210 lines
6.4 KiB
C++
210 lines
6.4 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, common code between Rotation matrix and Quaternion
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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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* @author Richard Roberts
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*/
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#include <gtsam/geometry/Rot3.h>
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#include <boost/math/constants/constants.hpp>
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#include <boost/random.hpp>
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#include <cmath>
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using namespace std;
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namespace gtsam {
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static const Matrix3 I3 = Matrix3::Identity();
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/* ************************************************************************* */
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void Rot3::print(const std::string& s) const {
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gtsam::print((Matrix)matrix(), s);
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}
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/* ************************************************************************* */
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Rot3 Rot3::rodriguez(const Point3& w, double theta) {
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return rodriguez((Vector)w.vector(),theta);
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}
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/* ************************************************************************* */
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Rot3 Rot3::rodriguez(const Sphere2& w, double theta) {
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return rodriguez(w.point3(),theta);
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}
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/* ************************************************************************* */
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Rot3 Rot3::Random(boost::random::mt19937 & rng) {
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// TODO allow any engine without including all of boost :-(
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Sphere2 w = Sphere2::Random(rng);
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boost::random::uniform_real_distribution<double> randomAngle(-M_PI,M_PI);
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double angle = randomAngle(rng);
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return rodriguez(w,angle);
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}
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/* ************************************************************************* */
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Rot3 Rot3::rodriguez(const Vector& w) {
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double t = w.norm();
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if (t < 1e-10) 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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Point3 Rot3::operator*(const Point3& p) const {
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return rotate(p);
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}
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/* ************************************************************************* */
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Sphere2 Rot3::rotate(const Sphere2& p,
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boost::optional<Matrix&> HR, boost::optional<Matrix&> Hp) const {
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Sphere2 q = rotate(p.point3(Hp));
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if (Hp)
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(*Hp) = q.basis().transpose() * matrix() * (*Hp);
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if (HR)
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(*HR) = -q.basis().transpose() * matrix() * p.skew();
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return q;
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}
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/* ************************************************************************* */
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Sphere2 Rot3::unrotate(const Sphere2& p,
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boost::optional<Matrix&> HR, boost::optional<Matrix&> Hp) const {
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Sphere2 q = unrotate(p.point3(Hp));
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if (Hp)
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(*Hp) = q.basis().transpose() * matrix().transpose () * (*Hp);
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if (HR)
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(*HR) = q.basis().transpose() * q.skew();
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return q;
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}
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/* ************************************************************************* */
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Sphere2 Rot3::operator*(const Sphere2& p) const {
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return rotate(p);
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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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/// Follow Iserles05an, B10, pg 147, with a sign change in the second term (left version)
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Matrix3 Rot3::dexpL(const Vector3& v) {
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if(zero(v)) return eye(3);
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Matrix x = skewSymmetric(v);
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Matrix x2 = x*x;
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double theta = v.norm(), vi = theta/2.0;
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double s1 = sin(vi)/vi;
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double s2 = (theta - sin(theta))/(theta*theta*theta);
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Matrix res = eye(3) - 0.5*s1*s1*x + s2*x2;
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return res;
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}
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/* ************************************************************************* */
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/// Follow Iserles05an, B11, pg 147, with a sign change in the second term (left version)
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Matrix3 Rot3::dexpInvL(const Vector3& v) {
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if(zero(v)) return eye(3);
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Matrix x = skewSymmetric(v);
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Matrix x2 = x*x;
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double theta = v.norm(), vi = theta/2.0;
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double s2 = (theta*tan(M_PI_2-vi) - 2)/(2*theta*theta);
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Matrix res = eye(3) + 0.5*x - s2*x2;
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return res;
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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 if(index == 1)
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return r1(); // default returns r1
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else
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throw invalid_argument("Argument to Rot3::column must be 1, 2, or 3");
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}
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/* ************************************************************************* */
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Vector3 Rot3::xyz() const {
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Matrix I;Vector3 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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/* ************************************************************************* */
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Vector3 Rot3::ypr() const {
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Vector3 q = xyz();
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return Vector3(q(2),q(1),q(0));
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}
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/* ************************************************************************* */
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Vector3 Rot3::rpy() const {
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return xyz();
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}
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/* ************************************************************************* */
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Vector Rot3::quaternion() const {
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Quaternion q = toQuaternion();
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Vector v(4);
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v(0) = q.w();
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v(1) = q.x();
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v(2) = q.y();
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v(3) = q.z();
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return v;
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}
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/* ************************************************************************* */
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pair<Matrix3, Vector3> RQ(const Matrix3& 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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Matrix3 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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Matrix3 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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Matrix3 R = C * Qz.matrix();
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Vector xyz = Vector3(x, y, z);
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return make_pair(R, xyz);
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}
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/* ************************************************************************* */
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ostream &operator<<(ostream &os, const Rot3& R) {
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os << "\n";
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os << '|' << R.r1().x() << ", " << R.r2().x() << ", " << R.r3().x() << "|\n";
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os << '|' << R.r1().y() << ", " << R.r2().y() << ", " << R.r3().y() << "|\n";
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os << '|' << R.r1().z() << ", " << R.r2().z() << ", " << R.r3().z() << "|\n";
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return os;
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}
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/* ************************************************************************* */
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} // namespace gtsam
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