Yoji KURODA / Eigen

Eigne Matrix Class Library

Dependents:   Eigen_test Odometry_test AttitudeEstimation_usingTicker MPU9250_Quaternion_Binary_Serial ... more

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Geometry module
Data Structures | Modules | Typedefs | Functions

Geometry module

This module provides support for:

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Data Structures

class  Map< const Quaternion< _Scalar >, _Options >
 Quaternion expression mapping a constant memory buffer. More...
class  Map< Quaternion< _Scalar >, _Options >
 Expression of a quaternion from a memory buffer. More...
class  AlignedBox< _Scalar, _AmbientDim >
  More...
class  AngleAxis< _Scalar >
  More...
class  Homogeneous< MatrixType, _Direction >
  More...
class  Hyperplane< _Scalar, _AmbientDim, _Options >
  More...
class  ParametrizedLine< _Scalar, _AmbientDim, _Options >
  More...
class  QuaternionBase< Derived >
  More...
class  Quaternion< _Scalar, _Options >
  More...
class  Rotation2D< _Scalar >
  More...
class  Scaling
  More...
class  Transform< _Scalar, _Dim, _Mode, _Options >
  More...
class  Translation< _Scalar, _Dim >
  More...

Modules

 Global aligned box typedefs
 

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


Typedefs

typedef AngleAxis< float > AngleAxisf
 single precision angle-axis type
typedef AngleAxis< double > AngleAxisd
 double precision angle-axis type
typedef Quaternion< float > Quaternionf
 single precision quaternion type
typedef Quaternion< double > Quaterniond
 double precision quaternion type
typedef Map< Quaternion< float >, 0 > QuaternionMapf
 Map an unaligned array of single precision scalars as a quaternion.
typedef Map< Quaternion
< double >, 0 > 		QuaternionMapd
 Map an unaligned array of double precision scalars as a quaternion.
typedef Map< Quaternion< float >
, Aligned > 		QuaternionMapAlignedf
 Map a 16-byte aligned array of single precision scalars as a quaternion.
typedef Map< Quaternion
< double >, Aligned > 		QuaternionMapAlignedd
 Map a 16-byte aligned array of double precision scalars as a quaternion.
typedef Rotation2D< float > Rotation2Df
 single precision 2D rotation type
typedef Rotation2D< double > Rotation2Dd
 double precision 2D rotation type
typedef DiagonalMatrix< float, 2 > AlignedScaling2f
typedef DiagonalMatrix< double, 2 > AlignedScaling2d
typedef DiagonalMatrix< float, 3 > AlignedScaling3f
typedef DiagonalMatrix< double, 3 > AlignedScaling3d

Functions

template<typename Derived , typename OtherDerived >
internal::umeyama_transform_matrix_type
< Derived, OtherDerived >
::type 		umeyama (const MatrixBase< Derived > &src, const MatrixBase< OtherDerived > &dst, bool with_scaling=true)
 
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
 

Detailed Description

This module provides support for:

 #include <Eigen/Geometry>

Typedef Documentation

typedef DiagonalMatrix<double,2> AlignedScaling2d

Definition at line 144 of file Scaling.h.

typedef DiagonalMatrix<float, 2> AlignedScaling2f

Definition at line 142 of file Scaling.h.

typedef DiagonalMatrix<double,3> AlignedScaling3d

Definition at line 148 of file Scaling.h.

typedef DiagonalMatrix<float, 3> AlignedScaling3f

Definition at line 146 of file Scaling.h.

typedef AngleAxis<double> AngleAxisd

double precision angle-axis type

Definition at line 156 of file AngleAxis.h.

typedef AngleAxis<float> AngleAxisf

single precision angle-axis type

Definition at line 153 of file AngleAxis.h.

typedef Quaternion<double> Quaterniond

double precision quaternion type

Definition at line 298 of file Quaternion.h.

typedef Quaternion<float> Quaternionf

single precision quaternion type

Definition at line 295 of file Quaternion.h.

typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd

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

Definition at line 410 of file Quaternion.h.

typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf

Map a 16-byte aligned array of single precision scalars as a quaternion.

Definition at line 407 of file Quaternion.h.

typedef Map<Quaternion<double>, 0> QuaternionMapd

Map an unaligned array of double precision scalars as a quaternion.

Definition at line 404 of file Quaternion.h.

typedef Map<Quaternion<float>, 0> QuaternionMapf

Map an unaligned array of single precision scalars as a quaternion.

Definition at line 401 of file Quaternion.h.

typedef Rotation2D<double> Rotation2Dd

double precision 2D rotation type

Definition at line 129 of file Rotation2D.h.

typedef Rotation2D<float> Rotation2Df

single precision 2D rotation type

Definition at line 126 of file Rotation2D.h.

Function Documentation

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

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

Definition at line 37 of file EulerAngles.h.

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.

Parameters:
srcSource points $ \mathbf{x} = \left( x_1, \hdots, x_n \right) $.
dstDestination points $ \mathbf{y} = \left( y_1, \hdots, y_n \right) $.
with_scalingSets $ 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.

Definition at line 95 of file Umeyama.h.

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