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Simplified Rot3 by having only one implementation available at a time

release/4.3a0
Richard Roberts 2012-01-02 20:24:23 +00:00
parent 4a9cfbc98a
commit b9bd2e61d8
6 changed files with 387 additions and 517 deletions
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67
gtsam/geometry/Rot3.h
View File

@ -16,20 +16,13 @@
*/ */
// \callgraph // \callgraph
#pragma once
#include <gtsam/geometry/Point3.h> #include <gtsam/geometry/Point3.h>
#include <gtsam/3rdparty/Eigen/Eigen/Geometry> #include <gtsam/3rdparty/Eigen/Eigen/Geometry>
/* ************************************************************************* */
// Below is the class definition of Rot3. By the macros at the end of this
// file, both Rot3M and Rot3Q are actually defined with this interface.
#if defined Rot3 || defined __DOXYGEN
namespace gtsam { namespace gtsam {
// Forward declarations;
class Rot3M;
class Rot3Q;
/// Typedef to an Eigen Quaternion<double>, we disable alignment because /// Typedef to an Eigen Quaternion<double>, we disable alignment because
/// geometry objects are stored in boost pool allocators, in Values /// geometry objects are stored in boost pool allocators, in Values
/// containers, and and these pool allocators do not support alignment. /// containers, and and these pool allocators do not support alignment.
@ -47,10 +40,10 @@ namespace gtsam {
static const size_t dimension = 3; static const size_t dimension = 3;
private: private:
#if defined ROT3_IS_MATRIX #ifndef GTSAM_DEFAULT_QUATERNIONS
/** We store columns ! */ /** We store columns ! */
Point3 r1_, r2_, r3_; Point3 r1_, r2_, r3_;
#elif defined ROT3_IS_QUATERNION #else
/** Internal Eigen Quaternion */ /** Internal Eigen Quaternion */
Quaternion quaternion_; Quaternion quaternion_;
#endif #endif
@ -85,9 +78,6 @@ namespace gtsam {
*/ */
Rot3(const Quaternion& q); Rot3(const Quaternion& q);
/** Constructor from a rotation matrix in a Rot3M */
Rot3(const Rot3M& r);
/* Static member function to generate some well known rotations */ /* Static member function to generate some well known rotations */
/// Rotation around X axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis. /// Rotation around X axis as in http://en.wikipedia.org/wiki/Rotation_matrix, counterclockwise when looking from unchanging axis.
@ -324,11 +314,11 @@ namespace gtsam {
template<class ARCHIVE> template<class ARCHIVE>
void serialize(ARCHIVE & ar, const unsigned int version) void serialize(ARCHIVE & ar, const unsigned int version)
{ {
#if defined ROT3_IS_MATRIX #ifndef GTSAM_DEFAULT_QUATERNIONS
ar & BOOST_SERIALIZATION_NVP(r1_); ar & BOOST_SERIALIZATION_NVP(r1_);
ar & BOOST_SERIALIZATION_NVP(r2_); ar & BOOST_SERIALIZATION_NVP(r2_);
ar & BOOST_SERIALIZATION_NVP(r3_); ar & BOOST_SERIALIZATION_NVP(r3_);
#elif defined ROT3_IS_QUATERNION #else
ar & BOOST_SERIALIZATION_NVP(quaternion_); ar & BOOST_SERIALIZATION_NVP(quaternion_);
#endif #endif
} }
@ -346,48 +336,3 @@ namespace gtsam {
*/ */
std::pair<Matrix,Vector> RQ(const Matrix& A); std::pair<Matrix,Vector> RQ(const Matrix& A);
} }
#endif // if defined Rot3 || defined __DOXYGEN
/* ************************************************************************* */
// This block of code defines both Rot3Q and Rot3M, by self-including Rot3.h
// twice and using preprocessor definitions of Rot3 to be Rot3M and Rot3Q. It
// then creates a typedef of Rot3 to either Rot3M or Rot3Q, depending on
// whether GTSAM_DEFAULT_QUATERNIONS is defined.
#if !defined __ROT3_H
#define __ROT3_H
// Define Rot3M
#define Rot3 Rot3M
#define ROT3_IS_MATRIX
#include <gtsam/geometry/Rot3.h>
#undef Rot3
#undef ROT3_IS_MATRIX
// Define Rot3Q
#define Rot3 Rot3Q
#define ROT3_IS_QUATERNION
#include <gtsam/geometry/Rot3.h>
#undef Rot3
#undef ROT3_IS_QUATERNION
// Create Rot3 typedef
namespace gtsam {
/**
* Typedef to the main 3D rotation implementation, which is Rot3M by default,
* or Rot3Q if GTSAM_DEFAULT_QUATERNIONS is defined. Depending on whether
* GTSAM_DEFAULT_QUATERNIONS is defined, Rot3M (the rotation matrix
* implementation) or Rot3Q (the quaternion implementation) will used in all
* built-in gtsam geometry types that involve 3D rotations, such as Pose3,
* SimpleCamera, CalibratedCamera, StereoCamera, etc.
*/
#ifdef GTSAM_DEFAULT_QUATERNIONS
typedef Rot3Q Rot3;
#else
typedef Rot3M Rot3;
#endif
}
#endif // if !defined Rot3

91
gtsam/geometry/Rot3M.cpp
View File

@ -10,13 +10,15 @@
* -------------------------------------------------------------------------- */ * -------------------------------------------------------------------------- */
/** /**
* @file Rot3M.cpp * @file Rot3.cpp
* @brief Rotation (internal: 3*3 matrix representation*) * @brief Rotation (internal: 3*3 matrix representation*)
* @author Alireza Fathi * @author Alireza Fathi
* @author Christian Potthast * @author Christian Potthast
* @author Frank Dellaert * @author Frank Dellaert
*/ */
#ifndef GTSAM_DEFAULT_QUATERNIONS
#include <boost/math/constants/constants.hpp> #include <boost/math/constants/constants.hpp>
#include <gtsam/geometry/Rot3.h> #include <gtsam/geometry/Rot3.h>
@ -27,17 +29,17 @@ namespace gtsam {
static const Matrix I3 = eye(3); static const Matrix I3 = eye(3);
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M::Rot3M() : Rot3::Rot3() :
r1_(Point3(1.0,0.0,0.0)), r1_(Point3(1.0,0.0,0.0)),
r2_(Point3(0.0,1.0,0.0)), r2_(Point3(0.0,1.0,0.0)),
r3_(Point3(0.0,0.0,1.0)) {} r3_(Point3(0.0,0.0,1.0)) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M::Rot3M(const Point3& r1, const Point3& r2, const Point3& r3) : Rot3::Rot3(const Point3& r1, const Point3& r2, const Point3& r3) :
r1_(r1), r2_(r2), r3_(r3) {} r1_(r1), r2_(r2), r3_(r3) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M::Rot3M(double R11, double R12, double R13, Rot3::Rot3(double R11, double R12, double R13,
double R21, double R22, double R23, double R21, double R22, double R23,
double R31, double R32, double R33) : double R31, double R32, double R33) :
r1_(Point3(R11, R21, R31)), r1_(Point3(R11, R21, R31)),
@ -45,13 +47,13 @@ Rot3M::Rot3M(double R11, double R12, double R13,
r3_(Point3(R13, R23, R33)) {} r3_(Point3(R13, R23, R33)) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M::Rot3M(const Matrix& R): Rot3::Rot3(const Matrix& R):
r1_(Point3(R(0,0), R(1,0), R(2,0))), r1_(Point3(R(0,0), R(1,0), R(2,0))),
r2_(Point3(R(0,1), R(1,1), R(2,1))), r2_(Point3(R(0,1), R(1,1), R(2,1))),
r3_(Point3(R(0,2), R(1,2), R(2,2))) {} r3_(Point3(R(0,2), R(1,2), R(2,2))) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M::Rot3M(const Quaternion& q) { Rot3::Rot3(const Quaternion& q) {
Eigen::Matrix3d R = q.toRotationMatrix(); Eigen::Matrix3d R = q.toRotationMatrix();
r1_ = Point3(R.col(0)); r1_ = Point3(R.col(0));
r2_ = Point3(R.col(1)); r2_ = Point3(R.col(1));
@ -59,30 +61,27 @@ Rot3M::Rot3M(const Quaternion& q) {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M::Rot3M(const Rot3M& r) : r1_(r.r1_), r2_(r.r2_), r3_(r.r3_) {} Rot3 Rot3::Rx(double t) {
/* ************************************************************************* */
Rot3M Rot3M::Rx(double t) {
double st = sin(t), ct = cos(t); double st = sin(t), ct = cos(t);
return Rot3M( return Rot3(
1, 0, 0, 1, 0, 0,
0, ct,-st, 0, ct,-st,
0, st, ct); 0, st, ct);
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::Ry(double t) { Rot3 Rot3::Ry(double t) {
double st = sin(t), ct = cos(t); double st = sin(t), ct = cos(t);
return Rot3M( return Rot3(
ct, 0, st, ct, 0, st,
0, 1, 0, 0, 1, 0,
-st, 0, ct); -st, 0, ct);
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::Rz(double t) { Rot3 Rot3::Rz(double t) {
double st = sin(t), ct = cos(t); double st = sin(t), ct = cos(t);
return Rot3M( return Rot3(
ct,-st, 0, ct,-st, 0,
st, ct, 0, st, ct, 0,
0, 0, 1); 0, 0, 1);
@ -90,7 +89,7 @@ Rot3M Rot3M::Rz(double t) {
/* ************************************************************************* */ /* ************************************************************************* */
// Considerably faster than composing matrices above ! // Considerably faster than composing matrices above !
Rot3M Rot3M::RzRyRx(double x, double y, double z) { Rot3 Rot3::RzRyRx(double x, double y, double z) {
double cx=cos(x),sx=sin(x); double cx=cos(x),sx=sin(x);
double cy=cos(y),sy=sin(y); double cy=cos(y),sy=sin(y);
double cz=cos(z),sz=sin(z); double cz=cos(z),sz=sin(z);
@ -105,7 +104,7 @@ Rot3M Rot3M::RzRyRx(double x, double y, double z) {
double s_c = sx * cz; double s_c = sx * cz;
double c_c = cx * cz; double c_c = cx * cz;
double ssc = ss_ * cz, csc = cs_ * cz, sss = ss_ * sz, css = cs_ * sz; double ssc = ss_ * cz, csc = cs_ * cz, sss = ss_ * sz, css = cs_ * sz;
return Rot3M( return Rot3(
_cc,- c_s + ssc, s_s + csc, _cc,- c_s + ssc, s_s + csc,
_cs, c_c + sss, -s_c + css, _cs, c_c + sss, -s_c + css,
-sy, sc_, cc_ -sy, sc_, cc_
@ -113,7 +112,7 @@ Rot3M Rot3M::RzRyRx(double x, double y, double z) {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::rodriguez(const Vector& w, double theta) { Rot3 Rot3::rodriguez(const Vector& w, double theta) {
// get components of axis \omega // get components of axis \omega
double wx = w(0), wy=w(1), wz=w(2); double wx = w(0), wy=w(1), wz=w(2);
double wwTxx = wx*wx, wwTyy = wy*wy, wwTzz = wz*wz; double wwTxx = wx*wx, wwTyy = wy*wy, wwTzz = wz*wz;
@ -129,26 +128,26 @@ Rot3M Rot3M::rodriguez(const Vector& w, double theta) {
double C11 = c_1*wwTyy, C12 = c_1*wy*wz; double C11 = c_1*wwTyy, C12 = c_1*wy*wz;
double C22 = c_1*wwTzz; double C22 = c_1*wwTzz;
return Rot3M( return Rot3(
c + C00, -swz + C01, swy + C02, c + C00, -swz + C01, swy + C02,
swz + C01, c + C11, -swx + C12, swz + C01, c + C11, -swx + C12,
-swy + C02, swx + C12, c + C22); -swy + C02, swx + C12, c + C22);
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::rodriguez(const Vector& w) { Rot3 Rot3::rodriguez(const Vector& w) {
double t = w.norm(); double t = w.norm();
if (t < 1e-10) return Rot3M(); if (t < 1e-10) return Rot3();
return rodriguez(w/t, t); return rodriguez(w/t, t);
} }
/* ************************************************************************* */ /* ************************************************************************* */
bool Rot3M::equals(const Rot3M & R, double tol) const { bool Rot3::equals(const Rot3 & R, double tol) const {
return equal_with_abs_tol(matrix(), R.matrix(), tol); return equal_with_abs_tol(matrix(), R.matrix(), tol);
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::compose (const Rot3M& R2, Rot3 Rot3::compose (const Rot3& R2,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
if (H1) *H1 = R2.transpose(); if (H1) *H1 = R2.transpose();
if (H2) *H2 = I3; if (H2) *H2 = I3;
@ -156,19 +155,19 @@ Rot3M Rot3M::compose (const Rot3M& R2,
} }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3M::operator*(const Point3& p) const { return rotate(p); } Point3 Rot3::operator*(const Point3& p) const { return rotate(p); }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::inverse(boost::optional<Matrix&> H1) const { Rot3 Rot3::inverse(boost::optional<Matrix&> H1) const {
if (H1) *H1 = -matrix(); if (H1) *H1 = -matrix();
return Rot3M( return Rot3(
r1_.x(), r1_.y(), r1_.z(), r1_.x(), r1_.y(), r1_.z(),
r2_.x(), r2_.y(), r2_.z(), r2_.x(), r2_.y(), r2_.z(),
r3_.x(), r3_.y(), r3_.z()); r3_.x(), r3_.y(), r3_.z());
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::between (const Rot3M& R2, Rot3 Rot3::between (const Rot3& R2,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
if (H1) *H1 = -(R2.transpose()*matrix()); if (H1) *H1 = -(R2.transpose()*matrix());
if (H2) *H2 = I3; if (H2) *H2 = I3;
@ -176,12 +175,12 @@ Rot3M Rot3M::between (const Rot3M& R2,
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3M Rot3M::operator*(const Rot3M& R2) const { Rot3 Rot3::operator*(const Rot3& R2) const {
return Rot3M(rotate(R2.r1_), rotate(R2.r2_), rotate(R2.r3_)); return Rot3(rotate(R2.r1_), rotate(R2.r2_), rotate(R2.r3_));
} }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3M::rotate(const Point3& p, Point3 Rot3::rotate(const Point3& p,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
if (H1) *H1 = matrix() * skewSymmetric(-p.x(), -p.y(), -p.z()); if (H1) *H1 = matrix() * skewSymmetric(-p.x(), -p.y(), -p.z());
if (H2) *H2 = matrix(); if (H2) *H2 = matrix();
@ -190,7 +189,7 @@ Point3 Rot3M::rotate(const Point3& p,
/* ************************************************************************* */ /* ************************************************************************* */
// see doc/math.lyx, SO(3) section // see doc/math.lyx, SO(3) section
Point3 Rot3M::unrotate(const Point3& p, Point3 Rot3::unrotate(const Point3& p,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
const Matrix Rt(transpose()); const Matrix Rt(transpose());
Point3 q(Rt*p.vector()); // q = Rt*p Point3 q(Rt*p.vector()); // q = Rt*p
@ -201,7 +200,7 @@ Point3 Rot3M::unrotate(const Point3& p,
/* ************************************************************************* */ /* ************************************************************************* */
// Log map at identity - return the canonical coordinates of this rotation // Log map at identity - return the canonical coordinates of this rotation
Vector Rot3M::Logmap(const Rot3M& R) { Vector Rot3::Logmap(const Rot3& R) {
double tr = R.r1().x()+R.r2().y()+R.r3().z(); double tr = R.r1().x()+R.r2().y()+R.r3().z();
// FIXME should tr in statement below be absolute value? // FIXME should tr in statement below be absolute value?
if (tr > 3.0 - 1e-17) { // when theta = 0, +-2pi, +-4pi, etc. (or tr > 3 + 1E-10) if (tr > 3.0 - 1e-17) { // when theta = 0, +-2pi, +-4pi, etc. (or tr > 3 + 1E-10)
@ -234,7 +233,7 @@ Vector Rot3M::Logmap(const Rot3M& R) {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Matrix Rot3M::matrix() const { Matrix Rot3::matrix() const {
Matrix R(3,3); Matrix R(3,3);
R << R <<
r1_.x(), r2_.x(), r3_.x(), r1_.x(), r2_.x(), r3_.x(),
@ -244,7 +243,7 @@ Matrix Rot3M::matrix() const {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Matrix Rot3M::transpose() const { Matrix Rot3::transpose() const {
Matrix Rt(3,3); Matrix Rt(3,3);
Rt << Rt <<
r1_.x(), r1_.y(), r1_.z(), r1_.x(), r1_.y(), r1_.z(),
@ -254,7 +253,7 @@ Matrix Rot3M::transpose() const {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3M::column(int index) const{ Point3 Rot3::column(int index) const{
if(index == 3) if(index == 3)
return r3_; return r3_;
else if(index == 2) else if(index == 2)
@ -266,35 +265,35 @@ Point3 Rot3M::column(int index) const{
} }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3M::r1() const { return r1_; } Point3 Rot3::r1() const { return r1_; }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3M::r2() const { return r2_; } Point3 Rot3::r2() const { return r2_; }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3M::r3() const { return r3_; } Point3 Rot3::r3() const { return r3_; }
/* ************************************************************************* */ /* ************************************************************************* */
Vector Rot3M::xyz() const { Vector Rot3::xyz() const {
Matrix I;Vector q; Matrix I;Vector q;
boost::tie(I,q)=RQ(matrix()); boost::tie(I,q)=RQ(matrix());
return q; return q;
} }
/* ************************************************************************* */ /* ************************************************************************* */
Vector Rot3M::ypr() const { Vector Rot3::ypr() const {
Vector q = xyz(); Vector q = xyz();
return Vector_(3,q(2),q(1),q(0)); return Vector_(3,q(2),q(1),q(0));
} }
/* ************************************************************************* */ /* ************************************************************************* */
Vector Rot3M::rpy() const { Vector Rot3::rpy() const {
Vector q = xyz(); Vector q = xyz();
return Vector_(3,q(0),q(1),q(2)); return Vector_(3,q(0),q(1),q(2));
} }
/* ************************************************************************* */ /* ************************************************************************* */
Quaternion Rot3M::toQuaternion() const { Quaternion Rot3::toQuaternion() const {
return Quaternion((Eigen::Matrix3d() << return Quaternion((Eigen::Matrix3d() <<
r1_.x(), r2_.x(), r3_.x(), r1_.x(), r2_.x(), r3_.x(),
r1_.y(), r2_.y(), r3_.y(), r1_.y(), r2_.y(), r3_.y(),
@ -305,15 +304,15 @@ Quaternion Rot3M::toQuaternion() const {
pair<Matrix, Vector> RQ(const Matrix& A) { pair<Matrix, Vector> RQ(const Matrix& A) {
double x = -atan2(-A(2, 1), A(2, 2)); double x = -atan2(-A(2, 1), A(2, 2));
Rot3M Qx = Rot3M::Rx(-x); Rot3 Qx = Rot3::Rx(-x);
Matrix B = A * Qx.matrix(); Matrix B = A * Qx.matrix();
double y = -atan2(B(2, 0), B(2, 2)); double y = -atan2(B(2, 0), B(2, 2));
Rot3M Qy = Rot3M::Ry(-y); Rot3 Qy = Rot3::Ry(-y);
Matrix C = B * Qy.matrix(); Matrix C = B * Qy.matrix();
double z = -atan2(-C(1, 0), C(1, 1)); double z = -atan2(-C(1, 0), C(1, 1));
Rot3M Qz = Rot3M::Rz(-z); Rot3 Qz = Rot3::Rz(-z);
Matrix R = C * Qz.matrix(); Matrix R = C * Qz.matrix();
Vector xyz = Vector_(3, x, y, z); Vector xyz = Vector_(3, x, y, z);
@ -323,3 +322,5 @@ pair<Matrix, Vector> RQ(const Matrix& A) {
/* ************************************************************************* */ /* ************************************************************************* */
} // namespace gtsam } // namespace gtsam
#endif

94
gtsam/geometry/Rot3Q.cpp
View File

@ -10,13 +10,15 @@
* -------------------------------------------------------------------------- */ * -------------------------------------------------------------------------- */
/** /**
* @file Rot3Q.cpp * @file Rot3.cpp
* @brief Rotation (internal: 3*3 matrix representation*) * @brief Rotation (internal: 3*3 matrix representation*)
* @author Alireza Fathi * @author Alireza Fathi
* @author Christian Potthast * @author Christian Potthast
* @author Frank Dellaert * @author Frank Dellaert
*/ */
#ifdef GTSAM_DEFAULT_QUATERNIONS
#include <boost/math/constants/constants.hpp> #include <boost/math/constants/constants.hpp>
#include <gtsam/geometry/Rot3.h> #include <gtsam/geometry/Rot3.h>
@ -27,17 +29,17 @@ namespace gtsam {
static const Matrix I3 = eye(3); static const Matrix I3 = eye(3);
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q::Rot3Q() : quaternion_(Quaternion::Identity()) {} Rot3::Rot3() : quaternion_(Quaternion::Identity()) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q::Rot3Q(const Point3& r1, const Point3& r2, const Point3& r3) : Rot3::Rot3(const Point3& r1, const Point3& r2, const Point3& r3) :
quaternion_((Eigen::Matrix3d() << quaternion_((Eigen::Matrix3d() <<
r1.x(), r2.x(), r3.x(), r1.x(), r2.x(), r3.x(),
r1.y(), r2.y(), r3.y(), r1.y(), r2.y(), r3.y(),
r1.z(), r2.z(), r3.z()).finished()) {} r1.z(), r2.z(), r3.z()).finished()) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q::Rot3Q(double R11, double R12, double R13, Rot3::Rot3(double R11, double R12, double R13,
double R21, double R22, double R23, double R21, double R22, double R23,
double R31, double R32, double R33) : double R31, double R32, double R33) :
quaternion_((Eigen::Matrix3d() << quaternion_((Eigen::Matrix3d() <<
@ -46,69 +48,66 @@ namespace gtsam {
R31, R32, R33).finished()) {} R31, R32, R33).finished()) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q::Rot3Q(const Matrix& R) : Rot3::Rot3(const Matrix& R) :
quaternion_(Eigen::Matrix3d(R)) {} quaternion_(Eigen::Matrix3d(R)) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q::Rot3Q(const Quaternion& q) : quaternion_(q) {} Rot3::Rot3(const Quaternion& q) : quaternion_(q) {}
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q::Rot3Q(const Rot3M& r) : quaternion_(Eigen::Matrix3d(r.matrix())) {} Rot3 Rot3::Rx(double t) { return Quaternion(Eigen::AngleAxisd(t, Eigen::Vector3d::UnitX())); }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::Rx(double t) { return Quaternion(Eigen::AngleAxisd(t, Eigen::Vector3d::UnitX())); } Rot3 Rot3::Ry(double t) { return Quaternion(Eigen::AngleAxisd(t, Eigen::Vector3d::UnitY())); }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::Ry(double t) { return Quaternion(Eigen::AngleAxisd(t, Eigen::Vector3d::UnitY())); } Rot3 Rot3::Rz(double t) { return Quaternion(Eigen::AngleAxisd(t, Eigen::Vector3d::UnitZ())); }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::Rz(double t) { return Quaternion(Eigen::AngleAxisd(t, Eigen::Vector3d::UnitZ())); } Rot3 Rot3::RzRyRx(double x, double y, double z) { return Rot3(
/* ************************************************************************* */
Rot3Q Rot3Q::RzRyRx(double x, double y, double z) { return Rot3Q(
Quaternion(Eigen::AngleAxisd(z, Eigen::Vector3d::UnitZ())) * Quaternion(Eigen::AngleAxisd(z, Eigen::Vector3d::UnitZ())) *
Quaternion(Eigen::AngleAxisd(y, Eigen::Vector3d::UnitY())) * Quaternion(Eigen::AngleAxisd(y, Eigen::Vector3d::UnitY())) *
Quaternion(Eigen::AngleAxisd(x, Eigen::Vector3d::UnitX()))); Quaternion(Eigen::AngleAxisd(x, Eigen::Vector3d::UnitX())));
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::rodriguez(const Vector& w, double theta) { Rot3 Rot3::rodriguez(const Vector& w, double theta) {
return Quaternion(Eigen::AngleAxisd(theta, w)); } return Quaternion(Eigen::AngleAxisd(theta, w)); }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::rodriguez(const Vector& w) { Rot3 Rot3::rodriguez(const Vector& w) {
double t = w.norm(); double t = w.norm();
if (t < 1e-10) return Rot3Q(); if (t < 1e-10) return Rot3();
return rodriguez(w/t, t); return rodriguez(w/t, t);
} }
/* ************************************************************************* */ /* ************************************************************************* */
bool Rot3Q::equals(const Rot3Q & R, double tol) const { bool Rot3::equals(const Rot3 & R, double tol) const {
return equal_with_abs_tol(matrix(), R.matrix(), tol); return equal_with_abs_tol(matrix(), R.matrix(), tol);
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::compose(const Rot3Q& R2, Rot3 Rot3::compose(const Rot3& R2,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
if (H1) *H1 = R2.transpose(); if (H1) *H1 = R2.transpose();
if (H2) *H2 = I3; if (H2) *H2 = I3;
return Rot3Q(quaternion_ * R2.quaternion_); return Rot3(quaternion_ * R2.quaternion_);
} }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3Q::operator*(const Point3& p) const { Point3 Rot3::operator*(const Point3& p) const {
Eigen::Vector3d r = quaternion_ * Eigen::Vector3d(p.x(), p.y(), p.z()); Eigen::Vector3d r = quaternion_ * Eigen::Vector3d(p.x(), p.y(), p.z());
return Point3(r(0), r(1), r(2)); return Point3(r(0), r(1), r(2));
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::inverse(boost::optional<Matrix&> H1) const { Rot3 Rot3::inverse(boost::optional<Matrix&> H1) const {
if (H1) *H1 = -matrix(); if (H1) *H1 = -matrix();
return Rot3Q(quaternion_.inverse()); return Rot3(quaternion_.inverse());
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::between(const Rot3Q& R2, Rot3 Rot3::between(const Rot3& R2,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
if (H1) *H1 = -(R2.transpose()*matrix()); if (H1) *H1 = -(R2.transpose()*matrix());
if (H2) *H2 = I3; if (H2) *H2 = I3;
@ -116,12 +115,12 @@ namespace gtsam {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Rot3Q Rot3Q::operator*(const Rot3Q& R2) const { Rot3 Rot3::operator*(const Rot3& R2) const {
return Rot3Q(quaternion_ * R2.quaternion_); return Rot3(quaternion_ * R2.quaternion_);
} }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3Q::rotate(const Point3& p, Point3 Rot3::rotate(const Point3& p,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
Matrix R = matrix(); Matrix R = matrix();
if (H1) *H1 = R * skewSymmetric(-p.x(), -p.y(), -p.z()); if (H1) *H1 = R * skewSymmetric(-p.x(), -p.y(), -p.z());
@ -132,7 +131,7 @@ namespace gtsam {
/* ************************************************************************* */ /* ************************************************************************* */
// see doc/math.lyx, SO(3) section // see doc/math.lyx, SO(3) section
Point3 Rot3Q::unrotate(const Point3& p, Point3 Rot3::unrotate(const Point3& p,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const { boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
const Matrix Rt(transpose()); const Matrix Rt(transpose());
Point3 q(Rt*p.vector()); // q = Rt*p Point3 q(Rt*p.vector()); // q = Rt*p
@ -143,7 +142,7 @@ namespace gtsam {
/* ************************************************************************* */ /* ************************************************************************* */
// Log map at identity - return the canonical coordinates of this rotation // Log map at identity - return the canonical coordinates of this rotation
Vector Rot3Q::Logmap(const Rot3Q& R) { Vector Rot3::Logmap(const Rot3& R) {
Eigen::AngleAxisd angleAxis(R.quaternion_); Eigen::AngleAxisd angleAxis(R.quaternion_);
if(angleAxis.angle() > M_PI) // Important: use the smallest possible if(angleAxis.angle() > M_PI) // Important: use the smallest possible
angleAxis.angle() -= 2.0*M_PI; // angle, e.g. no more than PI, to keep angleAxis.angle() -= 2.0*M_PI; // angle, e.g. no more than PI, to keep
@ -153,13 +152,13 @@ namespace gtsam {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Matrix Rot3Q::matrix() const { return quaternion_.toRotationMatrix(); } Matrix Rot3::matrix() const { return quaternion_.toRotationMatrix(); }
/* ************************************************************************* */ /* ************************************************************************* */
Matrix Rot3Q::transpose() const { return quaternion_.toRotationMatrix().transpose(); } Matrix Rot3::transpose() const { return quaternion_.toRotationMatrix().transpose(); }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3Q::column(int index) const{ Point3 Rot3::column(int index) const{
if(index == 3) if(index == 3)
return r3(); return r3();
else if(index == 2) else if(index == 2)
@ -171,36 +170,55 @@ namespace gtsam {
} }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3Q::r1() const { return Point3(quaternion_.toRotationMatrix().col(0)); } Point3 Rot3::r1() const { return Point3(quaternion_.toRotationMatrix().col(0)); }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3Q::r2() const { return Point3(quaternion_.toRotationMatrix().col(1)); } Point3 Rot3::r2() const { return Point3(quaternion_.toRotationMatrix().col(1)); }
/* ************************************************************************* */ /* ************************************************************************* */
Point3 Rot3Q::r3() const { return Point3(quaternion_.toRotationMatrix().col(2)); } Point3 Rot3::r3() const { return Point3(quaternion_.toRotationMatrix().col(2)); }
/* ************************************************************************* */ /* ************************************************************************* */
Vector Rot3Q::xyz() const { Vector Rot3::xyz() const {
Matrix I;Vector q; Matrix I;Vector q;
boost::tie(I,q)=RQ(matrix()); boost::tie(I,q)=RQ(matrix());
return q; return q;
} }
/* ************************************************************************* */ /* ************************************************************************* */
Vector Rot3Q::ypr() const { Vector Rot3::ypr() const {
Vector q = xyz(); Vector q = xyz();
return Vector_(3,q(2),q(1),q(0)); return Vector_(3,q(2),q(1),q(0));
} }
/* ************************************************************************* */ /* ************************************************************************* */
Vector Rot3Q::rpy() const { Vector Rot3::rpy() const {
Vector q = xyz(); Vector q = xyz();
return Vector_(3,q(0),q(1),q(2)); return Vector_(3,q(0),q(1),q(2));
} }
/* ************************************************************************* */ /* ************************************************************************* */
Quaternion Rot3Q::toQuaternion() const { return quaternion_; } Quaternion Rot3::toQuaternion() const { return quaternion_; }
/* ************************************************************************* */ /* ************************************************************************* */
pair<Matrix, Vector> RQ(const Matrix& A) {
double x = -atan2(-A(2, 1), A(2, 2));
Rot3 Qx = Rot3::Rx(-x);
Matrix B = A * Qx.matrix();
double y = -atan2(B(2, 0), B(2, 2));
Rot3 Qy = Rot3::Ry(-y);
Matrix C = B * Qy.matrix();
double z = -atan2(-C(1, 0), C(1, 1));
Rot3 Qz = Rot3::Rz(-z);
Matrix R = C * Qz.matrix();
Vector xyz = Vector_(3, x, y, z);
return make_pair(R, xyz);
}
} // namespace gtsam } // namespace gtsam
#endif

262
gtsam/geometry/tests/testRot3M.cpp
View File

@ -11,7 +11,7 @@
/** /**
* @file testRot3.cpp * @file testRot3.cpp
* @brief Unit tests for Rot3M class * @brief Unit tests for Rot3 class
* @author Alireza Fathi * @author Alireza Fathi
*/ */
@ -23,16 +23,18 @@
#include <gtsam/geometry/Point3.h> #include <gtsam/geometry/Point3.h>
#include <gtsam/geometry/Rot3.h> #include <gtsam/geometry/Rot3.h>
#ifndef GTSAM_DEFAULT_QUATERNIONS
using namespace gtsam; using namespace gtsam;
Rot3M R = Rot3M::rodriguez(0.1, 0.4, 0.2); Rot3 R = Rot3::rodriguez(0.1, 0.4, 0.2);
Point3 P(0.2, 0.7, -2.0); Point3 P(0.2, 0.7, -2.0);
double error = 1e-9, epsilon = 0.001; double error = 1e-9, epsilon = 0.001;
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, constructor) TEST( Rot3, constructor)
{ {
Rot3M expected(eye(3, 3)); Rot3 expected(eye(3, 3));
Vector r1(3), r2(3), r3(3); Vector r1(3), r2(3), r3(3);
r1(0) = 1; r1(0) = 1;
r1(1) = 0; r1(1) = 0;
@ -43,91 +45,91 @@ TEST( Rot3M, constructor)
r3(0) = 0; r3(0) = 0;
r3(1) = 0; r3(1) = 0;
r3(2) = 1; r3(2) = 1;
Rot3M actual(r1, r2, r3); Rot3 actual(r1, r2, r3);
CHECK(assert_equal(actual,expected)); CHECK(assert_equal(actual,expected));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, constructor2) TEST( Rot3, constructor2)
{ {
Matrix R = Matrix_(3, 3, 11., 12., 13., 21., 22., 23., 31., 32., 33.); Matrix R = Matrix_(3, 3, 11., 12., 13., 21., 22., 23., 31., 32., 33.);
Rot3M actual(R); Rot3 actual(R);
Rot3M expected(11, 12, 13, 21, 22, 23, 31, 32, 33); Rot3 expected(11, 12, 13, 21, 22, 23, 31, 32, 33);
CHECK(assert_equal(actual,expected)); CHECK(assert_equal(actual,expected));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, constructor3) TEST( Rot3, constructor3)
{ {
Rot3M expected(1, 2, 3, 4, 5, 6, 7, 8, 9); Rot3 expected(1, 2, 3, 4, 5, 6, 7, 8, 9);
Point3 r1(1, 4, 7), r2(2, 5, 8), r3(3, 6, 9); Point3 r1(1, 4, 7), r2(2, 5, 8), r3(3, 6, 9);
CHECK(assert_equal(Rot3M(r1,r2,r3),expected)); CHECK(assert_equal(Rot3(r1,r2,r3),expected));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, transpose) TEST( Rot3, transpose)
{ {
Rot3M R(1, 2, 3, 4, 5, 6, 7, 8, 9); Rot3 R(1, 2, 3, 4, 5, 6, 7, 8, 9);
Point3 r1(1, 2, 3), r2(4, 5, 6), r3(7, 8, 9); Point3 r1(1, 2, 3), r2(4, 5, 6), r3(7, 8, 9);
CHECK(assert_equal(R.inverse(),Rot3M(r1,r2,r3))); CHECK(assert_equal(R.inverse(),Rot3(r1,r2,r3)));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, equals) TEST( Rot3, equals)
{ {
CHECK(R.equals(R)); CHECK(R.equals(R));
Rot3M zero; Rot3 zero;
CHECK(!R.equals(zero)); CHECK(!R.equals(zero));
} }
/* ************************************************************************* */ /* ************************************************************************* */
// Notice this uses J^2 whereas fast uses w*w', and has cos(t)*I + .... // Notice this uses J^2 whereas fast uses w*w', and has cos(t)*I + ....
Rot3M slow_but_correct_rodriguez(const Vector& w) { Rot3 slow_but_correct_rodriguez(const Vector& w) {
double t = norm_2(w); double t = norm_2(w);
Matrix J = skewSymmetric(w / t); Matrix J = skewSymmetric(w / t);
if (t < 1e-5) return Rot3M(); if (t < 1e-5) return Rot3();
Matrix R = eye(3) + sin(t) * J + (1.0 - cos(t)) * (J * J); Matrix R = eye(3) + sin(t) * J + (1.0 - cos(t)) * (J * J);
return R; return R;
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, rodriguez) TEST( Rot3, rodriguez)
{ {
Rot3M R1 = Rot3M::rodriguez(epsilon, 0, 0); Rot3 R1 = Rot3::rodriguez(epsilon, 0, 0);
Vector w = Vector_(3, epsilon, 0., 0.); Vector w = Vector_(3, epsilon, 0., 0.);
Rot3M R2 = slow_but_correct_rodriguez(w); Rot3 R2 = slow_but_correct_rodriguez(w);
CHECK(assert_equal(R2,R1)); CHECK(assert_equal(R2,R1));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, rodriguez2) TEST( Rot3, rodriguez2)
{ {
Vector axis = Vector_(3,0.,1.,0.); // rotation around Y Vector axis = Vector_(3,0.,1.,0.); // rotation around Y
double angle = 3.14 / 4.0; double angle = 3.14 / 4.0;
Rot3M actual = Rot3M::rodriguez(axis, angle); Rot3 actual = Rot3::rodriguez(axis, angle);
Rot3M expected(0.707388, 0, 0.706825, Rot3 expected(0.707388, 0, 0.706825,
0, 1, 0, 0, 1, 0,
-0.706825, 0, 0.707388); -0.706825, 0, 0.707388);
CHECK(assert_equal(expected,actual,1e-5)); CHECK(assert_equal(expected,actual,1e-5));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, rodriguez3) TEST( Rot3, rodriguez3)
{ {
Vector w = Vector_(3, 0.1, 0.2, 0.3); Vector w = Vector_(3, 0.1, 0.2, 0.3);
Rot3M R1 = Rot3M::rodriguez(w / norm_2(w), norm_2(w)); Rot3 R1 = Rot3::rodriguez(w / norm_2(w), norm_2(w));
Rot3M R2 = slow_but_correct_rodriguez(w); Rot3 R2 = slow_but_correct_rodriguez(w);
CHECK(assert_equal(R2,R1)); CHECK(assert_equal(R2,R1));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, rodriguez4) TEST( Rot3, rodriguez4)
{ {
Vector axis = Vector_(3,0.,0.,1.); // rotation around Z Vector axis = Vector_(3,0.,0.,1.); // rotation around Z
double angle = M_PI_2; double angle = M_PI_2;
Rot3M actual = Rot3M::rodriguez(axis, angle); Rot3 actual = Rot3::rodriguez(axis, angle);
double c=cos(angle),s=sin(angle); double c=cos(angle),s=sin(angle);
Rot3M expected(c,-s, 0, Rot3 expected(c,-s, 0,
s, c, 0, s, c, 0,
0, 0, 1); 0, 0, 1);
CHECK(assert_equal(expected,actual,1e-5)); CHECK(assert_equal(expected,actual,1e-5));
@ -135,62 +137,62 @@ TEST( Rot3M, rodriguez4)
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, expmap) TEST( Rot3, expmap)
{ {
Vector v = zero(3); Vector v = zero(3);
CHECK(assert_equal(R.retract(v), R)); CHECK(assert_equal(R.retract(v), R));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3M, log) TEST(Rot3, log)
{ {
Vector w1 = Vector_(3, 0.1, 0.0, 0.0); Vector w1 = Vector_(3, 0.1, 0.0, 0.0);
Rot3M R1 = Rot3M::rodriguez(w1); Rot3 R1 = Rot3::rodriguez(w1);
CHECK(assert_equal(w1, Rot3M::Logmap(R1))); CHECK(assert_equal(w1, Rot3::Logmap(R1)));
Vector w2 = Vector_(3, 0.0, 0.1, 0.0); Vector w2 = Vector_(3, 0.0, 0.1, 0.0);
Rot3M R2 = Rot3M::rodriguez(w2); Rot3 R2 = Rot3::rodriguez(w2);
CHECK(assert_equal(w2, Rot3M::Logmap(R2))); CHECK(assert_equal(w2, Rot3::Logmap(R2)));
Vector w3 = Vector_(3, 0.0, 0.0, 0.1); Vector w3 = Vector_(3, 0.0, 0.0, 0.1);
Rot3M R3 = Rot3M::rodriguez(w3); Rot3 R3 = Rot3::rodriguez(w3);
CHECK(assert_equal(w3, Rot3M::Logmap(R3))); CHECK(assert_equal(w3, Rot3::Logmap(R3)));
Vector w = Vector_(3, 0.1, 0.4, 0.2); Vector w = Vector_(3, 0.1, 0.4, 0.2);
Rot3M R = Rot3M::rodriguez(w); Rot3 R = Rot3::rodriguez(w);
CHECK(assert_equal(w, Rot3M::Logmap(R))); CHECK(assert_equal(w, Rot3::Logmap(R)));
Vector w5 = Vector_(3, 0.0, 0.0, 0.0); Vector w5 = Vector_(3, 0.0, 0.0, 0.0);
Rot3M R5 = Rot3M::rodriguez(w5); Rot3 R5 = Rot3::rodriguez(w5);
CHECK(assert_equal(w5, Rot3M::Logmap(R5))); CHECK(assert_equal(w5, Rot3::Logmap(R5)));
Vector w6 = Vector_(3, boost::math::constants::pi<double>(), 0.0, 0.0); Vector w6 = Vector_(3, boost::math::constants::pi<double>(), 0.0, 0.0);
Rot3M R6 = Rot3M::rodriguez(w6); Rot3 R6 = Rot3::rodriguez(w6);
CHECK(assert_equal(w6, Rot3M::Logmap(R6))); CHECK(assert_equal(w6, Rot3::Logmap(R6)));
Vector w7 = Vector_(3, 0.0, boost::math::constants::pi<double>(), 0.0); Vector w7 = Vector_(3, 0.0, boost::math::constants::pi<double>(), 0.0);
Rot3M R7 = Rot3M::rodriguez(w7); Rot3 R7 = Rot3::rodriguez(w7);
CHECK(assert_equal(w7, Rot3M::Logmap(R7))); CHECK(assert_equal(w7, Rot3::Logmap(R7)));
Vector w8 = Vector_(3, 0.0, 0.0, boost::math::constants::pi<double>()); Vector w8 = Vector_(3, 0.0, 0.0, boost::math::constants::pi<double>());
Rot3M R8 = Rot3M::rodriguez(w8); Rot3 R8 = Rot3::rodriguez(w8);
CHECK(assert_equal(w8, Rot3M::Logmap(R8))); CHECK(assert_equal(w8, Rot3::Logmap(R8)));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3M, manifold) TEST(Rot3, manifold)
{ {
Rot3M gR1 = Rot3M::rodriguez(0.1, 0.4, 0.2); Rot3 gR1 = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3M gR2 = Rot3M::rodriguez(0.3, 0.1, 0.7); Rot3 gR2 = Rot3::rodriguez(0.3, 0.1, 0.7);
Rot3M origin; Rot3 origin;
// log behaves correctly // log behaves correctly
Vector d12 = gR1.localCoordinates(gR2); Vector d12 = gR1.localCoordinates(gR2);
CHECK(assert_equal(gR2, gR1.retract(d12))); CHECK(assert_equal(gR2, gR1.retract(d12)));
CHECK(assert_equal(gR2, gR1*Rot3M::Expmap(d12))); CHECK(assert_equal(gR2, gR1*Rot3::Expmap(d12)));
Vector d21 = gR2.localCoordinates(gR1); Vector d21 = gR2.localCoordinates(gR1);
CHECK(assert_equal(gR1, gR2.retract(d21))); CHECK(assert_equal(gR1, gR2.retract(d21)));
CHECK(assert_equal(gR1, gR2*Rot3M::Expmap(d21))); CHECK(assert_equal(gR1, gR2*Rot3::Expmap(d21)));
// Check that log(t1,t2)=-log(t2,t1) // Check that log(t1,t2)=-log(t2,t1)
CHECK(assert_equal(d12,-d21)); CHECK(assert_equal(d12,-d21));
@ -198,11 +200,11 @@ TEST(Rot3M, manifold)
// lines in canonical coordinates correspond to Abelian subgroups in SO(3) // lines in canonical coordinates correspond to Abelian subgroups in SO(3)
Vector d = Vector_(3, 0.1, 0.2, 0.3); Vector d = Vector_(3, 0.1, 0.2, 0.3);
// exp(-d)=inverse(exp(d)) // exp(-d)=inverse(exp(d))
CHECK(assert_equal(Rot3M::Expmap(-d),Rot3M::Expmap(d).inverse())); CHECK(assert_equal(Rot3::Expmap(-d),Rot3::Expmap(d).inverse()));
// exp(5d)=exp(2*d+3*d)=exp(2*d)exp(3*d)=exp(3*d)exp(2*d) // exp(5d)=exp(2*d+3*d)=exp(2*d)exp(3*d)=exp(3*d)exp(2*d)
Rot3M R2 = Rot3M::Expmap (2 * d); Rot3 R2 = Rot3::Expmap (2 * d);
Rot3M R3 = Rot3M::Expmap (3 * d); Rot3 R3 = Rot3::Expmap (3 * d);
Rot3M R5 = Rot3M::Expmap (5 * d); Rot3 R5 = Rot3::Expmap (5 * d);
CHECK(assert_equal(R5,R2*R3)); CHECK(assert_equal(R5,R2*R3));
CHECK(assert_equal(R5,R3*R2)); CHECK(assert_equal(R5,R3*R2));
} }
@ -223,106 +225,106 @@ AngularVelocity bracket(const AngularVelocity& X, const AngularVelocity& Y) {
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3M, BCH) TEST(Rot3, BCH)
{ {
// Approximate exmap by BCH formula // Approximate exmap by BCH formula
AngularVelocity w1(0.2, -0.1, 0.1); AngularVelocity w1(0.2, -0.1, 0.1);
AngularVelocity w2(0.01, 0.02, -0.03); AngularVelocity w2(0.01, 0.02, -0.03);
Rot3M R1 = Rot3M::Expmap (w1.vector()), R2 = Rot3M::Expmap (w2.vector()); Rot3 R1 = Rot3::Expmap (w1.vector()), R2 = Rot3::Expmap (w2.vector());
Rot3M R3 = R1 * R2; Rot3 R3 = R1 * R2;
Vector expected = Rot3M::Logmap(R3); Vector expected = Rot3::Logmap(R3);
Vector actual = BCH(w1, w2).vector(); Vector actual = BCH(w1, w2).vector();
CHECK(assert_equal(expected, actual,1e-5)); CHECK(assert_equal(expected, actual,1e-5));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, rotate_derivatives) TEST( Rot3, rotate_derivatives)
{ {
Matrix actualDrotate1a, actualDrotate1b, actualDrotate2; Matrix actualDrotate1a, actualDrotate1b, actualDrotate2;
R.rotate(P, actualDrotate1a, actualDrotate2); R.rotate(P, actualDrotate1a, actualDrotate2);
R.inverse().rotate(P, actualDrotate1b, boost::none); R.inverse().rotate(P, actualDrotate1b, boost::none);
Matrix numerical1 = numericalDerivative21(testing::rotate<Rot3M,Point3>, R, P); Matrix numerical1 = numericalDerivative21(testing::rotate<Rot3,Point3>, R, P);
Matrix numerical2 = numericalDerivative21(testing::rotate<Rot3M,Point3>, R.inverse(), P); Matrix numerical2 = numericalDerivative21(testing::rotate<Rot3,Point3>, R.inverse(), P);
Matrix numerical3 = numericalDerivative22(testing::rotate<Rot3M,Point3>, R, P); Matrix numerical3 = numericalDerivative22(testing::rotate<Rot3,Point3>, R, P);
EXPECT(assert_equal(numerical1,actualDrotate1a,error)); EXPECT(assert_equal(numerical1,actualDrotate1a,error));
EXPECT(assert_equal(numerical2,actualDrotate1b,error)); EXPECT(assert_equal(numerical2,actualDrotate1b,error));
EXPECT(assert_equal(numerical3,actualDrotate2, error)); EXPECT(assert_equal(numerical3,actualDrotate2, error));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, unrotate) TEST( Rot3, unrotate)
{ {
Point3 w = R * P; Point3 w = R * P;
Matrix H1,H2; Matrix H1,H2;
Point3 actual = R.unrotate(w,H1,H2); Point3 actual = R.unrotate(w,H1,H2);
CHECK(assert_equal(P,actual)); CHECK(assert_equal(P,actual));
Matrix numerical1 = numericalDerivative21(testing::unrotate<Rot3M,Point3>, R, w); Matrix numerical1 = numericalDerivative21(testing::unrotate<Rot3,Point3>, R, w);
CHECK(assert_equal(numerical1,H1,error)); CHECK(assert_equal(numerical1,H1,error));
Matrix numerical2 = numericalDerivative22(testing::unrotate<Rot3M,Point3>, R, w); Matrix numerical2 = numericalDerivative22(testing::unrotate<Rot3,Point3>, R, w);
CHECK(assert_equal(numerical2,H2,error)); CHECK(assert_equal(numerical2,H2,error));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, compose ) TEST( Rot3, compose )
{ {
Rot3M R1 = Rot3M::rodriguez(0.1, 0.2, 0.3); Rot3 R1 = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3M R2 = Rot3M::rodriguez(0.2, 0.3, 0.5); Rot3 R2 = Rot3::rodriguez(0.2, 0.3, 0.5);
Rot3M expected = R1 * R2; Rot3 expected = R1 * R2;
Matrix actualH1, actualH2; Matrix actualH1, actualH2;
Rot3M actual = R1.compose(R2, actualH1, actualH2); Rot3 actual = R1.compose(R2, actualH1, actualH2);
CHECK(assert_equal(expected,actual)); CHECK(assert_equal(expected,actual));
Matrix numericalH1 = numericalDerivative21(testing::compose<Rot3M>, R1, Matrix numericalH1 = numericalDerivative21(testing::compose<Rot3>, R1,
R2, 1e-2); R2, 1e-2);
CHECK(assert_equal(numericalH1,actualH1)); CHECK(assert_equal(numericalH1,actualH1));
Matrix numericalH2 = numericalDerivative22(testing::compose<Rot3M>, R1, Matrix numericalH2 = numericalDerivative22(testing::compose<Rot3>, R1,
R2, 1e-2); R2, 1e-2);
CHECK(assert_equal(numericalH2,actualH2)); CHECK(assert_equal(numericalH2,actualH2));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, inverse ) TEST( Rot3, inverse )
{ {
Rot3M R = Rot3M::rodriguez(0.1, 0.2, 0.3); Rot3 R = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3M I; Rot3 I;
Matrix actualH; Matrix actualH;
CHECK(assert_equal(I,R*R.inverse(actualH))); CHECK(assert_equal(I,R*R.inverse(actualH)));
CHECK(assert_equal(I,R.inverse()*R)); CHECK(assert_equal(I,R.inverse()*R));
Matrix numericalH = numericalDerivative11(testing::inverse<Rot3M>, R); Matrix numericalH = numericalDerivative11(testing::inverse<Rot3>, R);
CHECK(assert_equal(numericalH,actualH)); CHECK(assert_equal(numericalH,actualH));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, between ) TEST( Rot3, between )
{ {
Rot3M R = Rot3M::rodriguez(0.1, 0.4, 0.2); Rot3 R = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3M origin; Rot3 origin;
CHECK(assert_equal(R, origin.between(R))); CHECK(assert_equal(R, origin.between(R)));
CHECK(assert_equal(R.inverse(), R.between(origin))); CHECK(assert_equal(R.inverse(), R.between(origin)));
Rot3M R1 = Rot3M::rodriguez(0.1, 0.2, 0.3); Rot3 R1 = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3M R2 = Rot3M::rodriguez(0.2, 0.3, 0.5); Rot3 R2 = Rot3::rodriguez(0.2, 0.3, 0.5);
Rot3M expected = R1.inverse() * R2; Rot3 expected = R1.inverse() * R2;
Matrix actualH1, actualH2; Matrix actualH1, actualH2;
Rot3M actual = R1.between(R2, actualH1, actualH2); Rot3 actual = R1.between(R2, actualH1, actualH2);
CHECK(assert_equal(expected,actual)); CHECK(assert_equal(expected,actual));
Matrix numericalH1 = numericalDerivative21(testing::between<Rot3M> , R1, R2); Matrix numericalH1 = numericalDerivative21(testing::between<Rot3> , R1, R2);
CHECK(assert_equal(numericalH1,actualH1)); CHECK(assert_equal(numericalH1,actualH1));
Matrix numericalH2 = numericalDerivative22(testing::between<Rot3M> , R1, R2); Matrix numericalH2 = numericalDerivative22(testing::between<Rot3> , R1, R2);
CHECK(assert_equal(numericalH2,actualH2)); CHECK(assert_equal(numericalH2,actualH2));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, xyz ) TEST( Rot3, xyz )
{ {
double t = 0.1, st = sin(t), ct = cos(t); double t = 0.1, st = sin(t), ct = cos(t);
@ -332,47 +334,47 @@ TEST( Rot3M, xyz )
// z // z
// | * Y=(ct,st) // | * Y=(ct,st)
// x----y // x----y
Rot3M expected1(1, 0, 0, 0, ct, -st, 0, st, ct); Rot3 expected1(1, 0, 0, 0, ct, -st, 0, st, ct);
CHECK(assert_equal(expected1,Rot3M::Rx(t))); CHECK(assert_equal(expected1,Rot3::Rx(t)));
// x // x
// | * Z=(ct,st) // | * Z=(ct,st)
// y----z // y----z
Rot3M expected2(ct, 0, st, 0, 1, 0, -st, 0, ct); Rot3 expected2(ct, 0, st, 0, 1, 0, -st, 0, ct);
CHECK(assert_equal(expected2,Rot3M::Ry(t))); CHECK(assert_equal(expected2,Rot3::Ry(t)));
// y // y
// | X=* (ct,st) // | X=* (ct,st)
// z----x // z----x
Rot3M expected3(ct, -st, 0, st, ct, 0, 0, 0, 1); Rot3 expected3(ct, -st, 0, st, ct, 0, 0, 0, 1);
CHECK(assert_equal(expected3,Rot3M::Rz(t))); CHECK(assert_equal(expected3,Rot3::Rz(t)));
// Check compound rotation // Check compound rotation
Rot3M expected = Rot3M::Rz(0.3) * Rot3M::Ry(0.2) * Rot3M::Rx(0.1); Rot3 expected = Rot3::Rz(0.3) * Rot3::Ry(0.2) * Rot3::Rx(0.1);
CHECK(assert_equal(expected,Rot3M::RzRyRx(0.1,0.2,0.3))); CHECK(assert_equal(expected,Rot3::RzRyRx(0.1,0.2,0.3)));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, yaw_pitch_roll ) TEST( Rot3, yaw_pitch_roll )
{ {
double t = 0.1; double t = 0.1;
// yaw is around z axis // yaw is around z axis
CHECK(assert_equal(Rot3M::Rz(t),Rot3M::yaw(t))); CHECK(assert_equal(Rot3::Rz(t),Rot3::yaw(t)));
// pitch is around y axis // pitch is around y axis
CHECK(assert_equal(Rot3M::Ry(t),Rot3M::pitch(t))); CHECK(assert_equal(Rot3::Ry(t),Rot3::pitch(t)));
// roll is around x axis // roll is around x axis
CHECK(assert_equal(Rot3M::Rx(t),Rot3M::roll(t))); CHECK(assert_equal(Rot3::Rx(t),Rot3::roll(t)));
// Check compound rotation // Check compound rotation
Rot3M expected = Rot3M::yaw(0.1) * Rot3M::pitch(0.2) * Rot3M::roll(0.3); Rot3 expected = Rot3::yaw(0.1) * Rot3::pitch(0.2) * Rot3::roll(0.3);
CHECK(assert_equal(expected,Rot3M::ypr(0.1,0.2,0.3))); CHECK(assert_equal(expected,Rot3::ypr(0.1,0.2,0.3)));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, RQ) TEST( Rot3, RQ)
{ {
// Try RQ on a pure rotation // Try RQ on a pure rotation
Matrix actualK; Matrix actualK;
@ -382,18 +384,18 @@ TEST( Rot3M, RQ)
CHECK(assert_equal(eye(3),actualK)); CHECK(assert_equal(eye(3),actualK));
CHECK(assert_equal(expected,actual,1e-6)); CHECK(assert_equal(expected,actual,1e-6));
// Try using xyz call, asserting that Rot3M::RzRyRx(x,y,z).xyz()==[x;y;z] // Try using xyz call, asserting that Rot3::RzRyRx(x,y,z).xyz()==[x;y;z]
CHECK(assert_equal(expected,R.xyz(),1e-6)); CHECK(assert_equal(expected,R.xyz(),1e-6));
CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3M::RzRyRx(0.1,0.2,0.3).xyz())); CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3::RzRyRx(0.1,0.2,0.3).xyz()));
// Try using ypr call, asserting that Rot3M::ypr(y,p,r).ypr()==[y;p;r] // Try using ypr call, asserting that Rot3::ypr(y,p,r).ypr()==[y;p;r]
CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3M::ypr(0.1,0.2,0.3).ypr())); CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3::ypr(0.1,0.2,0.3).ypr()));
CHECK(assert_equal(Vector_(3,0.3,0.2,0.1),Rot3M::ypr(0.1,0.2,0.3).rpy())); CHECK(assert_equal(Vector_(3,0.3,0.2,0.1),Rot3::ypr(0.1,0.2,0.3).rpy()));
// Try ypr for pure yaw-pitch-roll matrices // Try ypr for pure yaw-pitch-roll matrices
CHECK(assert_equal(Vector_(3,0.1,0.0,0.0),Rot3M::yaw (0.1).ypr())); CHECK(assert_equal(Vector_(3,0.1,0.0,0.0),Rot3::yaw (0.1).ypr()));
CHECK(assert_equal(Vector_(3,0.0,0.1,0.0),Rot3M::pitch(0.1).ypr())); CHECK(assert_equal(Vector_(3,0.0,0.1,0.0),Rot3::pitch(0.1).ypr()));
CHECK(assert_equal(Vector_(3,0.0,0.0,0.1),Rot3M::roll (0.1).ypr())); CHECK(assert_equal(Vector_(3,0.0,0.0,0.1),Rot3::roll (0.1).ypr()));
// Try RQ to recover calibration from 3*3 sub-block of projection matrix // Try RQ to recover calibration from 3*3 sub-block of projection matrix
Matrix K = Matrix_(3, 3, 500.0, 0.0, 320.0, 0.0, 500.0, 240.0, 0.0, 0.0, 1.0); Matrix K = Matrix_(3, 3, 500.0, 0.0, 320.0, 0.0, 500.0, 240.0, 0.0, 0.0, 1.0);
@ -404,60 +406,60 @@ TEST( Rot3M, RQ)
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, expmapStability ) { TEST( Rot3, expmapStability ) {
Vector w = Vector_(3, 78e-9, 5e-8, 97e-7); Vector w = Vector_(3, 78e-9, 5e-8, 97e-7);
double theta = w.norm(); double theta = w.norm();
double theta2 = theta*theta; double theta2 = theta*theta;
Rot3M actualR = Rot3M::Expmap(w); Rot3 actualR = Rot3::Expmap(w);
Matrix W = Matrix_(3,3, 0.0, -w(2), w(1), Matrix W = Matrix_(3,3, 0.0, -w(2), w(1),
w(2), 0.0, -w(0), w(2), 0.0, -w(0),
-w(1), w(0), 0.0 ); -w(1), w(0), 0.0 );
Matrix W2 = W*W; Matrix W2 = W*W;
Matrix Rmat = eye(3) + (1.0-theta2/6.0 + theta2*theta2/120.0 Matrix Rmat = eye(3) + (1.0-theta2/6.0 + theta2*theta2/120.0
- theta2*theta2*theta2/5040.0)*W + (0.5 - theta2/24.0 + theta2*theta2/720.0)*W2 ; - theta2*theta2*theta2/5040.0)*W + (0.5 - theta2/24.0 + theta2*theta2/720.0)*W2 ;
Rot3M expectedR( Rmat ); Rot3 expectedR( Rmat );
CHECK(assert_equal(expectedR, actualR, 1e-10)); CHECK(assert_equal(expectedR, actualR, 1e-10));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3M, logmapStability ) { TEST( Rot3, logmapStability ) {
Vector w = Vector_(3, 1e-8, 0.0, 0.0); Vector w = Vector_(3, 1e-8, 0.0, 0.0);
Rot3M R = Rot3M::Expmap(w); Rot3 R = Rot3::Expmap(w);
// double tr = R.r1().x()+R.r2().y()+R.r3().z(); // double tr = R.r1().x()+R.r2().y()+R.r3().z();
// std::cout.precision(5000); // std::cout.precision(5000);
// std::cout << "theta: " << w.norm() << std::endl; // std::cout << "theta: " << w.norm() << std::endl;
// std::cout << "trace: " << tr << std::endl; // std::cout << "trace: " << tr << std::endl;
// R.print("R = "); // R.print("R = ");
Vector actualw = Rot3M::Logmap(R); Vector actualw = Rot3::Logmap(R);
CHECK(assert_equal(w, actualw, 1e-15)); CHECK(assert_equal(w, actualw, 1e-15));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3M, quaternion) { TEST(Rot3, quaternion) {
// NOTE: This is also verifying the ability to convert Vector to Quaternion // NOTE: This is also verifying the ability to convert Vector to Quaternion
Quaternion q1(0.710997408193224, 0.360544029310185, 0.594459869568306, 0.105395217842782); Quaternion q1(0.710997408193224, 0.360544029310185, 0.594459869568306, 0.105395217842782);
Rot3M R1 = Rot3M(Matrix_(3,3, Rot3 R1 = Rot3(Matrix_(3,3,
0.271018623057411, 0.278786459830371, 0.921318086098018, 0.271018623057411, 0.278786459830371, 0.921318086098018,
0.578529366719085, 0.717799701969298, -0.387385285854279, 0.578529366719085, 0.717799701969298, -0.387385285854279,
-0.769319620053772, 0.637998195662053, 0.033250932803219)); -0.769319620053772, 0.637998195662053, 0.033250932803219));
Quaternion q2(0.263360579192421, 0.571813128030932, 0.494678363680335, 0.599136268678053); Quaternion q2(0.263360579192421, 0.571813128030932, 0.494678363680335, 0.599136268678053);
Rot3M R2 = Rot3M(Matrix_(3,3, Rot3 R2 = Rot3(Matrix_(3,3,
-0.207341903877828, 0.250149415542075, 0.945745528564780, -0.207341903877828, 0.250149415542075, 0.945745528564780,
0.881304914479026, -0.371869043667957, 0.291573424846290, 0.881304914479026, -0.371869043667957, 0.291573424846290,
0.424630407073532, 0.893945571198514, -0.143353873763946)); 0.424630407073532, 0.893945571198514, -0.143353873763946));
// Check creating Rot3M from quaternion // Check creating Rot3 from quaternion
EXPECT(assert_equal(R1, Rot3M(q1))); EXPECT(assert_equal(R1, Rot3(q1)));
EXPECT(assert_equal(R1, Rot3M::quaternion(q1.w(), q1.x(), q1.y(), q1.z()))); EXPECT(assert_equal(R1, Rot3::quaternion(q1.w(), q1.x(), q1.y(), q1.z())));
EXPECT(assert_equal(R2, Rot3M(q2))); EXPECT(assert_equal(R2, Rot3(q2)));
EXPECT(assert_equal(R2, Rot3M::quaternion(q2.w(), q2.x(), q2.y(), q2.z()))); EXPECT(assert_equal(R2, Rot3::quaternion(q2.w(), q2.x(), q2.y(), q2.z())));
// Check converting Rot3M to quaterion // Check converting Rot3 to quaterion
EXPECT(assert_equal(Vector(R1.toQuaternion().coeffs()), Vector(q1.coeffs()))); EXPECT(assert_equal(Vector(R1.toQuaternion().coeffs()), Vector(q1.coeffs())));
EXPECT(assert_equal(Vector(R2.toQuaternion().coeffs()), Vector(q2.coeffs()))); EXPECT(assert_equal(Vector(R2.toQuaternion().coeffs()), Vector(q2.coeffs())));
// Check that quaternion and Rot3M represent the same rotation // Check that quaternion and Rot3 represent the same rotation
Point3 p1(1.0, 2.0, 3.0); Point3 p1(1.0, 2.0, 3.0);
Point3 p2(8.0, 7.0, 9.0); Point3 p2(8.0, 7.0, 9.0);
@ -471,6 +473,8 @@ TEST(Rot3M, quaternion) {
EXPECT(assert_equal(expected2, actual2)); EXPECT(assert_equal(expected2, actual2));
} }
#endif
/* ************************************************************************* */ /* ************************************************************************* */
int main() { int main() {
TestResult tr; TestResult tr;

298
gtsam/geometry/tests/testRot3Q.cpp
View File

@ -11,7 +11,7 @@
/** /**
* @file testRot3.cpp * @file testRot3.cpp
* @brief Unit tests for Rot3Q class * @brief Unit tests for Rot3 class
* @author Alireza Fathi * @author Alireza Fathi
*/ */
@ -23,16 +23,18 @@
#include <gtsam/geometry/Point3.h> #include <gtsam/geometry/Point3.h>
#include <gtsam/geometry/Rot3.h> #include <gtsam/geometry/Rot3.h>
#ifdef GTSAM_DEFAULT_QUATERNIONS
using namespace gtsam; using namespace gtsam;
Rot3Q R = Rot3Q::rodriguez(0.1, 0.4, 0.2); Rot3 R = Rot3::rodriguez(0.1, 0.4, 0.2);
Point3 P(0.2, 0.7, -2.0); Point3 P(0.2, 0.7, -2.0);
double error = 1e-9, epsilon = 0.001; double error = 1e-9, epsilon = 0.001;
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, constructor) TEST( Rot3, constructor)
{ {
Rot3Q expected(eye(3, 3)); Rot3 expected(eye(3, 3));
Vector r1(3), r2(3), r3(3); Vector r1(3), r2(3), r3(3);
r1(0) = 1; r1(0) = 1;
r1(1) = 0; r1(1) = 0;
@ -43,178 +45,146 @@ TEST( Rot3Q, constructor)
r3(0) = 0; r3(0) = 0;
r3(1) = 0; r3(1) = 0;
r3(2) = 1; r3(2) = 1;
Rot3Q actual(r1, r2, r3); Rot3 actual(r1, r2, r3);
CHECK(assert_equal(actual,expected)); CHECK(assert_equal(actual,expected));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, constructor2) TEST( Rot3, constructor2)
{ {
Matrix R = Matrix_(3, 3, 11., 12., 13., 21., 22., 23., 31., 32., 33.); Matrix R = Matrix_(3, 3, 11., 12., 13., 21., 22., 23., 31., 32., 33.);
Rot3Q actual(R); Rot3 actual(R);
Rot3Q expected(11, 12, 13, 21, 22, 23, 31, 32, 33); Rot3 expected(11, 12, 13, 21, 22, 23, 31, 32, 33);
CHECK(assert_equal(actual,expected)); CHECK(assert_equal(actual,expected));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, constructor3) TEST( Rot3, constructor3)
{ {
Rot3Q expected(1, 2, 3, 4, 5, 6, 7, 8, 9); Rot3 expected(1, 2, 3, 4, 5, 6, 7, 8, 9);
Point3 r1(1, 4, 7), r2(2, 5, 8), r3(3, 6, 9); Point3 r1(1, 4, 7), r2(2, 5, 8), r3(3, 6, 9);
CHECK(assert_equal(Rot3Q(r1,r2,r3),expected)); CHECK(assert_equal(Rot3(r1,r2,r3),expected));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, equals) TEST( Rot3, equals)
{ {
CHECK(R.equals(R)); CHECK(R.equals(R));
Rot3Q zero; Rot3 zero;
CHECK(!R.equals(zero)); CHECK(!R.equals(zero));
} }
/* ************************************************************************* */ /* ************************************************************************* */
// Notice this uses J^2 whereas fast uses w*w', and has cos(t)*I + .... // Notice this uses J^2 whereas fast uses w*w', and has cos(t)*I + ....
Rot3Q slow_but_correct_rodriguez(const Vector& w) { Rot3 slow_but_correct_rodriguez(const Vector& w) {
double t = norm_2(w); double t = norm_2(w);
Matrix J = skewSymmetric(w / t); Matrix J = skewSymmetric(w / t);
if (t < 1e-5) return Rot3Q(); if (t < 1e-5) return Rot3();
Matrix R = eye(3) + sin(t) * J + (1.0 - cos(t)) * (J * J); Matrix R = eye(3) + sin(t) * J + (1.0 - cos(t)) * (J * J);
return R; return R;
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, rodriguez) TEST( Rot3, rodriguez)
{ {
Rot3Q R1 = Rot3Q::rodriguez(epsilon, 0, 0); Rot3 R1 = Rot3::rodriguez(epsilon, 0, 0);
Vector w = Vector_(3, epsilon, 0., 0.); Vector w = Vector_(3, epsilon, 0., 0.);
Rot3Q R2 = slow_but_correct_rodriguez(w); Rot3 R2 = slow_but_correct_rodriguez(w);
Rot3Q expected2(Rot3M::rodriguez(epsilon, 0, 0));
CHECK(assert_equal(expected2,R1,1e-5));
CHECK(assert_equal(R2,R1)); CHECK(assert_equal(R2,R1));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, rodriguez2) TEST( Rot3, rodriguez2)
{ {
Vector axis = Vector_(3,0.,1.,0.); // rotation around Y Vector axis = Vector_(3,0.,1.,0.); // rotation around Y
double angle = 3.14 / 4.0; double angle = 3.14 / 4.0;
Rot3Q actual = Rot3Q::rodriguez(axis, angle); Rot3 actual = Rot3::rodriguez(axis, angle);
Rot3Q expected(0.707388, 0, 0.706825, Rot3 expected(0.707388, 0, 0.706825,
0, 1, 0, 0, 1, 0,
-0.706825, 0, 0.707388); -0.706825, 0, 0.707388);
Rot3Q expected2(Rot3M::rodriguez(axis, angle));
CHECK(assert_equal(expected,actual,1e-5)); CHECK(assert_equal(expected,actual,1e-5));
CHECK(assert_equal(expected2,actual,1e-5));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, rodriguez3) TEST( Rot3, rodriguez3)
{ {
Vector w = Vector_(3, 0.1, 0.2, 0.3); Vector w = Vector_(3, 0.1, 0.2, 0.3);
Rot3Q R1 = Rot3Q::rodriguez(w / norm_2(w), norm_2(w)); Rot3 R1 = Rot3::rodriguez(w / norm_2(w), norm_2(w));
Rot3Q R2 = slow_but_correct_rodriguez(w); Rot3 R2 = slow_but_correct_rodriguez(w);
Rot3Q expected2(Rot3M::rodriguez(w / norm_2(w), norm_2(w)));
CHECK(assert_equal(expected2,R1));
CHECK(assert_equal(R2,R1)); CHECK(assert_equal(R2,R1));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, rodriguez4) TEST( Rot3, rodriguez4)
{ {
Vector axis = Vector_(3,0.,0.,1.); // rotation around Z Vector axis = Vector_(3,0.,0.,1.); // rotation around Z
double angle = M_PI_2; double angle = M_PI_2;
Rot3Q actual = Rot3Q::rodriguez(axis, angle); Rot3 actual = Rot3::rodriguez(axis, angle);
double c=cos(angle),s=sin(angle); double c=cos(angle),s=sin(angle);
Rot3Q expected1(c,-s, 0, Rot3 expected(c,-s, 0,
s, c, 0, s, c, 0,
0, 0, 1); 0, 0, 1);
Rot3Q expected2(Rot3M::rodriguez(axis, angle)); CHECK(assert_equal(expected,actual,1e-5));
CHECK(assert_equal(expected1,actual,1e-5));
CHECK(assert_equal(expected2,actual,1e-5));
CHECK(assert_equal(slow_but_correct_rodriguez(axis*angle),actual,1e-5)); CHECK(assert_equal(slow_but_correct_rodriguez(axis*angle),actual,1e-5));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, expmap) TEST( Rot3, expmap)
{ {
Vector v = zero(3); Vector v = zero(3);
CHECK(assert_equal(R.retract(v), R)); CHECK(assert_equal(R.retract(v), R));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3Q, log) TEST(Rot3, log)
{ {
Vector w1 = Vector_(3, 0.1, 0.0, 0.0); Vector w1 = Vector_(3, 0.1, 0.0, 0.0);
Rot3Q R1 = Rot3Q::rodriguez(w1); Rot3 R1 = Rot3::rodriguez(w1);
Rot3Q R1m = Rot3M::rodriguez(w1); CHECK(assert_equal(w1, Rot3::Logmap(R1)));
CHECK(assert_equal(w1, Rot3Q::Logmap(R1)));
CHECK(assert_equal(R1m, R1));
Vector w2 = Vector_(3, 0.0, 0.1, 0.0); Vector w2 = Vector_(3, 0.0, 0.1, 0.0);
Rot3Q R2 = Rot3Q::rodriguez(w2); Rot3 R2 = Rot3::rodriguez(w2);
Rot3Q R2m = Rot3M::rodriguez(w2); CHECK(assert_equal(w2, Rot3::Logmap(R2)));
CHECK(assert_equal(w2, Rot3Q::Logmap(R2)));
CHECK(assert_equal(R2m, R2));
Vector w3 = Vector_(3, 0.0, 0.0, 0.1); Vector w3 = Vector_(3, 0.0, 0.0, 0.1);
Rot3Q R3 = Rot3Q::rodriguez(w3); Rot3 R3 = Rot3::rodriguez(w3);
Rot3Q R3m = Rot3M::rodriguez(w3); CHECK(assert_equal(w3, Rot3::Logmap(R3)));
CHECK(assert_equal(w3, Rot3Q::Logmap(R3)));
CHECK(assert_equal(R3m, R3));
Vector w = Vector_(3, 0.1, 0.4, 0.2); Vector w = Vector_(3, 0.1, 0.4, 0.2);
Rot3Q R = Rot3Q::rodriguez(w); Rot3 R = Rot3::rodriguez(w);
Rot3Q Rm = Rot3M::rodriguez(w); CHECK(assert_equal(w, Rot3::Logmap(R)));
CHECK(assert_equal(w, Rot3Q::Logmap(R)));
CHECK(assert_equal(Rm, R));
Vector w5 = Vector_(3, 0.0, 0.0, 0.0); Vector w5 = Vector_(3, 0.0, 0.0, 0.0);
Rot3Q R5 = Rot3Q::rodriguez(w5); Rot3 R5 = Rot3::rodriguez(w5);
Rot3Q R5m = Rot3M::rodriguez(w5); CHECK(assert_equal(w5, Rot3::Logmap(R5)));
CHECK(assert_equal(w5, Rot3Q::Logmap(R5)));
CHECK(assert_equal(R5m, R5));
Vector w6 = Vector_(3, boost::math::constants::pi<double>(), 0.0, 0.0); Vector w6 = Vector_(3, boost::math::constants::pi<double>(), 0.0, 0.0);
Rot3Q R6 = Rot3Q::rodriguez(w6); Rot3 R6 = Rot3::rodriguez(w6);
Rot3Q R6m = Rot3M::rodriguez(w6); CHECK(assert_equal(w6, Rot3::Logmap(R6)));
CHECK(assert_equal(w6, Rot3Q::Logmap(R6)));
CHECK(assert_equal(R6m, R6));
Vector w7 = Vector_(3, 0.0, boost::math::constants::pi<double>(), 0.0); Vector w7 = Vector_(3, 0.0, boost::math::constants::pi<double>(), 0.0);
Rot3Q R7 = Rot3Q::rodriguez(w7); Rot3 R7 = Rot3::rodriguez(w7);
Rot3Q R7m = Rot3M::rodriguez(w7); CHECK(assert_equal(w7, Rot3::Logmap(R7)));
CHECK(assert_equal(w7, Rot3Q::Logmap(R7)));
CHECK(assert_equal(R7m, R7));
Vector w8 = Vector_(3, 0.0, 0.0, boost::math::constants::pi<double>()); Vector w8 = Vector_(3, 0.0, 0.0, boost::math::constants::pi<double>());
Rot3Q R8 = Rot3Q::rodriguez(w8); Rot3 R8 = Rot3::rodriguez(w8);
Rot3Q R8m = Rot3M::rodriguez(w8); CHECK(assert_equal(w8, Rot3::Logmap(R8)));
CHECK(assert_equal(w8, Rot3Q::Logmap(R8)));
CHECK(assert_equal(R8m, R8));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3Q, manifold) TEST(Rot3, manifold)
{ {
Rot3Q gR1 = Rot3Q::rodriguez(0.1, 0.4, 0.2); Rot3 gR1 = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3Q gR2 = Rot3Q::rodriguez(0.3, 0.1, 0.7); Rot3 gR2 = Rot3::rodriguez(0.3, 0.1, 0.7);
Rot3Q origin; Rot3 origin;
Rot3M gR1m = Rot3M::rodriguez(0.1, 0.4, 0.2);
Rot3M gR2m = Rot3M::rodriguez(0.3, 0.1, 0.7);
EXPECT(assert_equal(gR1m.matrix(), gR1.matrix()));
EXPECT(assert_equal(gR2m.matrix(), gR2.matrix()));
// log behaves correctly // log behaves correctly
Vector d12 = gR1.localCoordinates(gR2); Vector d12 = gR1.localCoordinates(gR2);
EXPECT(assert_equal(gR1m.localCoordinates(gR2m), d12));
CHECK(assert_equal(gR2, gR1.retract(d12))); CHECK(assert_equal(gR2, gR1.retract(d12)));
CHECK(assert_equal(gR2, gR1*Rot3Q::Expmap(d12))); CHECK(assert_equal(gR2, gR1*Rot3::Expmap(d12)));
Vector d21 = gR2.localCoordinates(gR1); Vector d21 = gR2.localCoordinates(gR1);
EXPECT(assert_equal(gR2m.localCoordinates(gR1m), d21));
CHECK(assert_equal(gR1, gR2.retract(d21))); CHECK(assert_equal(gR1, gR2.retract(d21)));
CHECK(assert_equal(gR1, gR2*Rot3Q::Expmap(d21))); CHECK(assert_equal(gR1, gR2*Rot3::Expmap(d21)));
// Check that log(t1,t2)=-log(t2,t1) // Check that log(t1,t2)=-log(t2,t1)
CHECK(assert_equal(d12,-d21)); CHECK(assert_equal(d12,-d21));
@ -222,11 +192,11 @@ TEST(Rot3Q, manifold)
// lines in canonical coordinates correspond to Abelian subgroups in SO(3) // lines in canonical coordinates correspond to Abelian subgroups in SO(3)
Vector d = Vector_(3, 0.1, 0.2, 0.3); Vector d = Vector_(3, 0.1, 0.2, 0.3);
// exp(-d)=inverse(exp(d)) // exp(-d)=inverse(exp(d))
CHECK(assert_equal(Rot3Q::Expmap(-d),Rot3Q::Expmap(d).inverse())); CHECK(assert_equal(Rot3::Expmap(-d),Rot3::Expmap(d).inverse()));
// exp(5d)=exp(2*d+3*d)=exp(2*d)exp(3*d)=exp(3*d)exp(2*d) // exp(5d)=exp(2*d+3*d)=exp(2*d)exp(3*d)=exp(3*d)exp(2*d)
Rot3Q R2 = Rot3Q::Expmap (2 * d); Rot3 R2 = Rot3::Expmap (2 * d);
Rot3Q R3 = Rot3Q::Expmap (3 * d); Rot3 R3 = Rot3::Expmap (3 * d);
Rot3Q R5 = Rot3Q::Expmap (5 * d); Rot3 R5 = Rot3::Expmap (5 * d);
CHECK(assert_equal(R5,R2*R3)); CHECK(assert_equal(R5,R2*R3));
CHECK(assert_equal(R5,R3*R2)); CHECK(assert_equal(R5,R3*R2));
} }
@ -247,86 +217,86 @@ AngularVelocity bracket(const AngularVelocity& X, const AngularVelocity& Y) {
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3Q, BCH) TEST(Rot3, BCH)
{ {
// Approximate exmap by BCH formula // Approximate exmap by BCH formula
AngularVelocity w1(0.2, -0.1, 0.1); AngularVelocity w1(0.2, -0.1, 0.1);
AngularVelocity w2(0.01, 0.02, -0.03); AngularVelocity w2(0.01, 0.02, -0.03);
Rot3Q R1 = Rot3Q::Expmap (w1.vector()), R2 = Rot3Q::Expmap (w2.vector()); Rot3 R1 = Rot3::Expmap (w1.vector()), R2 = Rot3::Expmap (w2.vector());
Rot3Q R3 = R1 * R2; Rot3 R3 = R1 * R2;
Vector expected = Rot3Q::Logmap(R3); Vector expected = Rot3::Logmap(R3);
Vector actual = BCH(w1, w2).vector(); Vector actual = BCH(w1, w2).vector();
CHECK(assert_equal(expected, actual,1e-5)); CHECK(assert_equal(expected, actual,1e-5));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, rotate_derivatives) TEST( Rot3, rotate_derivatives)
{ {
Matrix actualDrotate1a, actualDrotate1b, actualDrotate2; Matrix actualDrotate1a, actualDrotate1b, actualDrotate2;
R.rotate(P, actualDrotate1a, actualDrotate2); R.rotate(P, actualDrotate1a, actualDrotate2);
R.inverse().rotate(P, actualDrotate1b, boost::none); R.inverse().rotate(P, actualDrotate1b, boost::none);
Matrix numerical1 = numericalDerivative21(testing::rotate<Rot3Q,Point3>, R, P); Matrix numerical1 = numericalDerivative21(testing::rotate<Rot3,Point3>, R, P);
Matrix numerical2 = numericalDerivative21(testing::rotate<Rot3Q,Point3>, R.inverse(), P); Matrix numerical2 = numericalDerivative21(testing::rotate<Rot3,Point3>, R.inverse(), P);
Matrix numerical3 = numericalDerivative22(testing::rotate<Rot3Q,Point3>, R, P); Matrix numerical3 = numericalDerivative22(testing::rotate<Rot3,Point3>, R, P);
EXPECT(assert_equal(numerical1,actualDrotate1a,error)); EXPECT(assert_equal(numerical1,actualDrotate1a,error));
EXPECT(assert_equal(numerical2,actualDrotate1b,error)); EXPECT(assert_equal(numerical2,actualDrotate1b,error));
EXPECT(assert_equal(numerical3,actualDrotate2, error)); EXPECT(assert_equal(numerical3,actualDrotate2, error));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, unrotate) TEST( Rot3, unrotate)
{ {
Point3 w = R * P; Point3 w = R * P;
Matrix H1,H2; Matrix H1,H2;
Point3 actual = R.unrotate(w,H1,H2); Point3 actual = R.unrotate(w,H1,H2);
CHECK(assert_equal(P,actual)); CHECK(assert_equal(P,actual));
Matrix numerical1 = numericalDerivative21(testing::unrotate<Rot3Q,Point3>, R, w); Matrix numerical1 = numericalDerivative21(testing::unrotate<Rot3,Point3>, R, w);
CHECK(assert_equal(numerical1,H1,error)); CHECK(assert_equal(numerical1,H1,error));
Matrix numerical2 = numericalDerivative22(testing::unrotate<Rot3Q,Point3>, R, w); Matrix numerical2 = numericalDerivative22(testing::unrotate<Rot3,Point3>, R, w);
CHECK(assert_equal(numerical2,H2,error)); CHECK(assert_equal(numerical2,H2,error));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, compose ) TEST( Rot3, compose )
{ {
Rot3Q R1 = Rot3Q::rodriguez(0.1, 0.2, 0.3); Rot3 R1 = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3Q R2 = Rot3Q::rodriguez(0.2, 0.3, 0.5); Rot3 R2 = Rot3::rodriguez(0.2, 0.3, 0.5);
Rot3Q expected = R1 * R2; Rot3 expected = R1 * R2;
Matrix actualH1, actualH2; Matrix actualH1, actualH2;
Rot3Q actual = R1.compose(R2, actualH1, actualH2); Rot3 actual = R1.compose(R2, actualH1, actualH2);
CHECK(assert_equal(expected,actual)); CHECK(assert_equal(expected,actual));
Matrix numericalH1 = numericalDerivative21(testing::compose<Rot3Q>, R1, Matrix numericalH1 = numericalDerivative21(testing::compose<Rot3>, R1,
R2, 1e-2); R2, 1e-2);
CHECK(assert_equal(numericalH1,actualH1)); CHECK(assert_equal(numericalH1,actualH1));
Matrix numericalH2 = numericalDerivative22(testing::compose<Rot3Q>, R1, Matrix numericalH2 = numericalDerivative22(testing::compose<Rot3>, R1,
R2, 1e-2); R2, 1e-2);
CHECK(assert_equal(numericalH2,actualH2)); CHECK(assert_equal(numericalH2,actualH2));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, inverse ) TEST( Rot3, inverse )
{ {
Rot3Q R = Rot3Q::rodriguez(0.1, 0.2, 0.3); Rot3 R = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3Q I; Rot3 I;
Matrix actualH; Matrix actualH;
CHECK(assert_equal(I,R*R.inverse(actualH))); CHECK(assert_equal(I,R*R.inverse(actualH)));
CHECK(assert_equal(I,R.inverse()*R)); CHECK(assert_equal(I,R.inverse()*R));
Matrix numericalH = numericalDerivative11(testing::inverse<Rot3Q>, R); Matrix numericalH = numericalDerivative11(testing::inverse<Rot3>, R);
CHECK(assert_equal(numericalH,actualH, 1e-4)); CHECK(assert_equal(numericalH,actualH, 1e-4));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, between ) TEST( Rot3, between )
{ {
Rot3Q r1 = Rot3Q::Rz(M_PI/3.0); Rot3 r1 = Rot3::Rz(M_PI/3.0);
Rot3Q r2 = Rot3Q::Rz(2.0*M_PI/3.0); Rot3 r2 = Rot3::Rz(2.0*M_PI/3.0);
Matrix expectedr1 = Matrix_(3,3, Matrix expectedr1 = Matrix_(3,3,
0.5, -sqrt(3.0)/2.0, 0.0, 0.5, -sqrt(3.0)/2.0, 0.0,
@ -334,32 +304,28 @@ TEST( Rot3Q, between )
0.0, 0.0, 1.0); 0.0, 0.0, 1.0);
EXPECT(assert_equal(expectedr1, r1.matrix())); EXPECT(assert_equal(expectedr1, r1.matrix()));
Rot3Q R = Rot3Q::rodriguez(0.1, 0.4, 0.2); Rot3 R = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3Q origin; Rot3 origin;
CHECK(assert_equal(R, origin.between(R))); CHECK(assert_equal(R, origin.between(R)));
CHECK(assert_equal(R.inverse(), R.between(origin))); CHECK(assert_equal(R.inverse(), R.between(origin)));
Rot3Q R1 = Rot3Q::rodriguez(0.1, 0.2, 0.3); Rot3 R1 = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3Q R2 = Rot3Q::rodriguez(0.2, 0.3, 0.5); Rot3 R2 = Rot3::rodriguez(0.2, 0.3, 0.5);
Rot3Q expected = R1.inverse() * R2; Rot3 expected = R1.inverse() * R2;
Matrix actualH1, actualH2; Matrix actualH1, actualH2;
Rot3Q actual = R1.between(R2, actualH1, actualH2); Rot3 actual = R1.between(R2, actualH1, actualH2);
CHECK(assert_equal(expected,actual)); CHECK(assert_equal(expected,actual));
Matrix numericalH1 = numericalDerivative21(testing::between<Rot3Q> , R1, R2); Matrix numericalH1 = numericalDerivative21(testing::between<Rot3> , R1, R2);
CHECK(assert_equal(numericalH1,actualH1, 1e-4)); CHECK(assert_equal(numericalH1,actualH1, 1e-4));
Matrix numericalH1M = numericalDerivative21(testing::between<Rot3M> , Rot3M(R1.matrix()), Rot3M(R2.matrix()));
CHECK(assert_equal(numericalH1M,actualH1, 1e-4));
Matrix numericalH2 = numericalDerivative22(testing::between<Rot3Q> , R1, R2); Matrix numericalH2 = numericalDerivative22(testing::between<Rot3> , R1, R2);
CHECK(assert_equal(numericalH2,actualH2, 1e-4)); CHECK(assert_equal(numericalH2,actualH2, 1e-4));
Matrix numericalH2M = numericalDerivative22(testing::between<Rot3M> , Rot3M(R1.matrix()), Rot3M(R2.matrix()));
CHECK(assert_equal(numericalH2M,actualH2, 1e-4));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, xyz ) TEST( Rot3, xyz )
{ {
double t = 0.1, st = sin(t), ct = cos(t); double t = 0.1, st = sin(t), ct = cos(t);
@ -369,47 +335,47 @@ TEST( Rot3Q, xyz )
// z // z
// | * Y=(ct,st) // | * Y=(ct,st)
// x----y // x----y
Rot3Q expected1(1, 0, 0, 0, ct, -st, 0, st, ct); Rot3 expected1(1, 0, 0, 0, ct, -st, 0, st, ct);
CHECK(assert_equal(expected1,Rot3Q::Rx(t))); CHECK(assert_equal(expected1,Rot3::Rx(t)));
// x // x
// | * Z=(ct,st) // | * Z=(ct,st)
// y----z // y----z
Rot3Q expected2(ct, 0, st, 0, 1, 0, -st, 0, ct); Rot3 expected2(ct, 0, st, 0, 1, 0, -st, 0, ct);
CHECK(assert_equal(expected2,Rot3Q::Ry(t))); CHECK(assert_equal(expected2,Rot3::Ry(t)));
// y // y
// | X=* (ct,st) // | X=* (ct,st)
// z----x // z----x
Rot3Q expected3(ct, -st, 0, st, ct, 0, 0, 0, 1); Rot3 expected3(ct, -st, 0, st, ct, 0, 0, 0, 1);
CHECK(assert_equal(expected3,Rot3Q::Rz(t))); CHECK(assert_equal(expected3,Rot3::Rz(t)));
// Check compound rotation // Check compound rotation
Rot3Q expected = Rot3Q::Rz(0.3) * Rot3Q::Ry(0.2) * Rot3Q::Rx(0.1); Rot3 expected = Rot3::Rz(0.3) * Rot3::Ry(0.2) * Rot3::Rx(0.1);
CHECK(assert_equal(expected,Rot3Q::RzRyRx(0.1,0.2,0.3))); CHECK(assert_equal(expected,Rot3::RzRyRx(0.1,0.2,0.3)));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, yaw_pitch_roll ) TEST( Rot3, yaw_pitch_roll )
{ {
double t = 0.1; double t = 0.1;
// yaw is around z axis // yaw is around z axis
CHECK(assert_equal(Rot3Q::Rz(t),Rot3Q::yaw(t))); CHECK(assert_equal(Rot3::Rz(t),Rot3::yaw(t)));
// pitch is around y axis // pitch is around y axis
CHECK(assert_equal(Rot3Q::Ry(t),Rot3Q::pitch(t))); CHECK(assert_equal(Rot3::Ry(t),Rot3::pitch(t)));
// roll is around x axis // roll is around x axis
CHECK(assert_equal(Rot3Q::Rx(t),Rot3Q::roll(t))); CHECK(assert_equal(Rot3::Rx(t),Rot3::roll(t)));
// Check compound rotation // Check compound rotation
Rot3Q expected = Rot3Q::yaw(0.1) * Rot3Q::pitch(0.2) * Rot3Q::roll(0.3); Rot3 expected = Rot3::yaw(0.1) * Rot3::pitch(0.2) * Rot3::roll(0.3);
CHECK(assert_equal(expected,Rot3Q::ypr(0.1,0.2,0.3))); CHECK(assert_equal(expected,Rot3::ypr(0.1,0.2,0.3)));
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, RQ) TEST( Rot3, RQ)
{ {
// Try RQ on a pure rotation // Try RQ on a pure rotation
Matrix actualK; Matrix actualK;
@ -419,18 +385,18 @@ TEST( Rot3Q, RQ)
CHECK(assert_equal(eye(3),actualK)); CHECK(assert_equal(eye(3),actualK));
CHECK(assert_equal(expected,actual,1e-6)); CHECK(assert_equal(expected,actual,1e-6));
// Try using xyz call, asserting that Rot3Q::RzRyRx(x,y,z).xyz()==[x;y;z] // Try using xyz call, asserting that Rot3::RzRyRx(x,y,z).xyz()==[x;y;z]
CHECK(assert_equal(expected,R.xyz(),1e-6)); CHECK(assert_equal(expected,R.xyz(),1e-6));
CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3Q::RzRyRx(0.1,0.2,0.3).xyz())); CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3::RzRyRx(0.1,0.2,0.3).xyz()));
// Try using ypr call, asserting that Rot3Q::ypr(y,p,r).ypr()==[y;p;r] // Try using ypr call, asserting that Rot3::ypr(y,p,r).ypr()==[y;p;r]
CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3Q::ypr(0.1,0.2,0.3).ypr())); CHECK(assert_equal(Vector_(3,0.1,0.2,0.3),Rot3::ypr(0.1,0.2,0.3).ypr()));
CHECK(assert_equal(Vector_(3,0.3,0.2,0.1),Rot3Q::ypr(0.1,0.2,0.3).rpy())); CHECK(assert_equal(Vector_(3,0.3,0.2,0.1),Rot3::ypr(0.1,0.2,0.3).rpy()));
// Try ypr for pure yaw-pitch-roll matrices // Try ypr for pure yaw-pitch-roll matrices
CHECK(assert_equal(Vector_(3,0.1,0.0,0.0),Rot3Q::yaw (0.1).ypr())); CHECK(assert_equal(Vector_(3,0.1,0.0,0.0),Rot3::yaw (0.1).ypr()));
CHECK(assert_equal(Vector_(3,0.0,0.1,0.0),Rot3Q::pitch(0.1).ypr())); CHECK(assert_equal(Vector_(3,0.0,0.1,0.0),Rot3::pitch(0.1).ypr()));
CHECK(assert_equal(Vector_(3,0.0,0.0,0.1),Rot3Q::roll (0.1).ypr())); CHECK(assert_equal(Vector_(3,0.0,0.0,0.1),Rot3::roll (0.1).ypr()));
// Try RQ to recover calibration from 3*3 sub-block of projection matrix // Try RQ to recover calibration from 3*3 sub-block of projection matrix
Matrix K = Matrix_(3, 3, 500.0, 0.0, 320.0, 0.0, 500.0, 240.0, 0.0, 0.0, 1.0); Matrix K = Matrix_(3, 3, 500.0, 0.0, 320.0, 0.0, 500.0, 240.0, 0.0, 0.0, 1.0);
@ -441,61 +407,61 @@ TEST( Rot3Q, RQ)
} }
/* ************************************************************************* */ /* ************************************************************************* */
TEST( Rot3Q, expmapStability ) { TEST( Rot3, expmapStability ) {
Vector w = Vector_(3, 78e-9, 5e-8, 97e-7); Vector w = Vector_(3, 78e-9, 5e-8, 97e-7);
double theta = w.norm(); double theta = w.norm();
double theta2 = theta*theta; double theta2 = theta*theta;
Rot3Q actualR = Rot3Q::Expmap(w); Rot3 actualR = Rot3::Expmap(w);
Matrix W = Matrix_(3,3, 0.0, -w(2), w(1), Matrix W = Matrix_(3,3, 0.0, -w(2), w(1),
w(2), 0.0, -w(0), w(2), 0.0, -w(0),
-w(1), w(0), 0.0 ); -w(1), w(0), 0.0 );
Matrix W2 = W*W; Matrix W2 = W*W;
Matrix Rmat = eye(3) + (1.0-theta2/6.0 + theta2*theta2/120.0 Matrix Rmat = eye(3) + (1.0-theta2/6.0 + theta2*theta2/120.0
- theta2*theta2*theta2/5040.0)*W + (0.5 - theta2/24.0 + theta2*theta2/720.0)*W2 ; - theta2*theta2*theta2/5040.0)*W + (0.5 - theta2/24.0 + theta2*theta2/720.0)*W2 ;
Rot3Q expectedR( Rmat ); Rot3 expectedR( Rmat );
CHECK(assert_equal(expectedR, actualR, 1e-10)); CHECK(assert_equal(expectedR, actualR, 1e-10));
} }
// Does not work with Quaternions // Does not work with Quaternions
///* ************************************************************************* */ ///* ************************************************************************* */
//TEST( Rot3Q, logmapStability ) { //TEST( Rot3, logmapStability ) {
// Vector w = Vector_(3, 1e-8, 0.0, 0.0); // Vector w = Vector_(3, 1e-8, 0.0, 0.0);
// Rot3Q R = Rot3Q::Expmap(w); // Rot3 R = Rot3::Expmap(w);
//// double tr = R.r1().x()+R.r2().y()+R.r3().z(); //// double tr = R.r1().x()+R.r2().y()+R.r3().z();
//// std::cout.precision(5000); //// std::cout.precision(5000);
//// std::cout << "theta: " << w.norm() << std::endl; //// std::cout << "theta: " << w.norm() << std::endl;
//// std::cout << "trace: " << tr << std::endl; //// std::cout << "trace: " << tr << std::endl;
//// R.print("R = "); //// R.print("R = ");
// Vector actualw = Rot3Q::Logmap(R); // Vector actualw = Rot3::Logmap(R);
// CHECK(assert_equal(w, actualw, 1e-15)); // CHECK(assert_equal(w, actualw, 1e-15));
//} //}
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3Q, quaternion) { TEST(Rot3, quaternion) {
// NOTE: This is also verifying the ability to convert Vector to Quaternion // NOTE: This is also verifying the ability to convert Vector to Quaternion
Quaternion q1(0.710997408193224, 0.360544029310185, 0.594459869568306, 0.105395217842782); Quaternion q1(0.710997408193224, 0.360544029310185, 0.594459869568306, 0.105395217842782);
Rot3Q R1 = Rot3Q(Matrix_(3,3, Rot3 R1 = Rot3(Matrix_(3,3,
0.271018623057411, 0.278786459830371, 0.921318086098018, 0.271018623057411, 0.278786459830371, 0.921318086098018,
0.578529366719085, 0.717799701969298, -0.387385285854279, 0.578529366719085, 0.717799701969298, -0.387385285854279,
-0.769319620053772, 0.637998195662053, 0.033250932803219)); -0.769319620053772, 0.637998195662053, 0.033250932803219));
Quaternion q2(0.263360579192421, 0.571813128030932, 0.494678363680335, 0.599136268678053); Quaternion q2(0.263360579192421, 0.571813128030932, 0.494678363680335, 0.599136268678053);
Rot3Q R2 = Rot3Q(Matrix_(3,3, Rot3 R2 = Rot3(Matrix_(3,3,
-0.207341903877828, 0.250149415542075, 0.945745528564780, -0.207341903877828, 0.250149415542075, 0.945745528564780,
0.881304914479026, -0.371869043667957, 0.291573424846290, 0.881304914479026, -0.371869043667957, 0.291573424846290,
0.424630407073532, 0.893945571198514, -0.143353873763946)); 0.424630407073532, 0.893945571198514, -0.143353873763946));
// Check creating Rot3Q from quaternion // Check creating Rot3 from quaternion
EXPECT(assert_equal(R1, Rot3Q(q1))); EXPECT(assert_equal(R1, Rot3(q1)));
EXPECT(assert_equal(R1, Rot3Q::quaternion(q1.w(), q1.x(), q1.y(), q1.z()))); EXPECT(assert_equal(R1, Rot3::quaternion(q1.w(), q1.x(), q1.y(), q1.z())));
EXPECT(assert_equal(R2, Rot3Q(q2))); EXPECT(assert_equal(R2, Rot3(q2)));
EXPECT(assert_equal(R2, Rot3Q::quaternion(q2.w(), q2.x(), q2.y(), q2.z()))); EXPECT(assert_equal(R2, Rot3::quaternion(q2.w(), q2.x(), q2.y(), q2.z())));
// Check converting Rot3Q to quaterion // Check converting Rot3 to quaterion
EXPECT(assert_equal(Vector(R1.toQuaternion().coeffs()), Vector(q1.coeffs()))); EXPECT(assert_equal(Vector(R1.toQuaternion().coeffs()), Vector(q1.coeffs())));
EXPECT(assert_equal(Vector(R2.toQuaternion().coeffs()), Vector(q2.coeffs()))); EXPECT(assert_equal(Vector(R2.toQuaternion().coeffs()), Vector(q2.coeffs())));
// Check that quaternion and Rot3Q represent the same rotation // Check that quaternion and Rot3 represent the same rotation
Point3 p1(1.0, 2.0, 3.0); Point3 p1(1.0, 2.0, 3.0);
Point3 p2(8.0, 7.0, 9.0); Point3 p2(8.0, 7.0, 9.0);
@ -509,6 +475,8 @@ TEST(Rot3Q, quaternion) {
EXPECT(assert_equal(expected2, actual2)); EXPECT(assert_equal(expected2, actual2));
} }
#endif
/* ************************************************************************* */ /* ************************************************************************* */
int main() { int main() {
TestResult tr; TestResult tr;

92
tests/testRot3Optimization.cpp
View File

@ -30,94 +30,28 @@
using namespace gtsam; using namespace gtsam;
typedef TypedSymbol<Rot3Q, 'r'> KeyQ; typedef TypedSymbol<Rot3, 'r'> Key;
typedef Values<KeyQ> ValuesQ; typedef Values<Key> Rot3Values;
typedef PriorFactor<ValuesQ, KeyQ> PriorQ; typedef PriorFactor<Rot3Values, Key> Prior;
typedef BetweenFactor<ValuesQ, KeyQ> BetweenQ; typedef BetweenFactor<Rot3Values, Key> Between;
typedef NonlinearFactorGraph<ValuesQ> GraphQ; typedef NonlinearFactorGraph<Rot3Values> Graph;
typedef TypedSymbol<Rot3M, 'r'> KeyM;
typedef Values<KeyM> ValuesM;
typedef PriorFactor<ValuesM, KeyM> PriorM;
typedef BetweenFactor<ValuesM, KeyM> BetweenM;
typedef NonlinearFactorGraph<ValuesM> GraphM;
/* ************************************************************************* */
TEST(Rot3, optimize1) {
// Compare Rot3Q and Rot3M optimization
GraphQ fgQ;
fgQ.add(PriorQ(0, Rot3Q(), sharedSigma(3, 0.01)));
fgQ.add(BetweenQ(0, 1, Rot3Q::Rz(M_PI/3.0), sharedSigma(3, 0.01)));
fgQ.add(BetweenQ(1, 0, Rot3Q::Rz(5.0*M_PI/3.0), sharedSigma(3, 0.01)));
GraphM fgM;
fgM.add(PriorM(0, Rot3M(), sharedSigma(3, 0.01)));
fgM.add(BetweenM(0, 1, Rot3M::Rz(M_PI/3.0), sharedSigma(3, 0.01)));
fgM.add(BetweenM(1, 0, Rot3M::Rz(5.0*M_PI/3.0), sharedSigma(3, 0.01)));
ValuesQ initialQ;
initialQ.insert(0, Rot3Q::Rz(0.0));
initialQ.insert(1, Rot3Q::Rz(M_PI/3.0 + 0.1));
ValuesM initialM;
initialM.insert(0, Rot3M::Rz(0.0));
initialM.insert(1, Rot3M::Rz(M_PI/3.0 + 0.1));
ValuesQ truthQ;
truthQ.insert(0, Rot3Q::Rz(0.0));
truthQ.insert(1, Rot3Q::Rz(M_PI/3.0));
ValuesM truthM;
truthM.insert(0, Rot3M::Rz(0.0));
truthM.insert(1, Rot3M::Rz(M_PI/3.0));
// Compare Matrix and Quaternion between
Matrix H1M, H2M;
Rot3M betwM = initialM[1].between(initialM[0], H1M, H2M);
Matrix H1Q, H2Q;
Rot3Q betwQ = initialM[1].between(initialM[0], H1Q, H2Q);
EXPECT(assert_equal(betwM.matrix(), betwQ.matrix()));
EXPECT(assert_equal(H1M, H1Q));
EXPECT(assert_equal(H2M, H2Q));
Point3 x1(1.0,0.0,0.0), x2(0.0,1.0,0.0);
EXPECT(assert_equal(betwM*x1, betwQ*x1));
EXPECT(assert_equal(betwM*x2, betwQ*x2));
// Compare Matrix and Quaternion logmap
Vector logM = initialM[1].localCoordinates(initialM[0]);
Vector logQ = initialQ[1].localCoordinates(initialQ[0]);
EXPECT(assert_equal(logM, logQ));
// Compare Matrix and Quaternion linear graph
Ordering ordering; ordering += KeyQ(0), KeyQ(1);
GaussianFactorGraph gfgQ(*fgQ.linearize(initialQ, ordering));
GaussianFactorGraph gfgM(*fgM.linearize(initialM, ordering));
EXPECT(assert_equal(gfgQ, gfgM, 1e-5));
NonlinearOptimizationParameters params;
//params.verbosity_ = NonlinearOptimizationParameters::TRYLAMBDA;
ValuesQ final = optimize(fgQ, initialQ, params);
EXPECT(assert_equal(truthQ, final, 1e-5));
}
/* ************************************************************************* */ /* ************************************************************************* */
TEST(Rot3, optimize) { TEST(Rot3, optimize) {
// Optimize a circle // Optimize a circle
ValuesQ truth; Rot3Values truth;
ValuesQ initial; Rot3Values initial;
GraphQ fg; Graph fg;
fg.add(PriorQ(0, Rot3Q(), sharedSigma(3, 0.01))); fg.add(Prior(0, Rot3(), sharedSigma(3, 0.01)));
for(int j=0; j<6; ++j) { for(int j=0; j<6; ++j) {
truth.insert(j, Rot3Q::Rz(M_PI/3.0 * double(j))); truth.insert(j, Rot3::Rz(M_PI/3.0 * double(j)));
initial.insert(j, Rot3Q::Rz(M_PI/3.0 * double(j) + 0.1 * double(j%2))); initial.insert(j, Rot3::Rz(M_PI/3.0 * double(j) + 0.1 * double(j%2)));
fg.add(BetweenQ(j, (j+1)%6, Rot3Q::Rz(M_PI/3.0), sharedSigma(3, 0.01))); fg.add(Between(j, (j+1)%6, Rot3::Rz(M_PI/3.0), sharedSigma(3, 0.01)));
} }
NonlinearOptimizationParameters params; NonlinearOptimizationParameters params;
ValuesQ final = optimize(fg, initial, params); Rot3Values final = optimize(fg, initial, params);
EXPECT(assert_equal(truth, final, 1e-5)); EXPECT(assert_equal(truth, final, 1e-5));
} }