Open CASCADE Technology
7.2.0

Defines a nonpersistent transformation in 3D space. The following transformations are implemented : . Translation, Rotation, Scale . Symmetry with respect to a point, a line, a plane. Complex transformations can be obtained by combining the previous elementary transformations using the method Multiply. The transformations can be represented as follow : More...
#include <gp_Trsf.hxx>
Public Member Functions  
gp_Trsf ()  
Returns the identity transformation. More...  
gp_Trsf (const gp_Trsf2d &T)  
Creates a 3D transformation from the 2D transformation T. The resulting transformation has a homogeneous vectorial part, V3, and a translation part, T3, built from T: a11 a12 0 a13 V3 = a21 a22 0 T3 = a23 0 0 1. 0 It also has the same scale factor as T. This guarantees (by projection) that the transformation which would be performed by T in a plane (2D space) is performed by the resulting transformation in the xOy plane of the 3D space, (i.e. in the plane defined by the origin (0., 0., 0.) and the vectors DX (1., 0., 0.), and DY (0., 1., 0.)). The scale factor is applied to the entire space. More...  
void  SetMirror (const gp_Pnt &P) 
Makes the transformation into a symmetrical transformation. P is the center of the symmetry. More...  
void  SetMirror (const gp_Ax1 &A1) 
Makes the transformation into a symmetrical transformation. A1 is the center of the axial symmetry. More...  
void  SetMirror (const gp_Ax2 &A2) 
Makes the transformation into a symmetrical transformation. A2 is the center of the planar symmetry and defines the plane of symmetry by its origin, "X
Direction" and "Y Direction". More...  
void  SetRotation (const gp_Ax1 &A1, const Standard_Real Ang) 
Changes the transformation into a rotation. A1 is the rotation axis and Ang is the angular value of the rotation in radians. More...  
void  SetRotation (const gp_Quaternion &R) 
Changes the transformation into a rotation defined by quaternion. Note that rotation is performed around origin, i.e. no translation is involved. More...  
void  SetScale (const gp_Pnt &P, const Standard_Real S) 
Changes the transformation into a scale. P is the center of the scale and S is the scaling value. Raises ConstructionError If <S> is null. More...  
void  SetDisplacement (const gp_Ax3 &FromSystem1, const gp_Ax3 &ToSystem2) 
Modifies this transformation so that it transforms the coordinate system defined by FromSystem1 into the one defined by ToSystem2. After this modification, this transformation transforms: More...  
void  SetTransformation (const gp_Ax3 &FromSystem1, const gp_Ax3 &ToSystem2) 
Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the coordinate system "FromSystem1" to the coordinate system "ToSystem2". Example : In a C++ implementation : Real x1, y1, z1; // are the coordinates of a point in the // local system FromSystem1 Real x2, y2, z2; // are the coordinates of a point in the // local system ToSystem2 gp_Pnt P1 (x1, y1, z1) Trsf T; T.SetTransformation (FromSystem1, ToSystem2); gp_Pnt P2 = P1.Transformed (T); P2.Coord (x2, y2, z2);. More...  
void  SetTransformation (const gp_Ax3 &ToSystem) 
Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the default coordinate system {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.), VZ (0., 0. ,1.) } to the local coordinate system defined with the Ax3 ToSystem. Use in the same way as the previous method. FromSystem1 is defaulted to the absolute coordinate system. More...  
void  SetTransformation (const gp_Quaternion &R, const gp_Vec &T) 
Sets transformation by directly specified rotation and translation. More...  
void  SetTranslation (const gp_Vec &V) 
Changes the transformation into a translation. V is the vector of the translation. More...  
void  SetTranslation (const gp_Pnt &P1, const gp_Pnt &P2) 
Makes the transformation into a translation where the translation vector is the vector (P1, P2) defined from point P1 to point P2. More...  
void  SetTranslationPart (const gp_Vec &V) 
Replaces the translation vector with the vector V. More...  
void  SetScaleFactor (const Standard_Real S) 
Modifies the scale factor. Raises ConstructionError If S is null. More...  
void  SetForm (const gp_TrsfForm P) 
void  SetValues (const Standard_Real a11, const Standard_Real a12, const Standard_Real a13, const Standard_Real a14, const Standard_Real a21, const Standard_Real a22, const Standard_Real a23, const Standard_Real a24, const Standard_Real a31, const Standard_Real a32, const Standard_Real a33, const Standard_Real a34) 
Sets the coefficients of the transformation. The transformation of the point x,y,z is the point x',y',z' with : More...  
Standard_Boolean  IsNegative () const 
Returns true if the determinant of the vectorial part of this transformation is negative. More...  
gp_TrsfForm  Form () const 
Returns the nature of the transformation. It can be: an identity transformation, a rotation, a translation, a mirror transformation (relative to a point, an axis or a plane), a scaling transformation, or a compound transformation. More...  
Standard_Real  ScaleFactor () const 
Returns the scale factor. More...  
const gp_XYZ &  TranslationPart () const 
Returns the translation part of the transformation's matrix. More...  
Standard_Boolean  GetRotation (gp_XYZ &theAxis, Standard_Real &theAngle) const 
Returns the boolean True if there is nonzero rotation. In the presence of rotation, the output parameters store the axis and the angle of rotation. The method always returns positive value "theAngle", i.e., 0. < theAngle <= PI. Note that this rotation is defined only by the vectorial part of the transformation; generally you would need to check also the translational part to obtain the axis (gp_Ax1) of rotation. More...  
gp_Quaternion  GetRotation () const 
Returns quaternion representing rotational part of the transformation. More...  
gp_Mat  VectorialPart () const 
Returns the vectorial part of the transformation. It is a 3*3 matrix which includes the scale factor. More...  
const gp_Mat &  HVectorialPart () const 
Computes the homogeneous vectorial part of the transformation. It is a 3*3 matrix which doesn't include the scale factor. In other words, the vectorial part of this transformation is equal to its homogeneous vectorial part, multiplied by the scale factor. The coefficients of this matrix must be multiplied by the scale factor to obtain the coefficients of the transformation. More...  
Standard_Real  Value (const Standard_Integer Row, const Standard_Integer Col) const 
Returns the coefficients of the transformation's matrix. It is a 3 rows * 4 columns matrix. This coefficient includes the scale factor. Raises OutOfRanged if Row < 1 or Row > 3 or Col < 1 or Col > 4. More...  
void  Invert () 
gp_Trsf  Inverted () const 
Computes the reverse transformation Raises an exception if the matrix of the transformation is not inversible, it means that the scale factor is lower or equal to Resolution from package gp. Computes the transformation composed with T and <me>. In a C++ implementation you can also write Tcomposed = <me> * T. Example : Trsf T1, T2, Tcomp; ............... Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1) Pnt P1(10.,3.,4.); Pnt P2 = P1.Transformed(Tcomp); //using Tcomp Pnt P3 = P1.Transformed(T1); //using T1 then T2 P3.Transform(T2); // P3 = P2 !!! More...  
gp_Trsf  Multiplied (const gp_Trsf &T) const 
gp_Trsf  operator* (const gp_Trsf &T) const 
void  Multiply (const gp_Trsf &T) 
Computes the transformation composed with <me> and T. <me> = <me> * T. More...  
void  operator*= (const gp_Trsf &T) 
void  PreMultiply (const gp_Trsf &T) 
Computes the transformation composed with <me> and T. <me> = T * <me> More...  
void  Power (const Standard_Integer N) 
gp_Trsf  Powered (const Standard_Integer N) const 
Computes the following composition of transformations <me> * <me> * .......* <me>, N time. if N = 0 <me> = Identity if N < 0 <me> = <me>.Inverse() *...........* <me>.Inverse(). More...  
void  Transforms (Standard_Real &X, Standard_Real &Y, Standard_Real &Z) const 
void  Transforms (gp_XYZ &Coord) const 
Transformation of a triplet XYZ with a Trsf. More...  
template<class T >  
void  GetMat4 (NCollection_Mat4< T > &theMat) const 
Convert transformation to 4x4 matrix. More...  
Protected Member Functions  
void  Orthogonalize () 
Makes orthogonalization of "matrix". More...  
Defines a nonpersistent transformation in 3D space. The following transformations are implemented : . Translation, Rotation, Scale . Symmetry with respect to a point, a line, a plane. Complex transformations can be obtained by combining the previous elementary transformations using the method Multiply. The transformations can be represented as follow :
V1 V2 V3 T XYZ XYZ  a11 a12 a13 a14   x   x'  a21 a22 a23 a24   y   y'  a31 a32 a33 a34   z  =  z'  0 0 0 1   1   1 
where {V1, V2, V3} defines the vectorial part of the transformation and T defines the translation part of the transformation. This transformation never change the nature of the objects.
gp_Trsf::gp_Trsf  (  ) 
Returns the identity transformation.
gp_Trsf::gp_Trsf  (  const gp_Trsf2d &  T  ) 
Creates a 3D transformation from the 2D transformation T. The resulting transformation has a homogeneous vectorial part, V3, and a translation part, T3, built from T: a11 a12 0 a13 V3 = a21 a22 0 T3 = a23 0 0 1. 0 It also has the same scale factor as T. This guarantees (by projection) that the transformation which would be performed by T in a plane (2D space) is performed by the resulting transformation in the xOy plane of the 3D space, (i.e. in the plane defined by the origin (0., 0., 0.) and the vectors DX (1., 0., 0.), and DY (0., 1., 0.)). The scale factor is applied to the entire space.
gp_TrsfForm gp_Trsf::Form  (  )  const 
Returns the nature of the transformation. It can be: an identity transformation, a rotation, a translation, a mirror transformation (relative to a point, an axis or a plane), a scaling transformation, or a compound transformation.

inline 
Convert transformation to 4x4 matrix.
Standard_Boolean gp_Trsf::GetRotation  (  gp_XYZ &  theAxis, 
Standard_Real &  theAngle  
)  const 
Returns the boolean True if there is nonzero rotation. In the presence of rotation, the output parameters store the axis and the angle of rotation. The method always returns positive value "theAngle", i.e., 0. < theAngle <= PI. Note that this rotation is defined only by the vectorial part of the transformation; generally you would need to check also the translational part to obtain the axis (gp_Ax1) of rotation.
gp_Quaternion gp_Trsf::GetRotation  (  )  const 
Returns quaternion representing rotational part of the transformation.
const gp_Mat& gp_Trsf::HVectorialPart  (  )  const 
Computes the homogeneous vectorial part of the transformation. It is a 3*3 matrix which doesn't include the scale factor. In other words, the vectorial part of this transformation is equal to its homogeneous vectorial part, multiplied by the scale factor. The coefficients of this matrix must be multiplied by the scale factor to obtain the coefficients of the transformation.
void gp_Trsf::Invert  (  ) 
gp_Trsf gp_Trsf::Inverted  (  )  const 
Computes the reverse transformation Raises an exception if the matrix of the transformation is not inversible, it means that the scale factor is lower or equal to Resolution from package gp. Computes the transformation composed with T and <me>. In a C++ implementation you can also write Tcomposed = <me> * T. Example : Trsf T1, T2, Tcomp; ............... Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1) Pnt P1(10.,3.,4.); Pnt P2 = P1.Transformed(Tcomp); //using Tcomp Pnt P3 = P1.Transformed(T1); //using T1 then T2 P3.Transform(T2); // P3 = P2 !!!
Standard_Boolean gp_Trsf::IsNegative  (  )  const 
Returns true if the determinant of the vectorial part of this transformation is negative.
void gp_Trsf::Multiply  (  const gp_Trsf &  T  ) 
Computes the transformation composed with <me> and T. <me> = <me> * T.

inline 

protected 
Makes orthogonalization of "matrix".
void gp_Trsf::Power  (  const Standard_Integer  N  ) 
gp_Trsf gp_Trsf::Powered  (  const Standard_Integer  N  )  const 
Computes the following composition of transformations <me> * <me> * .......* <me>, N time. if N = 0 <me> = Identity if N < 0 <me> = <me>.Inverse() *...........* <me>.Inverse().
Raises if N < 0 and if the matrix of the transformation not inversible.
void gp_Trsf::PreMultiply  (  const gp_Trsf &  T  ) 
Computes the transformation composed with <me> and T. <me> = T * <me>
Standard_Real gp_Trsf::ScaleFactor  (  )  const 
Returns the scale factor.
Modifies this transformation so that it transforms the coordinate system defined by FromSystem1 into the one defined by ToSystem2. After this modification, this transformation transforms:
void gp_Trsf::SetForm  (  const gp_TrsfForm  P  ) 
void gp_Trsf::SetMirror  (  const gp_Pnt &  P  ) 
Makes the transformation into a symmetrical transformation. P is the center of the symmetry.
void gp_Trsf::SetMirror  (  const gp_Ax1 &  A1  ) 
Makes the transformation into a symmetrical transformation. A1 is the center of the axial symmetry.
void gp_Trsf::SetMirror  (  const gp_Ax2 &  A2  ) 
Makes the transformation into a symmetrical transformation. A2 is the center of the planar symmetry and defines the plane of symmetry by its origin, "X Direction" and "Y Direction".
void gp_Trsf::SetRotation  (  const gp_Ax1 &  A1, 
const Standard_Real  Ang  
) 
Changes the transformation into a rotation. A1 is the rotation axis and Ang is the angular value of the rotation in radians.
void gp_Trsf::SetRotation  (  const gp_Quaternion &  R  ) 
Changes the transformation into a rotation defined by quaternion. Note that rotation is performed around origin, i.e. no translation is involved.
void gp_Trsf::SetScale  (  const gp_Pnt &  P, 
const Standard_Real  S  
) 
Changes the transformation into a scale. P is the center of the scale and S is the scaling value. Raises ConstructionError If <S> is null.
void gp_Trsf::SetScaleFactor  (  const Standard_Real  S  ) 
Modifies the scale factor. Raises ConstructionError If S is null.
Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the coordinate system "FromSystem1" to the coordinate system "ToSystem2". Example : In a C++ implementation : Real x1, y1, z1; // are the coordinates of a point in the // local system FromSystem1 Real x2, y2, z2; // are the coordinates of a point in the // local system ToSystem2 gp_Pnt P1 (x1, y1, z1) Trsf T; T.SetTransformation (FromSystem1, ToSystem2); gp_Pnt P2 = P1.Transformed (T); P2.Coord (x2, y2, z2);.
void gp_Trsf::SetTransformation  (  const gp_Ax3 &  ToSystem  ) 
Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the default coordinate system {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.), VZ (0., 0. ,1.) } to the local coordinate system defined with the Ax3 ToSystem. Use in the same way as the previous method. FromSystem1 is defaulted to the absolute coordinate system.
void gp_Trsf::SetTransformation  (  const gp_Quaternion &  R, 
const gp_Vec &  T  
) 
Sets transformation by directly specified rotation and translation.
void gp_Trsf::SetTranslation  (  const gp_Vec &  V  ) 
Changes the transformation into a translation. V is the vector of the translation.
Makes the transformation into a translation where the translation vector is the vector (P1, P2) defined from point P1 to point P2.
void gp_Trsf::SetTranslationPart  (  const gp_Vec &  V  ) 
Replaces the translation vector with the vector V.
void gp_Trsf::SetValues  (  const Standard_Real  a11, 
const Standard_Real  a12,  
const Standard_Real  a13,  
const Standard_Real  a14,  
const Standard_Real  a21,  
const Standard_Real  a22,  
const Standard_Real  a23,  
const Standard_Real  a24,  
const Standard_Real  a31,  
const Standard_Real  a32,  
const Standard_Real  a33,  
const Standard_Real  a34  
) 
Sets the coefficients of the transformation. The transformation of the point x,y,z is the point x',y',z' with :
x' = a11 x + a12 y + a13 z + a14 y' = a21 x + a22 y + a23 z + a24 z' = a31 x + a32 y + a33 z + a34
The method Value(i,j) will return aij. Raises ConstructionError if the determinant of the aij is null. The matrix is orthogonalized before future using.
void gp_Trsf::Transforms  (  Standard_Real &  X, 
Standard_Real &  Y,  
Standard_Real &  Z  
)  const 
void gp_Trsf::Transforms  (  gp_XYZ &  Coord  )  const 
Transformation of a triplet XYZ with a Trsf.
const gp_XYZ& gp_Trsf::TranslationPart  (  )  const 
Returns the translation part of the transformation's matrix.
Standard_Real gp_Trsf::Value  (  const Standard_Integer  Row, 
const Standard_Integer  Col  
)  const 
Returns the coefficients of the transformation's matrix. It is a 3 rows * 4 columns matrix. This coefficient includes the scale factor. Raises OutOfRanged if Row < 1 or Row > 3 or Col < 1 or Col > 4.
gp_Mat gp_Trsf::VectorialPart  (  )  const 
Returns the vectorial part of the transformation. It is a 3*3 matrix which includes the scale factor.