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gtsam/gtsam/geometry/tests/testRot3M.cpp

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/* ----------------------------------------------------------------------------
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
* Atlanta, Georgia 30332-0415
* All Rights Reserved
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
* See LICENSE for the license information
* -------------------------------------------------------------------------- */
/**
* @file testRot3.cpp
* @brief Unit tests for Rot3 class
* @author Alireza Fathi
*/
#include <gtsam/base/Testable.h>
#include <gtsam/base/numericalDerivative.h>
#include <gtsam/base/lieProxies.h>
#include <gtsam/geometry/Point3.h>
#include <gtsam/geometry/Rot3.h>
#include <boost/math/constants/constants.hpp>
#include <CppUnitLite/TestHarness.h>
#ifndef GTSAM_USE_QUATERNIONS
using namespace std;
using namespace gtsam;
GTSAM_CONCEPT_TESTABLE_INST(Rot3)
GTSAM_CONCEPT_LIE_INST(Rot3)
static Rot3 R = Rot3::rodriguez(0.1, 0.4, 0.2);
static Point3 P(0.2, 0.7, -2.0);
static double error = 1e-9, epsilon = 0.001;
static const Matrix I3 = eye(3);
/* ************************************************************************* */
TEST( Rot3, constructor)
{
Rot3 expected(I3);
Vector r1(3), r2(3), r3(3);
r1(0) = 1;
r1(1) = 0;
r1(2) = 0;
r2(0) = 0;
r2(1) = 1;
r2(2) = 0;
r3(0) = 0;
r3(1) = 0;
r3(2) = 1;
Rot3 actual(r1, r2, r3);
CHECK(assert_equal(actual,expected));
}
/* ************************************************************************* */
TEST( Rot3, constructor2)
{
Matrix R = (Matrix(3, 3) << 11., 12., 13., 21., 22., 23., 31., 32., 33.);
Rot3 actual(R);
Rot3 expected(11, 12, 13, 21, 22, 23, 31, 32, 33);
CHECK(assert_equal(actual,expected));
}
/* ************************************************************************* */
TEST( Rot3, constructor3)
{
Rot3 expected(1, 2, 3, 4, 5, 6, 7, 8, 9);
Point3 r1(1, 4, 7), r2(2, 5, 8), r3(3, 6, 9);
CHECK(assert_equal(Rot3(r1,r2,r3),expected));
}
/* ************************************************************************* */
TEST( Rot3, transpose)
{
Rot3 R(1, 2, 3, 4, 5, 6, 7, 8, 9);
Point3 r1(1, 2, 3), r2(4, 5, 6), r3(7, 8, 9);
CHECK(assert_equal(R.inverse(),Rot3(r1,r2,r3)));
}
/* ************************************************************************* */
TEST( Rot3, equals)
{
CHECK(R.equals(R));
Rot3 zero;
CHECK(!R.equals(zero));
}
/* ************************************************************************* */
// Notice this uses J^2 whereas fast uses w*w', and has cos(t)*I + ....
Rot3 slow_but_correct_rodriguez(const Vector& w) {
double t = norm_2(w);
Matrix J = skewSymmetric(w / t);
if (t < 1e-5) return Rot3();
Matrix R = I3 + sin(t) * J + (1.0 - cos(t)) * (J * J);
return R;
}
/* ************************************************************************* */
TEST( Rot3, rodriguez)
{
Rot3 R1 = Rot3::rodriguez(epsilon, 0, 0);
Vector w = (Vector(3) << epsilon, 0., 0.);
Rot3 R2 = slow_but_correct_rodriguez(w);
CHECK(assert_equal(R2,R1));
}
/* ************************************************************************* */
TEST( Rot3, rodriguez2)
{
Vector axis = (Vector(3) << 0., 1., 0.); // rotation around Y
double angle = 3.14 / 4.0;
Rot3 actual = Rot3::rodriguez(axis, angle);
Rot3 expected(0.707388, 0, 0.706825,
0, 1, 0,
-0.706825, 0, 0.707388);
CHECK(assert_equal(expected,actual,1e-5));
}
/* ************************************************************************* */
TEST( Rot3, rodriguez3)
{
Vector w = (Vector(3) << 0.1, 0.2, 0.3);
Rot3 R1 = Rot3::rodriguez(w / norm_2(w), norm_2(w));
Rot3 R2 = slow_but_correct_rodriguez(w);
CHECK(assert_equal(R2,R1));
}
/* ************************************************************************* */
TEST( Rot3, rodriguez4)
{
Vector axis = (Vector(3) << 0., 0., 1.); // rotation around Z
double angle = M_PI/2.0;
Rot3 actual = Rot3::rodriguez(axis, angle);
double c=cos(angle),s=sin(angle);
Rot3 expected(c,-s, 0,
s, c, 0,
0, 0, 1);
CHECK(assert_equal(expected,actual,1e-5));
CHECK(assert_equal(slow_but_correct_rodriguez(axis*angle),actual,1e-5));
}
/* ************************************************************************* */
TEST( Rot3, expmap)
{
Vector v = zero(3);
CHECK(assert_equal(R.retract(v), R));
}
/* ************************************************************************* */
TEST(Rot3, log)
{
static const double PI = boost::math::constants::pi<double>();
Vector w;
Rot3 R;
#define CHECK_OMEGA(X,Y,Z) \
w = (Vector(3) << (double)X, (double)Y, double(Z)); \
R = Rot3::rodriguez(w); \
EXPECT(assert_equal(w, Rot3::Logmap(R),1e-12));
// Check zero
CHECK_OMEGA( 0, 0, 0)
// create a random direction:
double norm=sqrt(1.0+16.0+4.0);
double x=1.0/norm, y=4.0/norm, z=2.0/norm;
// Check very small rotation for Taylor expansion
// Note that tolerance above is 1e-12, so Taylor is pretty good !
double d = 0.0001;
CHECK_OMEGA( d, 0, 0)
CHECK_OMEGA( 0, d, 0)
CHECK_OMEGA( 0, 0, d)
CHECK_OMEGA(x*d, y*d, z*d)
// check normal rotation
d = 0.1;
CHECK_OMEGA( d, 0, 0)
CHECK_OMEGA( 0, d, 0)
CHECK_OMEGA( 0, 0, d)
CHECK_OMEGA(x*d, y*d, z*d)
// Check 180 degree rotations
CHECK_OMEGA( PI, 0, 0)
CHECK_OMEGA( 0, PI, 0)
CHECK_OMEGA( 0, 0, PI)
CHECK_OMEGA(x*PI,y*PI,z*PI)
// Check 360 degree rotations
#define CHECK_OMEGA_ZERO(X,Y,Z) \
w = (Vector(3) << (double)X, (double)Y, double(Z)); \
R = Rot3::rodriguez(w); \
EXPECT(assert_equal(zero(3), Rot3::Logmap(R)));
CHECK_OMEGA_ZERO( 2.0*PI, 0, 0)
CHECK_OMEGA_ZERO( 0, 2.0*PI, 0)
CHECK_OMEGA_ZERO( 0, 0, 2.0*PI)
CHECK_OMEGA_ZERO(x*2.*PI,y*2.*PI,z*2.*PI)
}
Rot3 evaluateRotation(const Vector3 thetahat){
return Rot3::Expmap(thetahat);
}
Vector3 evaluateLogRotation(const Vector3 thetahat, const Vector3 deltatheta){
return Rot3::Logmap( Rot3::Expmap(thetahat).compose( Rot3::Expmap(deltatheta) ) );
}
/* ************************************************************************* */
TEST( Rot3, rightJacobianExpMapSO3 )
{
// Linearization point
Vector3 thetahat; thetahat << 0.1, 0, 0;
Matrix expectedJacobian = numericalDerivative11<Rot3, Vector3>(boost::bind(&evaluateRotation, _1), thetahat);
Matrix actualJacobian = Rot3::rightJacobianExpMapSO3(thetahat);
EXPECT(assert_equal(expectedJacobian, actualJacobian));
}
/* ************************************************************************* */
TEST( Rot3, rightJacobianExpMapSO3inverse )
{
// Linearization point
Vector3 thetahat; thetahat << 0.1,0.1,0; ///< Current estimate of rotation rate bias
Vector3 deltatheta; deltatheta << 0, 0, 0;
Matrix expectedJacobian = numericalDerivative11<Vector3,Vector3>(
boost::bind(&evaluateLogRotation, thetahat, _1), deltatheta);
Matrix actualJacobian = Rot3::rightJacobianExpMapSO3inverse(thetahat);
EXPECT(assert_equal(expectedJacobian, actualJacobian));
}
/* ************************************************************************* */
TEST(Rot3, manifold_caley)
{
Rot3 gR1 = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3 gR2 = Rot3::rodriguez(0.3, 0.1, 0.7);
Rot3 origin;
// log behaves correctly
Vector d12 = gR1.localCoordinates(gR2, Rot3::CAYLEY);
CHECK(assert_equal(gR2, gR1.retract(d12, Rot3::CAYLEY)));
Vector d21 = gR2.localCoordinates(gR1, Rot3::CAYLEY);
CHECK(assert_equal(gR1, gR2.retract(d21, Rot3::CAYLEY)));
// Check that log(t1,t2)=-log(t2,t1)
CHECK(assert_equal(d12,-d21));
// lines in canonical coordinates correspond to Abelian subgroups in SO(3)
Vector d = (Vector(3) << 0.1, 0.2, 0.3);
// exp(-d)=inverse(exp(d))
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)
Rot3 R2 = Rot3::Expmap (2 * d);
Rot3 R3 = Rot3::Expmap (3 * d);
Rot3 R5 = Rot3::Expmap (5 * d);
CHECK(assert_equal(R5,R2*R3));
CHECK(assert_equal(R5,R3*R2));
}
/* ************************************************************************* */
TEST(Rot3, manifold_slow_caley)
{
Rot3 gR1 = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3 gR2 = Rot3::rodriguez(0.3, 0.1, 0.7);
Rot3 origin;
// log behaves correctly
Vector d12 = gR1.localCoordinates(gR2, Rot3::SLOW_CAYLEY);
CHECK(assert_equal(gR2, gR1.retract(d12, Rot3::SLOW_CAYLEY)));
Vector d21 = gR2.localCoordinates(gR1, Rot3::SLOW_CAYLEY);
CHECK(assert_equal(gR1, gR2.retract(d21, Rot3::SLOW_CAYLEY)));
// Check that log(t1,t2)=-log(t2,t1)
CHECK(assert_equal(d12,-d21));
// lines in canonical coordinates correspond to Abelian subgroups in SO(3)
Vector d = (Vector(3) << 0.1, 0.2, 0.3);
// exp(-d)=inverse(exp(d))
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)
Rot3 R2 = Rot3::Expmap (2 * d);
Rot3 R3 = Rot3::Expmap (3 * d);
Rot3 R5 = Rot3::Expmap (5 * d);
CHECK(assert_equal(R5,R2*R3));
CHECK(assert_equal(R5,R3*R2));
}
/* ************************************************************************* */
TEST(Rot3, manifold_expmap)
{
Rot3 gR1 = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3 gR2 = Rot3::rodriguez(0.3, 0.1, 0.7);
Rot3 origin;
// log behaves correctly
Vector d12 = gR1.localCoordinates(gR2, Rot3::EXPMAP);
CHECK(assert_equal(gR2, gR1.retract(d12, Rot3::EXPMAP)));
Vector d21 = gR2.localCoordinates(gR1, Rot3::EXPMAP);
CHECK(assert_equal(gR1, gR2.retract(d21, Rot3::EXPMAP)));
// Check that it is expmap
CHECK(assert_equal(gR2, gR1*Rot3::Expmap(d12)));
CHECK(assert_equal(gR1, gR2*Rot3::Expmap(d21)));
// Check that log(t1,t2)=-log(t2,t1)
CHECK(assert_equal(d12,-d21));
// lines in canonical coordinates correspond to Abelian subgroups in SO(3)
Vector d = (Vector(3) << 0.1, 0.2, 0.3);
// exp(-d)=inverse(exp(d))
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)
Rot3 R2 = Rot3::Expmap (2 * d);
Rot3 R3 = Rot3::Expmap (3 * d);
Rot3 R5 = Rot3::Expmap (5 * d);
CHECK(assert_equal(R5,R2*R3));
CHECK(assert_equal(R5,R3*R2));
}
/* ************************************************************************* */
class AngularVelocity: public Point3 {
public:
AngularVelocity(const Point3& p) :
Point3(p) {
}
AngularVelocity(double wx, double wy, double wz) :
Point3(wx, wy, wz) {
}
};
AngularVelocity bracket(const AngularVelocity& X, const AngularVelocity& Y) {
return X.cross(Y);
}
/* ************************************************************************* */
TEST(Rot3, BCH)
{
// Approximate exmap by BCH formula
AngularVelocity w1(0.2, -0.1, 0.1);
AngularVelocity w2(0.01, 0.02, -0.03);
Rot3 R1 = Rot3::Expmap (w1.vector()), R2 = Rot3::Expmap (w2.vector());
Rot3 R3 = R1 * R2;
Vector expected = Rot3::Logmap(R3);
Vector actual = BCH(w1, w2).vector();
CHECK(assert_equal(expected, actual,1e-5));
}
/* ************************************************************************* */
TEST( Rot3, rotate_derivatives)
{
Matrix actualDrotate1a, actualDrotate1b, actualDrotate2;
R.rotate(P, actualDrotate1a, actualDrotate2);
R.inverse().rotate(P, actualDrotate1b, boost::none);
Matrix numerical1 = numericalDerivative21(testing::rotate<Rot3,Point3>, R, P);
Matrix numerical2 = numericalDerivative21(testing::rotate<Rot3,Point3>, R.inverse(), P);
Matrix numerical3 = numericalDerivative22(testing::rotate<Rot3,Point3>, R, P);
EXPECT(assert_equal(numerical1,actualDrotate1a,error));
EXPECT(assert_equal(numerical2,actualDrotate1b,error));
EXPECT(assert_equal(numerical3,actualDrotate2, error));
}
/* ************************************************************************* */
TEST( Rot3, unrotate)
{
Point3 w = R * P;
Matrix H1,H2;
Point3 actual = R.unrotate(w,H1,H2);
CHECK(assert_equal(P,actual));
Matrix numerical1 = numericalDerivative21(testing::unrotate<Rot3,Point3>, R, w);
CHECK(assert_equal(numerical1,H1,error));
Matrix numerical2 = numericalDerivative22(testing::unrotate<Rot3,Point3>, R, w);
CHECK(assert_equal(numerical2,H2,error));
}
/* ************************************************************************* */
TEST( Rot3, compose )
{
Rot3 R1 = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3 R2 = Rot3::rodriguez(0.2, 0.3, 0.5);
Rot3 expected = R1 * R2;
Matrix actualH1, actualH2;
Rot3 actual = R1.compose(R2, actualH1, actualH2);
CHECK(assert_equal(expected,actual));
Matrix numericalH1 = numericalDerivative21(testing::compose<Rot3>, R1,
R2, 1e-2);
CHECK(assert_equal(numericalH1,actualH1));
Matrix numericalH2 = numericalDerivative22(testing::compose<Rot3>, R1,
R2, 1e-2);
CHECK(assert_equal(numericalH2,actualH2));
}
/* ************************************************************************* */
TEST( Rot3, inverse )
{
Rot3 R = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3 I;
Matrix actualH;
CHECK(assert_equal(I,R*R.inverse(actualH)));
CHECK(assert_equal(I,R.inverse()*R));
Matrix numericalH = numericalDerivative11(testing::inverse<Rot3>, R);
CHECK(assert_equal(numericalH,actualH));
}
/* ************************************************************************* */
TEST( Rot3, between )
{
Rot3 R = Rot3::rodriguez(0.1, 0.4, 0.2);
Rot3 origin;
CHECK(assert_equal(R, origin.between(R)));
CHECK(assert_equal(R.inverse(), R.between(origin)));
Rot3 R1 = Rot3::rodriguez(0.1, 0.2, 0.3);
Rot3 R2 = Rot3::rodriguez(0.2, 0.3, 0.5);
Rot3 expected = R1.inverse() * R2;
Matrix actualH1, actualH2;
Rot3 actual = R1.between(R2, actualH1, actualH2);
CHECK(assert_equal(expected,actual));
Matrix numericalH1 = numericalDerivative21(testing::between<Rot3> , R1, R2);
CHECK(assert_equal(numericalH1,actualH1));
Matrix numericalH2 = numericalDerivative22(testing::between<Rot3> , R1, R2);
CHECK(assert_equal(numericalH2,actualH2));
}
/* ************************************************************************* */
Vector w = (Vector(3) << 0.1, 0.27, -0.2);
// Left trivialization Derivative of exp(w) wrpt w:
// How does exp(w) change when w changes?
// We find a y such that: exp(w) exp(y) = exp(w + dw) for dw --> 0
// => y = log (exp(-w) * exp(w+dw))
Vector3 testDexpL(const Vector3& dw) {
return Rot3::Logmap(Rot3::Expmap(-w) * Rot3::Expmap(w + dw));
}
TEST( Rot3, dexpL) {
Matrix actualDexpL = Rot3::dexpL(w);
Matrix expectedDexpL = numericalDerivative11<Vector3, Vector3>(testDexpL,
Vector3::Zero(), 1e-2);
EXPECT(assert_equal(expectedDexpL, actualDexpL, 1e-5));
Matrix actualDexpInvL = Rot3::dexpInvL(w);
EXPECT(assert_equal(expectedDexpL.inverse(), actualDexpInvL, 1e-5));
}
/* ************************************************************************* */
TEST( Rot3, xyz )
{
double t = 0.1, st = sin(t), ct = cos(t);
// Make sure all counterclockwise
// Diagrams below are all from from unchanging axis
// z
// | * Y=(ct,st)
// x----y
Rot3 expected1(1, 0, 0, 0, ct, -st, 0, st, ct);
CHECK(assert_equal(expected1,Rot3::Rx(t)));
// x
// | * Z=(ct,st)
// y----z
Rot3 expected2(ct, 0, st, 0, 1, 0, -st, 0, ct);
CHECK(assert_equal(expected2,Rot3::Ry(t)));
// y
// | X=* (ct,st)
// z----x
Rot3 expected3(ct, -st, 0, st, ct, 0, 0, 0, 1);
CHECK(assert_equal(expected3,Rot3::Rz(t)));
// Check compound rotation
Rot3 expected = Rot3::Rz(0.3) * Rot3::Ry(0.2) * Rot3::Rx(0.1);
CHECK(assert_equal(expected,Rot3::RzRyRx(0.1,0.2,0.3)));
}
/* ************************************************************************* */
TEST( Rot3, yaw_pitch_roll )
{
double t = 0.1;
// yaw is around z axis
CHECK(assert_equal(Rot3::Rz(t),Rot3::yaw(t)));
// pitch is around y axis
CHECK(assert_equal(Rot3::Ry(t),Rot3::pitch(t)));
// roll is around x axis
CHECK(assert_equal(Rot3::Rx(t),Rot3::roll(t)));
// Check compound rotation
Rot3 expected = Rot3::yaw(0.1) * Rot3::pitch(0.2) * Rot3::roll(0.3);
CHECK(assert_equal(expected,Rot3::ypr(0.1,0.2,0.3)));
CHECK(assert_equal((Vector)(Vector(3) << 0.1, 0.2, 0.3),expected.ypr()));
}
/* ************************************************************************* */
TEST( Rot3, RQ)
{
// Try RQ on a pure rotation
Matrix actualK;
Vector actual;
boost::tie(actualK, actual) = RQ(R.matrix());
Vector expected = (Vector(3) << 0.14715, 0.385821, 0.231671);
CHECK(assert_equal(I3,actualK));
CHECK(assert_equal(expected,actual,1e-6));
// 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((Vector)(Vector(3) << 0.1,0.2,0.3),Rot3::RzRyRx(0.1,0.2,0.3).xyz()));
// Try using ypr call, asserting that Rot3::ypr(y,p,r).ypr()==[y;p;r]
CHECK(assert_equal((Vector)(Vector(3) << 0.1,0.2,0.3),Rot3::ypr(0.1,0.2,0.3).ypr()));
CHECK(assert_equal((Vector)(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
CHECK(assert_equal((Vector)(Vector(3) << 0.1,0.0,0.0),Rot3::yaw (0.1).ypr()));
CHECK(assert_equal((Vector)(Vector(3) << 0.0,0.1,0.0),Rot3::pitch(0.1).ypr()));
CHECK(assert_equal((Vector)(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
Matrix K = (Matrix(3, 3) << 500.0, 0.0, 320.0, 0.0, 500.0, 240.0, 0.0, 0.0, 1.0);
Matrix A = K * R.matrix();
boost::tie(actualK, actual) = RQ(A);
CHECK(assert_equal(K,actualK));
CHECK(assert_equal(expected,actual,1e-6));
}
/* ************************************************************************* */
TEST( Rot3, expmapStability ) {
Vector w = (Vector(3) << 78e-9, 5e-8, 97e-7);
double theta = w.norm();
double theta2 = theta*theta;
Rot3 actualR = Rot3::Expmap(w);
Matrix W = (Matrix(3, 3) << 0.0, -w(2), w(1),
w(2), 0.0, -w(0),
-w(1), w(0), 0.0 );
Matrix W2 = W*W;
Matrix Rmat = I3 + (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 ;
Rot3 expectedR( Rmat );
CHECK(assert_equal(expectedR, actualR, 1e-10));
}
/* ************************************************************************* */
TEST( Rot3, logmapStability ) {
Vector w = (Vector(3) << 1e-8, 0.0, 0.0);
Rot3 R = Rot3::Expmap(w);
// double tr = R.r1().x()+R.r2().y()+R.r3().z();
// std::cout.precision(5000);
// std::cout << "theta: " << w.norm() << std::endl;
// std::cout << "trace: " << tr << std::endl;
// R.print("R = ");
Vector actualw = Rot3::Logmap(R);
CHECK(assert_equal(w, actualw, 1e-15));
}
/* ************************************************************************* */
TEST(Rot3, quaternion) {
// NOTE: This is also verifying the ability to convert Vector to Quaternion
Quaternion q1(0.710997408193224, 0.360544029310185, 0.594459869568306, 0.105395217842782);
Rot3 R1 = Rot3((Matrix)(Matrix(3, 3) <<
0.271018623057411, 0.278786459830371, 0.921318086098018,
0.578529366719085, 0.717799701969298, -0.387385285854279,
-0.769319620053772, 0.637998195662053, 0.033250932803219));
Quaternion q2(0.263360579192421, 0.571813128030932, 0.494678363680335, 0.599136268678053);
Rot3 R2 = Rot3((Matrix)(Matrix(3, 3) <<
-0.207341903877828, 0.250149415542075, 0.945745528564780,
0.881304914479026, -0.371869043667957, 0.291573424846290,
0.424630407073532, 0.893945571198514, -0.143353873763946));
// Check creating Rot3 from quaternion
EXPECT(assert_equal(R1, Rot3(q1)));
EXPECT(assert_equal(R1, Rot3::quaternion(q1.w(), q1.x(), q1.y(), q1.z())));
EXPECT(assert_equal(R2, Rot3(q2)));
EXPECT(assert_equal(R2, Rot3::quaternion(q2.w(), q2.x(), q2.y(), q2.z())));
// Check converting Rot3 to quaterion
EXPECT(assert_equal(Vector(R1.toQuaternion().coeffs()), Vector(q1.coeffs())));
EXPECT(assert_equal(Vector(R2.toQuaternion().coeffs()), Vector(q2.coeffs())));
// Check that quaternion and Rot3 represent the same rotation
Point3 p1(1.0, 2.0, 3.0);
Point3 p2(8.0, 7.0, 9.0);
Point3 expected1 = R1*p1;
Point3 expected2 = R2*p2;
Point3 actual1 = Point3(q1*p1.vector());
Point3 actual2 = Point3(q2*p2.vector());
EXPECT(assert_equal(expected1, actual1));
EXPECT(assert_equal(expected2, actual2));
}
/* ************************************************************************* */
TEST( Rot3, Cayley ) {
Matrix A = skewSymmetric(1,2,-3);
Matrix Q = Cayley(A);
EXPECT(assert_equal(I3, trans(Q)*Q));
EXPECT(assert_equal(A, Cayley(Q)));
}
/* ************************************************************************* */
TEST( Rot3, stream)
{
Rot3 R;
std::ostringstream os;
os << R;
EXPECT(os.str() == "\n|1, 0, 0|\n|0, 1, 0|\n|0, 0, 1|\n");
}
#endif
/* ************************************************************************* */
int main() {
TestResult tr;
return TestRegistry::runAllTests(tr);
}
/* ************************************************************************* */
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