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---Copyright: Matra Datavision 1991
class Trsf2d from gp inherits Storable
--- Purpose :
-- Defines a non-persistent transformation in 2D space.
-- The following transformations are implemented :
-- . Translation, Rotation, Scale
-- . Symmetry with respect to a point and a line.
-- Complex transformations can be obtained by combining the
-- previous elementary transformations using the method Multiply.
-- The transformations can be represented as follow :
--
-- V1 V2 T XY XY
-- | a11 a12 a13 | | x | | x'|
-- | a21 a22 a23 | | 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.
uses Ax2d from gp,
Mat2d from gp,
Pnt2d from gp,
TrsfForm from gp,
Trsf from gp,
Vec2d from gp,
XY from gp
raises ConstructionError from Standard,
OutOfRange from Standard
is
Create returns Trsf2d from gp;
---C++: inline
--- Purpose : Returns identity transformation.
Create(T : Trsf from gp)
returns Trsf2d from gp
raises ConstructionError;
---C++: inline
---Purpose: Creates a 2d transformation in the XY plane from a
-- 3d transformation .
SetMirror (me : in out; P : Pnt2d) is static;
---C++: inline
--- Purpose :
-- Changes the transformation into a symmetrical transformation.
-- P is the center of the symmetry.
SetMirror (me : in out; A : Ax2d) is static;
--- Purpose :
-- Changes the transformation into a symmetrical transformation.
-- A is the center of the axial symmetry.
SetRotation (me : in out; P : Pnt2d; Ang : Real) is static;
---C++: inline
--- Purpose :
-- Changes the transformation into a rotation.
-- P is the rotation's center and Ang is the angular value of the
-- rotation in radian.
SetScale (me : in out; P : Pnt2d; S : Real) is static;
---C++: inline
--- Purpose :
-- Changes the transformation into a scale.
-- P is the center of the scale and S is the scaling value.
SetTransformation (me : in out; FromSystem1, ToSystem2 : Ax2d) is static;
--- Purpose :
-- Changes a transformation allowing passage from the coordinate
-- system "FromSystem1" to the coordinate system "ToSystem2".
SetTransformation (me : in out; ToSystem : Ax2d) is static;
--- Purpose :
-- Changes the transformation allowing passage from the basic
-- coordinate system
-- {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.)}
-- to the local coordinate system defined with the Ax2d ToSystem.
SetTranslation (me : in out; V : Vec2d) is static;
---C++: inline
--- Purpose :
-- Changes the transformation into a translation.
-- V is the vector of the translation.
SetTranslation (me: in out; P1, P2 : Pnt2d) is static;
---C++: inline
--- Purpose :
-- Makes the transformation into a translation from
-- the point P1 to the point P2.
SetTranslationPart (me : in out; V : Vec2d) is static;
--- Purpose : Replaces the translation vector with V.
SetScaleFactor (me : in out; S : Real) is static;
--- Purpose : Modifies the scale factor.
IsNegative (me) returns Boolean is static;
--- Purpose : Returns true if the determinant of the vectorial part of
-- this transformation is negative..
---C++: inline
Form (me) returns TrsfForm is static;
--- Purpose :
-- Returns the nature of the transformation. It can be an
-- identity transformation, a rotation, a translation, a mirror
-- (relative to a point or an axis), a scaling transformation,
-- or a compound transformation.
---C++: inline
ScaleFactor (me) returns Real is static;
--- Purpose : Returns the scale factor.
---C++: inline
TranslationPart (me) returns XY is static;
--- Purpose :
-- Returns the translation part of the transformation's matrix
---C++: inline
---C++: return const&
VectorialPart (me) returns Mat2d is static;
--- Purpose :
-- Returns the vectorial part of the transformation. It is a
-- 2*2 matrix which includes the scale factor.
HVectorialPart (me) returns Mat2d is static;
--- Purpose :
-- Returns the homogeneous vectorial part of the transformation.
-- It is a 2*2 matrix which doesn't include the scale factor.
-- The coefficients of this matrix must be multiplied by the
-- scale factor to obtain the coefficients of the transformation.
---C++: inline
---C++: return const&
RotationPart (me) returns Real is static;
--- Purpose :
-- Returns the angle corresponding to the rotational component
-- of the transformation matrix (operation opposite to SetRotation()).
Value (me; Row, Col : Integer) returns Real
---C++: inline
--- Purpose :
-- Returns the coefficients of the transformation's matrix.
-- It is a 2 rows * 3 columns matrix.
-- Raises OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3
raises OutOfRange
is static;
Invert (me : in out) raises ConstructionError is static;
Inverted (me) returns Trsf2d raises ConstructionError is static;
--- Purpose :
-- 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.
---C++: inline
Multiplied (me; T : Trsf2d) returns Trsf2d is static;
---C++: inline
---C++: alias operator *
Multiply (me : in out; T : Trsf2d) is static;
---C++: alias operator *=
--- Purpose :
-- Computes the transformation composed from <T> and <me>.
-- In a C++ implementation you can also write Tcomposed = <me> * T.
-- Example :
-- Trsf2d T1, T2, Tcomp; ...............
-- //composition :
-- Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
-- // transformation of a point
-- Pnt2d P1(10.,3.,4.);
-- Pnt2d P2 = P1.Transformed(Tcomp); //using Tcomp
-- Pnt2d P3 = P1.Transformed(T1); //using T1 then T2
-- P3.Transform(T2); // P3 = P2 !!!
PreMultiply (me : in out; T : Trsf2d) is static;
--- Purpose :
-- Computes the transformation composed from <me> and T.
-- <me> = T * <me>
Power (me : in out; N : Integer) raises ConstructionError is static;
Powered (me : in out; N : Integer) returns Trsf2d
raises ConstructionError
is static;
--- Purpose :
-- 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.
---C++: inline
Transforms (me; X, Y : out Real) is static;
---C++: inline
Transforms (me; Coord : out XY) is static;
---C++: inline
--- Purpose : Transforms a doublet XY with a Trsf2d
fields
scale : Real;
shape : TrsfForm;
matrix : Mat2d;
loc : XY;
friends
class GTrsf2d
end;
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