Modules
	Global aligned box typedefs
	Eigen defines several typedef shortcuts for most common aligned box types.

Classes
class	Eigen::Map< const Quaternion< _Scalar >, _Options >
	Quaternion expression mapping a constant memory buffer. More...

class	Eigen::Map< Quaternion< _Scalar >, _Options >
	Expression of a quaternion from a memory buffer. More...

class	Eigen::AlignedBox< _Scalar, _AmbientDim >

class	Eigen::AngleAxis< _Scalar >

class	Eigen::Hyperplane< _Scalar, _AmbientDim >

class	Eigen::ParametrizedLine< _Scalar, _AmbientDim >

class	Eigen::Quaternion< _Scalar >

class	Eigen::Rotation2D< _Scalar >

class	Eigen::Scaling< _Scalar, _Dim >

class	Eigen::Transform< _Scalar, _Dim >

class	Eigen::Translation< _Scalar, _Dim >

class	Eigen::Homogeneous< MatrixType, _Direction >

class	Eigen::QuaternionBase< Derived >

Typedefs
typedef AngleAxis< float >	Eigen::AngleAxisf
	single precision angle-axis type

typedef AngleAxis< double >	Eigen::AngleAxisd
	double precision angle-axis type

typedef Quaternion< float >	Eigen::Quaternionf
	single precision quaternion type

typedef Quaternion< double >	Eigen::Quaterniond
	double precision quaternion type

typedef Rotation2D< float >	Eigen::Rotation2Df
	single precision 2D rotation type

typedef Rotation2D< double >	Eigen::Rotation2Dd
	double precision 2D rotation type

typedef Scaling< float, 2 >	Eigen::Scaling2f

typedef Scaling< double, 2 >	Eigen::Scaling2d

typedef Scaling< float, 3 >	Eigen::Scaling3f

typedef Scaling< double, 3 >	Eigen::Scaling3d

typedef Transform< float, 2 >	Eigen::Transform2f

typedef Transform< float, 3 >	Eigen::Transform3f

typedef Transform< double, 2 >	Eigen::Transform2d

typedef Transform< double, 3 >	Eigen::Transform3d

typedef Translation< float, 2 >	Eigen::Translation2f

typedef Translation< double, 2 >	Eigen::Translation2d

typedef Translation< float, 3 >	Eigen::Translation3f

typedef Translation< double, 3 >	Eigen::Translation3d

typedef Map< Quaternion< float >, 0 >	Eigen::QuaternionMapf
	Map an unaligned array of single precision scalars as a quaternion.

typedef Map< Quaternion< double >, 0 >	Eigen::QuaternionMapd
	Map an unaligned array of double precision scalars as a quaternion.

typedef Map< Quaternion< float >, Aligned >	Eigen::QuaternionMapAlignedf
	Map a 16-byte aligned array of single precision scalars as a quaternion.

typedef Map< Quaternion< double >, Aligned >	Eigen::QuaternionMapAlignedd
	Map a 16-byte aligned array of double precision scalars as a quaternion.

typedef DiagonalMatrix< float, 2 >	Eigen::AlignedScaling2f

typedef DiagonalMatrix< double, 2 >	Eigen::AlignedScaling2d

typedef DiagonalMatrix< float, 3 >	Eigen::AlignedScaling3f

typedef DiagonalMatrix< double, 3 >	Eigen::AlignedScaling3d

typedef Transform< float, 2, Isometry >	Eigen::Isometry2f

typedef Transform< float, 3, Isometry >	Eigen::Isometry3f

typedef Transform< double, 2, Isometry >	Eigen::Isometry2d

typedef Transform< double, 3, Isometry >	Eigen::Isometry3d

typedef Transform< float, 2, Affine >	Eigen::Affine2f

typedef Transform< float, 3, Affine >	Eigen::Affine3f

typedef Transform< double, 2, Affine >	Eigen::Affine2d

typedef Transform< double, 3, Affine >	Eigen::Affine3d

typedef Transform< float, 2, AffineCompact >	Eigen::AffineCompact2f

typedef Transform< float, 3, AffineCompact >	Eigen::AffineCompact3f

typedef Transform< double, 2, AffineCompact >	Eigen::AffineCompact2d

typedef Transform< double, 3, AffineCompact >	Eigen::AffineCompact3d

typedef Transform< float, 2, Projective >	Eigen::Projective2f

typedef Transform< float, 3, Projective >	Eigen::Projective3f

typedef Transform< double, 2, Projective >	Eigen::Projective2d

typedef Transform< double, 3, Projective >	Eigen::Projective3d

Functions
template<typename Derived , typename OtherDerived >
internal::umeyama_transform_matrix_type< Derived, OtherDerived >::type	Eigen::umeyama (const MatrixBase< Derived > &src, const MatrixBase< OtherDerived > &dst, bool with_scaling=true)

Matrix< Scalar, 3, 1 >	Eigen::MatrixBase< Derived >::eulerAngles (Index a0, Index a1, Index a2) const

Detailed Description

Typedef Documentation

§ AlignedScaling2d

typedef DiagonalMatrix<double,2> Eigen::AlignedScaling2d

Deprecated:

§ AlignedScaling2f

typedef DiagonalMatrix<float, 2> Eigen::AlignedScaling2f

Deprecated:

§ AlignedScaling3d

typedef DiagonalMatrix<double,3> Eigen::AlignedScaling3d

Deprecated:

§ AlignedScaling3f

typedef DiagonalMatrix<float, 3> Eigen::AlignedScaling3f

Deprecated:

Function Documentation

§ eulerAngles()

template<typename Derived >

Matrix< typename MatrixBase< Derived >::Scalar, 3, 1 > Eigen::MatrixBase< Derived >::eulerAngles	(	Index	a0,
		Index	a1,
		Index	a2
	)		const

inline

Returns: the Euler-angles of the rotation matrix *this using the convention defined by the triplet (a0,a1,a2)

Each of the three parameters a0,a1,a2 represents the respective rotation axis as an integer in {0,1,2}. For instance, in:

Vector3f ea = mat.eulerAngles(2, 0, 2);

"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:

mat == AngleAxisf(ea[0], Vector3f::UnitZ())
     * AngleAxisf(ea[1], Vector3f::UnitX())
     * AngleAxisf(ea[2], Vector3f::UnitZ()); 

This corresponds to the right-multiply conventions (with right hand side frames).

The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].

See also: class AngleAxis

§ umeyama()

template<typename Derived , typename OtherDerived >

internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type Eigen::umeyama	(	const MatrixBase< Derived > &	src,
		const MatrixBase< OtherDerived > &	dst,
		bool	with_scaling = `true`
	)

Returns the transformation between two point sets.

The algorithm is based on: "Least-squares estimation of transformation parameters between two point patterns", Shinji Umeyama, PAMI 1991, DOI: 10.1109/34.88573

It estimates parameters \( c, \mathbf{R}, \) and \( \mathbf{t} \) such that

\begin{align*} \frac{1}{n} \sum_{i=1}^n \vert\vert y_i - (c\mathbf{R}x_i + \mathbf{t}) \vert\vert_2^2 \end{align*}

is minimized.

The algorithm is based on the analysis of the covariance matrix \( \Sigma_{\mathbf{x}\mathbf{y}} \in \mathbb{R}^{d \times d} \) of the input point sets \( \mathbf{x} \) and \( \mathbf{y} \) where \(d\) is corresponding to the dimension (which is typically small). The analysis is involving the SVD having a complexity of \(O(d^3)\) though the actual computational effort lies in the covariance matrix computation which has an asymptotic lower bound of \(O(dm)\) when the input point sets have dimension \(d \times m\).

Currently the method is working only for floating point matrices.

Todo:: Should the return type of umeyama() become a Transform?

Parameters

src	Source points \( \mathbf{x} = \left( x_1, \hdots, x_n \right) \).
dst	Destination points \( \mathbf{y} = \left( y_1, \hdots, y_n \right) \).
with_scaling	Sets \( c=1 \) when `false` is passed.

Returns: The homogeneous transformation
\begin{align*} T = \begin{bmatrix} c\mathbf{R} & \mathbf{t} \\ \mathbf{0} & 1 \end{bmatrix} \end{align*}
minimizing the resudiual above. This transformation is always returned as an Eigen::Matrix.

Modules

Classes

Typedefs

Functions