|
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, _Options > |
| 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, _Options > |
| A parametrized line. More...
|
|
class | Eigen::Quaternion< _Scalar, _Options > |
| 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 | Scaling |
| Represents a generic uniform scaling transformation. More...
|
|
class | Eigen::Transform< _Scalar, _Dim, _Mode, _Options > |
| Represents an homogeneous transformation in a N dimensional space. More...
|
|
class | Eigen::Translation< _Scalar, _Dim > |
| Represents a translation transformation. More...
|
|
|
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 |
|
|
template<typename OtherDerived > |
PlainObject | Eigen::MatrixBase< Derived >::cross (const MatrixBase< OtherDerived > &other) const |
|
template<typename OtherDerived > |
const CrossReturnType | Eigen::VectorwiseOp< ExpressionType, Direction >::cross (const MatrixBase< OtherDerived > &other) const |
|
template<typename OtherDerived > |
PlainObject | Eigen::MatrixBase< Derived >::cross3 (const MatrixBase< OtherDerived > &other) const |
|
Matrix< Scalar, 3, 1 > | Eigen::MatrixBase< Derived >::eulerAngles (Index a0, Index a1, Index a2) const |
|
const HNormalizedReturnType | Eigen::MatrixBase< Derived >::hnormalized () const |
| homogeneous normalization More...
|
|
const HNormalizedReturnType | Eigen::VectorwiseOp< ExpressionType, Direction >::hnormalized () const |
| column or row-wise homogeneous normalization More...
|
|
HomogeneousReturnType | Eigen::MatrixBase< Derived >::homogeneous () const |
|
HomogeneousReturnType | Eigen::VectorwiseOp< ExpressionType, Direction >::homogeneous () const |
|
template<typename Derived , typename Scalar > |
| operator* (const MatrixBase< Derived > &matrix, const UniformScaling< Scalar > &s) |
|
UniformScaling< float > | Eigen::Scaling (float s) |
|
UniformScaling< double > | Eigen::Scaling (double s) |
|
template<typename RealScalar > |
UniformScaling< std::complex< RealScalar > > | Eigen::Scaling (const std::complex< RealScalar > &s) |
|
template<typename Scalar > |
DiagonalMatrix< Scalar, 2 > | Eigen::Scaling (const Scalar &sx, const Scalar &sy) |
|
template<typename Scalar > |
DiagonalMatrix< Scalar, 3 > | Eigen::Scaling (const Scalar &sx, const Scalar &sy, const Scalar &sz) |
|
template<typename Derived > |
const DiagonalWrapper< const Derived > | Eigen::Scaling (const MatrixBase< Derived > &coeffs) |
|
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...
|
|
PlainObject | Eigen::MatrixBase< Derived >::unitOrthogonal (void) const |
|
template<typename Derived >
This is defined in the Geometry module.
#include <Eigen/Geometry>
- 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:
"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:
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
template<typename Derived >
homogeneous normalization
This is defined in the Geometry module.
#include <Eigen/Geometry>
- Returns
- a vector expression of the N-1 first coefficients of
*this
divided by that last coefficient.
This can be used to convert homogeneous coordinates to affine coordinates.
It is essentially a shortcut for:
Example:
cout << "v = " << v.transpose() << "]^T" << endl;
cout << "v.hnormalized() = " << v.hnormalized().transpose() << "]^T" << endl;
cout <<
"P*v = " << (P*v).
transpose() <<
"]^T" << endl;
cout <<
"(P*v).hnormalized() = " << (P*v).
hnormalized().transpose() <<
"]^T" << endl;
Output:
v = 0.68 -0.211 0.566 0.597]^T
v.hnormalized() = 1.14 -0.354 0.949]^T
P*v = 0.663 -0.16 -0.13 0.91]^T
(P*v).hnormalized() = 0.729 -0.176 -0.143]^T
- See also
- VectorwiseOp::hnormalized()
template<typename ExpressionType , int Direction>
column or row-wise homogeneous normalization
This is defined in the Geometry module.
#include <Eigen/Geometry>
- Returns
- an expression of the first N-1 coefficients of each column (or row) of
*this
divided by the last coefficient of each column (or row).
This can be used to convert homogeneous coordinates to affine coordinates.
It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of *this
.
Example:
cout << "The matrix M is:" << endl << M << endl << endl;
cout << "M.colwise().hnormalized():" << endl << M.colwise().hnormalized() << endl << endl;
cout << "P*M:" << endl << P*M << endl << endl;
cout << "(P*M).colwise().hnormalized():" << endl << (P*M).colwise().hnormalized() << endl << endl;
Output:
The matrix M is:
0.68 0.823 -0.444 -0.27 0.271
-0.211 -0.605 0.108 0.0268 0.435
0.566 -0.33 -0.0452 0.904 -0.717
0.597 0.536 0.258 0.832 0.214
M.colwise().hnormalized():
1.14 1.53 -1.72 -0.325 1.27
-0.354 -1.13 0.419 0.0322 2.03
0.949 -0.614 -0.175 1.09 -3.35
P*M:
0.186 -0.589 0.369 1.33 -1.23
-0.871 -0.337 0.127 -0.715 0.091
-0.158 -0.0104 0.312 0.429 -0.478
0.992 0.777 -0.373 0.468 -0.651
(P*M).colwise().hnormalized():
0.188 -0.759 -0.989 2.85 1.89
-0.877 -0.433 -0.342 -1.53 -0.14
-0.16 -0.0134 -0.837 0.915 0.735
- See also
- MatrixBase::hnormalized()
template<typename Derived >
This is defined in the Geometry module.
#include <Eigen/Geometry>
- Returns
- a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as the last coefficient.
This can be used to convert affine coordinates to homogeneous coordinates.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
cout << "v = [" << v.transpose() << "]^T" << endl;
cout << "h.homogeneous() = [" << v.homogeneous().transpose() << "]^T" << endl;
cout <<
"(P * v.homogeneous()) = [" << (P * v.homogeneous()).
transpose() <<
"]^T" << endl;
cout <<
"(P * v.homogeneous()).hnormalized() = [" << (P * v.homogeneous()).
eval().hnormalized().transpose() <<
"]^T" << endl;
Output:
v = [ 0.68 -0.211 0.566]^T
h.homogeneous() = [ 0.68 -0.211 0.566 1]^T
(P * v.homogeneous()) = [ 1.27 0.772 0.0154 -0.419]^T
(P * v.homogeneous()).hnormalized() = [ -3.03 -1.84 -0.0367]^T
- See also
- VectorwiseOp::homogeneous(), class Homogeneous
template<typename ExpressionType , int Direction>
This is defined in the Geometry module.
#include <Eigen/Geometry>
- Returns
- an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of the matrix.
This can be used to convert affine coordinates to homogeneous coordinates.
Example:
cout << "The matrix M is:" << endl << M << endl << endl;
cout << "M.colwise().homogeneous():" << endl << M.colwise().homogeneous() << endl << endl;
cout << "P * M.colwise().homogeneous():" << endl << P * M.colwise().homogeneous() << endl << endl;
cout << "P * M.colwise().homogeneous().hnormalized(): " << endl << (P * M.colwise().homogeneous()).colwise().hnormalized() << endl << endl;
Output:
The matrix M is:
0.68 0.597 -0.33 0.108 -0.27
-0.211 0.823 0.536 -0.0452 0.0268
0.566 -0.605 -0.444 0.258 0.904
M.colwise().homogeneous():
0.68 0.597 -0.33 0.108 -0.27
-0.211 0.823 0.536 -0.0452 0.0268
0.566 -0.605 -0.444 0.258 0.904
1 1 1 1 1
P * M.colwise().homogeneous():
0.0832 -0.477 -1.21 -0.545 -0.452
0.998 0.779 0.695 0.894 0.277
-0.271 -0.608 -0.895 -0.544 -0.874
-0.728 -0.551 0.202 -0.21 -0.469
P * M.colwise().homogeneous().hnormalized():
-0.114 0.866 -6 2.6 0.962
-1.37 -1.41 3.44 -4.27 -0.591
0.373 1.1 -4.43 2.6 1.86
- See also
- MatrixBase::homogeneous(), class Homogeneous
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.
This is defined in the Geometry module.
#include <Eigen/Geometry>
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
and
such that
is minimized.
The algorithm is based on the analysis of the covariance matrix
of the input point sets
and
where
is corresponding to the dimension (which is typically small). The analysis is involving the SVD having a complexity of
though the actual computational effort lies in the covariance matrix computation which has an asymptotic lower bound of
when the input point sets have dimension
.
Currently the method is working only for floating point matrices.
- Parameters
-
src | Source points . |
dst | Destination points . |
with_scaling | Sets when false is passed. |
- Returns
- The homogeneous transformation
minimizing the resudiual above. This transformation is always returned as an Eigen::Matrix.