API reference - Class IMatrix3d

Notation used in Ruby API documentation

Module: db

Description: A 3d matrix object used mainly for representing rotation, shear, displacement and perspective transformations (integer coordinate version).

This object represents a 3x3 matrix. This matrix is used to implement generic geometrical transformations in the 2d space mainly. It can be decomposed into basic transformations: mirroring, rotation, shear, displacement and perspective distortion. In that case, the assumed execution order of the basic transformations is mirroring at the x axis, rotation, magnification, shear, displacement and perspective distortion.

The integer variant was introduced in version 0.27.

Public constructors

new IMatrix3d ptrnewCreate a new Matrix3d representing a unit transformation
new IMatrix3d ptrnew(double m)Create a new Matrix3d representing a magnification
new IMatrix3d ptrnew(const ICplxTrans t)Create a new Matrix3d from the given complex transformation@param t The transformation from which to create the matrix
new IMatrix3d ptrnew(double m11,
double m12,
double m21,
double m22)
Create a new Matrix3d from the four coefficients of a Matrix2d
new IMatrix3d ptrnew(double m11,
double m12,
double m21,
double m22,
double dx,
double dy)
Create a new Matrix3d from the four coefficients of a Matrix2d plus a displacement
new IMatrix3d ptrnew(double m11,
double m12,
double m13,
double m21,
double m22,
double m23,
double m31,
double m32,
double m33)
Create a new Matrix3d from the nine matrix coefficients

Public methods

[const]IMatrix3d*(const IMatrix3d m)Product of two matrices.
[const]Point*(const Point p)Transforms a point with this matrix.
[const]Vector*(const Vector v)Transforms a vector with this matrix.
[const]Edge*(const Edge e)Transforms an edge with this matrix.
[const]Box*(const Box box)Transforms a box with this matrix.
[const]SimplePolygon*(const SimplePolygon p)Transforms a simple polygon with this matrix.
[const]Polygon*(const Polygon p)Transforms a polygon with this matrix.
[const]IMatrix3d+(const IMatrix3d m)Sum of two matrices.
void_createEnsures the C++ object is created
void_destroyExplicitly destroys the object
[const]bool_destroyed?Returns a value indicating whether the object was already destroyed
[const]bool_is_const_object?Returns a value indicating whether the reference is a const reference
void_manageMarks the object as managed by the script side.
void_unmanageMarks the object as no longer owned by the script side.
[const]doubleangleReturns the rotation angle of the rotation component of this matrix.
voidassign(const IMatrix3d other)Assigns another object to self
[const]DCplxTranscplx_transConverts this matrix to a complex transformation (if possible).
[const]VectordispReturns the displacement vector of this transformation.
[const]new IMatrix3d ptrdupCreates a copy of self
[const]IMatrix3dinvertedThe inverse of this matrix.
[const]boolis_mirror?Returns the mirror flag of this matrix.
[const]doublem(int i,
int j)
Gets the m coefficient with the given index.
[const]doublemag_xReturns the x magnification of the magnification component of this matrix.
[const]doublemag_yReturns the y magnification of the magnification component of this matrix.
[const]doubleshear_angleReturns the magnitude of the shear component of this matrix.
[const]stringto_sConvert the matrix to a string.
[const]Pointtrans(const Point p)Transforms a point with this matrix.
[const]doubletx(double z)Returns the perspective tilt angle tx.
[const]doublety(double z)Returns the perspective tilt angle ty.

Public static methods and constants

new IMatrix3d ptrnewc(double mag,
double rotation,
bool mirrx)
Create a new Matrix3d representing a isotropic magnification, rotation and mirroring
new IMatrix3d ptrnewc(double shear,
double mx,
double my,
double rotation,
bool mirrx)
Create a new Matrix3d representing a shear, anisotropic magnification, rotation and mirroring
new IMatrix3d ptrnewc(const Vector u,
double shear,
double mx,
double my,
double rotation,
bool mirrx)
Create a new Matrix3d representing a displacement, shear, anisotropic magnification, rotation and mirroring
new IMatrix3d ptrnewc(double tx,
double ty,
double z,
const Vector u,
double shear,
double mx,
double my,
double rotation,
bool mirrx)
Create a new Matrix3d representing a perspective distortion, displacement, shear, anisotropic magnification, rotation and mirroring

Deprecated methods (protected, public, static, non-static and constructors)

voidcreateUse of this method is deprecated. Use _create instead
voiddestroyUse of this method is deprecated. Use _destroy instead
[const]booldestroyed?Use of this method is deprecated. Use _destroyed? instead
[const]boolis_const_object?Use of this method is deprecated. Use _is_const_object? instead

Detailed description

*

(1) Signature: [const] IMatrix3d * (const IMatrix3d m)

Description: Product of two matrices.

m:The other matrix.
Returns:The matrix product self*m

Python specific notes:
This method is also available as '__rmul__'

(2) Signature: [const] Point * (const Point p)

Description: Transforms a point with this matrix.

p:The point to transform.
Returns:The transformed point

Python specific notes:
This method is also available as '__rmul__'

(3) Signature: [const] Vector * (const Vector v)

Description: Transforms a vector with this matrix.

v:The vector to transform.
Returns:The transformed vector

Python specific notes:
This method is also available as '__rmul__'

(4) Signature: [const] Edge * (const Edge e)

Description: Transforms an edge with this matrix.

e:The edge to transform.
Returns:The transformed edge

Python specific notes:
This method is also available as '__rmul__'

(5) Signature: [const] Box * (const Box box)

Description: Transforms a box with this matrix.

box:The box to transform.
Returns:The transformed box

Please note that the box remains a box, even though the matrix supports shear and rotation. The returned box will be the bounding box of the sheared and rotated rectangle.

Python specific notes:
This method is also available as '__rmul__'

(6) Signature: [const] SimplePolygon * (const SimplePolygon p)

Description: Transforms a simple polygon with this matrix.

p:The simple polygon to transform.
Returns:The transformed simple polygon

Python specific notes:
This method is also available as '__rmul__'

(7) Signature: [const] Polygon * (const Polygon p)

Description: Transforms a polygon with this matrix.

p:The polygon to transform.
Returns:The transformed polygon

Python specific notes:
This method is also available as '__rmul__'

+

Signature: [const] IMatrix3d + (const IMatrix3d m)

Description: Sum of two matrices.

m:The other matrix.
Returns:The (element-wise) sum of self+m

_create

Signature: void _create

Description: Ensures the C++ object is created

Use this method to ensure the C++ object is created, for example to ensure that resources are allocated. Usually C++ objects are created on demand and not necessarily when the script object is created.

_destroy

Signature: void _destroy

Description: Explicitly destroys the object

Explicitly destroys the object on C++ side if it was owned by the script interpreter. Subsequent access to this object will throw an exception. If the object is not owned by the script, this method will do nothing.

_destroyed?

Signature: [const] bool _destroyed?

Description: Returns a value indicating whether the object was already destroyed

This method returns true, if the object was destroyed, either explicitly or by the C++ side. The latter may happen, if the object is owned by a C++ object which got destroyed itself.

_is_const_object?

Signature: [const] bool _is_const_object?

Description: Returns a value indicating whether the reference is a const reference

This method returns true, if self is a const reference. In that case, only const methods may be called on self.

_manage

Signature: void _manage

Description: Marks the object as managed by the script side.

After calling this method on an object, the script side will be responsible for the management of the object. This method may be called if an object is returned from a C++ function and the object is known not to be owned by any C++ instance. If necessary, the script side may delete the object if the script's reference is no longer required.

Usually it's not required to call this method. It has been introduced in version 0.24.

_unmanage

Signature: void _unmanage

Description: Marks the object as no longer owned by the script side.

Calling this method will make this object no longer owned by the script's memory management. Instead, the object must be managed in some other way. Usually this method may be called if it is known that some C++ object holds and manages this object. Technically speaking, this method will turn the script's reference into a weak reference. After the script engine decides to delete the reference, the object itself will still exist. If the object is not managed otherwise, memory leaks will occur.

Usually it's not required to call this method. It has been introduced in version 0.24.

angle

Signature: [const] double angle

Description: Returns the rotation angle of the rotation component of this matrix.

Returns:The angle in degree.

See the description of this class for details about the basic transformations.

assign

Signature: void assign (const IMatrix3d other)

Description: Assigns another object to self

cplx_trans

Signature: [const] DCplxTrans cplx_trans

Description: Converts this matrix to a complex transformation (if possible).

Returns:The complex transformation.

This method is successful only if the matrix does not contain shear or perspective distortion components and the magnification must be isotropic.

create

Signature: void create

Description: Ensures the C++ object is created

Use of this method is deprecated. Use _create instead

Use this method to ensure the C++ object is created, for example to ensure that resources are allocated. Usually C++ objects are created on demand and not necessarily when the script object is created.

destroy

Signature: void destroy

Description: Explicitly destroys the object

Use of this method is deprecated. Use _destroy instead

Explicitly destroys the object on C++ side if it was owned by the script interpreter. Subsequent access to this object will throw an exception. If the object is not owned by the script, this method will do nothing.

destroyed?

Signature: [const] bool destroyed?

Description: Returns a value indicating whether the object was already destroyed

Use of this method is deprecated. Use _destroyed? instead

This method returns true, if the object was destroyed, either explicitly or by the C++ side. The latter may happen, if the object is owned by a C++ object which got destroyed itself.

disp

Signature: [const] Vector disp

Description: Returns the displacement vector of this transformation.

Returns:The displacement vector.

Starting with version 0.25 this method returns a vector type instead of a point.

dup

Signature: [const] new IMatrix3d ptr dup

Description: Creates a copy of self

Python specific notes:
This method also implements '__copy__'

inverted

Signature: [const] IMatrix3d inverted

Description: The inverse of this matrix.

Returns:The inverse of this matrix

is_const_object?

Signature: [const] bool is_const_object?

Description: Returns a value indicating whether the reference is a const reference

Use of this method is deprecated. Use _is_const_object? instead

This method returns true, if self is a const reference. In that case, only const methods may be called on self.

is_mirror?

Signature: [const] bool is_mirror?

Description: Returns the mirror flag of this matrix.

Returns:True if this matrix has a mirror component.

See the description of this class for details about the basic transformations.

m

Signature: [const] double m (int i, int j)

Description: Gets the m coefficient with the given index.

Returns:The coefficient [i,j]

mag_x

Signature: [const] double mag_x

Description: Returns the x magnification of the magnification component of this matrix.

Returns:The magnification factor.

mag_y

Signature: [const] double mag_y

Description: Returns the y magnification of the magnification component of this matrix.

Returns:The magnification factor.

new

(1) Signature: [static] new IMatrix3d ptr new

Description: Create a new Matrix3d representing a unit transformation

Python specific notes:
This method is the default initializer of the object

(2) Signature: [static] new IMatrix3d ptr new (double m)

Description: Create a new Matrix3d representing a magnification

m:The magnification

Python specific notes:
This method is the default initializer of the object

(3) Signature: [static] new IMatrix3d ptr new (const ICplxTrans t)

Description: Create a new Matrix3d from the given complex transformation@param t The transformation from which to create the matrix

Python specific notes:
This method is the default initializer of the object

(4) Signature: [static] new IMatrix3d ptr new (double m11, double m12, double m21, double m22)

Description: Create a new Matrix3d from the four coefficients of a Matrix2d

Python specific notes:
This method is the default initializer of the object

(5) Signature: [static] new IMatrix3d ptr new (double m11, double m12, double m21, double m22, double dx, double dy)

Description: Create a new Matrix3d from the four coefficients of a Matrix2d plus a displacement

Python specific notes:
This method is the default initializer of the object

(6) Signature: [static] new IMatrix3d ptr new (double m11, double m12, double m13, double m21, double m22, double m23, double m31, double m32, double m33)

Description: Create a new Matrix3d from the nine matrix coefficients

Python specific notes:
This method is the default initializer of the object

newc

(1) Signature: [static] new IMatrix3d ptr newc (double mag, double rotation, bool mirrx)

Description: Create a new Matrix3d representing a isotropic magnification, rotation and mirroring

mag:The magnification
rotation:The rotation angle (in degree)
mirrx:The mirror flag (at x axis)

The order of execution of the operations is mirror, magnification and rotation. This constructor is called 'newc' to distinguish it from the constructors taking coefficients ('c' is for composite).

(2) Signature: [static] new IMatrix3d ptr newc (double shear, double mx, double my, double rotation, bool mirrx)

Description: Create a new Matrix3d representing a shear, anisotropic magnification, rotation and mirroring

shear:The shear angle
mx:The magnification in x direction
mx:The magnification in y direction
rotation:The rotation angle (in degree)
mirrx:The mirror flag (at x axis)

The order of execution of the operations is mirror, magnification, rotation and shear. This constructor is called 'newc' to distinguish it from the constructor taking the four matrix coefficients ('c' is for composite).

(3) Signature: [static] new IMatrix3d ptr newc (const Vector u, double shear, double mx, double my, double rotation, bool mirrx)

Description: Create a new Matrix3d representing a displacement, shear, anisotropic magnification, rotation and mirroring

u:The displacement
shear:The shear angle
mx:The magnification in x direction
mx:The magnification in y direction
rotation:The rotation angle (in degree)
mirrx:The mirror flag (at x axis)

The order of execution of the operations is mirror, magnification, rotation, shear and displacement. This constructor is called 'newc' to distinguish it from the constructor taking the four matrix coefficients ('c' is for composite).

Starting with version 0.25 the displacement is of vector type.

(4) Signature: [static] new IMatrix3d ptr newc (double tx, double ty, double z, const Vector u, double shear, double mx, double my, double rotation, bool mirrx)

Description: Create a new Matrix3d representing a perspective distortion, displacement, shear, anisotropic magnification, rotation and mirroring

tx:The perspective tilt angle x (around the y axis)
ty:The perspective tilt angle y (around the x axis)
z:The observer distance at which the tilt angles are given
u:The displacement
shear:The shear angle
mx:The magnification in x direction
mx:The magnification in y direction
rotation:The rotation angle (in degree)
mirrx:The mirror flag (at x axis)

The order of execution of the operations is mirror, magnification, rotation, shear, perspective distortion and displacement. This constructor is called 'newc' to distinguish it from the constructor taking the four matrix coefficients ('c' is for composite).

The tx and ty parameters represent the perspective distortion. They denote a tilt of the xy plane around the y axis (tx) or the x axis (ty) in degree. The same effect is achieved for different tilt angles for different observer distances. Hence, the observer distance must be given at which the tilt angles are given. If the magnitude of the tilt angle is not important, z can be set to 1.

Starting with version 0.25 the displacement is of vector type.

shear_angle

Signature: [const] double shear_angle

Description: Returns the magnitude of the shear component of this matrix.

Returns:The shear angle in degree.

The shear basic transformation will tilt the x axis towards the y axis and vice versa. The shear angle gives the tilt angle of the axes towards the other one. The possible range for this angle is -45 to 45 degree.See the description of this class for details about the basic transformations.

to_s

Signature: [const] string to_s

Description: Convert the matrix to a string.

Returns:The string representing this matrix

Python specific notes:
This method is also available as 'str(object)'

trans

Signature: [const] Point trans (const Point p)

Description: Transforms a point with this matrix.

p:The point to transform.
Returns:The transformed point

Python specific notes:
This method is also available as '__rmul__'

tx

Signature: [const] double tx (double z)

Description: Returns the perspective tilt angle tx.

z:The observer distance at which the tilt angle is computed.
Returns:The tilt angle tx.

The tx and ty parameters represent the perspective distortion. They denote a tilt of the xy plane around the y axis (tx) or the x axis (ty) in degree. The same effect is achieved for different tilt angles at different observer distances. Hence, the observer distance must be specified at which the tilt angle is computed. If the magnitude of the tilt angle is not important, z can be set to 1.

ty

Signature: [const] double ty (double z)

Description: Returns the perspective tilt angle ty.

z:The observer distance at which the tilt angle is computed.
Returns:The tilt angle ty.

The tx and ty parameters represent the perspective distortion. They denote a tilt of the xy plane around the y axis (tx) or the x axis (ty) in degree. The same effect is achieved for different tilt angles at different observer distances. Hence, the observer distance must be specified at which the tilt angle is computed. If the magnitude of the tilt angle is not important, z can be set to 1.