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Mathematics CATMathBox

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

public class CATMathBox

Class representing a 3D box, parallel to the canonical axis.
Role:
The box is defined by two CATMathPoint, the first (XMin, YMin, ZMin) called the low extremity, and the other one ((XMax, YMax, ZMax)) the high extremity.
A box can be seen as a set. If one of the cooordinates of the low extremity is greater than the corresponding coordinate of the high extremity, the box is empty. In other words, a box is not empty if XMin < XMax and YMin < YMax and ZMin < ZMax.

Constructor and Destructor Index

o CATMathBox(): Constructs an empty CATMathBox.
o CATMathBox(CATMathBox&): Copy Constructor.
o CATMathBox(double,double,double,double,double,double): Constructs a CATMathBox from its extremities.
o CATMathBox(CATMathPoint&,CATMathPoint&,CATBoolean): Constructs a CATMathBox from two CATMathPoint.
o ~CATMathBox(): Destructor.

Method Index

o AddInside(CATMathBox&): Replaces this CATMathBox by its union with another CATMathBox.
o AddInside(CATMathPoint&): Modifies this CATMathBox by forcing a CATMathPoint to belong to it.
o DistanceTo(CATMathPoint&): Returns the distance between this CATMathBox and a CATMathPoint.
o GetBoxCenter(CATMathPoint&): Retrieves the center of this CATMathBox.
o GetExtremities(double&,double&,double&,double&,double&,double&)
o GetHigh(CATMathPoint&)
o GetHighLimit(CATMathPoint&): Retrieves the high extremity of this CATMathBox.
o GetLimits(double&,double&,double&,double&,double&,double&): Retrieves the extremities of this CATMathBox.
o GetLow(CATMathPoint&)
o GetLowLimit(CATMathPoint&): Retrieves the low extremity of this CATMathBox.
o Inflate(double): Modifies this CATMathBox by adding a given thickness on each direction.
o IsContaining(CATMathBox&): Returns TRUE if this CATMathBox is completely containing an other CATMathBox.
o IsContaining(CATMathPoint&,double): Returns TRUE if this CATMathBox defined at a given tolerance is containing a CATMathPoint.
o IsEmpty(): Tests if this CATMathBox is empty.
o IsIntersecting(CATMathLine&): Returns TRUE if this CATMathBox is intersecting a CATMathLine.
o IsIntersecting(CATMathPlane&): Returns TRUE if this CATMathBox is intersecting a CATMathPlane.
o IsIntersecting(CATMathBox&,double): Returns TRUE if this CATMathBox is intersecting an another one.
o IsIntersecting(CATMathPoint&,CATMathPoint&): Returns TRUE if this CATMathBox is intersecting the segment [iP1,iP2].
o IsIntersectingAlongDir(CATMathBox&,CATMathDirection&,double): Returns TRUE if the projection of this CATMathBox onto the plane perpendicular to the direction The test takes into account a given tolerance (the result is equivalent to inflating one of the box of iTol and to compute IsIntersectingAlongDir with no tolerance.
o LocalScale(double): Modifies this CATMathBox by having it larger at the same place.
o SetExtremities(double,double,double,double,double,double): Sets the extremities of this CATMathBox.
o SetHigh(CATMathPoint&): Modifies the high extremity of this CATMathBox.
o SetLow(CATMathPoint&): Modifies the low extremity of this CATMathBox.
o SetToEmpty(): Resets this CATMathBox to an empty one.
o SetToIntersection(CATMathBox&,CATMathBox&): Replaces this CATMathBox with the intersection of two other CATMathBox.
o SetToUnion(CATMathBox&,CATMathBox&): Replaces this CATMathBox with the union of two other CATMathBox.
o SquareDistanceTo(CATMathPoint&): Returns the square distance between this CATMathBox and a CATMathPoint.
o SquareMaxDistanceTo(CATMathPoint&): Returns the square of the maximal distance between this CATMathBox and a CATMathPoint.
o Volume(): Returns the geometric volume included in this CATMathBox.

Constructor and Destructor

o CATMathBox

public CATMathBox(

)

Constructs an empty CATMathBox.

o CATMathBox

public CATMathBox( const iBoxToCopy)

Copy Constructor.

o CATMathBox

public CATMathBox(	const	`iXMin`,
	const	`iXMax`,
	const	`iYMin`,
	const	`iYMax`,
	const	`iZMin`,
	const	`iZMax`)

Constructs a CATMathBox from its extremities.
No verification is performed.

o CATMathBox

public CATMathBox(	const	`iLowExtremity`,
	const	`iHighExtremity`,
	const	`iCheck`	`=TRUE`)

Constructs a CATMathBox from two CATMathPoint.

Parameters:

iCheck

FALSE: The two CATMathPoint are assumed to be the lowest one and the highest one. This can create an empty box if it is not the case.
TRUE: It creates the smallest box that contains the two CATMathPoint (default mode).

o ~CATMathBox

public ~CATMathBox(

)

Destructor.

Methods

o AddInside

public AddInside( const iBoxToAdd)

Replaces this CATMathBox by its union with another CATMathBox.

o AddInside

public AddInside( const iPointToAdd)

Modifies this CATMathBox by forcing a CATMathPoint to belong to it.

o DistanceTo

public DistanceTo( const iPoint)

Returns the distance between this CATMathBox and a CATMathPoint.

o GetBoxCenter

public GetBoxCenter( ioCenterPoint)

Retrieves the center of this CATMathBox.

Returns:: E_FAIL if the box is empty, S_OK otherwise.

o GetExtremities

public GetExtremities(		`ioXMin`,
		`ioXMax`,
		`ioYMin`,
		`ioYMax`,
		`ioZMin`,
		`ioZMax`)

Deprecated:: V5R15 GetLimits Retrieves the extremities of this CATMathBox.
Throws an error if the box is empty.

o GetHigh

public GetHigh( ioHighPoint)

Deprecated:: V5R15 GetHighLimit Retrieves the high extremity of this CATMathBox.
Throws an error if the box is empty.

o GetHighLimit

public GetHighLimit( ioHighPoint)

Retrieves the high extremity of this CATMathBox.

Returns:: E_FAIL if the box is empty, S_OK otherwise.

o GetLimits

public GetLimits(		`ioXMin`,
		`ioXMax`,
		`ioYMin`,
		`ioYMax`,
		`ioZMin`,
		`ioZMax`)

Retrieves the extremities of this CATMathBox.

Returns:: E_FAIL if the box is empty, S_OK otherwise.

o GetLow

public GetLow( ioLowPoint)

Deprecated:: V5R15 GetLowLimit Retrieves the low extremity of this CATMathBox.
Throws an error if the box is empty.

o GetLowLimit

public GetLowLimit( ioLowPoint)

Retrieves the low extremity of this CATMathBox.

Returns:: E_FAIL if the box is empty, S_OK otherwise.

o Inflate

public Inflate( iThickness)

Modifies this CATMathBox by adding a given thickness on each direction.
Hence, the low extremity of the box becomes (XMin-iThickness, YMin-iThickness, ZMin-iThickness) and the high extremity becomes (XMax+iThickness, YMax+iThickness, ZMax+iThickness).
This method does not apply on an empty box, but no error is thrown in this case.

o IsContaining

public IsContaining( const iOtherBox)

Returns TRUE if this CATMathBox is completely containing an other CATMathBox.
Note that the empty CATMathBox is contained by all CATMathBox and does not contain any CATMathBox, even an empty one.

o IsContaining

public IsContaining(	const	`iPoint`,
		`iTol`	`=0.`)

Returns TRUE if this CATMathBox defined at a given tolerance is containing a CATMathPoint.
The CATMathBox used is defined by: [_XMin-iTol, _XMax+iTol] x [_YMin-iTol, _YMax+iTol] x [_ZMin-iTol, _ZMax+iTol]

o IsEmpty

public IsEmpty(

)

Tests if this CATMathBox is empty.

Returns:: TRUE if the CATMathBox is empty, FALSE otherwise.

o IsIntersecting

public IsIntersecting( const iLine)

Returns TRUE if this CATMathBox is intersecting a CATMathLine.
Note that if the intersection is a point or a line, the result is true.

o IsIntersecting

public IsIntersecting( const iPlane)

Returns TRUE if this CATMathBox is intersecting a CATMathPlane.
Note that if the intersection is a point or a line, the result is true.

o IsIntersecting

public IsIntersecting(	const	`iBox`,
		`iTol`	`=0.`)

Returns TRUE if this CATMathBox is intersecting an another one. The test takes a given tolerance into account (the result is equivalent to inflating one of the box of iTol and to compute IsIntersecting with no tolerance.
Note that if the intersection is a point or a line, the result is true.

o IsIntersecting

public IsIntersecting(	const	`iP1`,
	const	`iP2`)

Returns TRUE if this CATMathBox is intersecting the segment [iP1,iP2].
Note that if the intersection is a point or a line, the result is true.

o IsIntersectingAlongDir

public IsIntersectingAlongDir(		`iBox`,
	const	`iDir`,
		`iTol`	`=0.`)

Returns TRUE if the projection of this CATMathBox onto the plane perpendicular to the direction The test takes into account a given tolerance (the result is equivalent to inflating one of the box of iTol and to compute IsIntersectingAlongDir with no tolerance.

o LocalScale

public LocalScale( iScaleRatio)

Modifies this CATMathBox by having it larger at the same place.
The CATMathBox increases as follows: Let f=(iScaleRatio-1)/2 be the multiplicative ratio on each direction and dX=XMax-XMin, dY=YMax-YMin, dZ=ZMax-ZMin be the lengths of the box in each direction. The low extremity of the box becomes (XMin-dX*f, YMin-dY*f, ZMin-dZ*f) and the high extremity becomes (XMax+dX*f, YMax+dY*f, ZMax+dZ*f). In particular, if the length of the box is null in one direction, it still remains null after a local scale.
This method does not apply on an empty box, but no error is thrown in this case.

o SetExtremities

public SetExtremities(	const	`iXMin`,
	const	`iXMax`,
	const	`iYMin`,
	const	`iYMax`,
	const	`iZMin`,
	const	`iZMax`)

Sets the extremities of this CATMathBox.
No verification is done.

o SetHigh

public SetHigh( const iHighPoint)

Modifies the high extremity of this CATMathBox.
No verification is performed.

o SetLow

public SetLow( const iLowPoint)

Modifies the low extremity of this CATMathBox.
No verification is performed.

o SetToEmpty

public SetToEmpty(

)

Resets this CATMathBox to an empty one.

o SetToIntersection

public SetToIntersection(	const	`iBox1`,
	const	`iBox2`)

Replaces this CATMathBox with the intersection of two other CATMathBox.
It can lead to an empty CATMathBox.

o SetToUnion

public SetToUnion(	const	`iBox1`,
	const	`iBox2`)

Replaces this CATMathBox with the union of two other CATMathBox.

o SquareDistanceTo

public SquareDistanceTo( const iPoint)

Returns the square distance between this CATMathBox and a CATMathPoint.

o SquareMaxDistanceTo

public SquareMaxDistanceTo( const iPoint)

Returns the square of the maximal distance between this CATMathBox and a CATMathPoint. For a point inside the box, the maximal distance is the distance between it and the furthest point of the box from it.

o Volume

public Volume(

)

Returns the geometric volume included in this CATMathBox.

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

Mathematics writeClassCharacteristic(); CATMathBox

Constructor and Destructor Index

Method Index

Constructor and Destructor

Methods

Mathematics CATMathBox