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---Copyright: Matra Datavision 1991, 1992
class GTrsf2d from gp inherits Storable
--- Purpose :
-- 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.
uses Ax2d from gp,
Mat2d from gp,
Trsf2d from gp,
Vec2d from gp,
XY from gp,
TrsfForm from gp
raises ConstructionError from Standard,
OutOfRange from Standard
is
Create returns GTrsf2d;
---C++: inline
--- Purpose : returns identity transformation.
Create (T : Trsf2d) returns GTrsf2d;
---C++: inline
--- Purpose : Converts the gp_Trsf2d transformation T into a
-- general transformation.
Create (M : Mat2d; V : XY) returns GTrsf2d;
---C++: inline
--- Purpose : 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.
SetAffinity (me : in out; A : Ax2d; Ratio : Real) is static;
--- Purpose :
-- 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.
SetValue (me : in out; Row, Col : Integer; Value : Real)
---C++: inline
--- Purpose :
-- 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
raises OutOfRange
is static;
SetTranslationPart (me : in out; Coord : XY) is static;
--- Purpose : Replacesthe translation part of this
-- transformation by the coordinates of the number pair Coord.
SetTrsf2d (me : in out; T : Trsf2d) is static;
---C++: inline
--- Purpose :
-- Assigns the vectorial and translation parts of T to this transformation.
SetVectorialPart (me : in out; Matrix : Mat2d) is static;
---C++: inline
--- Purpose :
-- Replaces the vectorial part of this transformation by Matrix.
IsNegative (me) returns Boolean is static;
---C++: inline
--- Purpose :
-- Returns true if the determinant of the vectorial part of
-- this transformation is negative.
IsSingular (me) returns Boolean is static;
---C++: inline
--- Purpose : 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.
Form (me) returns TrsfForm is static;
---C++: inline
--- Purpose :
-- 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.
TranslationPart (me) returns XY is static;
--- Purpose : Returns the translation part of the GTrsf2d.
---C++: inline
---C++: return const&
VectorialPart (me) returns Mat2d is static;
--- Purpose :
-- Computes the vectorial part of the GTrsf2d. The returned
-- Matrix is a 2*2 matrix.
---C++: inline
---C++: return const&
Value (me; Row, Col : Integer) returns Real
--- Purpose :
-- Returns the coefficients of the global matrix of transformation.
--- Raised OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3
---C++: inline
---C++: alias operator()
raises OutOfRange
is static;
Invert (me : in out) raises ConstructionError is static;
Inverted (me) returns GTrsf2d raises ConstructionError is static;
---C++: inline
--- Purpose :
-- Computes the reverse transformation.
-- Raised an exception if the matrix of the transformation
-- is not inversible.
Multiply (me : in out; T : GTrsf2d) is static;
---C++: alias operator *=
Multiplied (me; T : GTrsf2d) returns GTrsf2d is static;
---C++: inline
---C++: alias operator *
--- Purpose :
-- 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 !!!
PreMultiply (me : in out; T : GTrsf2d) is static;
--- Purpose :
-- Computes the product of the transformation T and this
-- transformation, and assigns the result to this transformation:
-- this = T * this
Power (me : in out; N : Integer) raises ConstructionError is static;
Powered (me; N : Integer) returns GTrsf2d raises ConstructionError is static;
---C++: inline
--- 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 an exception if N < 0 and if the matrix of the
-- transformation is not inversible.
Transforms (me; Coord : in out XY) is static;
---C++: inline
Transformed(me; Coord : in XY from gp)
returns XY from gp
is static;
---C++: inline
Transforms (me; X, Y : in out Real) is static;
---C++: inline
---Purpose:
-- Applies this transformation to the coordinates:
-- - of the number pair Coord, or
-- - X and Y.
--
-- Note:
-- - Transforms modifies X, Y, or the coordinate pair Coord, while
-- - Transformed creates a new coordinate pair.
Trsf2d (me) returns Trsf2d raises ConstructionError is static;
---Purpose:
-- 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.
fields
matrix : Mat2d;
loc : XY;
shape : TrsfForm;
scale : Real;
end;
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