0 <= iCoordIndex < N) of the coordinate.

Returns:

The corresponding interval.

o GetMax

public GetMax( const iCoordIndex)

Returns the high limitation of a coordinate of this CATMathIntervalND.

Parameters:

iCoordIndex: The index (0 <= iCoordIndex < N) of the coordinate.

Returns:

The high limitation of iCoordIndex.

o GetMin

public GetMin( const iCoordIndex)

Returns the low limitation of a coordinate of this CATMathIntervalND.

Parameters:

iCoordIndex: The index (0 <= iCoordIndex < N) of the coordinate.

Returns:

The low limitation of iCoordIndex.

o Intersection

public virtual Intersection(	const	`iFirstPoint`,
	const	`iSecondPoint`,
		`oWeight`,
		`oPosition`)

Intersects this CATMathIntervalND with a segment.

Parameters:

iFirstPoint

The array of the coordinates of the first point.

iSecondPoint

The array of the coordinates of the second point.

oWeight

The intersection parameter on the segment [iFirstPoint,iSecondPoint].
IntersectionPoint = iFirstPoint + oWeight * (iSecondPoint - iFirstPoint) .

oPosition

2*i + d
i being the index of the first coordinate of IntersectionPoint such as

either IntersectionPoint_i=Low_i and then d = 0
or IntersectionPoint_i=High_i and then d = 1

Returns:

TRUE: if this contains iFirstPoint and does not contain iSecondPoint.
FALSE: otherwise.

o IsEmpty

public virtual IsEmpty(

)

Tests whether this CATMathIntervalND is empty.
A CATMathIntervalND is empty if there exists one coordinate for which Low_i > High_i. Note that if Low_i = High_i, it does not make an empty interval.

Returns:

The result of the test.
Legal values:

TRUE: if the interval is empty.
FALSE: otherwise.

o MinSquareDistance

public virtual MinSquareDistance(	const	`iPointToProject`,
		`ioSolution`)

Projects a given point onto this CATMathIntervalND.

Parameters:

iPointToProject: The array of the coordinates of the point to project.
oSolution: The array (already allocated) of coordinates of the point realizing the minimum distance between iPointToProject and this. If iPointToProject belongs to this, oSolution = iPointToProject. Otherwise, oSolution is on this boundaries.

Returns:

The square of the distance between oSolution and this.

o SetCoords

public SetCoords( const iMinMax)

Sets the limitations of this CATMathIntervalND with an array.

Parameters:

iMinMax[2,N]: The array of the limitation.
The domain is then [iMinMax[0], iMinMax[1]] X ... X [iMinMax[2N-2], iMinMax[2N-1]]

o SetInterval

public SetInterval(	const	`iCoordIndex`,
	const	`iNewLimit`)

Modifies the limitations associated with a coordinate of this CATMathIntervalND.

Parameters:

iCoordIndex: The index (0 <= iCoordIndex < N) of the coordinate.
iNewLimit: The new corresponding interval.

o SetMax

public SetMax(	const	`iCoordIndex`,
	const	`iNewMax`)

Modifies the high limitation of a coordinate of this CATMathIntervalND.

Parameters:

iCoordIndex: The index (0 <= iCoordIndex < N) of the coordinate.
iNewMax: The new high limitation of iCoordIndex.

o SetMin

public SetMin(	const	`iCoordIndex`,
	const	`iNewMin`)

Modifies the low limitation of a coordinate of this CATMathIntervalND.

Parameters:

iCoordIndex: The index (0 <= iCoordIndex < N) of the coordinate.
iNewMin: The new low limitation of iCoordIndex.

o Width

public Width(

)

Returns the sum of the interval width of each coordinate of this CATMathIntervalND.

Returns:: The width: (High_1-Low_1) + ... + (High_N-Low_N).

o operator =

public operator =( const iToAffect)

Assignement operator.

This object is included in the file: CATMathIntervalND.h
If needed, your Imakefile.mk should include the module: CATAdvancedMathematics

AdvancedMathematics writeClassCharacteristic(); CATMathIntervalND

Constructor and Destructor Index

Method Index

Constructor and Destructor

Methods

AdvancedMathematics CATMathIntervalND