# FoundationClasses
TKMath
gp

# gp_Trsf Class Reference

Defines a non-persistent 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 |
.

`#include <gp_Trsf.hxx>`

## Public Member Functions

void * | operator new (size_t, void *anAddress)
void * | operator new (size_t size)
void | operator delete (void *anAddress)
| gp_Trsf ()
| Returns the identity transformation. .
| 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.
.

void | SetMirror (const gp_Pnt &P)
| Makes the transformation into a symmetrical transformation. P is the center of the symmetry. .
Standard_EXPORT void | SetMirror (const gp_Ax1 &A1)
| Makes the transformation into a symmetrical transformation. A1 is the center of the axial symmetry. .
Standard_EXPORT 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 <br> Direction" and "Y Direction". .
Standard_EXPORT 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. .
Standard_EXPORT 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. .
Standard_EXPORT 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:
- the origin of FromSystem1 into the origin of ToSystem2,
- the "X Direction" of FromSystem1 into the "X <br> Direction" of ToSystem2,
- the "Y Direction" of FromSystem1 into the "Y <br> Direction" of ToSystem2, and
- the "main Direction" of FromSystem1 into the "main <br> Direction" of ToSystem2.
Warning
When you know the coordinates of a point in one
coordinate system and you want to express these
coordinates in another one, do not use the
transformation resulting from this function. Use the
transformation that results from SetTransformation instead.
SetDisplacement and SetTransformation create
related transformations: the vectorial part of one is the
inverse of the vectorial part of the other.
.

Standard_EXPORT 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);
.

Standard_EXPORT 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.
.

void | SetTranslation (const gp_Vec &V)
| Changes the transformation into a translation. V is the vector of the translation. .
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. .
Standard_EXPORT void | SetTranslationPart (const gp_Vec &V)
| Replaces the translation vector with the vector V. .
Standard_EXPORT void | SetScaleFactor (const Standard_Real S)
| Modifies the scale factor. Raises ConstructionError If S is null. .
Standard_EXPORT 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, const Standard_Real Tolang, const Standard_Real TolDist)

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 + a43 z + a34
Tolang and TolDist are used to test for null
angles and null distances to determine the form of
the transformation (identity, translation, etc..).
The method Value(i,j) will return aij.
Raises ConstructionError if the determinant of the aij is null. Or if
the matrix as not a uniform scale.
.

Standard_Boolean | IsNegative () const
| Returns true if the determinant of the vectorial part of this transformation is negative. .
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. .
Standard_Real | ScaleFactor () const
| Returns the scale factor. .
const gp_XYZ & | TranslationPart () const
| Returns the translation part of the transformation's matrix .
Standard_EXPORT Standard_Boolean | GetRotation (gp_XYZ &theAxis, Standard_Real &theAngle) const

Returns the boolean True if there is non-zero 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.
.

Standard_EXPORT gp_Mat | VectorialPart () const
| Returns the vectorial part of the transformation. It is a 3*3 matrix which includes the scale factor. .
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. .
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 .
Standard_EXPORT 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 !!!
.

gp_Trsf | Multiplied (const gp_Trsf &T) const
gp_Trsf | operator * (const gp_Trsf &T) const
Standard_EXPORT void | Multiply (const gp_Trsf &T)

Computes the transformation composed with T and <me>.
In a C++ implementation you can also write Tcomposed = <me> * T.
Example :
Trsf T1, T2, Tcomp; ...............
//composition :
Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
// transformation of a point
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 !!!
Computes the transformation composed with <me> and T.
<me> = T * <me>
.

void | operator *= (const gp_Trsf &T)
Standard_EXPORT void | PreMultiply (const gp_Trsf &T)
| Computes the transformation composed with <me> and T. <me> = T * <me> .
Standard_EXPORT void | Power (const Standard_Integer N)
gp_Trsf | Powered (const Standard_Integer N)
| Computes the following composition of transformations <me> * <me> * .......* <me>, N time. if N = 0 <me> = Identity if N < 0 <me> = <me>.Inverse() *...........* <me>.Inverse(). .
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 .
Standard_Real | _CSFDB_Getgp_Trsfscale () const
void | _CSFDB_Setgp_Trsfscale (const Standard_Real p)
gp_TrsfForm | _CSFDB_Getgp_Trsfshape () const
void | _CSFDB_Setgp_Trsfshape (const gp_TrsfForm p)
const gp_Mat & | _CSFDB_Getgp_Trsfmatrix () const
const gp_XYZ & | _CSFDB_Getgp_Trsfloc () const

## Private Attributes

Standard_Real | scale
gp_TrsfForm | shape
gp_Mat | matrix
gp_XYZ | loc

## Friends

Standard_EXPORT friend Handle_Standard_Type & | gp_Trsf_Type_ ()

## Constructor & Destructor Documentation

gp_Trsf::gp_Trsf | ( |  | ) | `[inline]`

gp_Trsf::gp_Trsf | ( | const gp_Trsf2d & | T | ) | `[inline]`

## Member Function Documentation

const gp_XYZ& gp_Trsf::_CSFDB_Getgp_Trsfloc | ( |  | ) | const`[inline]`

const gp_Mat& gp_Trsf::_CSFDB_Getgp_Trsfmatrix | ( |  | ) | const`[inline]`

Standard_Real gp_Trsf::_CSFDB_Getgp_Trsfscale | ( |  | ) | const`[inline]`

gp_TrsfForm gp_Trsf::_CSFDB_Getgp_Trsfshape | ( |  | ) | const`[inline]`

void gp_Trsf::_CSFDB_Setgp_Trsfscale | ( | const Standard_Real | p | ) | `[inline]`

void gp_Trsf::_CSFDB_Setgp_Trsfshape | ( | const gp_TrsfForm | p | ) | `[inline]`

gp_TrsfForm gp_Trsf::Form | ( |  | ) | const`[inline]`

Standard_EXPORT Standard_Boolean gp_Trsf::GetRotation | ( | gp_XYZ & | theAxis,
|  | Standard_Real & | theAngle
| ) | const

const gp_Mat & gp_Trsf::HVectorialPart | ( |  | ) | const`[inline]`

Standard_EXPORT void gp_Trsf::Invert | ( |  | ) |

gp_Trsf gp_Trsf::Inverted | ( |  | ) | const`[inline]`

Standard_Boolean gp_Trsf::IsNegative | ( |  | ) | const`[inline]`

gp_Trsf gp_Trsf::Multiplied | ( | const gp_Trsf & | T | ) | const`[inline]`

Standard_EXPORT void gp_Trsf::Multiply | ( | const gp_Trsf & | T | ) |

gp_Trsf gp_Trsf::operator * | ( | const gp_Trsf & | T | ) | const`[inline]`

void gp_Trsf::operator *= | ( | const gp_Trsf & | T | ) | `[inline]`

void gp_Trsf::operator delete | ( | void * | anAddress | ) | `[inline]`

void* gp_Trsf::operator new | ( | size_t | size | ) | `[inline]`

void* gp_Trsf::operator new | ( | size_t | ,
|  | void * | anAddress
| ) | `[inline]`

Standard_EXPORT void gp_Trsf::Power | ( | const Standard_Integer | N | ) |

gp_Trsf gp_Trsf::Powered | ( | const Standard_Integer | N | ) | `[inline]`

Standard_EXPORT void gp_Trsf::PreMultiply | ( | const gp_Trsf & | T | ) |

Standard_Real gp_Trsf::ScaleFactor | ( |  | ) | const`[inline]`

Standard_EXPORT void gp_Trsf::SetDisplacement | ( | const gp_Ax3 & | FromSystem1,
|  | const gp_Ax3 & | ToSystem2
| ) |

Standard_EXPORT void gp_Trsf::SetMirror | ( | const gp_Ax2 & | A2 | ) |

Standard_EXPORT void gp_Trsf::SetMirror | ( | const gp_Ax1 & | A1 | ) |

void gp_Trsf::SetMirror | ( | const gp_Pnt & | P | ) | `[inline]`

Standard_EXPORT void gp_Trsf::SetRotation | ( | const gp_Ax1 & | A1,
|  | const Standard_Real | Ang
| ) |

Standard_EXPORT void gp_Trsf::SetScale | ( | const gp_Pnt & | P,
|  | const Standard_Real | S
| ) |

Standard_EXPORT void gp_Trsf::SetScaleFactor | ( | const Standard_Real | S | ) |

Standard_EXPORT void gp_Trsf::SetTransformation | ( | const gp_Ax3 & | ToSystem | ) |

Standard_EXPORT void gp_Trsf::SetTransformation | ( | const gp_Ax3 & | FromSystem1,
|  | const gp_Ax3 & | ToSystem2
| ) |

void gp_Trsf::SetTranslation | ( | const gp_Pnt & | P1,
|  | const gp_Pnt & | P2
| ) | `[inline]`

void gp_Trsf::SetTranslation | ( | const gp_Vec & | V | ) | `[inline]`

Standard_EXPORT void gp_Trsf::SetTranslationPart | ( | const gp_Vec & | V | ) |

Standard_EXPORT 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,
|  | const Standard_Real | Tolang,
|  | const Standard_Real | TolDist
| ) |

void gp_Trsf::Transforms | ( | gp_XYZ & | Coord | ) | const`[inline]`

void gp_Trsf::Transforms | ( | Standard_Real & | X,
|  | Standard_Real & | Y,
|  | Standard_Real & | Z
| ) | const`[inline]`

const gp_XYZ & gp_Trsf::TranslationPart | ( |  | ) | const`[inline]`

Standard_Real gp_Trsf::Value | ( | const Standard_Integer | Row,
|  | const Standard_Integer | Col
| ) | const`[inline]`

Standard_EXPORT gp_Mat gp_Trsf::VectorialPart | ( |  | ) | const

## Friends And Related Function Documentation

Standard_EXPORT friend Handle_Standard_Type& gp_Trsf_Type_ | ( |  | ) | `[friend]`

## Field Documentation

gp_XYZ gp_Trsf::loc `[private]`

gp_Mat gp_Trsf::matrix `[private]`

Standard_Real gp_Trsf::scale `[private]`

gp_TrsfForm gp_Trsf::shape `[private]`

The documentation for this class was generated from the following files:

- gp_Trsf.hxx
- gp_Trsf.lxx