template<typename _Derived>
manif::SO2Base struct

The base class of the SO2 group.

Base classes

template<class _Derived>
struct LieGroupBase<_Derived>
Base class for Lie groups. Defines the minimum common API.

Public types

using Rotation = typename internal::traits<_Derived>::Rotation
using Transformation = typename internal::traits<_Derived>::Transformation

Public functions

auto inverse(OptJacobianRef J_minv_m = {}) const -> LieGroup
Get the inverse of this.
auto log(OptJacobianRef J_t_m = {}) const -> Tangent
Get the SO2 corresponding Lie algebra element in vector form.
auto lift(OptJacobianRef J_t_m = {}) const -> MANIF_DEPRECATED Tangent
This function is deprecated. Please considere using log instead.
template<typename _DerivedOther>
auto compose(const LieGroupBase<_DerivedOther>& m, OptJacobianRef J_mc_ma = {}, OptJacobianRef J_mc_mb = {}) const -> LieGroup
Composition of this and another SO2 element.
template<typename _EigenDerived>
auto act(const Eigen::MatrixBase<_EigenDerived>& v, tl::optional<Eigen::Ref<Eigen::Matrix<Scalar, 2, 1>>> J_vout_m = {}, tl::optional<Eigen::Ref<Eigen::Matrix<Scalar, 2, 2>>> J_vout_v = {}) const -> Eigen::Matrix<Scalar, 2, 1>
Rotation action on a 2-vector.
auto adj() const -> Jacobian
Get the ajoint matrix of SO2 at this.
auto transform() const -> Transformation
Get the transformation matrix (2D isometry).
auto rotation() const -> Rotation
Get the rotation matrix R.
auto real() const -> Scalar
Get the real part of the underlying complex number.
auto imag() const -> Scalar
Get the imaginary part of the underlying complex number.
auto angle() const -> Scalar
Get the angle (rad.).
void normalize()
Normalize the underlying complex number.
template<typename _EigenDerived>
auto act(const Eigen::MatrixBase<_EigenDerived>& v, tl::optional<Eigen::Ref<Eigen::Matrix<Scalar, 2, 1>>> J_vout_m, tl::optional<Eigen::Ref<Eigen::Matrix<Scalar, 2, 2>>> J_vout_v) const -> Eigen::Matrix<typename SO2Base<_Derived>::Scalar, 2, 1>
auto coeffs() -> DataType&
Access the underlying data by const reference.
auto coeffs() const -> const DataType&
Access the underlying data by const reference.

Protected functions

auto derived() & -> _Derived& noexcept
auto derived() const & -> const _Derived& noexcept

Function documentation

template<typename _Derived>
LieGroup manif::SO2Base<_Derived>::inverse(OptJacobianRef J_minv_m = {}) const

Get the inverse of this.

template<typename _Derived>
Tangent manif::SO2Base<_Derived>::log(OptJacobianRef J_t_m = {}) const

Get the SO2 corresponding Lie algebra element in vector form.

Returns The SO2 tangent of this.

template<typename _Derived> template<typename _DerivedOther>
LieGroup manif::SO2Base<_Derived>::compose(const LieGroupBase<_DerivedOther>& m, OptJacobianRef J_mc_ma = {}, OptJacobianRef J_mc_mb = {}) const

Composition of this and another SO2 element.

Parameters
m in Another SO2 element.
J_mc_ma
J_mc_mb
Returns The composition of 'this . m'.

template<typename _Derived> template<typename _EigenDerived>
Eigen::Matrix<Scalar, 2, 1> manif::SO2Base<_Derived>::act(const Eigen::MatrixBase<_EigenDerived>& v, tl::optional<Eigen::Ref<Eigen::Matrix<Scalar, 2, 1>>> J_vout_m = {}, tl::optional<Eigen::Ref<Eigen::Matrix<Scalar, 2, 2>>> J_vout_v = {}) const

Rotation action on a 2-vector.

Parameters
v A 2-vector.
J_vout_m
J_vout_v
Returns The rotated 2-vector.

template<typename _Derived>
Jacobian manif::SO2Base<_Derived>::adj() const

Get the ajoint matrix of SO2 at this.

template<typename _Derived>
Transformation manif::SO2Base<_Derived>::transform() const

Get the transformation matrix (2D isometry).