657 lines
22 KiB
C++
657 lines
22 KiB
C++
/// @file
|
|
/// Direct product R X SO(2) - rotation and scaling in 2d.
|
|
|
|
#ifndef SOPHUS_RXSO2_HPP
|
|
#define SOPHUS_RXSO2_HPP
|
|
|
|
#include "so2.hpp"
|
|
|
|
namespace Sophus {
|
|
template <class Scalar_, int Options = 0>
|
|
class RxSO2;
|
|
using RxSO2d = RxSO2<double>;
|
|
using RxSO2f = RxSO2<float>;
|
|
} // namespace Sophus
|
|
|
|
namespace Eigen {
|
|
namespace internal {
|
|
|
|
template <class Scalar_, int Options_>
|
|
struct traits<Sophus::RxSO2<Scalar_, Options_>> {
|
|
static constexpr int Options = Options_;
|
|
using Scalar = Scalar_;
|
|
using ComplexType = Sophus::Vector2<Scalar, Options>;
|
|
};
|
|
|
|
template <class Scalar_, int Options_>
|
|
struct traits<Map<Sophus::RxSO2<Scalar_>, Options_>>
|
|
: traits<Sophus::RxSO2<Scalar_, Options_>> {
|
|
static constexpr int Options = Options_;
|
|
using Scalar = Scalar_;
|
|
using ComplexType = Map<Sophus::Vector2<Scalar>, Options>;
|
|
};
|
|
|
|
template <class Scalar_, int Options_>
|
|
struct traits<Map<Sophus::RxSO2<Scalar_> const, Options_>>
|
|
: traits<Sophus::RxSO2<Scalar_, Options_> const> {
|
|
static constexpr int Options = Options_;
|
|
using Scalar = Scalar_;
|
|
using ComplexType = Map<Sophus::Vector2<Scalar> const, Options>;
|
|
};
|
|
} // namespace internal
|
|
} // namespace Eigen
|
|
|
|
namespace Sophus {
|
|
|
|
/// RxSO2 base type - implements RxSO2 class but is storage agnostic
|
|
///
|
|
/// This class implements the group ``R+ x SO(2)``, the direct product of the
|
|
/// group of positive scalar 2x2 matrices (= isomorph to the positive
|
|
/// real numbers) and the two-dimensional special orthogonal group SO(2).
|
|
/// Geometrically, it is the group of rotation and scaling in two dimensions.
|
|
/// As a matrix groups, R+ x SO(2) consists of matrices of the form ``s * R``
|
|
/// where ``R`` is an orthogonal matrix with ``det(R) = 1`` and ``s > 0``
|
|
/// being a positive real number. In particular, it has the following form:
|
|
///
|
|
/// | s * cos(theta) s * -sin(theta) |
|
|
/// | s * sin(theta) s * cos(theta) |
|
|
///
|
|
/// where ``theta`` being the rotation angle. Internally, it is represented by
|
|
/// the first column of the rotation matrix, or in other words by a non-zero
|
|
/// complex number.
|
|
///
|
|
/// R+ x SO(2) is not compact, but a commutative group. First it is not compact
|
|
/// since the scale factor is not bound. Second it is commutative since
|
|
/// ``sR(alpha, s1) * sR(beta, s2) = sR(beta, s2) * sR(alpha, s1)``, simply
|
|
/// because ``alpha + beta = beta + alpha`` and ``s1 * s2 = s2 * s1`` with
|
|
/// ``alpha`` and ``beta`` being rotation angles and ``s1``, ``s2`` being scale
|
|
/// factors.
|
|
///
|
|
/// This class has the explicit class invariant that the scale ``s`` is not
|
|
/// too close to zero. Strictly speaking, it must hold that:
|
|
///
|
|
/// ``complex().norm() >= Constants::epsilon()``.
|
|
///
|
|
/// In order to obey this condition, group multiplication is implemented with
|
|
/// saturation such that a product always has a scale which is equal or greater
|
|
/// this threshold.
|
|
template <class Derived>
|
|
class RxSO2Base {
|
|
public:
|
|
static constexpr int Options = Eigen::internal::traits<Derived>::Options;
|
|
using Scalar = typename Eigen::internal::traits<Derived>::Scalar;
|
|
using ComplexType = typename Eigen::internal::traits<Derived>::ComplexType;
|
|
using ComplexTemporaryType = Sophus::Vector2<Scalar, Options>;
|
|
|
|
/// Degrees of freedom of manifold, number of dimensions in tangent space
|
|
/// (one for rotation and one for scaling).
|
|
static int constexpr DoF = 2;
|
|
/// Number of internal parameters used (complex number is a tuple).
|
|
static int constexpr num_parameters = 2;
|
|
/// Group transformations are 2x2 matrices.
|
|
static int constexpr N = 2;
|
|
using Transformation = Matrix<Scalar, N, N>;
|
|
using Point = Vector2<Scalar>;
|
|
using HomogeneousPoint = Vector3<Scalar>;
|
|
using Line = ParametrizedLine2<Scalar>;
|
|
using Tangent = Vector<Scalar, DoF>;
|
|
using Adjoint = Matrix<Scalar, DoF, DoF>;
|
|
|
|
/// For binary operations the return type is determined with the
|
|
/// ScalarBinaryOpTraits feature of Eigen. This allows mixing concrete and Map
|
|
/// types, as well as other compatible scalar types such as Ceres::Jet and
|
|
/// double scalars with RxSO2 operations.
|
|
template <typename OtherDerived>
|
|
using ReturnScalar = typename Eigen::ScalarBinaryOpTraits<
|
|
Scalar, typename OtherDerived::Scalar>::ReturnType;
|
|
|
|
template <typename OtherDerived>
|
|
using RxSO2Product = RxSO2<ReturnScalar<OtherDerived>>;
|
|
|
|
template <typename PointDerived>
|
|
using PointProduct = Vector2<ReturnScalar<PointDerived>>;
|
|
|
|
template <typename HPointDerived>
|
|
using HomogeneousPointProduct = Vector3<ReturnScalar<HPointDerived>>;
|
|
|
|
/// Adjoint transformation
|
|
///
|
|
/// This function return the adjoint transformation ``Ad`` of the group
|
|
/// element ``A`` such that for all ``x`` it holds that
|
|
/// ``hat(Ad_A * x) = A * hat(x) A^{-1}``. See hat-operator below.
|
|
///
|
|
/// For RxSO(2), it simply returns the identity matrix.
|
|
///
|
|
SOPHUS_FUNC Adjoint Adj() const { return Adjoint::Identity(); }
|
|
|
|
/// Returns rotation angle.
|
|
///
|
|
SOPHUS_FUNC Scalar angle() const { return SO2<Scalar>(complex()).log(); }
|
|
|
|
/// Returns copy of instance casted to NewScalarType.
|
|
///
|
|
template <class NewScalarType>
|
|
SOPHUS_FUNC RxSO2<NewScalarType> cast() const {
|
|
return RxSO2<NewScalarType>(complex().template cast<NewScalarType>());
|
|
}
|
|
|
|
/// This provides unsafe read/write access to internal data. RxSO(2) is
|
|
/// represented by a complex number (two parameters). When using direct
|
|
/// write access, the user needs to take care of that the complex number is
|
|
/// not set close to zero.
|
|
///
|
|
/// Note: The first parameter represents the real part, while the
|
|
/// second parameter represent the imaginary part.
|
|
///
|
|
SOPHUS_FUNC Scalar* data() { return complex_nonconst().data(); }
|
|
|
|
/// Const version of data() above.
|
|
///
|
|
SOPHUS_FUNC Scalar const* data() const { return complex().data(); }
|
|
|
|
/// Returns group inverse.
|
|
///
|
|
SOPHUS_FUNC RxSO2<Scalar> inverse() const {
|
|
Scalar squared_scale = complex().squaredNorm();
|
|
return RxSO2<Scalar>(complex().x() / squared_scale,
|
|
-complex().y() / squared_scale);
|
|
}
|
|
|
|
/// Logarithmic map
|
|
///
|
|
/// Computes the logarithm, the inverse of the group exponential which maps
|
|
/// element of the group (scaled rotation matrices) to elements of the tangent
|
|
/// space (rotation-vector plus logarithm of scale factor).
|
|
///
|
|
/// To be specific, this function computes ``vee(logmat(.))`` with
|
|
/// ``logmat(.)`` being the matrix logarithm and ``vee(.)`` the vee-operator
|
|
/// of RxSO2.
|
|
///
|
|
SOPHUS_FUNC Tangent log() const {
|
|
using std::log;
|
|
Tangent theta_sigma;
|
|
theta_sigma[1] = log(scale());
|
|
theta_sigma[0] = SO2<Scalar>(complex()).log();
|
|
return theta_sigma;
|
|
}
|
|
|
|
/// Returns 2x2 matrix representation of the instance.
|
|
///
|
|
/// For RxSO2, the matrix representation is an scaled orthogonal matrix ``sR``
|
|
/// with ``det(R)=s^2``, thus a scaled rotation matrix ``R`` with scale
|
|
/// ``s``.
|
|
///
|
|
SOPHUS_FUNC Transformation matrix() const {
|
|
Transformation sR;
|
|
// clang-format off
|
|
sR << complex()[0], -complex()[1],
|
|
complex()[1], complex()[0];
|
|
// clang-format on
|
|
return sR;
|
|
}
|
|
|
|
/// Assignment-like operator from OtherDerived.
|
|
///
|
|
template <class OtherDerived>
|
|
SOPHUS_FUNC RxSO2Base<Derived>& operator=(
|
|
RxSO2Base<OtherDerived> const& other) {
|
|
complex_nonconst() = other.complex();
|
|
return *this;
|
|
}
|
|
|
|
/// Group multiplication, which is rotation concatenation and scale
|
|
/// multiplication.
|
|
///
|
|
/// Note: This function performs saturation for products close to zero in
|
|
/// order to ensure the class invariant.
|
|
///
|
|
template <typename OtherDerived>
|
|
SOPHUS_FUNC RxSO2Product<OtherDerived> operator*(
|
|
RxSO2Base<OtherDerived> const& other) const {
|
|
using ResultT = ReturnScalar<OtherDerived>;
|
|
|
|
Scalar lhs_real = complex().x();
|
|
Scalar lhs_imag = complex().y();
|
|
typename OtherDerived::Scalar const& rhs_real = other.complex().x();
|
|
typename OtherDerived::Scalar const& rhs_imag = other.complex().y();
|
|
/// complex multiplication
|
|
typename RxSO2Product<OtherDerived>::ComplexType result_complex(
|
|
lhs_real * rhs_real - lhs_imag * rhs_imag,
|
|
lhs_real * rhs_imag + lhs_imag * rhs_real);
|
|
|
|
const ResultT squared_scale = result_complex.squaredNorm();
|
|
|
|
if (squared_scale <
|
|
Constants<ResultT>::epsilon() * Constants<ResultT>::epsilon()) {
|
|
/// Saturation to ensure class invariant.
|
|
result_complex.normalize();
|
|
result_complex *= Constants<ResultT>::epsilon();
|
|
}
|
|
return RxSO2Product<OtherDerived>(result_complex);
|
|
}
|
|
|
|
/// Group action on 2-points.
|
|
///
|
|
/// This function rotates a 2 dimensional point ``p`` by the SO2 element
|
|
/// ``bar_R_foo`` (= rotation matrix) and scales it by the scale factor ``s``:
|
|
///
|
|
/// ``p_bar = s * (bar_R_foo * p_foo)``.
|
|
///
|
|
template <typename PointDerived,
|
|
typename = typename std::enable_if<
|
|
IsFixedSizeVector<PointDerived, 2>::value>::type>
|
|
SOPHUS_FUNC PointProduct<PointDerived> operator*(
|
|
Eigen::MatrixBase<PointDerived> const& p) const {
|
|
return matrix() * p;
|
|
}
|
|
|
|
/// Group action on homogeneous 2-points. See above for more details.
|
|
///
|
|
template <typename HPointDerived,
|
|
typename = typename std::enable_if<
|
|
IsFixedSizeVector<HPointDerived, 3>::value>::type>
|
|
SOPHUS_FUNC HomogeneousPointProduct<HPointDerived> operator*(
|
|
Eigen::MatrixBase<HPointDerived> const& p) const {
|
|
const auto rsp = *this * p.template head<2>();
|
|
return HomogeneousPointProduct<HPointDerived>(rsp(0), rsp(1), p(2));
|
|
}
|
|
|
|
/// Group action on lines.
|
|
///
|
|
/// This function rotates a parameterized line ``l(t) = o + t * d`` by the SO2
|
|
/// element and scales it by the scale factor
|
|
///
|
|
/// Origin ``o`` is rotated and scaled
|
|
/// Direction ``d`` is rotated (preserving it's norm)
|
|
///
|
|
SOPHUS_FUNC Line operator*(Line const& l) const {
|
|
return Line((*this) * l.origin(), (*this) * l.direction() / scale());
|
|
}
|
|
|
|
/// In-place group multiplication. This method is only valid if the return
|
|
/// type of the multiplication is compatible with this SO2's Scalar type.
|
|
///
|
|
/// Note: This function performs saturation for products close to zero in
|
|
/// order to ensure the class invariant.
|
|
///
|
|
template <typename OtherDerived,
|
|
typename = typename std::enable_if<
|
|
std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type>
|
|
SOPHUS_FUNC RxSO2Base<Derived>& operator*=(
|
|
RxSO2Base<OtherDerived> const& other) {
|
|
*static_cast<Derived*>(this) = *this * other;
|
|
return *this;
|
|
}
|
|
|
|
/// Returns internal parameters of RxSO(2).
|
|
///
|
|
/// It returns (c[0], c[1]), with c being the complex number.
|
|
///
|
|
SOPHUS_FUNC Sophus::Vector<Scalar, num_parameters> params() const {
|
|
return complex();
|
|
}
|
|
|
|
/// Sets non-zero complex
|
|
///
|
|
/// Precondition: ``z`` must not be close to zero.
|
|
SOPHUS_FUNC void setComplex(Vector2<Scalar> const& z) {
|
|
SOPHUS_ENSURE(z.squaredNorm() > Constants<Scalar>::epsilon() *
|
|
Constants<Scalar>::epsilon(),
|
|
"Scale factor must be greater-equal epsilon.");
|
|
static_cast<Derived*>(this)->complex_nonconst() = z;
|
|
}
|
|
|
|
/// Accessor of complex.
|
|
///
|
|
SOPHUS_FUNC ComplexType const& complex() const {
|
|
return static_cast<Derived const*>(this)->complex();
|
|
}
|
|
|
|
/// Returns rotation matrix.
|
|
///
|
|
SOPHUS_FUNC Transformation rotationMatrix() const {
|
|
ComplexTemporaryType norm_quad = complex();
|
|
norm_quad.normalize();
|
|
return SO2<Scalar>(norm_quad).matrix();
|
|
}
|
|
|
|
/// Returns scale.
|
|
///
|
|
SOPHUS_FUNC
|
|
Scalar scale() const { return complex().norm(); }
|
|
|
|
/// Setter of rotation angle, leaves scale as is.
|
|
///
|
|
SOPHUS_FUNC void setAngle(Scalar const& theta) { setSO2(SO2<Scalar>(theta)); }
|
|
|
|
/// Setter of complex using rotation matrix ``R``, leaves scale as is.
|
|
///
|
|
/// Precondition: ``R`` must be orthogonal with determinant of one.
|
|
///
|
|
SOPHUS_FUNC void setRotationMatrix(Transformation const& R) {
|
|
setSO2(SO2<Scalar>(R));
|
|
}
|
|
|
|
/// Sets scale and leaves rotation as is.
|
|
///
|
|
SOPHUS_FUNC void setScale(Scalar const& scale) {
|
|
using std::sqrt;
|
|
complex_nonconst().normalize();
|
|
complex_nonconst() *= scale;
|
|
}
|
|
|
|
/// Setter of complex number using scaled rotation matrix ``sR``.
|
|
///
|
|
/// Precondition: The 2x2 matrix must be "scaled orthogonal"
|
|
/// and have a positive determinant.
|
|
///
|
|
SOPHUS_FUNC void setScaledRotationMatrix(Transformation const& sR) {
|
|
SOPHUS_ENSURE(isScaledOrthogonalAndPositive(sR),
|
|
"sR must be scaled orthogonal:\n %", sR);
|
|
complex_nonconst() = sR.col(0);
|
|
}
|
|
|
|
/// Setter of SO(2) rotations, leaves scale as is.
|
|
///
|
|
SOPHUS_FUNC void setSO2(SO2<Scalar> const& so2) {
|
|
using std::sqrt;
|
|
Scalar saved_scale = scale();
|
|
complex_nonconst() = so2.unit_complex();
|
|
complex_nonconst() *= saved_scale;
|
|
}
|
|
|
|
SOPHUS_FUNC SO2<Scalar> so2() const { return SO2<Scalar>(complex()); }
|
|
|
|
private:
|
|
/// Mutator of complex is private to ensure class invariant.
|
|
///
|
|
SOPHUS_FUNC ComplexType& complex_nonconst() {
|
|
return static_cast<Derived*>(this)->complex_nonconst();
|
|
}
|
|
};
|
|
|
|
/// RxSO2 using storage; derived from RxSO2Base.
|
|
template <class Scalar_, int Options>
|
|
class RxSO2 : public RxSO2Base<RxSO2<Scalar_, Options>> {
|
|
public:
|
|
using Base = RxSO2Base<RxSO2<Scalar_, Options>>;
|
|
using Scalar = Scalar_;
|
|
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 ComplexMember = Eigen::Matrix<Scalar, 2, 1, Options>;
|
|
|
|
/// ``Base`` is friend so complex_nonconst can be accessed from ``Base``.
|
|
friend class RxSO2Base<RxSO2<Scalar_, Options>>;
|
|
|
|
using Base::operator=;
|
|
|
|
EIGEN_MAKE_ALIGNED_OPERATOR_NEW
|
|
|
|
/// Default constructor initializes complex number to identity rotation and
|
|
/// scale to 1.
|
|
///
|
|
SOPHUS_FUNC RxSO2() : complex_(Scalar(1), Scalar(0)) {}
|
|
|
|
/// Copy constructor
|
|
///
|
|
SOPHUS_FUNC RxSO2(RxSO2 const& other) = default;
|
|
|
|
/// Copy-like constructor from OtherDerived.
|
|
///
|
|
template <class OtherDerived>
|
|
SOPHUS_FUNC RxSO2(RxSO2Base<OtherDerived> const& other)
|
|
: complex_(other.complex()) {}
|
|
|
|
/// Constructor from scaled rotation matrix
|
|
///
|
|
/// Precondition: rotation matrix need to be scaled orthogonal with
|
|
/// determinant of ``s^2``.
|
|
///
|
|
SOPHUS_FUNC explicit RxSO2(Transformation const& sR) {
|
|
this->setScaledRotationMatrix(sR);
|
|
}
|
|
|
|
/// Constructor from scale factor and rotation matrix ``R``.
|
|
///
|
|
/// Precondition: Rotation matrix ``R`` must to be orthogonal with determinant
|
|
/// of 1 and ``scale`` must to be close to zero.
|
|
///
|
|
SOPHUS_FUNC RxSO2(Scalar const& scale, Transformation const& R)
|
|
: RxSO2((scale * SO2<Scalar>(R).unit_complex()).eval()) {}
|
|
|
|
/// Constructor from scale factor and SO2
|
|
///
|
|
/// Precondition: ``scale`` must be close to zero.
|
|
///
|
|
SOPHUS_FUNC RxSO2(Scalar const& scale, SO2<Scalar> const& so2)
|
|
: RxSO2((scale * so2.unit_complex()).eval()) {}
|
|
|
|
/// Constructor from complex number.
|
|
///
|
|
/// Precondition: complex number must not be close to zero.
|
|
///
|
|
SOPHUS_FUNC explicit RxSO2(Vector2<Scalar> const& z) : complex_(z) {
|
|
SOPHUS_ENSURE(complex_.squaredNorm() >= Constants<Scalar>::epsilon() *
|
|
Constants<Scalar>::epsilon(),
|
|
"Scale factor must be greater-equal epsilon: % vs %",
|
|
complex_.squaredNorm(),
|
|
Constants<Scalar>::epsilon() * Constants<Scalar>::epsilon());
|
|
}
|
|
|
|
/// Constructor from complex number.
|
|
///
|
|
/// Precondition: complex number must not be close to zero.
|
|
///
|
|
SOPHUS_FUNC explicit RxSO2(Scalar const& real, Scalar const& imag)
|
|
: RxSO2(Vector2<Scalar>(real, imag)) {}
|
|
|
|
/// Accessor of complex.
|
|
///
|
|
SOPHUS_FUNC ComplexMember const& complex() const { return complex_; }
|
|
|
|
/// Returns derivative of exp(x).matrix() wrt. ``x_i at x=0``.
|
|
///
|
|
SOPHUS_FUNC static Transformation Dxi_exp_x_matrix_at_0(int i) {
|
|
return generator(i);
|
|
}
|
|
/// Group exponential
|
|
///
|
|
/// This functions takes in an element of tangent space (= rotation angle
|
|
/// plus logarithm of scale) and returns the corresponding element of the
|
|
/// group RxSO2.
|
|
///
|
|
/// To be more specific, this function computes ``expmat(hat(theta))``
|
|
/// with ``expmat(.)`` being the matrix exponential and ``hat(.)`` being the
|
|
/// hat()-operator of RSO2.
|
|
///
|
|
SOPHUS_FUNC static RxSO2<Scalar> exp(Tangent const& a) {
|
|
using std::exp;
|
|
|
|
Scalar const theta = a[0];
|
|
Scalar const sigma = a[1];
|
|
Scalar s = exp(sigma);
|
|
Vector2<Scalar> z = SO2<Scalar>::exp(theta).unit_complex();
|
|
z *= s;
|
|
return RxSO2<Scalar>(z);
|
|
}
|
|
|
|
/// Returns the ith infinitesimal generators of ``R+ x SO(2)``.
|
|
///
|
|
/// The infinitesimal generators of RxSO2 are:
|
|
///
|
|
/// ```
|
|
/// | 0 -1 |
|
|
/// G_0 = | 1 0 |
|
|
///
|
|
/// | 1 0 |
|
|
/// G_1 = | 0 1 |
|
|
/// ```
|
|
///
|
|
/// Precondition: ``i`` must be 0, or 1.
|
|
///
|
|
SOPHUS_FUNC static Transformation generator(int i) {
|
|
SOPHUS_ENSURE(i >= 0 && i <= 1, "i should be 0 or 1.");
|
|
Tangent e;
|
|
e.setZero();
|
|
e[i] = Scalar(1);
|
|
return hat(e);
|
|
}
|
|
|
|
/// hat-operator
|
|
///
|
|
/// It takes in the 2-vector representation ``a`` (= rotation angle plus
|
|
/// logarithm of scale) and returns the corresponding matrix representation
|
|
/// of Lie algebra element.
|
|
///
|
|
/// Formally, the hat()-operator of RxSO2 is defined as
|
|
///
|
|
/// ``hat(.): R^2 -> R^{2x2}, hat(a) = sum_i a_i * G_i`` (for i=0,1,2)
|
|
///
|
|
/// with ``G_i`` being the ith infinitesimal generator of RxSO2.
|
|
///
|
|
/// The corresponding inverse is the vee()-operator, see below.
|
|
///
|
|
SOPHUS_FUNC static Transformation hat(Tangent const& a) {
|
|
Transformation A;
|
|
// clang-format off
|
|
A << a(1), -a(0),
|
|
a(0), a(1);
|
|
// clang-format on
|
|
return A;
|
|
}
|
|
|
|
/// Lie bracket
|
|
///
|
|
/// It computes the Lie bracket of RxSO(2). To be more specific, it computes
|
|
///
|
|
/// ``[omega_1, omega_2]_rxso2 := 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 RxSO2.
|
|
///
|
|
SOPHUS_FUNC static Tangent lieBracket(Tangent const&, Tangent const&) {
|
|
Vector2<Scalar> res;
|
|
res.setZero();
|
|
return res;
|
|
}
|
|
|
|
/// Draw uniform sample from RxSO(2) manifold.
|
|
///
|
|
/// The scale factor is drawn uniformly in log2-space from [-1, 1],
|
|
/// hence the scale is in [0.5, 2)].
|
|
///
|
|
template <class UniformRandomBitGenerator>
|
|
static RxSO2 sampleUniform(UniformRandomBitGenerator& generator) {
|
|
std::uniform_real_distribution<Scalar> uniform(Scalar(-1), Scalar(1));
|
|
using std::exp2;
|
|
return RxSO2(exp2(uniform(generator)),
|
|
SO2<Scalar>::sampleUniform(generator));
|
|
}
|
|
|
|
/// vee-operator
|
|
///
|
|
/// It takes the 2x2-matrix representation ``Omega`` and maps it to the
|
|
/// corresponding vector representation of Lie algebra.
|
|
///
|
|
/// This is the inverse of the hat()-operator, see above.
|
|
///
|
|
/// Precondition: ``Omega`` must have the following structure:
|
|
///
|
|
/// | d -x |
|
|
/// | x d |
|
|
///
|
|
SOPHUS_FUNC static Tangent vee(Transformation const& Omega) {
|
|
using std::abs;
|
|
return Tangent(Omega(1, 0), Omega(0, 0));
|
|
}
|
|
|
|
protected:
|
|
SOPHUS_FUNC ComplexMember& complex_nonconst() { return complex_; }
|
|
|
|
ComplexMember complex_;
|
|
};
|
|
|
|
} // namespace Sophus
|
|
|
|
namespace Eigen {
|
|
|
|
/// Specialization of Eigen::Map for ``RxSO2``; derived from RxSO2Base.
|
|
///
|
|
/// Allows us to wrap RxSO2 objects around POD array (e.g. external z style
|
|
/// complex).
|
|
template <class Scalar_, int Options>
|
|
class Map<Sophus::RxSO2<Scalar_>, Options>
|
|
: public Sophus::RxSO2Base<Map<Sophus::RxSO2<Scalar_>, Options>> {
|
|
using Base = Sophus::RxSO2Base<Map<Sophus::RxSO2<Scalar_>, Options>>;
|
|
|
|
public:
|
|
using Scalar = Scalar_;
|
|
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;
|
|
|
|
/// ``Base`` is friend so complex_nonconst can be accessed from ``Base``.
|
|
friend class Sophus::RxSO2Base<Map<Sophus::RxSO2<Scalar_>, Options>>;
|
|
|
|
using Base::operator=;
|
|
using Base::operator*=;
|
|
using Base::operator*;
|
|
|
|
SOPHUS_FUNC Map(Scalar* coeffs) : complex_(coeffs) {}
|
|
|
|
/// Accessor of complex.
|
|
///
|
|
SOPHUS_FUNC
|
|
Map<Sophus::Vector2<Scalar>, Options> const& complex() const {
|
|
return complex_;
|
|
}
|
|
|
|
protected:
|
|
SOPHUS_FUNC Map<Sophus::Vector2<Scalar>, Options>& complex_nonconst() {
|
|
return complex_;
|
|
}
|
|
|
|
Map<Sophus::Vector2<Scalar>, Options> complex_;
|
|
};
|
|
|
|
/// Specialization of Eigen::Map for ``RxSO2 const``; derived from RxSO2Base.
|
|
///
|
|
/// Allows us to wrap RxSO2 objects around POD array (e.g. external z style
|
|
/// complex).
|
|
template <class Scalar_, int Options>
|
|
class Map<Sophus::RxSO2<Scalar_> const, Options>
|
|
: public Sophus::RxSO2Base<Map<Sophus::RxSO2<Scalar_> const, Options>> {
|
|
public:
|
|
using Base = Sophus::RxSO2Base<Map<Sophus::RxSO2<Scalar_> const, Options>>;
|
|
using Scalar = Scalar_;
|
|
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 Base::operator*=;
|
|
using Base::operator*;
|
|
|
|
SOPHUS_FUNC
|
|
Map(Scalar const* coeffs) : complex_(coeffs) {}
|
|
|
|
/// Accessor of complex.
|
|
///
|
|
SOPHUS_FUNC
|
|
Map<Sophus::Vector2<Scalar> const, Options> const& complex() const {
|
|
return complex_;
|
|
}
|
|
|
|
protected:
|
|
Map<Sophus::Vector2<Scalar> const, Options> const complex_;
|
|
};
|
|
} // namespace Eigen
|
|
|
|
#endif /// SOPHUS_RXSO2_HPP
|