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	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...
class	Homogeneous< MatrixType, _Direction >
	Expression of one (or a set of) homogeneous vector(s). More...
Typedefs
typedef AngleAxis< float >	AngleAxisf
typedef AngleAxis< double >	AngleAxisd
typedef Quaternion< float >	Quaternionf
typedef Quaternion< double >	Quaterniond
typedef Rotation2D< float >	Rotation2Df
typedef Rotation2D< double >	Rotation2Dd
typedef Scaling< float, 2 >	Scaling2f
typedef Scaling< double, 2 >	Scaling2d
typedef Scaling< float, 3 >	Scaling3f
typedef Scaling< double, 3 >	Scaling3d
typedef Transform< float, 2 >	Transform2f
typedef Transform< float, 3 >	Transform3f
typedef Transform< double, 2 >	Transform2d
typedef Transform< double, 3 >	Transform3d
typedef Translation< float, 2 >	Translation2f
typedef Translation< double, 2 >	Translation2d
typedef Translation< float, 3 >	Translation3f
typedef Translation< double, 3 >	Translation3d
typedef AngleAxis< float >	AngleAxisf
typedef AngleAxis< double >	AngleAxisd
typedef Quaternion< float >	Quaternionf
typedef Quaternion< double >	Quaterniond
typedef Map< Quaternion< float >, 0 >	QuaternionMapf
typedef Map< Quaternion < double >, 0 >	QuaternionMapd
typedef Map< Quaternion< float > , Aligned >	QuaternionMapAlignedf
typedef Map< Quaternion < double >, Aligned >	QuaternionMapAlignedd
typedef Rotation2D< float >	Rotation2Df
typedef Rotation2D< double >	Rotation2Dd
typedef DiagonalMatrix< float, 2 >	AlignedScaling2f
typedef DiagonalMatrix< double, 2 >	AlignedScaling2d
typedef DiagonalMatrix< float, 3 >	AlignedScaling3f
typedef DiagonalMatrix< double, 3 >	AlignedScaling3d
typedef Transform< float, 2, Isometry >	Isometry2f
typedef Transform< float, 3, Isometry >	Isometry3f
typedef Transform< double, 2, Isometry >	Isometry2d
typedef Transform< double, 3, Isometry >	Isometry3d
typedef Transform< float, 2, Affine >	Affine2f
typedef Transform< float, 3, Affine >	Affine3f
typedef Transform< double, 2, Affine >	Affine2d
typedef Transform< double, 3, Affine >	Affine3d
typedef Transform< float, 2, AffineCompact >	AffineCompact2f
typedef Transform< float, 3, AffineCompact >	AffineCompact3f
typedef Transform< double, 2, AffineCompact >	AffineCompact2d
typedef Transform< double, 3, AffineCompact >	AffineCompact3d
typedef Transform< float, 2, Projective >	Projective2f
typedef Transform< float, 3, Projective >	Projective3f
typedef Transform< double, 2, Projective >	Projective2d
typedef Transform< double, 3, Projective >	Projective3d
typedef Translation< float, 2 >	Translation2f
typedef Translation< double, 2 >	Translation2d
typedef Translation< float, 3 >	Translation3f
typedef Translation< double, 3 >	Translation3d
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)
	Returns the transformation between two point sets.
Matrix< Scalar, 3, 1 >	MatrixBase::eulerAngles (Index a0, Index a1, Index a2) const

Typedef Documentation

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

Deprecated:

typedef DiagonalMatrix<float, 2> AlignedScaling2f

Deprecated:

typedef DiagonalMatrix<double,3> AlignedScaling3d

Deprecated:

typedef DiagonalMatrix<float, 3> AlignedScaling3f

Deprecated:

typedef AngleAxis<double> AngleAxisd

double precision angle-axis type

typedef AngleAxis<double> AngleAxisd

double precision angle-axis type

typedef AngleAxis<float> AngleAxisf

single precision angle-axis type

typedef AngleAxis<float> AngleAxisf

single precision angle-axis type

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

double precision quaternion type

typedef Quaternion<double> Quaterniond

double precision quaternion type

typedef Quaternion<float> Quaternionf

single precision quaternion type

typedef Quaternion<float> Quaternionf

single precision quaternion type

typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd

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

typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf

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

typedef Map<Quaternion<double>, 0> QuaternionMapd

Map an unaligned array of double precision scalar as a quaternion

typedef Map<Quaternion<float>, 0> QuaternionMapf

Map an unaligned array of single precision scalar as a quaternion

typedef Rotation2D<double> Rotation2Dd

double precision 2D rotation type

typedef Rotation2D<double> Rotation2Dd

double precision 2D rotation type

typedef Rotation2D<float> Rotation2Df

single precision 2D rotation type

typedef Rotation2D<float> Rotation2Df

single precision 2D rotation type

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<float, 2> Translation2f

typedef Translation<double,3> Translation3d

typedef Translation<float, 3> Translation3f

Function Documentation

template<typename Derived >

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

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:

	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.

Geometry_Module

Classes

Typedefs

Functions

Typedef Documentation

Function Documentation