Mathematics CATMathTransformation
Usage: you must use this class as is. You should never derive it.
public class CATMathTransformation
Class representing a transformation in dimension 3.
It is composed of a matrix Matrix,
and of a translation Vector.
| Matrix= | a11 | a12 | a13 |
Vector= | u1 |
| a21 | a22 | a23 |
| u2 |
| a31 | a32 | a33 |
| u3 |
Apply transformations by using the * operator.
Available transformations are scaling, translation, reflection,
rotation.
Constructor and Destructor Index
- o
CATMathTransformation()
- Constructs an Identity transformation.
- o
CATMathTransformation(double[],CATLONG32)
-
- o
CATMathTransformation(CATMathPlane&)
- Constructs a reflection on a plane.
- o
CATMathTransformation(CATMathVector&)
- Constructs a translation.
- o
CATMathTransformation(CATMathPlane&,double)
- Constructs an affinity with respect to a plane.
- o
CATMathTransformation(CATMathPoint&,double)
- Constructs a scaling.
- o
CATMathTransformation(CATMathAxis&,double[])
- Constructs an affinity with respect to a given ratio for each direction of a CATMathAxis.
- o
CATMathTransformation(CATMathTransformation&)
- Copy constructor.
- o
CATMathTransformation(CATAngle&,CATMathLine&)
- Constructs a rotation (radians).
- o
CATMathTransformation(CATMathAxis&,CATMathAxis&)
-
- o
CATMathTransformation(CATMathPoint&,CATMathVector&)
- Constructs a reflection from a CATMathPoint and a CATMathVector.
- o
CATMathTransformation(CATMath3x3Matrix&,CATMathVector&)
- Constructs a CATMathTransformation from a CATMath3x3Matrix and a CATMathVector.
- o
CATMathTransformation(double,CATMathTransformation&,CATMathTransformation&)
-
Method Index
- o
ApplyTo(CATMathLine&,CATMathLine&)
-
- o
ApplyTo(CATMathAxis&,CATMathAxis&)
-
- o
ApplyTo(CATMathPlane&,CATMathPlane&)
-
- o
ApplyToAxis(CATMathAxis&,CATMathAxis&)
- Computes the CATMathAxis transformation.
- o
ApplyToLine(CATMathLine&,CATMathLine&)
- Computes the CATMathLine transformation.
- o
ApplyToPlane(CATMathPlane&,CATMathPlane&)
- Computes the CATMathPlane transformation.
- o
ComputeInverse(CATMathTransformation&)
- Retrieves the inverse of this CATMathTransformation.
- o
Dump(ostream*)
- Dumps this CATMathTransformation.
- o
GetCoef(double[],CATLONG32)
-
- o
GetCoefficients(double[],CATLONG32)
- Retrieves the coefficients of this CATMathTransformation in an array[] of doubles.
- o
GetMatrix(CATMath3x3Matrix&)
- Retrieves the CATMath3x3Matrix associated with this CATMathTransformation.
- o
GetVector(CATMathVector&)
- Retrieves the CATMathVector associated with this CATMathTransformation.
- o
Inverse(CATMathTransformation&)
-
- o
IsIdentity()
- Tests if the matrix of this CATMathTransformation is the identity (invariant).
- o
IsIsometry()
- Tests if the matrix of this CATMathTransformation is an isometry (keeps the distances).
- o
IsReflection(CATMathPlane&)
- Tests if this CATMathTransformation is a reflection and retrieves the reflect plane.
- o
IsRotation(CATAngle&,CATMathLine&,double)
- Tests if the matrix of this CATMathTransformation is a rotation and retrieves the axis and the
angle in radian.
- o
IsScaling(CATMathPoint&,double&)
- Tests if this CATMathTransformation is a scaling and retrieves the Origin and
the Scale.
- o
IsSimilitude(double&)
- Tests if the matrix of this CATMathTransformation is a similitude and retrieves the scale.
- o
Set(CATMathAxis&,CATMathAxis&)
- Set an transformation of axis systems.
- o
Set(double,CATMathTransformation&,CATMathTransformation&)
- Set an interpolation of an isometry.
- o
SetCoef(double[],CATLONG32)
-
- o
SetCoefficients(double[],CATLONG32)
- Modifies the coefficients of this CATMathTransformation from an array[] of doubles.
- o
SetFromAxisToOIJK(CATMathAxis&)
- Set an transformation of axis systems.
- o
SetFromOIJKToAxis(CATMathAxis&)
- Set an transformation of axis systems.
- o
SetMatrix(CATMath3x3Matrix&)
- Sets the matrix of this CATMathTransformation.
- o
SetVector(CATMathVector&)
- Sets the vector of this CATMathTransformation.
Constructor and Destructor
o CATMathTransformation
| public CATMathTransformation( | ) |
-
Constructs an Identity transformation.
Matrix= Identity, Vector = (0,0,0)
o CATMathTransformation
| public CATMathTransformation( | const | iCoeff, |
| const | iNbCoeff | = 12) |
-
- Deprecated:
- V5R20 SetCoefficients
Throws an error if iNbCoeff value is not 12 or 16.
Constructs a transformation from an array[] of doubles.
If iNbCoeff=12, the array is:
| iCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
and the coefficients must be given COLUMN by COLUMN.
If iNbCoeff=16, DO NOT USE- the array is:
| iCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
| 0 | 0 | 0 |
1 |
and the coefficients must be given COLUMN by COLUMN.
o CATMathTransformation
| public CATMathTransformation( | const | iReflectPlane) |
-
Constructs a reflection on a plane.
o CATMathTransformation
| public CATMathTransformation( | const | iTranslation) |
-
Constructs a translation.
o CATMathTransformation
| public CATMathTransformation( | const | iPlane, |
| const | iScale) |
-
Constructs an affinity with respect to a plane.
o CATMathTransformation
| public CATMathTransformation( | const | iCenter, |
| const | iScale) |
-
Constructs a scaling.
o CATMathTransformation
| public CATMathTransformation( | const | iAxis, |
| const | iRatio) |
-
Constructs an affinity with respect to a given ratio for each direction of a CATMathAxis.
- Parameters:
-
- iAxis
- The three direction of the affinity.
- iRatio
- Array of 3 doubles, giving the ratio in each direction.
o CATMathTransformation
| public CATMathTransformation( | const | iTransfoToCopy) |
-
Copy constructor.
o CATMathTransformation
| public CATMathTransformation( | const | iAngle, |
| const | iAxis) |
-
Constructs a rotation (radians).
- Parameters:
-
- iAngle
- The angle in radians.
- iAxis
- The rotation axis.
o CATMathTransformation
| public CATMathTransformation( | const | iFromAxis, |
| const | iToAxis) |
-
- Deprecated:
- V5R15 Set
Constructs a transformation of axis systems.
This transformation transforms, in the global axis system
CATMathOIJK, the coordinates of a point M
into the coordinates of the point TM such that:
M and TM have the same coordinate values
in the axis iFromAxis and iToAxis.
Now, for defining the transformation from iFromAxis to iToAxis, you have to combine
two transformations, in the following way:
CATMathTransformation(iToAxis, CATMathOIJK) * CATMathTransformation(CATMathOIJK, iFromAxis)
o CATMathTransformation
| public CATMathTransformation( | const | iReflectPlaneOrigin, |
| const | iReflectPlaneNormal) |
-
Constructs a reflection from a CATMathPoint and a CATMathVector.
o CATMathTransformation
| public CATMathTransformation( | const | iMatrix, |
| const | iTranslation) |
-
Constructs a CATMathTransformation from a CATMath3x3Matrix and a CATMathVector.
o CATMathTransformation
| public CATMathTransformation( | const | iFactor, |
| const | iFromTansfo, |
| const | iToTransfo) |
-
- Deprecated:
- V5R15 Set
Creates an interpolation of an isometry.
This can be used for simulating intermediate steps of a displacement.
Throws an error if the two transformations are not compatible.
- Parameters:
-
- iFactor
- The ratio of the intermediate step: 0 < iFactor < 1.
Methods
o ApplyTo
| public ApplyTo( | const | iLineToTransfo, |
| | oLine) |
-
- Deprecated:
- V5R21 ApplyToLine
Computes the CATMathLine transformation.
- Parameters:
-
- iLineToTransfo
- The CATMathLine of origin
- oLine
- The transformed CATMathLine
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 CATMathAxis of origin
- oAxis
- The transformed CATMathAxis
Note that the second and third directions of the transformated axis are re-orthonormalized.
- Returns:
- E_FAIL if an error occurs, S_OK otherwise.
o ApplyTo
| public ApplyTo( | const | iPlaneToTransfo, |
| | oPlane) |
-
- Deprecated:
- V5R21 ApplyToPlane
Computes the CATMathPlane transformation.
- Parameters:
-
- iPlaneToTransfo
- The CATMathPlane of origin
- oPlane
- The transformed planed
Note that the second direction of the transformated plane is re-orthonormalized.
- Returns:
- E_FAIL if an error occurs, S_OK otherwise.
o ApplyToAxis
| public ApplyToAxis( | const | iAxisToTransfo, |
| | oAxis) |
-
Computes the CATMathAxis transformation.
- Parameters:
-
- iAxisToTransfo
- The CATMathAxis of origin
- oAxis
- The transformed CATMathAxis
Note that the second and third directions of the transformated axis are re-orthonormalized.
- Returns:
- E_FAIL if an error occurs, S_OK otherwise.
o ApplyToLine
| public ApplyToLine( | const | iLineToTransfo, |
| | oLine) |
-
Computes the CATMathLine transformation.
- Parameters:
-
- iLineToTransfo
- The CATMathLine of origin
- oLine
- The transformed CATMathLine
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 ApplyToPlane
| public ApplyToPlane( | const | iPlaneToTransfo, |
| | oPlane) |
-
Computes the CATMathPlane transformation.
- Parameters:
-
- iPlaneToTransfo
- The CATMathPlane of origin
- oPlane
- The transformed planed
Note that the second direction of the transformated plane is re-orthonormalized.
- Returns:
- E_FAIL if an error occurs, S_OK otherwise.
o ComputeInverse
| public ComputeInverse( | | ioInverse) |
-
Retrieves the inverse of this CATMathTransformation.
- Returns:
- S_OK if this CATMathTransformation is invertible, E_FAIL otherwise.
In this last case, oInverse is not modified.
o Dump
-
Dumps this CATMathTransformation.
This writes the following lines on the ostream:
| Matrix= | | | iA11 | iA12 |
iA13 | | |
| | | | iA21 | iA22 |
iA23 | | |
| | | | iA31 | iA32 |
iA33 | | |
| Translation= | ( | FirstCoord, | SecondCoord, |
ThirdCoord | ) |
- Parameters:
-
- iStream
- A pointer to the output. If 0L, the method dumps
on the cout output.
o GetCoef
| public GetCoef( | | iCoeff, |
| const | iNbCoeff | = 12) |
-
- Deprecated:
- V5R15 GetCoefficients
Throws an error if iNbCoeff value is not 12 or 16.
Retrieves the coefficients of this CATMathTransformation in an array[] of doubles.
If iNbCoeff=12, the array is:
| oCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
and the coefficients are given COLUMN by COLUMN.
If iNbCoeff=16, DO NOT USE - and the array is:
| oCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
| 0 | 0 | 0 |
1 |
and the coefficients are given COLUMN by COLUMN.
o GetCoefficients
| public GetCoefficients( | | iCoeff, |
| const | iNbCoeff | = 12) |
-
Retrieves the coefficients of this CATMathTransformation in an array[] of doubles.
If iNbCoeff=12, the array is:
| oCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
and the coefficients are given COLUMN by COLUMN.
If iNbCoeff=16, DO NOT USE - and the array is:
| oCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
| 0 | 0 | 0 |
1 |
and the coefficients are given COLUMN by COLUMN.
- Returns:
- E_FAIL if iNbCoeff value is not 12 or 16, S_OK otherwise.
o GetMatrix
| public GetMatrix( | | ioMatrix) |
-
Retrieves the CATMath3x3Matrix associated with this CATMathTransformation.
o GetVector
| public GetVector( | | ioVector) |
-
Retrieves the CATMathVector associated with this CATMathTransformation.
o Inverse
| public Inverse( | | ioInverse) |
-
- Deprecated:
- V5R15 ComputeInverse
Retrieves the inverse of this CATMathTransformation.
- Returns:
- TRUE if this CATMathTransformation is invertible, FALSE otherwise.
In this last case, oInverse is not modified.
o IsIdentity
-
Tests if the matrix of this CATMathTransformation is the identity (invariant).
- Returns:
-
- FALSE
- if it is not the identity.
- TRUE
- if it is the identity.
o IsIsometry
-
Tests if the matrix of this CATMathTransformation is an isometry (keeps the distances).
return
- FALSE
- if it is not an isometry.
- TRUE
- if it is a direct isometry.
o IsReflection
| public IsReflection( | | ioReflectPlane) |
-
Tests if this CATMathTransformation is a reflection and retrieves the reflect plane.
- Returns:
-
- FALSE
- if it is not a reflection.
- TRUE
- if it is a reflection.
o IsRotation
| public IsRotation( | | ioAngle, |
| | ioAxis, |
| const | iTol | = 0.) |
-
Tests if the matrix of this CATMathTransformation is a rotation and retrieves the axis and the
angle in radian.
- Returns:
-
- FALSE
- if it is not a rotation.
- TRUE
- if it is a rotation.
o IsScaling
| public IsScaling( | | ioOrigin, |
| | ioScale) |
-
Tests if this CATMathTransformation 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( | | ioScale) |
-
Tests if the matrix of this CATMathTransformation is a similitude and retrieves the scale.
- Returns:
-
- FALSE
- if it is not a similitude.
- TRUE
- if it is a similitude.
o Set
| public Set( | const | iFromAxis, |
| const | iToAxis) |
-
Set an transformation of axis systems.
This transformation transforms, in the global axis system
CATMathOIJK, the coordinates of a point M
into the coordinates of the point TM such that:
M and TM have the same coordinate values
in the axis iFromAxis and iToAxis.
Now, for defining the transformation from iFromAxis to iToAxis, you have to combine
two transformations, in the following way:
CATMathTransformation(iToAxis, CATMathOIJK) * CATMathTransformation(CATMathOIJK, iFromAxis)
- Returns:
- E_FAIL if an error occurs, S_OK otherwise.
o Set
| public Set( | const | iFactor, |
| const | iFromTansfo, |
| const | iToTransfo) |
-
Set an interpolation of an isometry.
This can be used for simulating intermediate steps of a displacement.
- Parameters:
-
- iFactor
- The ratio of the intermediate step: 0 < iFactor < 1.
- Returns:
- E_FAIL if the two transformations are not compatible, S_OK otherwise.
o SetCoef
| public SetCoef( | const | iCoeff, |
| const | iNbCoeff | = 12) |
-
- Deprecated:
- V5R15 SetCoefficients
Throws an error if iNbCoeff value is not 12 or 16.
Modifies the coefficients of this CATMathTransformation from an array[] of doubles.
If iNbCoeff=12, the array is:
| iCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
and the coefficients must be given COLUMN by COLUMN.
If iNbCoeff=16, DO NOT USE - the array is:
| iCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
| 0 | 0 | 0 |
1 |
and the coefficients must be given COLUMN by COLUMN.
o SetCoefficients
| public SetCoefficients( | const | iCoeff, |
| const | iNbCoeff | = 12) |
-
Modifies the coefficients of this CATMathTransformation from an array[] of doubles.
If iNbCoeff=12, the array is:
| iCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
and the coefficients must be given COLUMN by COLUMN.
If iNbCoeff=16, DO NOT USE - the array is:
| iCoeff | a11 | a12 | a13 |
u1 |
| a21 | a22 | a23 |
u2 |
| a31 | a32 | a33 |
u3 |
| 0 | 0 | 0 |
1 |
and the coefficients must be given COLUMN by COLUMN.
- Returns:
- E_FAIL if iNbCoeff value is not 12 or 16, S_OK otherwise.
o SetFromAxisToOIJK
| public SetFromAxisToOIJK( | const | iFromAxis) |
-
Set an transformation of axis systems.
This transformation transforms the coordinates of a point M
in the axis iFromAxis into the coordinates of the point TM
in the global axis system CATMathOIJK.
- Returns:
- E_FAIL if an error occurs, S_OK otherwise.
o SetFromOIJKToAxis
| public SetFromOIJKToAxis( | const | iToAxis) |
-
Set an transformation of axis systems.
This transformation transforms the coordinates of a point M
in the global axis system CATMathOIJK into the coordinates
of the point TM in the axis iToAxis.
- Returns:
- E_FAIL if an error occurs, S_OK otherwise.
o SetMatrix
| public SetMatrix( | const | iMatrix) |
-
Sets the matrix of this CATMathTransformation.
o SetVector
| public SetVector( | const | iVector) |
-
Sets the vector of this CATMathTransformation.
This object is included in the file: CATMathTransformation.h
If needed, your Imakefile.mk should include the module: CATMathematics
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