254 lines
7.7 KiB
C++
254 lines
7.7 KiB
C++
/* ----------------------------------------------------------------------------
|
|
|
|
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
|
|
* Atlanta, Georgia 30332-0415
|
|
* All Rights Reserved
|
|
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
|
|
|
|
* See LICENSE for the license information
|
|
|
|
* -------------------------------------------------------------------------- */
|
|
|
|
/**
|
|
* @file Rot3.cpp
|
|
* @brief Rotation, common code between Rotation matrix and Quaternion
|
|
* @author Alireza Fathi
|
|
* @author Christian Potthast
|
|
* @author Frank Dellaert
|
|
* @author Richard Roberts
|
|
*/
|
|
|
|
#include <gtsam/geometry/Rot3.h>
|
|
#include <boost/math/constants/constants.hpp>
|
|
#include <boost/random.hpp>
|
|
#include <cmath>
|
|
|
|
using namespace std;
|
|
|
|
namespace gtsam {
|
|
|
|
/* ************************************************************************* */
|
|
void Rot3::print(const std::string& s) const {
|
|
gtsam::print((Matrix)matrix(), s);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Rot3 Rot3::rodriguez(const Point3& w, double theta) {
|
|
return rodriguez((Vector)w.vector(),theta);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Rot3 Rot3::rodriguez(const Unit3& w, double theta) {
|
|
return rodriguez(w.point3(),theta);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Rot3 Rot3::Random(boost::mt19937 & rng) {
|
|
// TODO allow any engine without including all of boost :-(
|
|
Unit3 w = Unit3::Random(rng);
|
|
boost::uniform_real<double> randomAngle(-M_PI,M_PI);
|
|
double angle = randomAngle(rng);
|
|
return rodriguez(w,angle);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Rot3 Rot3::rodriguez(const Vector& w) {
|
|
double t = w.norm();
|
|
if (t < 1e-10) return Rot3();
|
|
return rodriguez(w/t, t);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
bool Rot3::equals(const Rot3 & R, double tol) const {
|
|
return equal_with_abs_tol(matrix(), R.matrix(), tol);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Point3 Rot3::operator*(const Point3& p) const {
|
|
return rotate(p);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Unit3 Rot3::rotate(const Unit3& p,
|
|
OptionalJacobian<2,3> HR, OptionalJacobian<2,2> Hp) const {
|
|
Matrix32 Dp;
|
|
Unit3 q = Unit3(rotate(p.point3(Hp ? &Dp : 0)));
|
|
if (Hp)
|
|
(*Hp) = q.basis().transpose() * matrix() * Dp;
|
|
if (HR)
|
|
(*HR) = -q.basis().transpose() * matrix() * p.skew();
|
|
return q;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Unit3 Rot3::unrotate(const Unit3& p,
|
|
OptionalJacobian<2,3> HR, OptionalJacobian<2,2> Hp) const {
|
|
Matrix32 Dp;
|
|
Unit3 q = Unit3(unrotate(p.point3(Dp)));
|
|
if (Hp)
|
|
(*Hp) = q.basis().transpose() * matrix().transpose () * Dp;
|
|
if (HR)
|
|
(*HR) = q.basis().transpose() * q.skew();
|
|
return q;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Unit3 Rot3::operator*(const Unit3& p) const {
|
|
return rotate(p);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
// see doc/math.lyx, SO(3) section
|
|
Point3 Rot3::unrotate(const Point3& p, OptionalJacobian<3,3> H1,
|
|
OptionalJacobian<3,3> H2) const {
|
|
const Matrix3& Rt = transpose();
|
|
Point3 q(Rt * p.vector()); // q = Rt*p
|
|
const double wx = q.x(), wy = q.y(), wz = q.z();
|
|
if (H1)
|
|
*H1 << 0.0, -wz, +wy, +wz, 0.0, -wx, -wy, +wx, 0.0;
|
|
if (H2)
|
|
*H2 = Rt;
|
|
return q;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
/// Follow Iserles05an, B10, pg 147, with a sign change in the second term (left version)
|
|
Matrix3 Rot3::dexpL(const Vector3& v) {
|
|
if(zero(v)) return eye(3);
|
|
Matrix3 x = skewSymmetric(v);
|
|
Matrix3 x2 = x*x;
|
|
double theta = v.norm(), vi = theta/2.0;
|
|
double s1 = sin(vi)/vi;
|
|
double s2 = (theta - sin(theta))/(theta*theta*theta);
|
|
Matrix3 res = I3 - 0.5*s1*s1*x + s2*x2;
|
|
return res;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
/// Follow Iserles05an, B11, pg 147, with a sign change in the second term (left version)
|
|
Matrix3 Rot3::dexpInvL(const Vector3& v) {
|
|
if(zero(v)) return eye(3);
|
|
Matrix3 x = skewSymmetric(v);
|
|
Matrix3 x2 = x*x;
|
|
double theta = v.norm(), vi = theta/2.0;
|
|
double s2 = (theta*tan(M_PI_2-vi) - 2)/(2*theta*theta);
|
|
Matrix3 res = I3 + 0.5*x - s2*x2;
|
|
return res;
|
|
}
|
|
|
|
|
|
/* ************************************************************************* */
|
|
Point3 Rot3::column(int index) const{
|
|
if(index == 3)
|
|
return r3();
|
|
else if(index == 2)
|
|
return r2();
|
|
else if(index == 1)
|
|
return r1(); // default returns r1
|
|
else
|
|
throw invalid_argument("Argument to Rot3::column must be 1, 2, or 3");
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Vector3 Rot3::xyz() const {
|
|
Matrix3 I;Vector3 q;
|
|
boost::tie(I,q)=RQ(matrix());
|
|
return q;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Vector3 Rot3::ypr() const {
|
|
Vector3 q = xyz();
|
|
return Vector3(q(2),q(1),q(0));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Vector3 Rot3::rpy() const {
|
|
return xyz();
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Vector Rot3::quaternion() const {
|
|
Quaternion q = toQuaternion();
|
|
Vector v(4);
|
|
v(0) = q.w();
|
|
v(1) = q.x();
|
|
v(2) = q.y();
|
|
v(3) = q.z();
|
|
return v;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Matrix3 Rot3::rightJacobianExpMapSO3(const Vector3& x) {
|
|
// x is the axis-angle representation (exponential coordinates) for a rotation
|
|
double normx = norm_2(x); // rotation angle
|
|
Matrix3 Jr;
|
|
if (normx < 10e-8){
|
|
Jr = I3;
|
|
}
|
|
else{
|
|
const Matrix3 X = skewSymmetric(x); // element of Lie algebra so(3): X = x^
|
|
Jr = I3 - ((1-cos(normx))/(normx*normx)) * X +
|
|
((normx-sin(normx))/(normx*normx*normx)) * X * X; // right Jacobian
|
|
}
|
|
return Jr;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Matrix3 Rot3::rightJacobianExpMapSO3inverse(const Vector3& x) {
|
|
// x is the axis-angle representation (exponential coordinates) for a rotation
|
|
double normx = norm_2(x); // rotation angle
|
|
Matrix3 Jrinv;
|
|
|
|
if (normx < 10e-8){
|
|
Jrinv = I3;
|
|
}
|
|
else{
|
|
const Matrix3 X = skewSymmetric(x); // element of Lie algebra so(3): X = x^
|
|
Jrinv = I3 +
|
|
0.5 * X + (1/(normx*normx) - (1+cos(normx))/(2*normx * sin(normx)) ) * X * X;
|
|
}
|
|
return Jrinv;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
pair<Matrix3, Vector3> RQ(const Matrix3& A) {
|
|
|
|
double x = -atan2(-A(2, 1), A(2, 2));
|
|
Rot3 Qx = Rot3::Rx(-x);
|
|
Matrix3 B = A * Qx.matrix();
|
|
|
|
double y = -atan2(B(2, 0), B(2, 2));
|
|
Rot3 Qy = Rot3::Ry(-y);
|
|
Matrix3 C = B * Qy.matrix();
|
|
|
|
double z = -atan2(-C(1, 0), C(1, 1));
|
|
Rot3 Qz = Rot3::Rz(-z);
|
|
Matrix3 R = C * Qz.matrix();
|
|
|
|
Vector xyz = Vector3(x, y, z);
|
|
return make_pair(R, xyz);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
ostream &operator<<(ostream &os, const Rot3& R) {
|
|
os << "\n";
|
|
os << '|' << R.r1().x() << ", " << R.r2().x() << ", " << R.r3().x() << "|\n";
|
|
os << '|' << R.r1().y() << ", " << R.r2().y() << ", " << R.r3().y() << "|\n";
|
|
os << '|' << R.r1().z() << ", " << R.r2().z() << ", " << R.r3().z() << "|\n";
|
|
return os;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Rot3 Rot3::slerp(double t, const Rot3& other) const {
|
|
// amazingly simple in GTSAM :-)
|
|
assert(t>=0 && t<=1);
|
|
Vector3 omega = localCoordinates(other, Rot3::EXPMAP);
|
|
return retract(t * omega, Rot3::EXPMAP);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
|
|
} // namespace gtsam
|
|
|