org.apache.commons.geometry.euclidean.twod

Class AffineTransformMatrix2D

java.lang.Object

org.apache.commons.geometry.euclidean.AbstractAffineTransformMatrix<Vector2D,AffineTransformMatrix2D>

org.apache.commons.geometry.euclidean.twod.AffineTransformMatrix2D

All Implemented Interfaces:

Function<Vector2D,Vector2D>, UnaryOperator<Vector2D>, Transform<Vector2D>, EuclideanTransform<Vector2D>

public final class AffineTransformMatrix2D
extends AbstractAffineTransformMatrix<Vector2D,AffineTransformMatrix2D>

Class using a matrix to represent affine transformations in 2 dimensional Euclidean space.

Instances of this class use a 3x3 matrix for all transform operations. The last row of this matrix is always set to the values [0 0 1] and so is not stored. Hence, the methods in this class that accept or return arrays always use arrays containing 6 elements, instead of 9.

Method Summary

Modifier and Type	Method and Description
Vector2D	apply(Vector2D pt) Apply this transform to the given point, returning the result as a new instance.
Vector2D.Unit	applyDirection(Vector2D vec) Apply this transform to the given vector, ignoring translations and normalizing the result.
Vector2D	applyVector(Vector2D vec) Apply this transform to the given vector, ignoring translations.
double	applyVectorX(double x, double y) Apply this transform to the given vector coordinates, ignoring translations, and return the transformed x value.
double	applyVectorY(double x, double y) Apply this transform to the given vector coordinates, ignoring translations, and return the transformed y value.
double	applyX(double x, double y) Apply this transform to the given point coordinates and return the transformed x value.
double	applyY(double x, double y) Apply this transform to the given point coordinates and return the transformed y value.
static AffineTransformMatrix2D	createRotation(double angle) Create a transform representing a counterclockwise rotation of angle radians around the origin.
static AffineTransformMatrix2D	createRotation(Vector2D center, double angle) Create a transform representing a counterclockwise rotation of angle radians around the given center point.
static AffineTransformMatrix2D	createRotation(Vector2D center, Rotation2D rotation) Create a transform representing a counterclockwise rotation around the given center point.
static AffineTransformMatrix2D	createScale(double factor) Create a transform representing a scale operation with the given scale factor applied to all axes.
static AffineTransformMatrix2D	createScale(double x, double y) Create a transform representing a scale operation.
static AffineTransformMatrix2D	createScale(Vector2D factors) Create a transform representing a scale operation.
static AffineTransformMatrix2D	createShear(double shx, double shy) Create a transform representing a shear operation.
static AffineTransformMatrix2D	createTranslation(double x, double y) Create a transform representing the given translation.
static AffineTransformMatrix2D	createTranslation(Vector2D translation) Create a transform representing the given translation.
double	determinant() Get the determinant of the matrix.
boolean	equals(Object obj) Return true if the given object is an instance of AffineTransformMatrix2D and all matrix element values are exactly equal.
static AffineTransformMatrix2D	from(UnaryOperator<Vector2D> fn) Construct a new transform representing the given function.
static AffineTransformMatrix2D	fromColumnVectors(Vector2D u, Vector2D v) Get a new transform create from the given column vectors.
static AffineTransformMatrix2D	fromColumnVectors(Vector2D u, Vector2D v, Vector2D t) Get a new transform created from the given column vectors.
int	hashCode()
static AffineTransformMatrix2D	identity() Get the transform representing the identity matrix.
AffineTransformMatrix2D	inverse()
AffineTransformMatrix2D	linear() Return a matrix containing only the linear portion of this transform.
AffineTransformMatrix2D	linearTranspose() Return a matrix containing the transpose of the linear portion of this transform.
AffineTransformMatrix2D	multiply(AffineTransformMatrix2D m) Get a new transform created by multiplying this instance by the argument.
static AffineTransformMatrix2D	of(double... arr) Get a new transform with the given matrix elements.
AffineTransformMatrix2D	premultiply(AffineTransformMatrix2D m) Get a new transform created by multiplying the argument by this instance.
AffineTransformMatrix2D	rotate(double angle) Apply a counterclockwise rotation to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	rotate(Rotation2D rotation) Apply a counterclockwise rotation to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	rotate(Vector2D center, double angle) Apply a counterclockwise rotation about the given center point to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	rotate(Vector2D center, Rotation2D rotation) Apply a counterclockwise rotation about the given center point to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	scale(double factor) Apply a scale operation to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	scale(double x, double y) Apply a scale operation to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	scale(Vector2D scaleFactors) Apply a scale operation to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	shear(double shx, double shy) Apply a shear to the current instance, returning the result as a new transform.
double[]	toArray() Return a 6 element array containing the variable elements from the internal transformation matrix.
String	toString()
AffineTransformMatrix2D	translate(double x, double y) Apply a translation to the current instance, returning the result as a new transform.
AffineTransformMatrix2D	translate(Vector2D translation) Apply a translation to the current instance, returning the result as a new transform.

Methods inherited from class org.apache.commons.geometry.euclidean.AbstractAffineTransformMatrix

normalTransform, preservesOrientation

Methods inherited from class java.lang.Object

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

Methods inherited from interface java.util.function.Function

andThen, compose

Method Detail

toArray

public double[] toArray()

Return a 6 element array containing the variable elements from the internal transformation matrix. The elements are in row-major order. The array indices map to the internal matrix as follows:

      [
          arr[0],   arr[1],   arr[2],
          arr[3],   arr[4],   arr[5],
          0         0         1
      ]
 

Returns:

6 element array containing the variable elements from the internal transformation matrix

apply

public Vector2D apply(Vector2D pt)

Apply this transform to the given point, returning the result as a new instance.

The transformed point is computed by creating a 3-element column vector from the coordinates in the input and setting the last element to 1. This is then multiplied with the 3x3 transform matrix to produce the transformed point. The 1 in the last position is ignored.

      [ m00  m01  m02 ]     [ x ]     [ x']
      [ m10  m11  m12 ]  *  [ y ]  =  [ y']
      [ 0    0    1   ]     [ 1 ]     [ 1 ]
 

applyX

public double applyX(double x,
                     double y)

Apply this transform to the given point coordinates and return the transformed x value. The return value is equal to (x * m00) + (y * m01) + m02.

Parameters:

x - x coordinate value

y - y coordinate value

Returns:

transformed x coordinate value

See Also:

apply(Vector2D)

applyY

public double applyY(double x,
                     double y)

Apply this transform to the given point coordinates and return the transformed y value. The return value is equal to (x * m10) + (y * m11) + m12.

Parameters:

x - x coordinate value

y - y coordinate value

Returns:

transformed y coordinate value

See Also:

apply(Vector2D)

applyVector

public Vector2D applyVector(Vector2D vec)

Apply this transform to the given vector, ignoring translations.

This method can be used to transform vector instances representing displacements between points. For example, if v represents the difference between points p1 and p2, then transform.applyVector(v) will represent the difference between p1 and p2 after transform is applied.

The transformed vector is computed by creating a 3-element column vector from the coordinates in the input and setting the last element to 0. This is then multiplied with the 3x3 transform matrix to produce the transformed vector. The 0 in the last position is ignored.

      [ m00  m01  m02 ]     [ x ]     [ x']
      [ m10  m11  m12 ]  *  [ y ]  =  [ y']
      [ 0    0    1   ]     [ 0 ]     [ 0 ]
 

Parameters:

vec - the vector to transform

Returns:

the new, transformed vector

See Also:

applyDirection(Vector2D)

applyVectorX

public double applyVectorX(double x,
                           double y)

Apply this transform to the given vector coordinates, ignoring translations, and return the transformed x value. The return value is equal to (x * m00) + (y * m01).

Parameters:

x - x coordinate value

y - y coordinate value

Returns:

transformed x coordinate value

See Also:

applyVector(Vector2D)

applyVectorY

public double applyVectorY(double x,
                           double y)

Apply this transform to the given vector coordinates, ignoring translations, and return the transformed y value. The return value is equal to (x * m10) + (y * m11).

Parameters:

x - x coordinate value

y - y coordinate value

Returns:

transformed y coordinate value

See Also:

applyVector(Vector2D)

applyDirection

public Vector2D.Unit applyDirection(Vector2D vec)

Apply this transform to the given vector, ignoring translations and normalizing the result. This is equivalent to transform.applyVector(vec).normalize() but without the intermediate vector instance.

Specified by:

applyDirection in class AbstractAffineTransformMatrix<Vector2D,AffineTransformMatrix2D>

Parameters:

vec - the vector to transform

Returns:

the new, transformed unit vector

See Also:

applyVector(Vector2D)

determinant

public double determinant()

Get the determinant of the matrix.

Specified by:

determinant in class AbstractAffineTransformMatrix<Vector2D,AffineTransformMatrix2D>

Returns:

the determinant of the matrix

linear

public AffineTransformMatrix2D linear()

Return a matrix containing only the linear portion of this transform. The returned instance contains the same matrix elements as this instance but with the translation component set to zero.

Example

      [ a, b, c ]   [ a, b, 0 ]
      [ d, e, f ] → [ d, e, 0 ]
      [ 0, 0, 1 ]   [ 0, 0, 1 ]
 

Specified by:

linear in class AbstractAffineTransformMatrix<Vector2D,AffineTransformMatrix2D>

Returns:

a matrix containing only the linear portion of this transform

linearTranspose

public AffineTransformMatrix2D linearTranspose()

Return a matrix containing the transpose of the linear portion of this transform. The returned instance is linear, meaning it has a translation component of zero.

Example

      [ a, b, c ]   [ a, d, 0 ]
      [ d, e, f ] → [ b, e, 0 ]
      [ 0, 0, 1 ]   [ 0, 0, 1 ]
 

Specified by:

linearTranspose in class AbstractAffineTransformMatrix<Vector2D,AffineTransformMatrix2D>

Returns:

a matrix containing the transpose of the linear portion of this transform

translate

public AffineTransformMatrix2D translate(Vector2D translation)

Apply a translation to the current instance, returning the result as a new transform.

Parameters:

translation - vector containing the translation values for each axis

Returns:

a new transform containing the result of applying a translation to the current instance

translate

public AffineTransformMatrix2D translate(double x,
                                         double y)

Apply a translation to the current instance, returning the result as a new transform.

Parameters:

x - translation in the x direction

y - translation in the y direction

Returns:

a new transform containing the result of applying a translation to the current instance

scale

public AffineTransformMatrix2D scale(double factor)

Apply a scale operation to the current instance, returning the result as a new transform.

Parameters:

factor - the scale factor to apply to all axes

Returns:

a new transform containing the result of applying a scale operation to the current instance

scale

public AffineTransformMatrix2D scale(Vector2D scaleFactors)

Apply a scale operation to the current instance, returning the result as a new transform.

Parameters:

scaleFactors - vector containing scale factors for each axis

Returns:

a new transform containing the result of applying a scale operation to the current instance

scale

public AffineTransformMatrix2D scale(double x,
                                     double y)

Apply a scale operation to the current instance, returning the result as a new transform.

Parameters:

x - scale factor for the x axis

y - scale factor for the y axis

Returns:

a new transform containing the result of applying a scale operation to the current instance

rotate

public AffineTransformMatrix2D rotate(double angle)

Apply a counterclockwise rotation to the current instance, returning the result as a new transform.

Parameters:

angle - the angle of counterclockwise rotation in radians

Returns:

a new transform containing the result of applying a rotation to the current instance

See Also:

Rotation2D.of(double)

rotate

public AffineTransformMatrix2D rotate(Rotation2D rotation)

Apply a counterclockwise rotation to the current instance, returning the result as a new transform.

Parameters:

rotation - the rotation to apply

Returns:

a new transform containing the result of applying the rotation to the current instance

rotate

public AffineTransformMatrix2D rotate(Vector2D center,
                                      double angle)

Apply a counterclockwise rotation about the given center point to the current instance, returning the result as a new transform. This is accomplished by translating the center to the origin, applying the rotation, and then translating back.

Parameters:

center - the center of rotation

angle - the angle of counterclockwise rotation in radians

Returns:

a new transform containing the result of applying a rotation about the given center point to the current instance

rotate

public AffineTransformMatrix2D rotate(Vector2D center,
                                      Rotation2D rotation)

Apply a counterclockwise rotation about the given center point to the current instance, returning the result as a new transform. This is accomplished by translating the center to the origin, applying the rotation, and then translating back.

Parameters:

center - the center of rotation

rotation - the rotation to apply

Returns:

a new transform containing the result of applying a rotation about the given center point to the current instance

shear

public AffineTransformMatrix2D shear(double shx,
                                     double shy)

Apply a shear to the current instance, returning the result as a new transform.

Parameters:

shx - multiplier by which coordinates are shifted along the positive x-axis as a factor of their y coordinate; a value of 0 indicates no shift along the x-axis

shy - multiplier by which coordinates are shifted along the positive y-axis as a factor of their x coordinate; a value of 0 indicates no shift along the y-axis

Returns:

a new transform containing the result of applying a shear to the current instance

multiply

public AffineTransformMatrix2D multiply(AffineTransformMatrix2D m)

Get a new transform created by multiplying this instance by the argument. This is equivalent to the expression A * M where A is the current transform matrix and M is the given transform matrix. In terms of transformations, applying the returned matrix is equivalent to applying M and then applying A. In other words, the rightmost transform is applied first.

Parameters:

m - the transform to multiply with

Returns:

the result of multiplying the current instance by the given transform matrix

premultiply

public AffineTransformMatrix2D premultiply(AffineTransformMatrix2D m)

Get a new transform created by multiplying the argument by this instance. This is equivalent to the expression M * A where A is the current transform matrix and M is the given transform matrix. In terms of transformations, applying the returned matrix is equivalent to applying A and then applying M. In other words, the rightmost transform is applied first.

Parameters:

m - the transform to multiply with

Returns:

the result of multiplying the given transform matrix by the current instance

inverse

public AffineTransformMatrix2D inverse()

Specified by:

inverse in interface Transform<Vector2D>

Specified by:

inverse in class AbstractAffineTransformMatrix<Vector2D,AffineTransformMatrix2D>

Throws:

IllegalStateException - if the matrix cannot be inverted

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Return true if the given object is an instance of AffineTransformMatrix2D and all matrix element values are exactly equal.

Overrides:

equals in class Object

Parameters:

obj - object to test for equality with the current instance

Returns:

true if all transform matrix elements are exactly equal; otherwise false

toString

public String toString()

Overrides:

toString in class Object

of

public static AffineTransformMatrix2D of(double... arr)

Get a new transform with the given matrix elements. The array must contain 6 elements.

Parameters:

arr - 6-element array containing values for the variable entries in the transform matrix

Returns:

a new transform initialized with the given matrix values

Throws:

IllegalArgumentException - if the array does not have 6 elements

from

public static AffineTransformMatrix2D from(UnaryOperator<Vector2D> fn)

Construct a new transform representing the given function. The function is sampled at the origin and along each axis and a matrix is created to perform the transformation.

Parameters:

fn - function to create a transform matrix from

Returns:

a transform matrix representing the given function

Throws:

IllegalArgumentException - if the given function does not represent a valid affine transform

fromColumnVectors

public static AffineTransformMatrix2D fromColumnVectors(Vector2D u,
                                                        Vector2D v)

Get a new transform create from the given column vectors. The returned transform does not include any translation component.

Parameters:

u - first column vector; this corresponds to the first basis vector in the coordinate frame

v - second column vector; this corresponds to the second basis vector in the coordinate frame

Returns:

a new transform with the given column vectors

fromColumnVectors

public static AffineTransformMatrix2D fromColumnVectors(Vector2D u,
                                                        Vector2D v,
                                                        Vector2D t)

Get a new transform created from the given column vectors.

Parameters:

u - first column vector; this corresponds to the first basis vector in the coordinate frame

v - second column vector; this corresponds to the second basis vector in the coordinate frame

t - third column vector; this corresponds to the translation of the transform

Returns:

a new transform with the given column vectors

identity

public static AffineTransformMatrix2D identity()

Get the transform representing the identity matrix. This transform does not modify point or vector values when applied.

Returns:

transform representing the identity matrix

createTranslation

public static AffineTransformMatrix2D createTranslation(Vector2D translation)

Create a transform representing the given translation.

Parameters:

translation - vector containing translation values for each axis

Returns:

a new transform representing the given translation

createTranslation

public static AffineTransformMatrix2D createTranslation(double x,
                                                        double y)

Create a transform representing the given translation.

Parameters:

x - translation in the x direction

y - translation in the y direction

Returns:

a new transform representing the given translation

createScale

public static AffineTransformMatrix2D createScale(double factor)

Create a transform representing a scale operation with the given scale factor applied to all axes.

Parameters:

factor - scale factor to apply to all axes

Returns:

a new transform representing a uniform scaling in all axes

createScale

public static AffineTransformMatrix2D createScale(Vector2D factors)

Create a transform representing a scale operation.

Parameters:

factors - vector containing scale factors for each axis

Returns:

a new transform representing a scale operation

createScale

public static AffineTransformMatrix2D createScale(double x,
                                                  double y)

Create a transform representing a scale operation.

Parameters:

x - scale factor for the x axis

y - scale factor for the y axis

Returns:

a new transform representing a scale operation

createRotation

public static AffineTransformMatrix2D createRotation(double angle)

Create a transform representing a counterclockwise rotation of angle radians around the origin.

Parameters:

angle - the angle of rotation in radians

Returns:

a new transform representing the rotation

See Also:

Rotation2D.toMatrix()

createRotation

public static AffineTransformMatrix2D createRotation(Vector2D center,
                                                     double angle)

Create a transform representing a counterclockwise rotation of angle radians around the given center point. This is accomplished by translating the center point to the origin, applying the rotation, and then translating back.

Parameters:

center - the center of rotation

angle - the angle of rotation in radians

Returns:

a new transform representing the rotation about the given center

createRotation

public static AffineTransformMatrix2D createRotation(Vector2D center,
                                                     Rotation2D rotation)

Create a transform representing a counterclockwise rotation around the given center point. This is accomplished by translating the center point to the origin, applying the rotation, and then translating back.

Parameters:

center - the center of rotation

rotation - the rotation to apply

Returns:

a new transform representing the rotation about the given center

createShear

public static AffineTransformMatrix2D createShear(double shx,
                                                  double shy)

Create a transform representing a shear operation. The returned instance contains the matrix values

      [ 1,    shx,  0 ]
      [ shy,  1,    0 ]
      [ 0,    0,    0 ]
 

Parameters:

shx - multiplier by which coordinates are shifted along the positive x-axis as a factor of their y coordinate; a value of 0 indicates no shift along the x-axis

shy - multiplier by which coordinates are shifted along the positive y-axis as a factor of their x coordinate; a value of 0 indicates no shift along the y-axis

Returns:

a new transform representing the shear operation