Open CASCADE Technology
6.5.4
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Defines a non persistent transformation in 2D space.
This transformation is a general transformation.
It can be a Trsf2d from package gp, an affinity, or you can
define your own transformation giving the corresponding
matrix of transformation.
With a GTrsf2d you can transform only a doublet of coordinates
XY. It is not possible to transform other geometric objects
because these transformations can change the nature of non-
elementary geometric objects.
A GTrsf2d is represented with a 2 rows * 3 columns matrix :
V1 V2 T XY XY
| a11 a12 a14 | | x | | x'|
| a21 a22 a24 | | y | | y'|
| 0 0 1 | | 1 | | 1 |
where {V1, V2} defines the vectorial part of the
transformation and T defines the translation part of
the transformation.
Warning
A GTrsf2d transformation is only applicable on
coordinates. Be careful if you apply such a
transformation to all the points of a geometric object,
as this can change the nature of the object and thus
render it incoherent!
Typically, a circle is transformed into an ellipse by an
affinity transformation. To avoid modifying the nature of
an object, use a gp_Trsf2d transformation instead, as
objects of this class respect the nature of geometric objects.
#include <gp_GTrsf2d.hxx>
Public Member Functions | |
DEFINE_STANDARD_ALLOC | gp_GTrsf2d () |
returns identity transformation. | |
gp_GTrsf2d (const gp_Trsf2d &T) | |
Converts the gp_Trsf2d transformation T into a general transformation. | |
gp_GTrsf2d (const gp_Mat2d &M, const gp_XY &V) | |
Creates a transformation based on the matrix M and the vector V where M defines the vectorial part of the transformation, and V the translation part. | |
void | SetAffinity (const gp_Ax2d &A, const Standard_Real Ratio) |
Changes this transformation into an affinity of ratio Ratio with respect to the axis A. Note: An affinity is a point-by-point transformation that transforms any point P into a point P' such that if H is the orthogonal projection of P on the axis A, the vectors HP and HP' satisfy: HP' = Ratio * HP. | |
void | SetValue (const Standard_Integer Row, const Standard_Integer Col, const Standard_Real Value) |
Replaces the coefficient (Row, Col) of the matrix representing this transformation by Value, Raises OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3 | |
void | SetTranslationPart (const gp_XY &Coord) |
Replacesthe translation part of this transformation by the coordinates of the number pair Coord. | |
void | SetTrsf2d (const gp_Trsf2d &T) |
Assigns the vectorial and translation parts of T to this transformation. | |
void | SetVectorialPart (const gp_Mat2d &Matrix) |
Replaces the vectorial part of this transformation by Matrix. | |
Standard_Boolean | IsNegative () const |
Returns true if the determinant of the vectorial part of this transformation is negative. | |
Standard_Boolean | IsSingular () const |
Returns true if this transformation is singular (and therefore, cannot be inverted). Note: The Gauss LU decomposition is used to invert the transformation matrix. Consequently, the transformation is considered as singular if the largest pivot found is less than or equal to gp::Resolution(). Warning If this transformation is singular, it cannot be inverted. | |
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 or axis), a scaling transformation, a compound transformation or some other type of transformation. | |
const gp_XY & | TranslationPart () const |
Returns the translation part of the GTrsf2d. | |
const gp_Mat2d & | VectorialPart () const |
Computes the vectorial part of the GTrsf2d. The returned Matrix is a 2*2 matrix. | |
Standard_Real | Value (const Standard_Integer Row, const Standard_Integer Col) const |
Returns the coefficients of the global matrix of transformation. Raised OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3 | |
Standard_Real | operator() (const Standard_Integer Row, const Standard_Integer Col) const |
void | Invert () |
gp_GTrsf2d | Inverted () const |
Computes the reverse transformation. Raised an exception if the matrix of the transformation is not inversible. | |
void | Multiply (const gp_GTrsf2d &T) |
void | operator*= (const gp_GTrsf2d &T) |
gp_GTrsf2d | Multiplied (const gp_GTrsf2d &T) const |
Computes the transformation composed with T and <me>. In a C++ implementation you can also write Tcomposed = <me> * T. Example : GTrsf2d T1, T2, Tcomp; ............... //composition : Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1) // transformation of a point XY P(10.,3.); XY P1(P); Tcomp.Transforms(P1); //using Tcomp XY P2(P); T1.Transforms(P2); //using T1 then T2 T2.Transforms(P2); // P1 = P2 !!! | |
gp_GTrsf2d | operator* (const gp_GTrsf2d &T) const |
void | PreMultiply (const gp_GTrsf2d &T) |
Computes the product of the transformation T and this transformation, and assigns the result to this transformation: this = T * this | |
void | Power (const Standard_Integer N) |
gp_GTrsf2d | 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 an exception if N < 0 and if the matrix of the transformation is not inversible. | |
void | Transforms (gp_XY &Coord) const |
gp_XY | Transformed (const gp_XY &Coord) const |
void | Transforms (Standard_Real &X, Standard_Real &Y) const |
Applies this transformation to the coordinates: | |
gp_Trsf2d | Trsf2d () const |
Converts this transformation into a gp_Trsf2d transformation. Exceptions Standard_ConstructionError if this transformation cannot be converted, i.e. if its form is gp_Other. | |
const gp_Mat2d & | _CSFDB_Getgp_GTrsf2dmatrix () const |
const gp_XY & | _CSFDB_Getgp_GTrsf2dloc () const |
gp_TrsfForm | _CSFDB_Getgp_GTrsf2dshape () const |
void | _CSFDB_Setgp_GTrsf2dshape (const gp_TrsfForm p) |
Standard_Real | _CSFDB_Getgp_GTrsf2dscale () const |
void | _CSFDB_Setgp_GTrsf2dscale (const Standard_Real p) |
gp_GTrsf2d::gp_GTrsf2d | ( | const gp_Trsf2d & | T | ) |
gp_GTrsf2d::gp_GTrsf2d | ( | const gp_Mat2d & | M, |
const gp_XY & | V | ||
) |
const gp_XY& gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dloc | ( | ) | const [inline] |
const gp_Mat2d& gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dmatrix | ( | ) | const [inline] |
Standard_Real gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dscale | ( | ) | const [inline] |
gp_TrsfForm gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dshape | ( | ) | const [inline] |
void gp_GTrsf2d::_CSFDB_Setgp_GTrsf2dscale | ( | const Standard_Real | p | ) | [inline] |
void gp_GTrsf2d::_CSFDB_Setgp_GTrsf2dshape | ( | const gp_TrsfForm | p | ) | [inline] |
gp_TrsfForm gp_GTrsf2d::Form | ( | ) | const |
gp_GTrsf2d gp_GTrsf2d::Inverted | ( | ) | const |
Standard_Boolean gp_GTrsf2d::IsNegative | ( | ) | const |
Standard_Boolean gp_GTrsf2d::IsSingular | ( | ) | const |
gp_GTrsf2d gp_GTrsf2d::Multiplied | ( | const gp_GTrsf2d & | T | ) | const |
void gp_GTrsf2d::Multiply | ( | const gp_GTrsf2d & | T | ) |
Standard_Real gp_GTrsf2d::operator() | ( | const Standard_Integer | Row, |
const Standard_Integer | Col | ||
) | const [inline] |
gp_GTrsf2d gp_GTrsf2d::operator* | ( | const gp_GTrsf2d & | T | ) | const [inline] |
void gp_GTrsf2d::operator*= | ( | const gp_GTrsf2d & | T | ) | [inline] |
gp_GTrsf2d gp_GTrsf2d::Powered | ( | const Standard_Integer | N | ) | const |
void gp_GTrsf2d::SetAffinity | ( | const gp_Ax2d & | A, |
const Standard_Real | Ratio | ||
) |
void gp_GTrsf2d::SetTranslationPart | ( | const gp_XY & | Coord | ) |
void gp_GTrsf2d::SetTrsf2d | ( | const gp_Trsf2d & | T | ) |
void gp_GTrsf2d::SetValue | ( | const Standard_Integer | Row, |
const Standard_Integer | Col, | ||
const Standard_Real | Value | ||
) |
void gp_GTrsf2d::SetVectorialPart | ( | const gp_Mat2d & | Matrix | ) |
gp_XY gp_GTrsf2d::Transformed | ( | const gp_XY & | Coord | ) | const |
void gp_GTrsf2d::Transforms | ( | gp_XY & | Coord | ) | const |
void gp_GTrsf2d::Transforms | ( | Standard_Real & | X, |
Standard_Real & | Y | ||
) | const |
const gp_XY& gp_GTrsf2d::TranslationPart | ( | ) | const |
gp_Trsf2d gp_GTrsf2d::Trsf2d | ( | ) | const |
Standard_Real gp_GTrsf2d::Value | ( | const Standard_Integer | Row, |
const Standard_Integer | Col | ||
) | const |
const gp_Mat2d& gp_GTrsf2d::VectorialPart | ( | ) | const |