237 lines
7.3 KiB
C++
237 lines
7.3 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file Rot3.cpp
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* @brief Rotation (internal: 3*3 matrix representation*)
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* @author Alireza Fathi
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* @author Christian Potthast
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* @author Frank Dellaert
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*/
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#include <boost/math/constants/constants.hpp>
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#include <gtsam/geometry/Rot3.h>
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#include <gtsam/base/Lie-inl.h>
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using namespace std;
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namespace gtsam {
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/** Explicit instantiation of base class to export members */
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INSTANTIATE_LIE(Rot3);
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static const Matrix I3 = eye(3);
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/* ************************************************************************* */
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// static member functions to construct rotations
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Rot3 Rot3::Rx(double t) {
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double st = sin(t), ct = cos(t);
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return Rot3(
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1, 0, 0,
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0, ct,-st,
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0, st, ct);
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}
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Rot3 Rot3::Ry(double t) {
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double st = sin(t), ct = cos(t);
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return Rot3(
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ct, 0, st,
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0, 1, 0,
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-st, 0, ct);
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}
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Rot3 Rot3::Rz(double t) {
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double st = sin(t), ct = cos(t);
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return Rot3(
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ct,-st, 0,
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st, ct, 0,
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0, 0, 1);
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}
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// Considerably faster than composing matrices above !
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Rot3 Rot3::RzRyRx(double x, double y, double z) {
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double cx=cos(x),sx=sin(x);
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double cy=cos(y),sy=sin(y);
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double cz=cos(z),sz=sin(z);
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double ss_ = sx * sy;
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double cs_ = cx * sy;
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double sc_ = sx * cy;
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double cc_ = cx * cy;
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double c_s = cx * sz;
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double s_s = sx * sz;
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double _cs = cy * sz;
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double _cc = cy * cz;
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double s_c = sx * cz;
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double c_c = cx * cz;
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double ssc = ss_ * cz, csc = cs_ * cz, sss = ss_ * sz, css = cs_ * sz;
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return Rot3(
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_cc,- c_s + ssc, s_s + csc,
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_cs, c_c + sss, -s_c + css,
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-sy, sc_, cc_
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);
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}
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/* ************************************************************************* */
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Rot3 Rot3::rodriguez(const Vector& w, double theta) {
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// get components of axis \omega
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double wx = w(0), wy=w(1), wz=w(2);
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double wwTxx = wx*wx, wwTyy = wy*wy, wwTzz = wz*wz;
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#ifndef NDEBUG
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double l_n = wwTxx + wwTyy + wwTzz;
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if (fabs(l_n-1.0)>1e-9) throw domain_error("rodriguez: length of n should be 1");
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#endif
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double c = cos(theta), s = sin(theta), c_1 = 1 - c;
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double swx = wx * s, swy = wy * s, swz = wz * s;
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double C00 = c_1*wwTxx, C01 = c_1*wx*wy, C02 = c_1*wx*wz;
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double C11 = c_1*wwTyy, C12 = c_1*wy*wz;
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double C22 = c_1*wwTzz;
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return Rot3( c + C00, -swz + C01, swy + C02,
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swz + C01, c + C11, -swx + C12,
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-swy + C02, swx + C12, c + C22);
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}
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/* ************************************************************************* */
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Rot3 Rot3::rodriguez(const Vector& w) {
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double t = norm_2(w);
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if (t < 1e-5) return Rot3();
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return rodriguez(w/t, t);
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}
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/* ************************************************************************* */
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bool Rot3::equals(const Rot3 & R, double tol) const {
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return equal_with_abs_tol(matrix(), R.matrix(), tol);
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}
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/* ************************************************************************* */
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Matrix Rot3::matrix() const {
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double r[] = { r1_.x(), r2_.x(), r3_.x(),
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r1_.y(), r2_.y(), r3_.y(),
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r1_.z(), r2_.z(), r3_.z() };
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return Matrix_(3,3, r);
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}
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/* ************************************************************************* */
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Matrix Rot3::transpose() const {
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double r[] = { r1_.x(), r1_.y(), r1_.z(),
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r2_.x(), r2_.y(), r2_.z(),
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r3_.x(), r3_.y(), r3_.z()};
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return Matrix_(3,3, r);
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}
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/* ************************************************************************* */
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Point3 Rot3::column(int index) const{
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if(index == 3)
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return r3_;
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else if (index == 2)
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return r2_;
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else
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return r1_; // default returns r1
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}
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/* ************************************************************************* */
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Vector Rot3::xyz() const {
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Matrix I;Vector q;
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boost::tie(I,q)=RQ(matrix());
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return q;
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}
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Vector Rot3::ypr() const {
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Vector q = xyz();
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return Vector_(3,q(2),q(1),q(0));
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}
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/* ************************************************************************* */
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// Log map at identity - return the canonical coordinates of this rotation
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Vector Rot3::Logmap(const Rot3& R) {
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double tr = R.r1().x()+R.r2().y()+R.r3().z();
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if (fabs(tr-3.0) < 1e-5) { // when theta = 0, +-2pi, +-4pi, etc.
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return zero(3);
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} else if (fabs(tr - -1.0) < 1e-5) { // when theta = +-pi, +-3pi, +-5pi, etc.
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if(R.r3().z() != -1.0)
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return (boost::math::constants::pi<double>() / sqrt(2.0+2.0*R.r3().z())) *
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Vector_(3, R.r3().x(), R.r3().y(), 1.0+R.r3().z());
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else if(R.r2().y() != -1.0)
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return (boost::math::constants::pi<double>() / sqrt(2.0+2.0*R.r2().y())) *
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Vector_(3, R.r2().x(), 1.0+R.r2().y(), R.r2().z());
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else // if(R.r1().x() != -1.0) TODO: fix this?
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return (boost::math::constants::pi<double>() / sqrt(2.0+2.0*R.r1().x())) *
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Vector_(3, 1.0+R.r1().x(), R.r1().y(), R.r1().z());
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} else {
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double theta = acos((tr-1.0)/2.0);
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return (theta/2.0/sin(theta))*Vector_(3,
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R.r2().z()-R.r3().y(),
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R.r3().x()-R.r1().z(),
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R.r1().y()-R.r2().x());
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}
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}
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/* ************************************************************************* */
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Point3 Rot3::rotate(const Point3& p,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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if (H1) *H1 = matrix() * skewSymmetric(-p.x(), -p.y(), -p.z());
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if (H2) *H2 = matrix();
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return r1_ * p.x() + r2_ * p.y() + r3_ * p.z();
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}
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/* ************************************************************************* */
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// see doc/math.lyx, SO(3) section
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Point3 Rot3::unrotate(const Point3& p,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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const Matrix Rt(transpose());
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Point3 q(Rt*p.vector()); // q = Rt*p
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if (H1) *H1 = skewSymmetric(q.x(), q.y(), q.z());
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if (H2) *H2 = Rt;
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return q;
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}
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/* ************************************************************************* */
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Rot3 Rot3::compose (const Rot3& R2,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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if (H1) *H1 = R2.transpose();
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if (H2) *H2 = I3;
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return *this * R2;
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}
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/* ************************************************************************* */
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Rot3 Rot3::between (const Rot3& R2,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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if (H1) *H1 = -(R2.transpose()*matrix());
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if (H2) *H2 = I3;
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return between_default(*this, R2);
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}
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/* ************************************************************************* */
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pair<Matrix, Vector> RQ(const Matrix& A) {
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double x = -atan2(-A(2, 1), A(2, 2));
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Rot3 Qx = Rot3::Rx(-x);
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Matrix B = A * Qx.matrix();
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double y = -atan2(B(2, 0), B(2, 2));
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Rot3 Qy = Rot3::Ry(-y);
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Matrix C = B * Qy.matrix();
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double z = -atan2(-C(1, 0), C(1, 1));
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Rot3 Qz = Rot3::Rz(-z);
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Matrix R = C * Qz.matrix();
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Vector xyz = Vector_(3, x, y, z);
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return make_pair(R, xyz);
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}
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/* ************************************************************************* */
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} // namespace gtsam
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