Module imagingbook.common

Package imagingbook.common.geometry.mappings.linear

Class Rotation2D

java.lang.Object

imagingbook.common.geometry.mappings.linear.LinearMapping2D

imagingbook.common.geometry.mappings.linear.ProjectiveMapping2D

imagingbook.common.geometry.mappings.linear.AffineMapping2D

imagingbook.common.geometry.mappings.linear.Rotation2D

All Implemented Interfaces:

Inversion, Jacobian, Mapping2D, Cloneable

public class Rotation2D
extends AffineMapping2D

This class represents a pure 2D rotation about the coordinate origin (as a special case of affine mapping). It can be assumed that every instance of this class is indeed a rotation. See Secs. 21.1.3 and 21.3.1 of [1] for details.

[1] W. Burger, M.J. Burge, Digital Image Processing – An Algorithmic Introduction, 3rd ed, Springer (2022).

Field Summary

Fields inherited from class imagingbook.common.geometry.mappings.linear.LinearMapping2D

a00, a01, a02, a10, a11, a12, a20, a21, a22

Constructor Summary

Constructors

Modifier	Constructor	Description
	Rotation2D(double alpha)	Constructor.
protected	Rotation2D(double a00, double a01, double a10, double a11)	Auxiliary constructor used internally for duplicating instances.
	Rotation2D(Rotation2D m)	Constructor.

Method Summary

Modifier and Type	Method	Description
Rotation2D	concat(Rotation2D B)	Concatenates this rotation (A) with another rotation (B) and returns a new rotation (C), such that C(x) = B(A(x)).
Rotation2D	duplicate()	Returns a copy of this mapping.
Rotation2D	getInverse()	Calculates and returns the inverse mapping.

Methods inherited from class imagingbook.common.geometry.mappings.linear.AffineMapping2D

applyTo, concat, fromPoints, fromPoints, getJacobian, isAffine

Methods inherited from class imagingbook.common.geometry.mappings.linear.ProjectiveMapping2D

concat, main

Methods inherited from class imagingbook.common.geometry.mappings.linear.LinearMapping2D

concat, concatenate, getTransformationMatrix, normalize, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface imagingbook.common.geometry.mappings.Mapping2D

applyTo

Constructor Details

Rotation2D

public Rotation2D(double alpha)

Constructor. Creates a 2D rotation by a given angle about the origin.

Parameters:

alpha - rotation angle (in radians)

Rotation2D

protected Rotation2D(double a00,
 double a01,
 double a10,
 double a11)

Auxiliary constructor used internally for duplicating instances.

Parameters:

a00 - matrix element A_00

a01 - matrix element A_01

a10 - matrix element A_10

a11 - matrix element A_11

Rotation2D

public Rotation2D(Rotation2D m)

Constructor. Creates a new Rotation2D object from an existing instance.

Parameters:

m - a Rotation2D instance

Method Details

concat

public Rotation2D concat(Rotation2D B)

Concatenates this rotation (A) with another rotation (B) and returns a new rotation (C), such that C(x) = B(A(x)).

Parameters:

B - the second rotation

Returns:

the concatenated rotations

duplicate

public Rotation2D duplicate()

Description copied from class: AffineMapping2D

Returns a copy of this mapping.

Overrides:

duplicate in class AffineMapping2D

Returns:

a new affine mapping

getInverse

public Rotation2D getInverse()

Description copied from class: AffineMapping2D

Calculates and returns the inverse mapping. Note that the inverse A' of a projective transformation matrix A is again a linear transformation but its a'2' element is generally not 1. Scaling A' to A'' = A' / a22' yields a projective transformation that reverses A. While A * A' = I, the result of A * A'' is a scaled identity matrix. Note that inverting an affine transformation always yields another affine transformation.

Specified by:

getInverse in interface Inversion

Overrides:

getInverse in class AffineMapping2D

Returns:

the inverse projective transformation