rxso3.hpp

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#ifndef SOPHUS_RXSO3_HPP
#define SOPHUS_RXSO3_HPP
 
#include "so3.hpp"
 
namespace Sophus {
template <class Scalar_, int Options = 0>
class RxSO3;
using RxSO3d = RxSO3<double>;
using RxSO3f = RxSO3<float>;
}  // namespace Sophus
 
namespace Eigen {
namespace internal {
 
template <class Scalar_, int Options>
struct traits<Sophus::RxSO3<Scalar_, Options>> {
  using Scalar = Scalar_;
  using QuaternionType = Eigen::Quaternion<Scalar, Options>;
};
 
template <class Scalar_, int Options>
struct traits<Map<Sophus::RxSO3<Scalar_>, Options>>
    : traits<Sophus::RxSO3<Scalar_, Options>> {
  using Scalar = Scalar_;
  using QuaternionType = Map<Eigen::Quaternion<Scalar>, Options>;
};
 
template <class Scalar_, int Options>
struct traits<Map<Sophus::RxSO3<Scalar_> const, Options>>
    : traits<Sophus::RxSO3<Scalar_, Options> const> {
  using Scalar = Scalar_;
  using QuaternionType = Map<Eigen::Quaternion<Scalar> const, Options>;
};
}  // namespace internal
}  // namespace Eigen
 
namespace Sophus {
 
template <class Derived>
class RxSO3Base {
 public:
  using Scalar = typename Eigen::internal::traits<Derived>::Scalar;
  using QuaternionType =
      typename Eigen::internal::traits<Derived>::QuaternionType;
 
  static int constexpr DoF = 4;
  static int constexpr num_parameters = 4;
  static int constexpr N = 3;
  using Transformation = Matrix<Scalar, N, N>;
  using Point = Vector3<Scalar>;
  using HomogeneousPoint = Vector4<Scalar>;
  using Line = ParametrizedLine3<Scalar>;
  using Tangent = Vector<Scalar, DoF>;
  using Adjoint = Matrix<Scalar, DoF, DoF>;
 
  struct TangentAndTheta {
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
    Tangent tangent;
    Scalar theta;
  };
 
  template <typename OtherDerived>
  using ReturnScalar = typename Eigen::ScalarBinaryOpTraits<
      Scalar, typename OtherDerived::Scalar>::ReturnType;
 
  template <typename OtherDerived>
  using RxSO3Product = RxSO3<ReturnScalar<OtherDerived>>;
 
  template <typename PointDerived>
  using PointProduct = Vector3<ReturnScalar<PointDerived>>;
 
  template <typename HPointDerived>
  using HomogeneousPointProduct = Vector4<ReturnScalar<HPointDerived>>;
 
  SOPHUS_FUNC Adjoint Adj() const {
    Adjoint res;
    res.setIdentity();
    res.template topLeftCorner<3, 3>() = rotationMatrix();
    return res;
  }
 
  template <class NewScalarType>
  SOPHUS_FUNC RxSO3<NewScalarType> cast() const {
    return RxSO3<NewScalarType>(quaternion().template cast<NewScalarType>());
  }
 
  SOPHUS_FUNC Scalar* data() { return quaternion_nonconst().coeffs().data(); }
 
  SOPHUS_FUNC Scalar const* data() const {
    return quaternion().coeffs().data();
  }
 
  SOPHUS_FUNC RxSO3<Scalar> inverse() const {
    return RxSO3<Scalar>(quaternion().inverse());
  }
 
  SOPHUS_FUNC Tangent log() const { return logAndTheta().tangent; }
 
  SOPHUS_FUNC TangentAndTheta logAndTheta() const {
    using std::log;
 
    Scalar scale = quaternion().squaredNorm();
    TangentAndTheta result;
    result.tangent[3] = log(scale);
    auto omega_and_theta = SO3<Scalar>(quaternion()).logAndTheta();
    result.tangent.template head<3>() = omega_and_theta.tangent;
    result.theta = omega_and_theta.theta;
    return result;
  }
  SOPHUS_FUNC Transformation matrix() const {
    Transformation sR;
 
    Scalar const vx_sq = quaternion().vec().x() * quaternion().vec().x();
    Scalar const vy_sq = quaternion().vec().y() * quaternion().vec().y();
    Scalar const vz_sq = quaternion().vec().z() * quaternion().vec().z();
    Scalar const w_sq = quaternion().w() * quaternion().w();
    Scalar const two_vx = Scalar(2) * quaternion().vec().x();
    Scalar const two_vy = Scalar(2) * quaternion().vec().y();
    Scalar const two_vz = Scalar(2) * quaternion().vec().z();
    Scalar const two_vx_vy = two_vx * quaternion().vec().y();
    Scalar const two_vx_vz = two_vx * quaternion().vec().z();
    Scalar const two_vx_w = two_vx * quaternion().w();
    Scalar const two_vy_vz = two_vy * quaternion().vec().z();
    Scalar const two_vy_w = two_vy * quaternion().w();
    Scalar const two_vz_w = two_vz * quaternion().w();
 
    sR(0, 0) = vx_sq - vy_sq - vz_sq + w_sq;
    sR(1, 0) = two_vx_vy + two_vz_w;
    sR(2, 0) = two_vx_vz - two_vy_w;
 
    sR(0, 1) = two_vx_vy - two_vz_w;
    sR(1, 1) = -vx_sq + vy_sq - vz_sq + w_sq;
    sR(2, 1) = two_vx_w + two_vy_vz;
 
    sR(0, 2) = two_vx_vz + two_vy_w;
    sR(1, 2) = -two_vx_w + two_vy_vz;
    sR(2, 2) = -vx_sq - vy_sq + vz_sq + w_sq;
    return sR;
  }
 
  SOPHUS_FUNC RxSO3Base& operator=(RxSO3Base const& other) = default;
 
  template <class OtherDerived>
  SOPHUS_FUNC RxSO3Base<Derived>& operator=(
      RxSO3Base<OtherDerived> const& other) {
    quaternion_nonconst() = other.quaternion();
    return *this;
  }
 
  template <typename OtherDerived>
  SOPHUS_FUNC RxSO3Product<OtherDerived> operator*(
      RxSO3Base<OtherDerived> const& other) const {
    using ResultT = ReturnScalar<OtherDerived>;
    typename RxSO3Product<OtherDerived>::QuaternionType result_quaternion(
        quaternion() * other.quaternion());
 
    ResultT scale = result_quaternion.squaredNorm();
    if (scale < Constants<ResultT>::epsilon()) {
      SOPHUS_ENSURE(scale > ResultT(0), "Scale must be greater zero.");
      result_quaternion.normalize();
      result_quaternion.coeffs() *= sqrt(Constants<Scalar>::epsilon());
    }
    return RxSO3Product<OtherDerived>(result_quaternion);
  }
 
  template <typename PointDerived,
            typename = typename std::enable_if<
                IsFixedSizeVector<PointDerived, 3>::value>::type>
  SOPHUS_FUNC PointProduct<PointDerived> operator*(
      Eigen::MatrixBase<PointDerived> const& p) const {
    // Follows http:///eigen.tuxfamily.org/bz/show_bug.cgi?id=459
    Scalar scale = quaternion().squaredNorm();
    PointProduct<PointDerived> two_vec_cross_p = quaternion().vec().cross(p);
    two_vec_cross_p += two_vec_cross_p;
    return scale * p + (quaternion().w() * two_vec_cross_p +
                        quaternion().vec().cross(two_vec_cross_p));
  }
 
  template <typename HPointDerived,
            typename = typename std::enable_if<
                IsFixedSizeVector<HPointDerived, 4>::value>::type>
  SOPHUS_FUNC HomogeneousPointProduct<HPointDerived> operator*(
      Eigen::MatrixBase<HPointDerived> const& p) const {
    const auto rsp = *this * p.template head<3>();
    return HomogeneousPointProduct<HPointDerived>(rsp(0), rsp(1), rsp(2), p(3));
  }
 
  SOPHUS_FUNC Line operator*(Line const& l) const {
    return Line((*this) * l.origin(),
                (*this) * l.direction() / quaternion().squaredNorm());
  }
 
  template <typename OtherDerived,
            typename = typename std::enable_if<
                std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type>
  SOPHUS_FUNC RxSO3Base<Derived>& operator*=(
      RxSO3Base<OtherDerived> const& other) {
    *static_cast<Derived*>(this) = *this * other;
    return *this;
  }
 
  SOPHUS_FUNC Sophus::Vector<Scalar, num_parameters> params() const {
    return quaternion().coeffs();
  }
 
  SOPHUS_FUNC void setQuaternion(Eigen::Quaternion<Scalar> const& quat) {
    SOPHUS_ENSURE(quat.squaredNorm() > Constants<Scalar>::epsilon() *
                                           Constants<Scalar>::epsilon(),
                  "Scale factor must be greater-equal epsilon.");
    static_cast<Derived*>(this)->quaternion_nonconst() = quat;
  }
 
  SOPHUS_FUNC QuaternionType const& quaternion() const {
    return static_cast<Derived const*>(this)->quaternion();
  }
 
  SOPHUS_FUNC Transformation rotationMatrix() const {
    QuaternionType norm_quad = quaternion();
    norm_quad.normalize();
    return norm_quad.toRotationMatrix();
  }
 
  SOPHUS_FUNC
  Scalar scale() const { return quaternion().squaredNorm(); }
 
  SOPHUS_FUNC void setRotationMatrix(Transformation const& R) {
    using std::sqrt;
    Scalar saved_scale = scale();
    quaternion_nonconst() = R;
    quaternion_nonconst().coeffs() *= sqrt(saved_scale);
  }
 
  SOPHUS_FUNC
  void setScale(Scalar const& scale) {
    using std::sqrt;
    quaternion_nonconst().normalize();
    quaternion_nonconst().coeffs() *= sqrt(scale);
  }
 
  SOPHUS_FUNC void setScaledRotationMatrix(Transformation const& sR) {
    Transformation squared_sR = sR * sR.transpose();
    Scalar squared_scale =
        Scalar(1. / 3.) *
        (squared_sR(0, 0) + squared_sR(1, 1) + squared_sR(2, 2));
    SOPHUS_ENSURE(squared_scale >= Constants<Scalar>::epsilon() *
                                       Constants<Scalar>::epsilon(),
                  "Scale factor must be greater-equal epsilon.");
    Scalar scale = sqrt(squared_scale);
    quaternion_nonconst() = sR / scale;
    quaternion_nonconst().coeffs() *= sqrt(scale);
  }
 
  SOPHUS_FUNC void setSO3(SO3<Scalar> const& so3) {
    using std::sqrt;
    Scalar saved_scale = scale();
    quaternion_nonconst() = so3.unit_quaternion();
    quaternion_nonconst().coeffs() *= sqrt(saved_scale);
  }
 
  SOPHUS_FUNC SO3<Scalar> so3() const { return SO3<Scalar>(quaternion()); }
 
 protected:
  SOPHUS_FUNC QuaternionType& quaternion_nonconst() {
    return static_cast<Derived*>(this)->quaternion_nonconst();
  }
};
 
template <class Scalar_, int Options>
class RxSO3 : public RxSO3Base<RxSO3<Scalar_, Options>> {
 public:
  using Base = RxSO3Base<RxSO3<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 QuaternionMember = Eigen::Quaternion<Scalar, Options>;
 
  friend class RxSO3Base<RxSO3<Scalar_, Options>>;
 
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 
  SOPHUS_FUNC RxSO3()
      : quaternion_(Scalar(1), Scalar(0), Scalar(0), Scalar(0)) {}
 
  SOPHUS_FUNC RxSO3(RxSO3 const& other) = default;
 
  template <class OtherDerived>
  SOPHUS_FUNC RxSO3(RxSO3Base<OtherDerived> const& other)
      : quaternion_(other.quaternion()) {}
 
  SOPHUS_FUNC explicit RxSO3(Transformation const& sR) {
    this->setScaledRotationMatrix(sR);
  }
 
  SOPHUS_FUNC RxSO3(Scalar const& scale, Transformation const& R)
      : quaternion_(R) {
    SOPHUS_ENSURE(scale >= Constants<Scalar>::epsilon(),
                  "Scale factor must be greater-equal epsilon.");
    using std::sqrt;
    quaternion_.coeffs() *= sqrt(scale);
  }
 
  SOPHUS_FUNC RxSO3(Scalar const& scale, SO3<Scalar> const& so3)
      : quaternion_(so3.unit_quaternion()) {
    SOPHUS_ENSURE(scale >= Constants<Scalar>::epsilon(),
                  "Scale factor must be greater-equal epsilon.");
    using std::sqrt;
    quaternion_.coeffs() *= sqrt(scale);
  }
 
  template <class D>
  SOPHUS_FUNC explicit RxSO3(Eigen::QuaternionBase<D> const& quat)
      : quaternion_(quat) {
    static_assert(std::is_same<typename D::Scalar, Scalar>::value,
                  "must be same Scalar type.");
    SOPHUS_ENSURE(quaternion_.squaredNorm() >= Constants<Scalar>::epsilon(),
                  "Scale factor must be greater-equal epsilon.");
  }
 
  SOPHUS_FUNC QuaternionMember const& quaternion() const { return quaternion_; }
 
  SOPHUS_FUNC static Transformation Dxi_exp_x_matrix_at_0(int i) {
    return generator(i);
  }
  SOPHUS_FUNC static RxSO3<Scalar> exp(Tangent const& a) {
    Scalar theta;
    return expAndTheta(a, &theta);
  }
 
  SOPHUS_FUNC static RxSO3<Scalar> expAndTheta(Tangent const& a,
                                               Scalar* theta) {
    SOPHUS_ENSURE(theta != nullptr, "must not be nullptr.");
    using std::exp;
    using std::sqrt;
 
    Vector3<Scalar> const omega = a.template head<3>();
    Scalar sigma = a[3];
    Scalar sqrt_scale = sqrt(exp(sigma));
    Eigen::Quaternion<Scalar> quat =
        SO3<Scalar>::expAndTheta(omega, theta).unit_quaternion();
    quat.coeffs() *= sqrt_scale;
    return RxSO3<Scalar>(quat);
  }
 
  SOPHUS_FUNC static Transformation generator(int i) {
    SOPHUS_ENSURE(i >= 0 && i <= 3, "i should be in range [0,3].");
    Tangent e;
    e.setZero();
    e[i] = Scalar(1);
    return hat(e);
  }
 
  SOPHUS_FUNC static Transformation hat(Tangent const& a) {
    Transformation A;
    // clang-format off
    A <<  a(3), -a(2),  a(1),
          a(2),  a(3), -a(0),
         -a(1),  a(0),  a(3);
    // clang-format on
    return A;
  }
 
  SOPHUS_FUNC static Tangent lieBracket(Tangent const& a, Tangent const& b) {
    Vector3<Scalar> const omega1 = a.template head<3>();
    Vector3<Scalar> const omega2 = b.template head<3>();
    Vector4<Scalar> res;
    res.template head<3>() = omega1.cross(omega2);
    res[3] = Scalar(0);
    return res;
  }
 
  template <class UniformRandomBitGenerator>
  static RxSO3 sampleUniform(UniformRandomBitGenerator& generator) {
    std::uniform_real_distribution<Scalar> uniform(Scalar(-1), Scalar(1));
    using std::exp2;
    return RxSO3(exp2(uniform(generator)),
                 SO3<Scalar>::sampleUniform(generator));
  }
 
  SOPHUS_FUNC static Tangent vee(Transformation const& Omega) {
    using std::abs;
    return Tangent(Omega(2, 1), Omega(0, 2), Omega(1, 0), Omega(0, 0));
  }
 
 protected:
  SOPHUS_FUNC QuaternionMember& quaternion_nonconst() { return quaternion_; }
 
  QuaternionMember quaternion_;
};
 
}  // namespace Sophus
 
namespace Eigen {
 
template <class Scalar_, int Options>
class Map<Sophus::RxSO3<Scalar_>, Options>
    : public Sophus::RxSO3Base<Map<Sophus::RxSO3<Scalar_>, Options>> {
 public:
  using Base = Sophus::RxSO3Base<Map<Sophus::RxSO3<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;
 
  friend class Sophus::RxSO3Base<Map<Sophus::RxSO3<Scalar_>, Options>>;
 
  // LCOV_EXCL_START
  EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Map);
  // LCOV_EXCL_STOP
 
  using Base::operator*=;
  using Base::operator*;
 
  SOPHUS_FUNC Map(Scalar* coeffs) : quaternion_(coeffs) {}
 
  SOPHUS_FUNC
  Map<Eigen::Quaternion<Scalar>, Options> const& quaternion() const {
    return quaternion_;
  }
 
 protected:
  SOPHUS_FUNC Map<Eigen::Quaternion<Scalar>, Options>& quaternion_nonconst() {
    return quaternion_;
  }
 
  Map<Eigen::Quaternion<Scalar>, Options> quaternion_;
};
 
template <class Scalar_, int Options>
class Map<Sophus::RxSO3<Scalar_> const, Options>
    : public Sophus::RxSO3Base<Map<Sophus::RxSO3<Scalar_> const, Options>> {
 public:
  using Base = Sophus::RxSO3Base<Map<Sophus::RxSO3<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) : quaternion_(coeffs) {}
 
  SOPHUS_FUNC
  Map<Eigen::Quaternion<Scalar> const, Options> const& quaternion() const {
    return quaternion_;
  }
 
 protected:
  Map<Eigen::Quaternion<Scalar> const, Options> const quaternion_;
};
}  // namespace Eigen
 
#endif