.. _program_listing_file_sophus_sim2.hpp:

Program Listing for File sim2.hpp
=================================

|exhale_lsh| :ref:`Return to documentation for file <file_sophus_sim2.hpp>` (``sophus/sim2.hpp``)

.. |exhale_lsh| unicode:: U+021B0 .. UPWARDS ARROW WITH TIP LEFTWARDS

.. code-block:: cpp

   
   #pragma once
   
   #include "rxso2.hpp"
   #include "sim_details.hpp"
   
   namespace Sophus {
   template <class Scalar_, int Options = 0>
   class Sim2;
   using Sim2d = Sim2<double>;
   using Sim2f = Sim2<float>;
   }  // namespace Sophus
   
   namespace Eigen {
   namespace internal {
   
   template <class Scalar_, int Options>
   struct traits<Sophus::Sim2<Scalar_, Options>> {
     using Scalar = Scalar_;
     using TranslationType = Sophus::Vector2<Scalar, Options>;
     using RxSO2Type = Sophus::RxSO2<Scalar, Options>;
   };
   
   template <class Scalar_, int Options>
   struct traits<Map<Sophus::Sim2<Scalar_>, Options>>
       : traits<Sophus::Sim2<Scalar_, Options>> {
     using Scalar = Scalar_;
     using TranslationType = Map<Sophus::Vector2<Scalar>, Options>;
     using RxSO2Type = Map<Sophus::RxSO2<Scalar>, Options>;
   };
   
   template <class Scalar_, int Options>
   struct traits<Map<Sophus::Sim2<Scalar_> const, Options>>
       : traits<Sophus::Sim2<Scalar_, Options> const> {
     using Scalar = Scalar_;
     using TranslationType = Map<Sophus::Vector2<Scalar> const, Options>;
     using RxSO2Type = Map<Sophus::RxSO2<Scalar> const, Options>;
   };
   }  // namespace internal
   }  // namespace Eigen
   
   namespace Sophus {
   
   template <class Derived>
   class Sim2Base {
    public:
     using Scalar = typename Eigen::internal::traits<Derived>::Scalar;
     using TranslationType =
         typename Eigen::internal::traits<Derived>::TranslationType;
     using RxSO2Type = typename Eigen::internal::traits<Derived>::RxSO2Type;
   
     static int constexpr DoF = 4;
     static int constexpr num_parameters = 4;
     static int constexpr N = 3;
     static int constexpr Dim = 2;
     using Transformation = Matrix<Scalar, N, N>;
     using Point = Vector2<Scalar>;
     using HomogeneousPoint = Vector3<Scalar>;
     using Line = ParametrizedLine2<Scalar>;
     using Hyperplane = Hyperplane2<Scalar>;
     using Tangent = Vector<Scalar, DoF>;
     using Adjoint = Matrix<Scalar, DoF, DoF>;
   
     template <typename OtherDerived>
     using ReturnScalar = typename Eigen::ScalarBinaryOpTraits<
         Scalar, typename OtherDerived::Scalar>::ReturnType;
   
     template <typename OtherDerived>
     using Sim2Product = Sim2<ReturnScalar<OtherDerived>>;
   
     template <typename PointDerived>
     using PointProduct = Vector2<ReturnScalar<PointDerived>>;
   
     template <typename HPointDerived>
     using HomogeneousPointProduct = Vector3<ReturnScalar<HPointDerived>>;
   
     SOPHUS_FUNC Adjoint Adj() const {
       Adjoint res;
       res.setZero();
       res.template block<2, 2>(0, 0) = rxso2().matrix();
       res(0, 2) = translation()[1];
       res(1, 2) = -translation()[0];
       res.template block<2, 1>(0, 3) = -translation();
   
       res(2, 2) = Scalar(1);
   
       res(3, 3) = Scalar(1);
       return res;
     }
   
     template <class NewScalarType>
     SOPHUS_FUNC Sim2<NewScalarType> cast() const {
       return Sim2<NewScalarType>(rxso2().template cast<NewScalarType>(),
                                  translation().template cast<NewScalarType>());
     }
   
     SOPHUS_FUNC Sim2<Scalar> inverse() const {
       RxSO2<Scalar> invR = rxso2().inverse();
       return Sim2<Scalar>(invR, invR * (translation() * Scalar(-1)));
     }
   
     SOPHUS_FUNC Tangent log() const {
       Tangent res;
       Vector2<Scalar> const theta_sigma = rxso2().log();
       Scalar const theta = theta_sigma[0];
       Scalar const sigma = theta_sigma[1];
       Matrix2<Scalar> const Omega = SO2<Scalar>::hat(theta);
       Matrix2<Scalar> const W_inv =
           details::calcWInv<Scalar, 2>(Omega, theta, sigma, scale());
   
       res.segment(0, 2) = W_inv * translation();
       res[2] = theta;
       res[3] = sigma;
       return res;
     }
   
     SOPHUS_FUNC Transformation matrix() const {
       Transformation homogeneous_matrix;
       homogeneous_matrix.template topLeftCorner<2, 3>() = matrix2x3();
       homogeneous_matrix.row(2) =
           Matrix<Scalar, 3, 1>(Scalar(0), Scalar(0), Scalar(1));
       return homogeneous_matrix;
     }
   
     SOPHUS_FUNC Matrix<Scalar, 2, 3> matrix2x3() const {
       Matrix<Scalar, 2, 3> matrix;
       matrix.template topLeftCorner<2, 2>() = rxso2().matrix();
       matrix.col(2) = translation();
       return matrix;
     }
   
     template <class OtherDerived>
     SOPHUS_FUNC Sim2Base<Derived>& operator=(
         Sim2Base<OtherDerived> const& other) {
       rxso2() = other.rxso2();
       translation() = other.translation();
       return *this;
     }
   
     template <typename OtherDerived>
     SOPHUS_FUNC Sim2Product<OtherDerived> operator*(
         Sim2Base<OtherDerived> const& other) const {
       return Sim2Product<OtherDerived>(
           rxso2() * other.rxso2(), translation() + rxso2() * other.translation());
     }
   
     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 rxso2() * p + translation();
     }
   
     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 PointProduct<HPointDerived> tp =
           rxso2() * p.template head<2>() + p(2) * translation();
       return HomogeneousPointProduct<HPointDerived>(tp(0), tp(1), p(2));
     }
   
     SOPHUS_FUNC Line operator*(Line const& l) const {
       Line rotatedLine = rxso2() * l;
       return Line(rotatedLine.origin() + translation(), rotatedLine.direction());
     }
   
     SOPHUS_FUNC Hyperplane operator*(Hyperplane const& p) const {
       Hyperplane const rotated = rxso2() * p;
       return Hyperplane(rotated.normal(),
                         rotated.offset() - translation().dot(rotated.normal()));
     }
   
     SOPHUS_FUNC Sophus::Vector<Scalar, num_parameters> params() const {
       Sophus::Vector<Scalar, num_parameters> p;
       p << rxso2().params(), translation();
       return p;
     }
   
     template <typename OtherDerived,
               typename = typename std::enable_if<
                   std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type>
     SOPHUS_FUNC Sim2Base<Derived>& operator*=(
         Sim2Base<OtherDerived> const& other) {
       *static_cast<Derived*>(this) = *this * other;
       return *this;
     }
   
     SOPHUS_FUNC Matrix<Scalar, num_parameters, DoF> Dx_this_mul_exp_x_at_0()
         const {
       Matrix<Scalar, num_parameters, DoF> J;
       J.template block<2, 2>(0, 0).setZero();
       J.template block<2, 2>(0, 2) = rxso2().Dx_this_mul_exp_x_at_0();
       J.template block<2, 2>(2, 2).setZero();
       J.template block<2, 2>(2, 0) = rxso2().matrix();
       return J;
     }
   
     SOPHUS_FUNC Matrix<Scalar, DoF, num_parameters> Dx_log_this_inv_by_x_at_this()
         const {
       Matrix<Scalar, num_parameters, DoF> J;
       J.template block<2, 2>(0, 0).setZero();
       J.template block<2, 2>(0, 2) = rxso2().inverse().matrix();
       J.template block<2, 2>(2, 0) = rxso2().Dx_log_this_inv_by_x_at_this();
       J.template block<2, 2>(2, 2).setZero();
       return J;
     }
   
     SOPHUS_FUNC void setComplex(Vector2<Scalar> const& z) {
       rxso2().setComplex(z);
     }
   
     SOPHUS_FUNC
     typename Eigen::internal::traits<Derived>::RxSO2Type::ComplexType const&
     complex() const {
       return rxso2().complex();
     }
   
     SOPHUS_FUNC Matrix2<Scalar> rotationMatrix() const {
       return rxso2().rotationMatrix();
     }
   
     SOPHUS_FUNC RxSO2Type& rxso2() {
       return static_cast<Derived*>(this)->rxso2();
     }
   
     SOPHUS_FUNC RxSO2Type const& rxso2() const {
       return static_cast<Derived const*>(this)->rxso2();
     }
   
     SOPHUS_FUNC Scalar scale() const { return rxso2().scale(); }
   
     SOPHUS_FUNC void setRotationMatrix(Matrix2<Scalar>& R) {
       rxso2().setRotationMatrix(R);
     }
   
     SOPHUS_FUNC void setScale(Scalar const& scale) { rxso2().setScale(scale); }
   
     SOPHUS_FUNC void setScaledRotationMatrix(Matrix2<Scalar> const& sR) {
       rxso2().setScaledRotationMatrix(sR);
     }
   
     SOPHUS_FUNC TranslationType& translation() {
       return static_cast<Derived*>(this)->translation();
     }
   
     SOPHUS_FUNC TranslationType const& translation() const {
       return static_cast<Derived const*>(this)->translation();
     }
   };
   
   template <class Scalar_, int Options>
   class Sim2 : public Sim2Base<Sim2<Scalar_, Options>> {
    public:
     using Base = Sim2Base<Sim2<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 RxSo2Member = RxSO2<Scalar, Options>;
     using TranslationMember = Vector2<Scalar, Options>;
   
     using Base::operator=;
   
     SOPHUS_FUNC Sim2& operator=(Sim2 const& other) = default;
   
     static int constexpr DoF = Base::DoF;
     static int constexpr num_parameters = Base::num_parameters;
   
     EIGEN_MAKE_ALIGNED_OPERATOR_NEW
   
     SOPHUS_FUNC Sim2();
   
     SOPHUS_FUNC Sim2(Sim2 const& other) = default;
   
     template <class OtherDerived>
     SOPHUS_FUNC Sim2(Sim2Base<OtherDerived> const& other)
         : rxso2_(other.rxso2()), translation_(other.translation()) {
       static_assert(std::is_same<typename OtherDerived::Scalar, Scalar>::value,
                     "must be same Scalar type");
     }
   
     template <class OtherDerived, class D>
     SOPHUS_FUNC Sim2(RxSO2Base<OtherDerived> const& rxso2,
                      Eigen::MatrixBase<D> const& translation)
         : rxso2_(rxso2), translation_(translation) {
       static_assert(std::is_same<typename OtherDerived::Scalar, Scalar>::value,
                     "must be same Scalar type");
       static_assert(std::is_same<typename D::Scalar, Scalar>::value,
                     "must be same Scalar type");
     }
   
     template <class D>
     SOPHUS_FUNC Sim2(Vector2<Scalar> const& complex_number,
                      Eigen::MatrixBase<D> const& translation)
         : rxso2_(complex_number), translation_(translation) {
       static_assert(std::is_same<typename D::Scalar, Scalar>::value,
                     "must be same Scalar type");
     }
   
     SOPHUS_FUNC explicit Sim2(Matrix<Scalar, 3, 3> const& T)
         : rxso2_((T.template topLeftCorner<2, 2>()).eval()),
           translation_(T.template block<2, 1>(0, 2)) {}
   
     SOPHUS_FUNC Scalar* data() {
       // rxso2_ and translation_ are laid out sequentially with no padding
       return rxso2_.data();
     }
   
     SOPHUS_FUNC Scalar const* data() const {
       // rxso2_ and translation_ are laid out sequentially with no padding
       return rxso2_.data();
     }
   
     SOPHUS_FUNC RxSo2Member& rxso2() { return rxso2_; }
   
     SOPHUS_FUNC RxSo2Member const& rxso2() const { return rxso2_; }
   
     SOPHUS_FUNC TranslationMember& translation() { return translation_; }
   
     SOPHUS_FUNC TranslationMember const& translation() const {
       return translation_;
     }
   
     SOPHUS_FUNC static Sophus::Matrix<Scalar, num_parameters, DoF>
     Dx_exp_x_at_0() {
       Sophus::Matrix<Scalar, num_parameters, DoF> J;
       J.template block<2, 2>(0, 0).setZero();
       J.template block<2, 2>(0, 2) = RxSO2<Scalar>::Dx_exp_x_at_0();
       J.template block<2, 2>(2, 0).setIdentity();
       J.template block<2, 2>(2, 2).setZero();
       return J;
     }
   
     SOPHUS_FUNC static Sophus::Matrix<Scalar, num_parameters, DoF> Dx_exp_x(
         const Tangent& a) {
       static Matrix2<Scalar> const I = Matrix2<Scalar>::Identity();
       static Scalar const one(1.0);
   
       Scalar const theta = a[2];
       Scalar const sigma = a[3];
   
       Matrix2<Scalar> const Omega = SO2<Scalar>::hat(theta);
       Matrix2<Scalar> const Omega_dtheta = SO2<Scalar>::hat(one);
       Matrix2<Scalar> const Omega2 = Omega * Omega;
       Matrix2<Scalar> const Omega2_dtheta =
           Omega_dtheta * Omega + Omega * Omega_dtheta;
       Matrix2<Scalar> const W = details::calcW<Scalar, 2>(Omega, theta, sigma);
       Vector2<Scalar> const upsilon = a.segment(0, 2);
   
       Sophus::Matrix<Scalar, num_parameters, DoF> J;
       J.template block<2, 2>(0, 0).setZero();
       J.template block<2, 2>(0, 2) =
           RxSO2<Scalar>::Dx_exp_x(a.template tail<2>());
       J.template block<2, 2>(2, 0) = W;
   
       Scalar A, B, C, A_dtheta, B_dtheta, A_dsigma, B_dsigma, C_dsigma;
       details::calcW_derivatives(theta, sigma, A, B, C, A_dsigma, B_dsigma,
                                  C_dsigma, A_dtheta, B_dtheta);
   
       J.template block<2, 1>(2, 2) = (A_dtheta * Omega + A * Omega_dtheta +
                                       B_dtheta * Omega2 + B * Omega2_dtheta) *
                                      upsilon;
       J.template block<2, 1>(2, 3) =
           (A_dsigma * Omega + B_dsigma * Omega2 + C_dsigma * I) * upsilon;
   
       return J;
     }
   
     SOPHUS_FUNC static Sophus::Matrix<Scalar, 2, DoF> Dx_exp_x_times_point_at_0(
         Point const& point) {
       Sophus::Matrix<Scalar, 2, DoF> J;
       J << Sophus::Matrix2<Scalar>::Identity(),
           Sophus::RxSO2<Scalar>::Dx_exp_x_times_point_at_0(point);
       return J;
     }
   
     SOPHUS_FUNC static Transformation Dxi_exp_x_matrix_at_0(int i) {
       return generator(i);
     }
   
   
     SOPHUS_FUNC static Sim2<Scalar> exp(Tangent const& a) {
       // For the derivation of the exponential map of Sim(N) see
       // H. Strasdat, "Local Accuracy and Global Consistency for Efficient Visual
       // SLAM", PhD thesis, 2012.
       // http:///hauke.strasdat.net/files/strasdat_thesis_2012.pdf (A.5, pp. 186)
       Vector2<Scalar> const upsilon = a.segment(0, 2);
       Scalar const theta = a[2];
       Scalar const sigma = a[3];
       RxSO2<Scalar> rxso2 = RxSO2<Scalar>::exp(a.template tail<2>());
       Matrix2<Scalar> const Omega = SO2<Scalar>::hat(theta);
       Matrix2<Scalar> const W = details::calcW<Scalar, 2>(Omega, theta, sigma);
       return Sim2<Scalar>(rxso2, W * upsilon);
     }
   
     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 Omega;
       Omega.template topLeftCorner<2, 2>() =
           RxSO2<Scalar>::hat(a.template tail<2>());
       Omega.col(2).template head<2>() = a.template head<2>();
       Omega.row(2).setZero();
       return Omega;
     }
   
     SOPHUS_FUNC static Tangent lieBracket(Tangent const& a, Tangent const& b) {
       Vector2<Scalar> const upsilon1 = a.template head<2>();
       Vector2<Scalar> const upsilon2 = b.template head<2>();
       Scalar const theta1 = a[2];
       Scalar const theta2 = b[2];
       Scalar const sigma1 = a[3];
       Scalar const sigma2 = b[3];
   
       Tangent res;
       res[0] = -theta1 * upsilon2[1] + theta2 * upsilon1[1] +
                sigma1 * upsilon2[0] - sigma2 * upsilon1[0];
       res[1] = theta1 * upsilon2[0] - theta2 * upsilon1[0] +
                sigma1 * upsilon2[1] - sigma2 * upsilon1[1];
       res[2] = Scalar(0);
       res[3] = Scalar(0);
   
       return res;
     }
   
     template <class UniformRandomBitGenerator>
     static Sim2 sampleUniform(UniformRandomBitGenerator& generator) {
       std::uniform_real_distribution<Scalar> uniform(Scalar(-1), Scalar(1));
       return Sim2(RxSO2<Scalar>::sampleUniform(generator),
                   Vector2<Scalar>(uniform(generator), uniform(generator)));
     }
   
     SOPHUS_FUNC static Tangent vee(Transformation const& Omega) {
       Tangent upsilon_omega_sigma;
       upsilon_omega_sigma.template head<2>() = Omega.col(2).template head<2>();
       upsilon_omega_sigma.template tail<2>() =
           RxSO2<Scalar>::vee(Omega.template topLeftCorner<2, 2>());
       return upsilon_omega_sigma;
     }
   
    protected:
     RxSo2Member rxso2_;
     TranslationMember translation_;
   };
   
   template <class Scalar, int Options>
   SOPHUS_FUNC Sim2<Scalar, Options>::Sim2()
       : translation_(TranslationMember::Zero()) {
     static_assert(std::is_standard_layout<Sim2>::value,
                   "Assume standard layout for the use of offset of check below.");
     static_assert(
         offsetof(Sim2, rxso2_) + sizeof(Scalar) * RxSO2<Scalar>::num_parameters ==
             offsetof(Sim2, translation_),
         "This class assumes packed storage and hence will only work "
         "correctly depending on the compiler (options) - in "
         "particular when using [this->data(), this-data() + "
         "num_parameters] to access the raw data in a contiguous fashion.");
   }
   
   }  // namespace Sophus
   
   namespace Eigen {
   
   template <class Scalar_, int Options>
   class Map<Sophus::Sim2<Scalar_>, Options>
       : public Sophus::Sim2Base<Map<Sophus::Sim2<Scalar_>, Options>> {
    public:
     using Base = Sophus::Sim2Base<Map<Sophus::Sim2<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 Base::operator=;
     using Base::operator*=;
     using Base::operator*;
   
     SOPHUS_FUNC explicit Map(Scalar* coeffs)
         : rxso2_(coeffs),
           translation_(coeffs + Sophus::RxSO2<Scalar>::num_parameters) {}
   
     SOPHUS_FUNC Map<Sophus::RxSO2<Scalar>, Options>& rxso2() { return rxso2_; }
   
     SOPHUS_FUNC Map<Sophus::RxSO2<Scalar>, Options> const& rxso2() const {
       return rxso2_;
     }
   
     SOPHUS_FUNC Map<Sophus::Vector2<Scalar>, Options>& translation() {
       return translation_;
     }
   
     SOPHUS_FUNC Map<Sophus::Vector2<Scalar>, Options> const& translation() const {
       return translation_;
     }
   
    protected:
     Map<Sophus::RxSO2<Scalar>, Options> rxso2_;
     Map<Sophus::Vector2<Scalar>, Options> translation_;
   };
   
   template <class Scalar_, int Options>
   class Map<Sophus::Sim2<Scalar_> const, Options>
       : public Sophus::Sim2Base<Map<Sophus::Sim2<Scalar_> const, Options>> {
    public:
     using Base = Sophus::Sim2Base<Map<Sophus::Sim2<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 explicit Map(Scalar const* coeffs)
         : rxso2_(coeffs),
           translation_(coeffs + Sophus::RxSO2<Scalar>::num_parameters) {}
   
     SOPHUS_FUNC Map<Sophus::RxSO2<Scalar> const, Options> const& rxso2() const {
       return rxso2_;
     }
   
     SOPHUS_FUNC Map<Sophus::Vector2<Scalar> const, Options> const& translation()
         const {
       return translation_;
     }
   
    protected:
     Map<Sophus::RxSO2<Scalar> const, Options> const rxso2_;
     Map<Sophus::Vector2<Scalar> const, Options> const translation_;
   };
   }  // namespace Eigen