Module org.arakhne.afc.core.mathgeom

Package org.arakhne.afc.math.geometry.d2

Class Transform2D

java.lang.Object

org.arakhne.afc.math.matrix.Matrix3d

org.arakhne.afc.math.geometry.d2.Transform2D

All Implemented Interfaces:

Serializable, Cloneable

public class Transform2D
extends Matrix3d

A 2D transformation. Is represented internally as a 3x3 floating point matrix. The mathematical representation is row major, as in traditional matrix mathematics.

The transformation matrix is:

 | cos(theta)   | -+sin(theta) | Tx |
 | -+sin(theta) |   cos(theta) | Ty |
 | 0            | 0            | 1  |
 

Version:

17.0 2020-01-04 14:41:43

Author:

Stéphane GALLAND

See Also:

Serialized Form

Maven Group Id:

org.arakhne.afc.core

Maven Artifact Id:

mathgeom

Field Summary

Fields

Modifier and Type	Field	Description
static Transform2D	IDENTITY	This is the identifity transformation.

Fields inherited from class org.arakhne.afc.math.matrix.Matrix3d

isIdentity, m00, m01, m02, m10, m11, m12, m20, m21, m22

Constructor Summary

Constructors

Constructor	Description
Transform2D()	Constructs a new Transform2D object and sets it to the identity transformation.
Transform2D(double m00, double m01, double m02, double m10, double m11, double m12)	Constructs and initializes a Matrix3f from the specified nine values.
Transform2D(Transform2D tranform)	Constructs a new Transform2D object and initializes it from the specified transform.
Transform2D(Matrix3d matrix)	Constructor by copy.

Method Summary

Modifier and Type	Method	Description
Transform2D	clone()	Creates a new object of the same class as this object.
Transform2D	createInverse()	Returns an Transform2D object representing the inverse transformation.
double	getRotation()	Performs an SVD normalization of this matrix to calculate and return the rotation angle.
double	getScale()	Performs an SVD normalization of this matrix to calculate and return the uniform scale factor.
protected void	getScaleRotate2x2(double[] scales, double[] rots)	Perform SVD on the 2x2 matrix containing the rotation and scaling factors.
void	getScaleVector(Tuple2D<?> scale)	Performs an SVD normalization of this matrix to calculate and return the scale factors for X and Y axess.
double	getScaleX()	Performs an SVD normalization of this matrix to calculate and return the scale factor for X axis.
double	getScaleY()	Performs an SVD normalization of this matrix to calculate and return the scale factor for Y axis.
void	getTranslationVector(Tuple2D<?> translation)	Replies the translation.
double	getTranslationX()	Replies the X translation.
double	getTranslationY()	Replies the Y translation.
void	invert()	Invert this transformation.
void	invert(Matrix3d matrix)	Invert this transformation.
void	makeRotationMatrix(double angle)	Sets the value of this matrix to a counter clockwise rotation about the x axis, and no translation
void	makeScaleMatrix(double scaleX, double scaleY)	Sets the value of this matrix to the given scaling, without rotation.
void	makeTranslationMatrix(double dx, double dy)	Sets the value of this matrix to the given translation, without rotation.
void	rotate(double theta)	Rotate the object (theta).
void	scale(double scale)	Concatenates this transform with a scaling transformation.
void	scale(double scaleX, double scaleY)	Concatenates this transform with a scaling transformation.
void	scale(Tuple2D<?> tuple)	Concatenates this transform with a scaling transformation.
void	set(double m00, double m01, double m02, double m10, double m11, double m12)	Set the components of the transformation.
void	setRotation(double angle)	Change the rotation of this matrix.
void	setScale(double scaleX, double scaleY)	Change the scale of this matrix.
void	setScale(Tuple2D<?> tuple)	Set the scale.
void	setTranslation(double x, double y)	Set the position.
void	setTranslation(Tuple2D<?> translation)	Set the position.
void	shear(double shearX, double shearY)	Concatenates this transform with a shearing transformation.
void	shear(Tuple2D<?> shear)	Concatenates this transform with a shearing transformation.
void	transform(Tuple2D<?> tuple)	Multiply this matrix by the tuple t and place the result back into the tuple (t = this*t).
void	transform(Tuple2D<?> tuple, Tuple2D<?> result)	Multiply this matrix by the tuple t and and place the result into the tuple "result".
void	translate(double dx, double dy)	Translate the position.
void	translate(Vector2D<?,?> translation)	Translate the position.

Methods inherited from class org.arakhne.afc.math.matrix.Matrix3d

$bang, $div, $minus, $minus, $minus, $plus, $plus, $times, $times, add, add, add, add, computeSVD, cov, cov, cov, determinant, eigenVectorsOfSymmetricMatrix, epsilonEquals, equals, equals, getColumn, getColumn, getElement, getM00, getM01, getM02, getM10, getM11, getM12, getM20, getM21, getM22, getRow, getRow, hashCode, isIdentity, isSymmetric, mul, mul, mul, mul, mul, mulNormalize, mulNormalize, mulTransposeBoth, mulTransposeLeft, mulTransposeLeft, mulTransposeRight, negate, negate, normalize, normalize, normalizeCP, normalizeCP, operator_add, operator_add, operator_divide, operator_minus, operator_minus, operator_minus, operator_moinsMoins, operator_multiply, operator_multiply, operator_not, operator_plus, operator_plus, operator_plusPlus, operator_remove, operator_remove, set, set, set, setColumn, setColumn, setColumn, setDiagonal, setElement, setIdentity, setM00, setM01, setM02, setM10, setM11, setM12, setM20, setM21, setM22, setRow, setRow, setRow, setZero, sub, sub, toString, transpose, transpose

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

IDENTITY

public static final Transform2D IDENTITY

This is the identifity transformation.

Constructor Detail

Transform2D

public Transform2D()

Constructs a new Transform2D object and sets it to the identity transformation.

Transform2D

public Transform2D(Transform2D tranform)

Constructs a new Transform2D object and initializes it from the specified transform.

Parameters:

tranform - the transformation to copy.

Transform2D

public Transform2D(Matrix3d matrix)

Constructor by copy.

Parameters:

matrix - the matrix to copy.

Transform2D

public Transform2D(double m00,
                   double m01,
                   double m02,
                   double m10,
                   double m11,
                   double m12)

Constructs and initializes a Matrix3f from the specified nine values.

Parameters:

m00 - the [0][0] element

m01 - the [0][1] element

m02 - the [0][2] element

m10 - the [1][0] element

m11 - the [1][1] element

m12 - the [1][2] element

Method Detail

clone

@Pure
public Transform2D clone()

Description copied from class: Matrix3d

Creates a new object of the same class as this object.

Overrides:

clone in class Matrix3d

Returns:

a clone of this instance.

See Also:

Cloneable

setTranslation

public void setTranslation(double x,
                           double y)

Set the position.

This function changes only the elements of the matrix related to the translation (m02, m12). The scaling and the shearing are not changed.

After a call to this function, the matrix will contains (? means any value):

          [   ?    ?    x   ]
          [   ?    ?    y   ]
          [   ?    ?    ?   ]
 

Parameters:

x - x translation.

y - y translation.

See Also:

makeTranslationMatrix(double, double)

setTranslation

public void setTranslation(Tuple2D<?> translation)

Set the position.

This function changes only the elements of the matrix related to the translation (m02, m12). The scaling and the shearing are not changed.

After a call to this function, the matrix will contains (? means any value):

          [   ?    ?    t.x   ]
          [   ?    ?    t.y   ]
          [   ?    ?    ?     ]
 

Parameters:

translation - the translation.

See Also:

makeTranslationMatrix(double, double)

translate

public void translate(double dx,
                      double dy)

Translate the position.

This function is equivalent to:

 this = this *  [   1    0    dx   ]
                [   0    1    dy   ]
                [   0    0    1    ]
 

Parameters:

dx - the x translation

dy - the y translation

translate

public void translate(Vector2D<?,?> translation)

Translate the position.

This function is equivalent to:

 this = this *  [   1    0    t.x   ]
                [   0    1    t.y   ]
                [   0    0    1     ]
 

Parameters:

translation - the translation.

getTranslationX

@Pure
public double getTranslationX()

Replies the X translation.

Returns:

the amount

getTranslationY

@Pure
public double getTranslationY()

Replies the Y translation.

Returns:

the amount

getTranslationVector

@Pure
public void getTranslationVector(Tuple2D<?> translation)

Replies the translation.

Parameters:

translation - the vector to set with the translation component.

rotate

public void rotate(double theta)

Rotate the object (theta).

This function is equivalent to:

 this = this *  [   cos(theta)    -sin(theta)    0   ]
                [   sin(theta)    cos(theta)     0   ]
                [   0             0              1   ]
 

Parameters:

theta - the rotation angle, in radians.

getScaleRotate2x2

protected void getScaleRotate2x2(double[] scales,
                                 double[] rots)

Perform SVD on the 2x2 matrix containing the rotation and scaling factors.

Parameters:

scales - the scaling factors.

rots - the rotation factors.

getRotation

@Pure
public double getRotation()

Performs an SVD normalization of this matrix to calculate and return the rotation angle.

Returns:

the rotation angle of this matrix. The value is in [-PI; PI]

setRotation

public void setRotation(double angle)

Change the rotation of this matrix. Performs an SVD normalization of this matrix for determining and preserving the scaling.

Parameters:

angle - the rotation angle.

scale

public void scale(double scaleX,
                  double scaleY)

Concatenates this transform with a scaling transformation.

This function is equivalent to:

 this = this *  [   sx   0    0   ]
                [   0    sy   0   ]
                [   0    0    1   ]
 

Parameters:

scaleX - scaling along x axis.

scaleY - scaling along y axis.

scale

public void scale(Tuple2D<?> tuple)

Concatenates this transform with a scaling transformation.

This function is equivalent to:

 this = this *  [   t.x   0     0   ]
                [   0     t.y   0   ]
                [   0     0     1   ]
 

Parameters:

tuple - the scaling factors.

scale

public void scale(double scale)

Concatenates this transform with a scaling transformation.

This function is equivalent to:

 this = this *  [   s    0    0   ]
                [   0    s    0   ]
                [   0    0    1   ]
 

Parameters:

scale - the scaling factor.

getScale

@Pure
public double getScale()

Performs an SVD normalization of this matrix to calculate and return the uniform scale factor. If the matrix has non-uniform scale factors, the largest of the x, y scale factors will be returned.

Returns:

the scale factor of this matrix.

getScaleX

@Pure
public double getScaleX()

Performs an SVD normalization of this matrix to calculate and return the scale factor for X axis.

Returns:

the x scale factor.

getScaleY

@Pure
public double getScaleY()

Performs an SVD normalization of this matrix to calculate and return the scale factor for Y axis.

Returns:

the y scale factor.

getScaleVector

@Pure
public void getScaleVector(Tuple2D<?> scale)

Performs an SVD normalization of this matrix to calculate and return the scale factors for X and Y axess.

Parameters:

scale - the tuple to set.

setScale

public void setScale(double scaleX,
                     double scaleY)

Change the scale of this matrix. Performs an SVD normalization of this matrix for determining and preserving the rotation.

Parameters:

scaleX - the scaling factor along x axis.

scaleY - the scaling factor along y axis.

See Also:

makeScaleMatrix(double, double)

setScale

public void setScale(Tuple2D<?> tuple)

Set the scale.

This function changes only the elements of the matrix related to the scaling (m00, m11). The shearing and the translation are not changed. The rotation is lost.

After a call to this function, the matrix will contains (? means any value):

          [   t.x  ?    ?   ]
          [   ?    t.y  ?   ]
          [   ?    ?    ?   ]
 

Parameters:

tuple - the scaling factors.

See Also:

makeScaleMatrix(double, double)

shear

public void shear(double shearX,
                  double shearY)

Concatenates this transform with a shearing transformation.

This function is equivalent to:

 this = this *  [   1    shx  0   ]
                [   shy  1    0   ]
                [   0    0    1   ]
 

Parameters:

shearX - the shearing factory along x axis.

shearY - the shearing factory along y axis.

shear

public void shear(Tuple2D<?> shear)

Concatenates this transform with a shearing transformation.

This function is equivalent to:

 this = this *  [   1    shx  0   ]
                [   shy  1    0   ]
                [   0    0    1   ]
 

Parameters:

shear - the shear factors.

makeRotationMatrix

public void makeRotationMatrix(double angle)

Sets the value of this matrix to a counter clockwise rotation about the x axis, and no translation

This function changes all the elements of the matrix, icluding the translation.

After a call to this function, the matrix will contains (? means any value):

          [   cos(theta)  -sin(theta)  0   ]
          [   sin(theta)  cos(theta)   0   ]
          [   0           0            1   ]
 

Parameters:

angle - the angle to rotate about the X axis in radians

See Also:

setRotation(double)

makeTranslationMatrix

public void makeTranslationMatrix(double dx,
                                  double dy)

Sets the value of this matrix to the given translation, without rotation.

This function changes all the elements of the matrix including the scaling and the shearing.

After a call to this function, the matrix will contains (? means any value):

          [   1    0    x   ]
          [   0    1    y   ]
          [   0    0    1   ]
 

Parameters:

dx - is the translation along X.

dy - is the translation along Y.

See Also:

setTranslation(double, double), setTranslation(Tuple2D)

makeScaleMatrix

public void makeScaleMatrix(double scaleX,
                            double scaleY)

Sets the value of this matrix to the given scaling, without rotation.

This function changes all the elements of the matrix, including the shearing and the translation.

After a call to this function, the matrix will contains (? means any value):

          [   sx  0   0   ]
          [   0   sy  0   ]
          [   0   0   1   ]
 

Parameters:

scaleX - is the scaling along X.

scaleY - is the scaling along Y.

See Also:

setScale(double, double), setScale(Tuple2D)

transform

public void transform(Tuple2D<?> tuple)

Multiply this matrix by the tuple t and place the result back into the tuple (t = this*t).

Parameters:

tuple - the tuple to be multiplied by this matrix and then replaced

transform

public void transform(Tuple2D<?> tuple,
                      Tuple2D<?> result)

Multiply this matrix by the tuple t and and place the result into the tuple "result".

This function is equivalent to:

 result = this *  [   t.x   ]
                  [   t.y   ]
                  [   1     ]
 

Parameters:

tuple - the tuple to be multiplied by this matrix

result - the tuple into which the product is placed

createInverse

@Pure
public Transform2D createInverse()

Returns an Transform2D object representing the inverse transformation. The inverse transform Tx' of this transform Tx maps coordinates transformed by Tx back to their original coordinates. In other words, Tx'(Tx(p)) = p = Tx(Tx'(p)).

If this transform maps all coordinates onto a point or a line then it will not have an inverse, since coordinates that do not lie on the destination point or line will not have an inverse mapping. The determinant method can be used to determine if this transform has no inverse, in which case an exception will be thrown if the createInverse method is called.

Returns:

a new Transform2D object representing the inverse transformation.

See Also:

Matrix3d.determinant()

set

public void set(double m00,
                double m01,
                double m02,
                double m10,
                double m11,
                double m12)

Set the components of the transformation.

Parameters:

m00 - the [0][0] element

m01 - the [0][1] element

m02 - the [0][2] element

m10 - the [1][0] element

m11 - the [1][1] element

m12 - the [1][2] element

invert

public void invert()

Invert this transformation. The inverse transform Tx' of this transform Tx maps coordinates transformed by Tx back to their original coordinates. In other words, Tx'(Tx(p)) = p = Tx(Tx'(p)).

If this transform maps all coordinates onto a point or a line then it will not have an inverse, since coordinates that do not lie on the destination point or line will not have an inverse mapping. The determinant method can be used to determine if this transform has no inverse, in which case an exception will be thrown if the createInverse method is called.

Overrides:

invert in class Matrix3d

See Also:

Matrix3d.determinant()

invert

public void invert(Matrix3d matrix)

Invert this transformation. The inverse transform Tx' of this transform Tx maps coordinates transformed by Tx back to their original coordinates. In other words, Tx'(Tx(p)) = p = Tx(Tx'(p)).

If this transform maps all coordinates onto a point or a line then it will not have an inverse, since coordinates that do not lie on the destination point or line will not have an inverse mapping. The determinant method can be used to determine if this transform has no inverse, in which case an exception will be thrown if the createInverse method is called.

Overrides:

invert in class Matrix3d

Parameters:

matrix - is the matrix to invert

See Also:

Matrix3d.determinant()