Collaboration diagram for Geometry_Module:

Modules
	Global aligned box typedefs

Classes
class	Eigen::AlignedBox< _Scalar, _AmbientDim >
	An axis aligned box. More...

class	Eigen::AngleAxis< _Scalar >
	Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...

class	Eigen::Homogeneous< MatrixType, _Direction >
	Expression of one (or a set of) homogeneous vector(s) More...

class	Eigen::Hyperplane< _Scalar, _AmbientDim >
	A hyperplane. More...

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::ParametrizedLine< _Scalar, _AmbientDim >
	A parametrized line. More...

class	Eigen::Quaternion< _Scalar >
	The quaternion class used to represent 3D orientations and rotations. More...

class	Eigen::QuaternionBase< Derived >
	Base class for quaternion expressions. More...

class	Eigen::Rotation2D< _Scalar >
	Represents a rotation/orientation in a 2 dimensional space. More...

class	Eigen::Scaling< _Scalar, _Dim >
	Represents a possibly non uniform scaling transformation. More...

class	Eigen::Transform< _Scalar, _Dim >
	Represents an homogeneous transformation in a N dimensional space. More...

class	Eigen::Translation< _Scalar, _Dim >
	Represents a translation transformation. More...

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

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

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

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

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

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

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

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

typedef DiagonalMatrix< double, 2 >	Eigen::AlignedScaling2d

typedef DiagonalMatrix< float, 2 >	Eigen::AlignedScaling2f

typedef DiagonalMatrix< double, 3 >	Eigen::AlignedScaling3d

typedef DiagonalMatrix< float, 3 >	Eigen::AlignedScaling3f

typedef AngleAxis< double >	Eigen::AngleAxisd

typedef AngleAxis< float >	Eigen::AngleAxisf

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

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

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

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

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

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

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

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

typedef Quaternion< double >	Eigen::Quaterniond

typedef Quaternion< float >	Eigen::Quaternionf

typedef Map< Quaternion< double >, Aligned >	Eigen::QuaternionMapAlignedd

typedef Map< Quaternion< float >, Aligned >	Eigen::QuaternionMapAlignedf

typedef Map< Quaternion< double >, 0 >	Eigen::QuaternionMapd

typedef Map< Quaternion< float >, 0 >	Eigen::QuaternionMapf

typedef Rotation2D< double >	Eigen::Rotation2Dd

typedef Rotation2D< float >	Eigen::Rotation2Df

typedef Scaling< double, 2 >	Eigen::Scaling2d

typedef Scaling< float, 2 >	Eigen::Scaling2f

typedef Scaling< double, 3 >	Eigen::Scaling3d

typedef Scaling< float, 3 >	Eigen::Scaling3f

typedef Transform< double, 2 >	Eigen::Transform2d

typedef Transform< float, 2 >	Eigen::Transform2f

typedef Transform< double, 3 >	Eigen::Transform3d

typedef Transform< float, 3 >	Eigen::Transform3f

typedef Translation< double, 2 >	Eigen::Translation2d

typedef Translation< float, 2 >	Eigen::Translation2f

typedef Translation< double, 3 >	Eigen::Translation3d

typedef Translation< float, 3 >	Eigen::Translation3f

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

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. More...

Detailed Description

Typedef Documentation

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

Definition at line 656 of file Geometry/Transform.h.

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

Definition at line 652 of file Geometry/Transform.h.

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

Definition at line 658 of file Geometry/Transform.h.

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

Definition at line 654 of file Geometry/Transform.h.

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

Definition at line 665 of file Geometry/Transform.h.

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

Definition at line 661 of file Geometry/Transform.h.

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

Definition at line 667 of file Geometry/Transform.h.

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

Definition at line 663 of file Geometry/Transform.h.

typedef DiagonalMatrix<double,2> Eigen::AlignedScaling2d

Deprecated:

Definition at line 144 of file Geometry/Scaling.h.

typedef DiagonalMatrix<float, 2> Eigen::AlignedScaling2f

Deprecated:

Definition at line 142 of file Geometry/Scaling.h.

typedef DiagonalMatrix<double,3> Eigen::AlignedScaling3d

Deprecated:

Definition at line 148 of file Geometry/Scaling.h.

typedef DiagonalMatrix<float, 3> Eigen::AlignedScaling3f

Deprecated:

Definition at line 146 of file Geometry/Scaling.h.

typedef AngleAxis< double > Eigen::AngleAxisd

double precision angle-axis type

Definition at line 152 of file Eigen2Support/Geometry/AngleAxis.h.

typedef AngleAxis< float > Eigen::AngleAxisf

single precision angle-axis type

Definition at line 149 of file Eigen2Support/Geometry/AngleAxis.h.

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

Definition at line 647 of file Geometry/Transform.h.

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

Definition at line 643 of file Geometry/Transform.h.

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

Definition at line 649 of file Geometry/Transform.h.

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

Definition at line 645 of file Geometry/Transform.h.

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

Definition at line 674 of file Geometry/Transform.h.

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

Definition at line 670 of file Geometry/Transform.h.

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

Definition at line 676 of file Geometry/Transform.h.

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

Definition at line 672 of file Geometry/Transform.h.

typedef Quaternion< double > Eigen::Quaterniond

double precision quaternion type

Definition at line 211 of file Eigen2Support/Geometry/Quaternion.h.

typedef Quaternion< float > Eigen::Quaternionf

single precision quaternion type

Definition at line 208 of file Eigen2Support/Geometry/Quaternion.h.

typedef Map<Quaternion<double>, Aligned> Eigen::QuaternionMapAlignedd

Map a 16-bits aligned array of double precision scalars as a quaternion

Definition at line 412 of file Geometry/Quaternion.h.

typedef Map<Quaternion<float>, Aligned> Eigen::QuaternionMapAlignedf

Map a 16-bits aligned array of double precision scalars as a quaternion

Definition at line 409 of file Geometry/Quaternion.h.

typedef Map<Quaternion<double>, 0> Eigen::QuaternionMapd

Map an unaligned array of double precision scalar as a quaternion

Definition at line 406 of file Geometry/Quaternion.h.

typedef Map<Quaternion<float>, 0> Eigen::QuaternionMapf

Map an unaligned array of single precision scalar as a quaternion

Definition at line 403 of file Geometry/Quaternion.h.

typedef Rotation2D< double > Eigen::Rotation2Dd

double precision 2D rotation type

Definition at line 119 of file Eigen2Support/Geometry/Rotation2D.h.

typedef Rotation2D< float > Eigen::Rotation2Df

single precision 2D rotation type

Definition at line 116 of file Eigen2Support/Geometry/Rotation2D.h.

typedef Scaling<double,2> Eigen::Scaling2d

Definition at line 141 of file Eigen2Support/Geometry/Scaling.h.

typedef Scaling<float, 2> Eigen::Scaling2f

Definition at line 140 of file Eigen2Support/Geometry/Scaling.h.

typedef Scaling<double,3> Eigen::Scaling3d

Definition at line 143 of file Eigen2Support/Geometry/Scaling.h.

typedef Scaling<float, 3> Eigen::Scaling3f

Definition at line 142 of file Eigen2Support/Geometry/Scaling.h.

typedef Transform<double,2> Eigen::Transform2d

Definition at line 286 of file Eigen2Support/Geometry/Transform.h.

typedef Transform<float,2> Eigen::Transform2f

Definition at line 282 of file Eigen2Support/Geometry/Transform.h.

typedef Transform<double,3> Eigen::Transform3d

Definition at line 288 of file Eigen2Support/Geometry/Transform.h.

typedef Transform<float,3> Eigen::Transform3f

Definition at line 284 of file Eigen2Support/Geometry/Transform.h.

typedef Translation< double, 2 > Eigen::Translation2d

Definition at line 144 of file Eigen2Support/Geometry/Translation.h.

typedef Translation< float, 2 > Eigen::Translation2f

Definition at line 143 of file Eigen2Support/Geometry/Translation.h.

typedef Translation< double, 3 > Eigen::Translation3d

Definition at line 146 of file Eigen2Support/Geometry/Translation.h.

typedef Translation< float, 3 > Eigen::Translation3f

Definition at line 145 of file Eigen2Support/Geometry/Translation.h.

Function Documentation

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[0:pi]x[-pi:pi].

See also: class AngleAxis

Definition at line 37 of file EulerAngles.h.

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 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.

Definition at line 95 of file Umeyama.h.

Modules

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation