template class sophus::Sim3¶
Overview¶
Sim3 using default storage; derived from Sim3Base. More…
#include <sim3.h> template <class TScalar, int kOptions> class Sim3 { public: // typedefs using Base = Sim3Base<Sim3<TScalar, kOptions>> ; using Scalar = TScalar ; using Transformation = typename Base::Transformation ; using Point = typename Base::Point ; using HomogeneousPoint = typename Base::HomogeneousPoint ; using Tangent = typename Base::Tangent ; using Adjoint = typename Base::Adjoint ; using RxSo3Member = RxSo3<Scalar, kOptions> ; using TranslationMember = Eigen::Matrix<Scalar, 3, 1, kOptions> ; // fields static constexpr int kDoF = Base::kDoF; static constexpr int kNumParameters = Base::kNumParameters; // construction Sim3(); Sim3(Sim3 const& other); template <class TOtherDerived> Sim3(Sim3Base<TOtherDerived> const& other); template <class TOtherDerived, class TD> Sim3( RxSo3Base<TOtherDerived> const& rxso3, Eigen::MatrixBase<TD> const& translation ); template <class TD1T, class TD2T> Sim3( Eigen::QuaternionBase<TD1T> const& quaternion, Eigen::MatrixBase<TD2T> const& translation ); template <class TD1T, class TD2T> Sim3( Scalar const& scale, Eigen::QuaternionBase<TD1T> const& unit_quaternion, Eigen::MatrixBase<TD2T> const& translation ); Sim3(Eigen::Matrix<Scalar, 4, 4> const& t); // methods SOPHUS_FUNC Sim3& operator=(Sim3 const& other); SOPHUS_FUNC Scalar* data(); SOPHUS_FUNC Scalar const* data() const; SOPHUS_FUNC RxSo3Member& rxso3(); SOPHUS_FUNC RxSo3Member const& rxso3() const; SOPHUS_FUNC TranslationMember& translation(); SOPHUS_FUNC TranslationMember const& translation() const; template <class TOtherDerived> SOPHUS_FUNC Sim3Base<TDerived>& operator=(Sim3Base<TOtherDerived> const& other); static SOPHUS_FUNC Eigen::Matrix<Scalar, kNumParameters, kDoF> dxExpXAt0(); static SOPHUS_FUNC Eigen::Matrix<Scalar, kNumParameters, kDoF> dxExpX(Tangent const& vec_a); static SOPHUS_FUNC Eigen::Matrix<Scalar, 3, kDoF> dxExpXTimesPointAt0(Point const& point); static SOPHUS_FUNC Transformation dxiExpmatXAt0(int i); static SOPHUS_FUNC Sim3<Scalar> exp(Tangent const& vec_a); static SOPHUS_FUNC Transformation generator(int i); static SOPHUS_FUNC Transformation hat(Tangent const& vec_a); static SOPHUS_FUNC Tangent lieBracket(Tangent const& vec_a, Tangent const& vec_b); template <class TUniformRandomBitGenerator> static Sim3 sampleUniform(TUniformRandomBitGenerator& generator); static SOPHUS_FUNC Tangent vee(Transformation const& mat_omega); protected: // fields RxSo3Member rxso3_; TranslationMember translation_; };
Detailed Documentation¶
Sim3 using default storage; derived from Sim3Base.
Construction¶
Sim3()
Default constructor initializes similarity transform to the identity.
Sim3(Sim3 const& other)
Copy constructor.
template <class TOtherDerived> Sim3(Sim3Base<TOtherDerived> const& other)
Copy-like constructor from OtherDerived.
template <class TOtherDerived, class TD> Sim3( RxSo3Base<TOtherDerived> const& rxso3, Eigen::MatrixBase<TD> const& translation )
Constructor from RxSo3 and translation vector.
template <class TD1T, class TD2T> Sim3( Eigen::QuaternionBase<TD1T> const& quaternion, Eigen::MatrixBase<TD2T> const& translation )
Constructor from quaternion and translation vector.
Precondition: quaternion must not be close to zero.
template <class TD1T, class TD2T> Sim3( Scalar const& scale, Eigen::QuaternionBase<TD1T> const& unit_quaternion, Eigen::MatrixBase<TD2T> const& translation )
Constructor from scale factor, unit quaternion, and translation vector.
Precondition: quaternion must not be close to zero.
Sim3(Eigen::Matrix<Scalar, 4, 4> const& t)
Constructor from 4x4 matrix.
Precondition: Top-left 3x3 matrix needs to be “scaled-orthogonal” with positive determinant. The last row must be (0, 0, 0, 1)
.
Methods¶
SOPHUS_FUNC Sim3& operator=(Sim3 const& other)
Define copy-assignment operator explicitly. The definition of implicit copy assignment operator is deprecated in presence of a user-declared copy constructor (-Wdeprecated-copy in clang >= 13).
SOPHUS_FUNC Scalar* data()
This provides unsafe read/write access to internal data. Sim(3) is represented by an Eigen::Quaternion (four parameters) and a 3-vector. When using direct write access, the user needs to take care of that the quaternion is not set close to zero.
SOPHUS_FUNC Scalar const* data() const
Const version of data() above.
SOPHUS_FUNC RxSo3Member& rxso3()
Accessor of RxSo3.
SOPHUS_FUNC RxSo3Member const& rxso3() const
Mutator of RxSo3.
SOPHUS_FUNC TranslationMember& translation()
Mutator of translation vector.
SOPHUS_FUNC TranslationMember const& translation() const
Accessor of translation vector.
template <class TOtherDerived> SOPHUS_FUNC Sim3Base<TDerived>& operator=(Sim3Base<TOtherDerived> const& other)
Assignment-like operator from OtherDerived.
static SOPHUS_FUNC Eigen::Matrix<Scalar, kNumParameters, kDoF> dxExpXAt0()
Returns derivative of exp(x) wrt. x_i at x=0.
static SOPHUS_FUNC Eigen::Matrix<Scalar, kNumParameters, kDoF> dxExpX(Tangent const& vec_a)
Returns derivative of exp(x) wrt. x.
static SOPHUS_FUNC Eigen::Matrix<Scalar, 3, kDoF> dxExpXTimesPointAt0(Point const& point)
Returns derivative of exp(x) * p wrt. x_i at x=0.
static SOPHUS_FUNC Transformation dxiExpmatXAt0(int i)
Returns derivative of expmat(x)
wrt. x_i at x=0
, with expmat(.)
being the matrix exponential.
static SOPHUS_FUNC Sim3<Scalar> exp(Tangent const& vec_a)
Group exponential.
This functions takes in an element of tangent space and returns the corresponding element of the group Sim(3).
The first three components of a
represent the translational part upsilon
in the tangent space of Sim(3), the following three components of a
represents the rotation vector omega
and the final component represents the logarithm of the scaling factor sigma
. To be more specific, this function computes expmat(hat(a))
with expmat(.)
being the matrix exponential and hat(.)
the hat-operator of Sim(3), see below.
static SOPHUS_FUNC Transformation generator(int i)
Returns the ith infinitesimal generators of Sim(3).
The infinitesimal generators of Sim(3) are:
| 0 0 0 1 | G_0 = | 0 0 0 0 | | 0 0 0 0 | | 0 0 0 0 | | 0 0 0 0 | G_1 = | 0 0 0 1 | | 0 0 0 0 | | 0 0 0 0 | | 0 0 0 0 | G_2 = | 0 0 0 0 | | 0 0 0 1 | | 0 0 0 0 | | 0 0 0 0 | G_3 = | 0 0 -1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 1 0 | G_4 = | 0 0 0 0 | | -1 0 0 0 | | 0 0 0 0 | | 0 -1 0 0 | G_5 = | 1 0 0 0 | | 0 0 0 0 | | 0 0 0 0 | | 1 0 0 0 | G_6 = | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 0 |
Precondition: i
must be in [0, 6].
static SOPHUS_FUNC Transformation hat(Tangent const& vec_a)
hat-operator
It takes in the 7-vector representation and returns the corresponding matrix representation of Lie algebra element.
Formally, the hat() -operator of Sim(3) is defined as
hat(.): R^7 -> R^{4x4}, hat(a) = sum_i a_i * G_i
(for i=0,…,6)
with G_i
being the ith infinitesimal generator of Sim(3).
The corresponding inverse is the vee() -operator, see below.
static SOPHUS_FUNC Tangent lieBracket(Tangent const& vec_a, Tangent const& vec_b)
Lie bracket.
It computes the Lie bracket of Sim(3). To be more specific, it computes
[omega_1, omega_2]_sim3 := vee([hat(omega_1), hat(omega_2)])
with [A,B] := AB-BA
being the matrix commutator, hat(.)
the hat() -operator and vee(.)
the vee() -operator of Sim(3).
template <class TUniformRandomBitGenerator> static Sim3 sampleUniform(TUniformRandomBitGenerator& generator)
Draw uniform sample from Sim(3) manifold.
Translations are drawn component-wise from the range [-1, 1]. The scale factor is drawn uniformly in log2-space from [-1, 1], hence the scale is in [0.5, 2].
static SOPHUS_FUNC Tangent vee(Transformation const& mat_omega)
vee-operator
It takes the 4x4-matrix representation Omega
and maps it to the corresponding 7-vector representation of Lie algebra.
This is the inverse of the hat() -operator, see above.
Precondition: Omega
must have the following structure:
| g -f e a |
| f g -d b |
| -e d g c |
| 0 0 0 0 |