All Frameworks Class Hierarchy This Framework Indexes Previous Next

AdvancedMathematics CATMathInterval

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

public class CATMathInterval

Class representing a closed bounded interval of R.

A CATMathInterval is the set of the reals x lying between two real bounds Low and High: Low <= x <= High. If Low > High, the interval is empty.

Constructor and Destructor Index

o CATMathInterval(): Constructs a CATMathInterval with Low = High = 0.
o CATMathInterval(CATMathInterval&): Copy Constructor.
o CATMathInterval(double&,double&): Constructs a CATMathInterval.

Method Index

o Center(): Returns the center of this CATMathInterval.
o ClosestPeriodicEndpoint(double&,double): Retrieves the closest external point of this CATMathInterval among those obtained by all the successive translations of length + or -iPeriod.
o DistanceTo(double&)
o DistanceTo(double&): Return the distance between this CATMathInterval and a point.
o GetMax(): Returns the high limitation of this CATMathInterval.
o GetMin(): Returns the low limitation of this CATMathInterval.
o InPeriodicTrim(double,double,double): Tests whether a point belongs to this CATMathInterval after a given number of translation of length + or -iPeriod+iTolerance.
o IsEmpty(): Tests if this CATMathInterval is empty.
o IsIncludedIn(CATMathInterval&): Tests if this CATMathInterval is included into an other one.
o IsIncludedIn(CATMathInterval&,double): Tests if this CATMathInterval is included into an other one at a given absolute tolerance.
o Norm()
o Norm(): Returns the norm of this CATMathInterval.
o PeriodicResidue(double&): Translates a point to locate it at this CATMathInterval point such that the distance between these two points is a multiple of this CATMathInterval width.
o SetMax(double&): Modifies the high limitation of this CATMathInterval.
o SetMin(double&): Modifies the low limitation of this CATMathInterval.
o Sign(): Tests the relative position of this CATMathInterval with regards to 0.
o Width(): Returns the width of this CATMathInterval.
o operator &&(CATMathInterval&,CATMathInterval&): Returns the interval resulting of the intersection of two CATMathIntervals.
o operator *(double&,CATMathInterval&): Defines the multiplication of a CATMathInterval with a scalar.
o operator *(CATMathInterval&,double&): Defines the multiplication of a scalar with a CATMathInterval.
o operator *=(CATMathInterval&,double): Defines the *= operator of a CATMathInterval with a scalar.
o operator +(double&,CATMathInterval&): Defines the scalar addition with a CATMathInterval.
o operator +(CATMathInterval&,double&): Defines the addition of a CATMathInterval with a scalar.
o operator +(CATMathInterval&,CATMathInterval&): Unary plus operator.
o operator +=(CATMathInterval&,double&): Defines the += operator of a CATMathInterval with a scalar.
o operator +=(CATMathInterval&,CATMathInterval&): Addition assignment operator.
o operator -(CATMathInterval&): Defines the opposite of a CATMathInterval.
o operator -(double&,CATMathInterval&): Defines the scalar substraction with a CATMathInterval.
o operator -(CATMathInterval&,double&): Defines the scalar substraction with a CATMathInterval.
o operator -(CATMathInterval&,CATMathInterval&): Subtraction operator.
o operator -=(CATMathInterval&,double&): Defines the -= operator of a CATMathInterval with a scalar.
o operator -=(CATMathInterval&,CATMathInterval&): Subtraction assignment operator.
o operator /(CATMathInterval&,double&): Defines the division of a CATMathInterval by a scalar.
o operator /(CATMathInterval&,CATMathInterval&): Defines the dividion of a CATMathInterval by another one.
o operator ||(CATMathInterval&,CATMathInterval&): Returns the interval resulting of the union of two CATMathIntervals.

Constructor and Destructor

o CATMathInterval

public CATMathInterval(

)

Constructs a CATMathInterval with Low = High = 0.

o CATMathInterval

public CATMathInterval( const iToCopy)

Copy Constructor.

o CATMathInterval

public CATMathInterval(	const	`iLow`,
	const	`iHigh`)

Constructs a CATMathInterval.
If iLow > iHigh, the interval is empty.

Methods

o Center

public Center(

)

Returns the center of this CATMathInterval.

Returns:: The center ((High + Low)*0.5).

o ClosestPeriodicEndpoint

public ClosestPeriodicEndpoint(		`ioPoint`,
	const	`iPeriod`)

Retrieves the closest external point of this CATMathInterval among those obtained by all the successive translations of length + or -iPeriod.

Parameters:

iPoint: The initial point (input) and the resulting one (output).
iPeriod: The period.

Returns:

The distance between this point and the initial one.

o DistanceTo

public DistanceTo( const iPoint)

o DistanceTo

public DistanceTo( const iPoint)

Return the distance between this CATMathInterval and a point.

Parameters:

iPoint: The value to which the distance is computed.

Returns:

0: if the point is included into this.
iPoint-High: if the point does not belong to this and iPoint >= High
Low-iPoint: if the point does not belong to this and Low>=iPoint

Returns:

o GetMax

public GetMax(

)

Returns the high limitation of this CATMathInterval.

Returns:: The high limitation.

o GetMin

public GetMin(

)

Returns the low limitation of this CATMathInterval.

Returns:: The low limitation.

o InPeriodicTrim

public InPeriodicTrim(	const	`iPoint`,
	const	`iPeriod`,
	const	`iTolerance`	`= 0.0`)

Tests whether a point belongs to this CATMathInterval after a given number of translation of length + or -iPeriod+iTolerance.
The difference with the preceding method, is that iPeriod is greater than the width of the CATMathInterval (the CATMathInterval may be seen as a trimmed interval of the [0,iPeriod] one.)

Parameters:

iPoint: The tested point.
iPeriod: A value greater than the with of this CATMathInterval.
iTol: The tolerance at which the tests is run.

Returns:

TRUE if iPoint is in the interval with regards to iPeriod, FALSE otherwise.

o IsEmpty

public IsEmpty(

)

Tests if this CATMathInterval is empty.

Returns:: The result of the test.
Legal values: 1 if Low > High, 0 otherwise.

o IsIncludedIn

public IsIncludedIn( const iOther)

Tests if this CATMathInterval is included into an other one.

Parameters:

iOther: The other interval.

Returns:

The result of the test.
Legal values:

1: if this is included.
0: otherwise

.
An empty interval is always included into another one, except if this other one is empty too.

o IsIncludedIn

public IsIncludedIn(	const	`iOther`,
	const	`iTol`)

Tests if this CATMathInterval is included into an other one at a given absolute tolerance.

Parameters:

iOther: The other interval
iTol: The tolerance at which the tests is run.

Returns:

The result of the test.
Legal values:

1: if this is included.
0: otherwise

.
An empty interval is always included into another one, except if this other one is empty too.

o Norm

public Norm(

)

o Norm

public Norm(

)

Returns the norm of this CATMathInterval.
This norm may be negative if the interval is empty.

Returns:

The norm.

High: if Low > 0.
-Low: if High < 0.
High: if High >= -Low(and the interval is not empty)
-Low: High < -Low(and the interval is not empty)

Returns:

The norm.

o PeriodicResidue

public PeriodicResidue( ioToTranslate)

Translates a point to locate it at this CATMathInterval point such that the distance between these two points is a multiple of this CATMathInterval width.
This is useful in case of periodic functions to find the parameter of the fundamental interval corresponding to a given point.

Parameters:

ioToTranslate: The point to translate (in input), and the resulting one (in output).

o SetMax

public SetMax( const iNewHigh)

Modifies the high limitation of this CATMathInterval.

Parameters:

iNewHigh: The new value of the high limitation.

o SetMin

public SetMin( const iNewLow)

Modifies the low limitation of this CATMathInterval.

Parameters:

iNewLow: The new value of the low limitation.

o Sign

public Sign(

)

Tests the relative position of this CATMathInterval with regards to 0.

Returns:

The result of the test.
Legal values:

1: if Low > 0 or the interval is empty.
-1: if Low < 0 and the interval is not empty.
0: otherwise. In this case, 0 belongs to the interval, which is not empty

o Width

public Width(

)

Returns the width of this CATMathInterval.

Returns:: The width ((High - Low)).

o operator &&

public operator &&(	const	`i1`,
	const	`i2`)

Returns the interval resulting of the intersection of two CATMathIntervals.

o operator *

public operator *(	const	`iScalar`,
	const	`i`)

Defines the multiplication of a CATMathInterval with a scalar.

Returns:

[i.GetMin()*iScalar,i.GetMax()*iScalar]: if iScalar>0
[i.GetMax()*iScalar,i.GetMin()*iScalar]: if iScalar<=0

o operator *

public operator *(	const	`i`,
	const	`iScalar`)

Defines the multiplication of a scalar with a CATMathInterval.

Returns:

[i.GetMin()*iScalar,i.GetMax()*iScalar]: if iScalar>0
[i.GetMax()*iScalar,i.GetMin()*iScalar]: if iScalar<=0

o operator *=

public *operator =**(		`io`,
	const	`iScalar`)

Defines the *= operator of a CATMathInterval with a scalar.

Returns:

[io.GetMin()*=iScalar,io.GetMax()*=iScalar]: if iScalar>0
[io.GetMax()*=iScalar,io.GetMin()*=iScalar]: if iScalar<=0

o operator +

public operator +(	const	`iScalar`,
	const	`i`)

Defines the scalar addition with a CATMathInterval.

Returns:: [i.GetMin()+iScalar,i.GetMax()+iScalar]

o operator +

public operator +(	const	`i`,
	const	`iScalar`)

Defines the addition of a CATMathInterval with a scalar.

Returns:: [i.GetMin()+iScalar,i.GetMax()+iScalar]

o operator +

public operator +(	const	`i1`,
	const	`i2`)

Unary plus operator.

Returns:: [i1.GetMin()+i2.GetMin(),i1.GetMax()+i2.GetMax()]

o operator +=

public operator +=(		`io`,
	const	`iScalar`)

Defines the += operator of a CATMathInterval with a scalar.

Returns:: io = [io.GetMin()+=iScalar,io.GetMax()+=iScalar]

o operator +=

public operator +=(		`io1`,
	const	`i2`)

Addition assignment operator.

Returns:: io1 = [io1.GetMin()+=i2.GetMin(),io1.GetMax()+=i2.GetMax()]

o operator -

public operator -( const i)

Defines the opposite of a CATMathInterval.

Returns:: [-i.GetMax(),-i.GetMin()]

o operator -

public operator -(	const	`iScalar`,
	const	`i`)

Defines the scalar substraction with a CATMathInterval.

Returns:: [iScalar-i.GetMin(),iScalar-i.GetMax()]

o operator -

public operator -(	const	`i`,
	const	`iScalar`)

Defines the scalar substraction with a CATMathInterval.

Returns:: [i.GetMin()-iScalar,i.GetMax()-iScalar]

o operator -

public operator -(	const	`i1`,
	const	`i2`)

Subtraction operator.

Returns:: [i1.GetMin()-i2.GetMin(),i1.GetMax()-i2.GetMax()]

o operator -=

public operator -=(		`io`,
	const	`iScalar`)

Defines the -= operator of a CATMathInterval with a scalar.

Returns:: io = [io.GetMin()-=iScalar,io.GetMax()-=iScalar]

o operator -=

public operator -=(		`io1`,
	const	`i2`)

Subtraction assignment operator.

Returns:: io1= [i1.GetMin()-=i2.GetMax(),i1.GetMax()-=i2.GetMin()]

o operator /

public operator /(	const	`i`,
	const	`iScalar`)

Defines the division of a CATMathInterval by a scalar.

Returns:

[i.GetMin()/iScalar,i.GetMax()/iScalar]: if iScalar>0
[i.GetMax()/iScalar,i.GetMin()/iScalar]: if iScalar<=0

o operator /

public operator /(	const	`i1`,
	const	`i2`)

Defines the dividion of a CATMathInterval by another one.

Returns:

i1*[1/i2.GetMax(), 1/i2.GetMin()]: if i2.GetMax()*i2.GetMin() >0
[-CATMathInfinite,CATMathInfinite]: if i2.GetMax()*i2.GetMin() <=0

o operator ||

public operator \|\|(	const	`i1`,
	const	`i2`)

Returns the interval resulting of the union of two CATMathIntervals.

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

AdvancedMathematics writeClassCharacteristic(); CATMathInterval

Constructor and Destructor Index

Method Index

Constructor and Destructor

Methods

AdvancedMathematics CATMathInterval