API reference - Class Matrix3d

Notation used in Ruby API documentation

Description: A 3d matrix object used mainly for representing rotation, shear, displacement and perspective transformations.

This object represents a 3x3 matrix. This matrix is used to represent 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.

This class was introduced in version 0.22.

Public constructors

new Matrix3dnewCreate a new Matrix3d representing a unit transformation
new Matrix3dnew(double m)Create a new Matrix3d representing a magnification
new Matrix3dnew(const DCplxTrans arg1)Create a new Matrix3d from the given complex transformation@args t
new Matrix3dnew(double m11,
double m12,
double m21,
double m22)
Create a new Matrix3d from the four coefficients of a Matrix2d
new Matrix3dnew(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 Matrix3dnew(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
new Matrix3dnewc(double mag,
double rotation,
bool mirrx)
Create a new Matrix3d representing a isotropic magnification, rotation and mirroring
new Matrix3dnewc(double shear,
double mx,
double my,
double rotation,
bool mirrx)
Create a new Matrix3d representing a shear, anisotropic magnification, rotation and mirroring
new Matrix3dnewc(const DPoint 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 Matrix3dnewc(double tx,
double ty,
double z,
const DPoint 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

Public methods

[const]Matrix3d*(const Matrix3d arg1)Product two matrices.
[const]DPoint*(const DPoint arg1)Transform a point.
[const]Matrix3d+(const Matrix3d arg1)Sum two matrices.
voidadjust(DPoint[] landmarks_before,
DPoint[] landmarks_after,
int flags,
int fixed_point)
Adjust a 3d matrix to match the given set of landmarks
[const]doubleangleReturns the rotation angle of the rotation component of this matrix.
[const]voidassign(const Matrix3d other)Assign the contents of another object to self
[const]DCplxTranscplx_transConverts this matrix to a complex transformation (if possible).
voidcreateEnsures the C++ object is created
voiddestroyExplicitly destroy the object
[const]booldestroyed?Returns a value indicating whether the object was already destroyed
[const]DPointdispReturns the displacement vector of this transformation.
[const]Matrix3ddupCreates a copy of self
[const]Matrix3dinvertedThe inverse of this matrix.
[const]boolis_const_object?Returns a value indicating whether the reference is a const reference
[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]DPointtrans(const DPoint arg1)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

intAdjustAllMode for adjust: currently equivalent to adjust_perspective
intAdjustDisplacementMode for adjust: adjust displacement only
intAdjustMagnificationMode for adjust: adjust rotation, mirror option and magnification
intAdjustNoneMode for adjust: adjust nothing
intAdjustPerspectiveMode for adjust: adjust whole matrix including perspective transformation
intAdjustRotationMode for adjust: adjust rotation only
intAdjustRotationMirrorMode for adjust: adjust rotation and mirror option
intAdjustShearMode for adjust: adjust rotation, mirror option, magnification and shear

Detailed description

[const] Matrix3d *(const Matrix3d arg1)

Description: Product two matrices.

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

@arg m

[const] DPoint *(const DPoint arg1)

Description: Transform a point.

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

@arg p

[const] Matrix3d +(const Matrix3d arg1)

Description: Sum two matrices.

m:The other matrix.
Returns:The sum self+m

@arg m

[static] int AdjustAll

Description: Mode for adjust: currently equivalent to adjust_perspective

[static] int AdjustDisplacement

Description: Mode for adjust: adjust displacement only

[static] int AdjustMagnification

Description: Mode for adjust: adjust rotation, mirror option and magnification

[static] int AdjustNone

Description: Mode for adjust: adjust nothing

[static] int AdjustPerspective

Description: Mode for adjust: adjust whole matrix including perspective transformation

[static] int AdjustRotation

Description: Mode for adjust: adjust rotation only

[static] int AdjustRotationMirror

Description: Mode for adjust: adjust rotation and mirror option

[static] int AdjustShear

Description: Mode for adjust: adjust rotation, mirror option, magnification and shear

void adjust(DPoint[] landmarks_before,DPoint[] landmarks_after,int flags,int fixed_point)

Description: Adjust a 3d matrix to match the given set of landmarks

landmarks_before:The points before the transformation.
landmarks_after:The points after the transformation.
mode:Selects the adjustment mode. Must be one of the Adjust... constants.
fixed_point:The index of the fixed point (one that is definitly mapped to the target) or -1 if there is none

This function tries to adjust the matrix such, that either the matrix is changed as little as possible (if few landmarks are given) or that the "after" landmarks will match as close as possible to the "before" landmarks (if the problem is overdetermined).

[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.

[const] void assign(const Matrix3d other)

Description: Assign the contents of another object to self

This method assigns the contents of another object to self. This is a deep copy that does not only copy the reference but the actual content.

[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.

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.

void destroy

Description: Explicitly destroy the object

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

[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.

[const] DPoint disp

Description: Returns the displacement vector of this transformation.

Returns:The displacement vector.

[const] Matrix3d dup

Description: Creates a copy of self

[const] Matrix3d inverted

Description: The inverse of this matrix.

Returns:The inverse of this matrix

[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.

[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.

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

Description: Gets the m coefficient with the given index.

Returns:The coefficient [i,j]

[const] double mag_x

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

Returns:The magnification factor.

[const] double mag_y

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

Returns:The magnification factor.

[static] new Matrix3d new

Description: Create a new Matrix3d representing a unit transformation

[static] new Matrix3d new(double m)

Description: Create a new Matrix3d representing a magnification

m:The magnification

[static] new Matrix3d new(const DCplxTrans arg1)

Description: Create a new Matrix3d from the given complex transformation@args t

t:The transformation from which to create the matrix

[static] new Matrix3d new(double m11,double m12,double m21,double m22)

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

[static] new Matrix3d 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

[static] new Matrix3d 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

[static] new Matrix3d 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).

[static] new Matrix3d 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).

[static] new Matrix3d newc(const DPoint 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).

[static] new Matrix3d newc(double tx,double ty,double z,const DPoint 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.

[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.

[const] string to_s

Description: Convert the matrix to a string.

Returns:The string representing this matrix

[const] DPoint trans(const DPoint arg1)

Description: Transforms a point with this matrix.

p:The point to transform.
Returns:The product if self and the point p

@arg p

[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.

[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.