All Frameworks Class Hierarchy This Framework Indexes Previous Next

Mathematics CATMathTransformation2D

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

public class CATMathTransformation2D

Class representing a transformation in dimension 2.

It is composed of a matrix Matrix, and of a translation Vector.
Matrix= a11 a12 Vector= u1 a21 a22 u2
Apply transformations by using the * operator.
Available transformations are scaling, translation, reflection, rotation.

Constructor and Destructor Index

o CATMathTransformation2D(): Constructs an Identity transformation.
o CATMathTransformation2D(CATMathLine2D&): Constructs a reflection.
o CATMathTransformation2D(double[],double[])
o CATMathTransformation2D(CATMathVector2D&): Constructs a translation.
o CATMathTransformation2D(CATMathTransformation2D&): Copy constructor.
o CATMathTransformation2D(CATMathAxis2D&,CATMathAxis2D&): Constructs a tranformation of axes systems.
o CATMathTransformation2D(CATMath2x2Matrix&,CATMathVector2D&): Constructs from a CATMath2x2Matrix and a CATMathVector2D.
o CATMathTransformation2D(double,CATMathPoint2D&,CATMathTransfoType): Constructs a CATMathTansformation2D from a scalar and a CATMathPoint2D.

Method Index

o ApplyTo(CATMathLine2D&,CATMathLine2D&)
o ApplyTo(CATMathAxis2D&,CATMathAxis2D&)
o ApplyToAxis(CATMathAxis2D&,CATMathAxis2D&): Computes the CATMathAxis transformation.
o ApplyToLine(CATMathLine2D&,CATMathLine2D&): Computes the CATMathLine2D transformation.
o GetCoef(double[]): Retrieves the coefficients of this CATMathTransformation2D in an array[] of doubles.
o GetMatrix(CATMath2x2Matrix&): Returns the CATMath2x2Matrix associated with this CATMathTransformation2D.
o GetVector(CATMathVector2D&): Returns the CATMathVector2D associated with this CATMathTransformation2D.
o Inverse(CATMathTransformation2D&): Retrieves the inverse of this CATMathTransformation2D.
o IsDirect(): Tests whether this transformation is direct.
o IsIsometry(): Tests whether this transformation is an isometry (keeps the distances).
o IsRotation(CATAngle&,CATMathPoint2D&): Tests whether this transformation is a rotation and retrieves the center and the angle in radians.
o IsScaling(CATMathPoint2D&,double&): Tests whether this transformation is a scaling and retrieves the Origin and the Scale.
o IsSimilitude(): Tests whether this transformation is a similitude (keeps the angles).
o IsSimilitude(double&): Retrieves the scale of this CATMathTransformation2D.
o Set(double[],double[]): Modifies the CATMathTransformation2D that transforms 3 2D points into 3 new 2D points.
o SetCoef(double[]): Retrieves the coefficients of this CATMathTransformation2D in an array[] of doubles.
o SetMatrix(CATMath2x2Matrix&): Sets the matrix of this CATMathTransformation2D.
o SetVector(CATMathVector2D&): Sets the vector of this CATMathTransformation2D.

Constructor and Destructor

o CATMathTransformation2D

public CATMathTransformation2D(

)

Constructs an Identity transformation.
Matrix= Identity, Vector = (0,0)

o CATMathTransformation2D

public CATMathTransformation2D( const iReflectLine)

Constructs a reflection.

o CATMathTransformation2D

public CATMathTransformation2D(	const	`iFrom`,
	const	`iTo`)

Deprecated:

V5R20 Set Constructs theCATMathTransformation2D that transforms 3 2D points into 3 new 2D points.
The points must be different.

Parameters:

iFrom[]: The array of the six coordinates (Point1.x, Point1.y, Point2.x, Point2.y, Point3.x, Point3.y) of the initial points.
iTo[]: The array of the six coordinates: (Result1.x, Result1.y, Result2.x, Result2.y, Result3.x, Result3.y)of the resulting points.

o CATMathTransformation2D

public CATMathTransformation2D( const iTranslation)

Constructs a translation.

o CATMathTransformation2D

public CATMathTransformation2D( const iTransfoToCopy)

Copy constructor.

o CATMathTransformation2D

public CATMathTransformation2D(	const	`iFromAxis`,
	const	`iToAxis`)

Constructs a tranformation of axes systems.

o CATMathTransformation2D

public CATMathTransformation2D(	const	`iMatrix`,
	const	`iVector`)

Constructs from a CATMath2x2Matrix and a CATMathVector2D.

o CATMathTransformation2D

public CATMathTransformation2D(	const	`iA`,
	const	`iCenter`,
	const	`iType`	`= CATMathScaling`)

Constructs a CATMathTansformation2D from a scalar and a CATMathPoint2D.

Returns:

If iType== CATMathScaling

Matrix=	iA	0
	0	iA

If iType== CATMathRotation, iA is in radians.

Matrix=	cos(iA)	-sin(iA)
	sin(iA)	cos(iA)

Methods

o ApplyTo

public ApplyTo(	const	`iLineToTransfo`,
		`oLine`)

Deprecated:

V5R21 ApplyToLine Computes the CATMathLine2D transformation.

Parameters:

iLineToTransfo: The CATMathLine2D of origin
oLine: The transformed CATMathLine2D Note that it could change the length if the transformation is not an isometry.

Returns:

E_FAIL if an error occurs, S_OK otherwise.

o ApplyTo

public ApplyTo(	const	`iAxisToTransfo`,
		`oAxis`)

Deprecated:

V5R21 ApplyToAxis Computes the CATMathAxis transformation.

Parameters:

iAxisToTransfo: The CATMathAxis2D of origin
oAxis: The transformed CATMathAxis2D Note that the directions of the transformated axis are re-orthonormalized.

Returns:

E_FAIL if an error occurs, S_OK otherwise.

o ApplyToAxis

public ApplyToAxis(	const	`p`,
		`oAxis`)

Computes the CATMathAxis transformation.

Parameters:

iAxisToTransfo: The CATMathAxis2D of origin
oAxis: The transformed CATMathAxis2D Note that the directions of the transformated axis are re-orthonormalized.

Returns:

E_FAIL if an error occurs, S_OK otherwise.

o ApplyToLine

public ApplyToLine(	const	`l`,
		`oLine`)

Computes the CATMathLine2D transformation.

Parameters:

iLineToTransfo: The CATMathLine2D of origin
oLine: The transformed CATMathLine2D Note that it could change the length if the transformation is not an isometry.

Returns:

E_FAIL if an error occurs, S_OK otherwise.

o GetCoef

public GetCoef( iCoef)

Retrieves the coefficients of this CATMathTransformation2D in an array[] of doubles.
The size of the array is 6. If the matrix is:
iCoeff a11 a12 u1 a21 a22 u2 the coefficients must be given COLUMN by COLUMN.

o GetMatrix

public GetMatrix( ioMatrix)

Returns the CATMath2x2Matrix associated with this CATMathTransformation2D.

o GetVector

public GetVector( ioVector)

Returns the CATMathVector2D associated with this CATMathTransformation2D.

o Inverse

public Inverse( ioInverse)

Retrieves the inverse of this CATMathTransformation2D.

Returns:: TRUE if this CATMathTransformation2D is invertible, FALSE otherwise. In this last case, ioInverse is not modified.

o IsDirect

public IsDirect(

)

Tests whether this transformation is direct.

Returns:

FALSE: if it is indirect.
TRUE: if it is direct.

o IsIsometry

public IsIsometry(

)

Tests whether this transformation is an isometry (keeps the distances).

Returns:

FALSE: if it is not an isometry.
TRUE: if it is a direct isometry.

o IsRotation

public IsRotation(		`ioAngle`,
		`ioCenter`)

Tests whether this transformation is a rotation and retrieves the center and the angle in radians.

Returns:

FALSE: if it is not a rotation.
TRUE: if it is a rotation.

o IsScaling

public IsScaling(		`oOrigin`,
		`oScale`)

Tests whether this transformation is a scaling and retrieves the Origin and the Scale.

Returns:

FALSE: if it is not a scaling.
TRUE: if it is a scaling.

o IsSimilitude

public IsSimilitude(

)

Tests whether this transformation is a similitude (keeps the angles).

Returns:

FALSE: if it is not an similitude.
TRUE: if it is a similitude.

o IsSimilitude

public IsSimilitude( oScale)

Retrieves the scale of this CATMathTransformation2D.

Returns:

FALSE: if it is not an similitude.
TRUE: if it is a similitude.

o Set

public Set(	const	`iFrom`,
	const	`iTo`)

Modifies the CATMathTransformation2D that transforms 3 2D points into 3 new 2D points.
The points must be different.

Parameters:

iFrom[]: The array of the six coordinates (Point1.x, Point1.y, Point2.x, Point2.y, Point3.x, Point3.y) of the initial points.
iTo[]: The array of the six coordinates: (Result1.x, Result1.y, Result2.x, Result2.y, Result3.x, Result3.y)of the resulting points.

Returns:

E_FAIL if an error occurs, S_OK otherwise.

o SetCoef

public SetCoef( const iCoeff)

o SetMatrix

public SetMatrix( const iMatrix)

Sets the matrix of this CATMathTransformation2D.

o SetVector

public SetVector( const iVector)

Sets the vector of this CATMathTransformation2D.

This object is included in the file: CATMathTransformation2D.h
If needed, your Imakefile.mk should include the module: CATMathematics

Mathematics writeClassCharacteristic(); CATMathTransformation2D

Constructor and Destructor Index

Method Index

Constructor and Destructor

Methods

Mathematics CATMathTransformation2D