Classes | Typedefs | Functions
Geometry_Module

Classes

class  AlignedBox< _Scalar, _AmbientDim >
 An axis aligned box. More...
class  AngleAxis< _Scalar >
 Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...
class  Homogeneous< MatrixType, _Direction >
 Expression of one (or a set of) homogeneous vector(s) More...
class  Hyperplane< _Scalar, _AmbientDim >
 A hyperplane. More...
class  ParametrizedLine< _Scalar, _AmbientDim >
 A parametrized line. More...
class  Quaternion< _Scalar >
 The quaternion class used to represent 3D orientations and rotations. More...
class  Rotation2D< _Scalar >
 Represents a rotation/orientation in a 2 dimensional space. More...
class  Scaling< _Scalar, _Dim >
 Represents a possibly non uniform scaling transformation. More...
class  Transform< _Scalar, _Dim >
 Represents an homogeneous transformation in a N dimensional space. More...
class  Translation< _Scalar, _Dim >
 Represents a translation transformation. More...

Typedefs

typedef Transform< double,
2, Affine > 		Affine2d
typedef Transform< float,
2, Affine > 		Affine2f
typedef Transform< double,
3, Affine > 		Affine3d
typedef Transform< float,
3, Affine > 		Affine3f
typedef Transform< double,
2, AffineCompact > 		AffineCompact2d
typedef Transform< float,
2, AffineCompact > 		AffineCompact2f
typedef Transform< double,
3, AffineCompact > 		AffineCompact3d
typedef Transform< float,
3, AffineCompact > 		AffineCompact3f
typedef DiagonalMatrix< double, 2 > AlignedScaling2d
typedef DiagonalMatrix< float, 2 > AlignedScaling2f
typedef DiagonalMatrix< double, 3 > AlignedScaling3d
typedef DiagonalMatrix< float, 3 > AlignedScaling3f
typedef AngleAxis< double > AngleAxisd
typedef AngleAxis< double > AngleAxisd
typedef AngleAxis< float > AngleAxisf
typedef AngleAxis< float > AngleAxisf
typedef Transform< double,
2, Isometry > 		Isometry2d
typedef Transform< float,
2, Isometry > 		Isometry2f
typedef Transform< double,
3, Isometry > 		Isometry3d
typedef Transform< float,
3, Isometry > 		Isometry3f
typedef Transform< double,
2, Projective > 		Projective2d
typedef Transform< float,
2, Projective > 		Projective2f
typedef Transform< double,
3, Projective > 		Projective3d
typedef Transform< float,
3, Projective > 		Projective3f
typedef Quaternion< double > Quaterniond
typedef Quaternion< double > Quaterniond
typedef Quaternion< float > Quaternionf
typedef Quaternion< float > Quaternionf
typedef Map< Quaternion
< double >, Aligned > 		QuaternionMapAlignedd
typedef Map< Quaternion< float >
, Aligned > 		QuaternionMapAlignedf
typedef Map< Quaternion
< double >, 0 > 		QuaternionMapd
typedef Map< Quaternion< float >, 0 > QuaternionMapf
typedef Rotation2D< double > Rotation2Dd
typedef Rotation2D< double > Rotation2Dd
typedef Rotation2D< float > Rotation2Df
typedef Rotation2D< float > Rotation2Df
typedef Scaling< double, 2 > Scaling2d
typedef Scaling< float, 2 > Scaling2f
typedef Scaling< double, 3 > Scaling3d
typedef Scaling< float, 3 > Scaling3f
typedef Transform< double, 2 > Transform2d
typedef Transform< float, 2 > Transform2f
typedef Transform< double, 3 > Transform3d
typedef Transform< float, 3 > Transform3f
typedef Translation< double, 2 > Translation2d
typedef Translation< double, 2 > Translation2d
typedef Translation< float, 2 > Translation2f
typedef Translation< float, 2 > Translation2f
typedef Translation< double, 3 > Translation3d
typedef Translation< double, 3 > Translation3d
typedef Translation< float, 3 > Translation3f
typedef Translation< float, 3 > Translation3f

Functions

Matrix< Scalar, 3, 1 > MatrixBase< Derived >::eulerAngles (Index a0, Index a1, Index a2) const
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)
 Returns the transformation between two point sets.

Typedef Documentation

typedef Transform<double,2,Affine> Affine2d

Definition at line 633 of file Geometry/Transform.h.

typedef Transform<float,2,Affine> Affine2f

Definition at line 629 of file Geometry/Transform.h.

typedef Transform<double,3,Affine> Affine3d

Definition at line 635 of file Geometry/Transform.h.

typedef Transform<float,3,Affine> Affine3f

Definition at line 631 of file Geometry/Transform.h.

typedef Transform<double,2,AffineCompact> AffineCompact2d

Definition at line 642 of file Geometry/Transform.h.

typedef Transform<float,2,AffineCompact> AffineCompact2f

Definition at line 638 of file Geometry/Transform.h.

typedef Transform<double,3,AffineCompact> AffineCompact3d

Definition at line 644 of file Geometry/Transform.h.

typedef Transform<float,3,AffineCompact> AffineCompact3f

Definition at line 640 of file Geometry/Transform.h.

typedef DiagonalMatrix<double,2> AlignedScaling2d
Deprecated:

Definition at line 152 of file Geometry/Scaling.h.

typedef DiagonalMatrix<float, 2> AlignedScaling2f
Deprecated:

Definition at line 150 of file Geometry/Scaling.h.

typedef DiagonalMatrix<double,3> AlignedScaling3d
Deprecated:

Definition at line 156 of file Geometry/Scaling.h.

typedef DiagonalMatrix<float, 3> AlignedScaling3f
Deprecated:

Definition at line 154 of file Geometry/Scaling.h.

typedef AngleAxis<double> AngleAxisd

double precision angle-axis type

Definition at line 162 of file Geometry/AngleAxis.h.

typedef AngleAxis<double> AngleAxisd

double precision angle-axis type

Definition at line 166 of file Eigen2Support/Geometry/AngleAxis.h.

typedef AngleAxis<float> AngleAxisf

single precision angle-axis type

Definition at line 159 of file Geometry/AngleAxis.h.

typedef AngleAxis<float> AngleAxisf

single precision angle-axis type

Definition at line 163 of file Eigen2Support/Geometry/AngleAxis.h.

typedef Transform<double,2,Isometry> Isometry2d

Definition at line 624 of file Geometry/Transform.h.

typedef Transform<float,2,Isometry> Isometry2f

Definition at line 620 of file Geometry/Transform.h.

typedef Transform<double,3,Isometry> Isometry3d

Definition at line 626 of file Geometry/Transform.h.

typedef Transform<float,3,Isometry> Isometry3f

Definition at line 622 of file Geometry/Transform.h.

typedef Transform<double,2,Projective> Projective2d

Definition at line 651 of file Geometry/Transform.h.

typedef Transform<float,2,Projective> Projective2f

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

typedef Transform<double,3,Projective> Projective3d

Definition at line 653 of file Geometry/Transform.h.

typedef Transform<float,3,Projective> Projective3f

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

typedef Quaternion<double> Quaterniond

double precision quaternion type

Definition at line 224 of file Eigen2Support/Geometry/Quaternion.h.

typedef Quaternion<double> Quaterniond

double precision quaternion type

Definition at line 294 of file Geometry/Quaternion.h.

typedef Quaternion<float> Quaternionf

single precision quaternion type

Definition at line 221 of file Eigen2Support/Geometry/Quaternion.h.

typedef Quaternion<float> Quaternionf

single precision quaternion type

Definition at line 291 of file Geometry/Quaternion.h.

typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd

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

Definition at line 417 of file Geometry/Quaternion.h.

typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf

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

Definition at line 414 of file Geometry/Quaternion.h.

typedef Map<Quaternion<double>, 0> QuaternionMapd

Map an unaligned array of double precision scalar as a quaternion

Definition at line 411 of file Geometry/Quaternion.h.

typedef Map<Quaternion<float>, 0> QuaternionMapf

Map an unaligned array of single precision scalar as a quaternion

Definition at line 408 of file Geometry/Quaternion.h.

typedef Rotation2D<double> Rotation2Dd

double precision 2D rotation type

Definition at line 133 of file Eigen2Support/Geometry/Rotation2D.h.

typedef Rotation2D<double> Rotation2Dd

double precision 2D rotation type

Definition at line 139 of file Geometry/Rotation2D.h.

typedef Rotation2D<float> Rotation2Df

single precision 2D rotation type

Definition at line 130 of file Eigen2Support/Geometry/Rotation2D.h.

typedef Rotation2D<float> Rotation2Df

single precision 2D rotation type

Definition at line 136 of file Geometry/Rotation2D.h.

typedef Scaling<double,2> Scaling2d

Definition at line 155 of file Eigen2Support/Geometry/Scaling.h.

typedef Scaling<float, 2> Scaling2f

Definition at line 154 of file Eigen2Support/Geometry/Scaling.h.

typedef Scaling<double,3> Scaling3d

Definition at line 157 of file Eigen2Support/Geometry/Scaling.h.

typedef Scaling<float, 3> Scaling3f

Definition at line 156 of file Eigen2Support/Geometry/Scaling.h.

typedef Transform<double,2> Transform2d

Definition at line 300 of file Eigen2Support/Geometry/Transform.h.

typedef Transform<float,2> Transform2f

Definition at line 296 of file Eigen2Support/Geometry/Transform.h.

typedef Transform<double,3> Transform3d

Definition at line 302 of file Eigen2Support/Geometry/Transform.h.

typedef Transform<float,3> Transform3f

Definition at line 298 of file Eigen2Support/Geometry/Transform.h.

typedef Translation<double,2> Translation2d

Definition at line 158 of file Eigen2Support/Geometry/Translation.h.

typedef Translation<double,2> Translation2d

Definition at line 184 of file Geometry/Translation.h.

typedef Translation<float, 2> Translation2f

Definition at line 157 of file Eigen2Support/Geometry/Translation.h.

typedef Translation<float, 2> Translation2f

Definition at line 183 of file Geometry/Translation.h.

typedef Translation<double,3> Translation3d

Definition at line 160 of file Eigen2Support/Geometry/Translation.h.

typedef Translation<double,3> Translation3d

Definition at line 186 of file Geometry/Translation.h.

typedef Translation<float, 3> Translation3f

Definition at line 159 of file Eigen2Support/Geometry/Translation.h.

typedef Translation<float, 3> Translation3f

Definition at line 185 of file Geometry/Translation.h.

Function Documentation

template<typename Derived >
Matrix< typename MatrixBase< Derived >::Scalar, 3, 1 > 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).

Definition at line 46 of file EulerAngles.h.

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 
)

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:
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 108 of file Umeyama.h.


re_vision
Author(s): Dorian Galvez-Lopez
autogenerated on Sun Jan 5 2014 11:33:51