gtsam/cpp/testRot3.cpp

/**
 * @file    testRot3.cpp
 * @brief   Unit tests for Rot3 class
 * @author  Alireza Fathi
 */

#include <CppUnitLite/TestHarness.h>
#include <boost/math/constants/constants.hpp>
#include "numericalDerivative.h"
#include "Point3.h"
#include "Rot3.h"

using namespace gtsam;

Rot3 R = rodriguez(0.1,0.4,0.2);
Point3 P(0.2,0.7,-2.0);
double error = 1e-9, epsilon=0.001;

/* ************************************************************************* */
TEST( Rot3, constructor) {
  Rot3 expected(eye(3,3));
  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(inverse(R),Rot3(r1,r2,r3)));
}

/* ************************************************************************* */
TEST( Rot3, equals) {
  CHECK(R.equals(R));
  Rot3 zero;
  CHECK(!R.equals(zero));
}

/* ************************************************************************* */
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 = eye(3, 3) + sin(t) * J + (1.0 - cos(t)) * (J * J);
	return R; // matrix constructor will be tripped
}

/* ************************************************************************* */
TEST( Rot3, rodriguez) {
  Rot3 R1 = rodriguez(epsilon, 0, 0);
  Vector w = Vector_(3,epsilon,0.,0.);
  Rot3 R2 = slow_but_correct_rodriguez(w);
  CHECK(assert_equal(R1,R2));
}

/* ************************************************************************* */
TEST( Rot3, rodriguez2) {
  Vector v(3); v(0) = 0; v(1) = 1; v(2) = 0;
  Rot3 R1 = rodriguez(v, 3.14/4.0);
  Rot3 R2(0.707388,0,0.706825,
  		0,1,0,
  		-0.706825,0,0.707388);
  CHECK(assert_equal(R1,R2,1e-5));
}

/* ************************************************************************* */
TEST( Rot3, rodriguez3) {
  Vector w = Vector_(3,0.1,0.2,0.3);
  Rot3 R1 = rodriguez(w/norm_2(w), norm_2(w));
  Rot3 R2 = slow_but_correct_rodriguez(w);
  CHECK(assert_equal(R1,R2));
}

/* ************************************************************************* */
TEST( Rot3, expmap)
{
  Vector v(3);
  fill(v.begin(), v.end(), 0);
  CHECK(assert_equal(expmap(R,v), R));
}

/* ************************************************************************* */
TEST(Rot3, log)
{
	Vector w1 = Vector_(3, 0.1, 0.0, 0.0);
	Rot3 R1 = rodriguez(w1);
	CHECK(assert_equal(w1, logmap(R1)));

	Vector w2 = Vector_(3, 0.0, 0.1, 0.0);
	Rot3 R2 = rodriguez(w2);
	CHECK(assert_equal(w2, logmap(R2)));

	Vector w3 = Vector_(3, 0.0, 0.0, 0.1);
	Rot3 R3 = rodriguez(w3);
	CHECK(assert_equal(w3, logmap(R3)));

	Vector w = Vector_(3, 0.1, 0.4, 0.2);
	Rot3 R = rodriguez(w);
	CHECK(assert_equal(w, logmap(R)));

	Vector w5 = Vector_(3, 0.0, 0.0, 0.0);
	Rot3 R5 = rodriguez(w5);
	CHECK(assert_equal(w5, logmap(R5)));

	Vector w6 = Vector_(3, boost::math::constants::pi<double>(), 0.0, 0.0);
	Rot3 R6 = rodriguez(w6);
	CHECK(assert_equal(w6, logmap(R6)));

    Vector w7 = Vector_(3, 0.0, boost::math::constants::pi<double>(), 0.0);
    Rot3 R7 = rodriguez(w7);
    CHECK(assert_equal(w7, logmap(R7)));

    Vector w8 = Vector_(3, 0.0, 0.0, boost::math::constants::pi<double>());
    Rot3 R8 = rodriguez(w8);
    CHECK(assert_equal(w8, logmap(R8)));
}

/* ************************************************************************* */
	TEST(Rot3, manifold)
{
	Rot3 t1 = rodriguez(0.1, 0.4, 0.2);
	Rot3 t2 = rodriguez(0.3, 0.1, 0.7);
	Rot3 origin;

	// log behaves correctly
	Vector d12 = logmap(t1, t2);
	CHECK(assert_equal(t2, expmap(t1,d12)));
	CHECK(assert_equal(t2, expmap<Rot3>(d12)*t1));
	Vector d21 = logmap(t2, t1);
	CHECK(assert_equal(t1, expmap(t2,d21)));
	CHECK(assert_equal(t1, expmap<Rot3>(d21)*t2));

	// 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(expmap<Rot3>(-d),inverse(expmap<Rot3>(d))));
	// exp(5d)=exp(2*d+3*d)=exp(2*d)exp(3*d)=exp(3*d)exp(2*d)
	Rot3 R2 = expmap<Rot3>(2*d);
	Rot3 R3 = expmap<Rot3>(3*d);
	Rot3 R5 = expmap<Rot3>(5*d);
	CHECK(assert_equal(R5,R2*R3));
	CHECK(assert_equal(R5,R3*R2));
}

/* ************************************************************************* */
// rotate derivatives

TEST( Rot3, Drotate1)
{
  Matrix computed = Drotate1(R, P);
  Matrix numerical = numericalDerivative21(rotate,R,P);
  CHECK(assert_equal(numerical,computed,error));
}

TEST( Rot3, Drotate1_)
  {
  Matrix computed = Drotate1(inverse(R), P);
  Matrix numerical = numericalDerivative21(rotate,inverse(R),P);
  CHECK(assert_equal(numerical,computed,error));
}

TEST( Rot3, Drotate2_DNrotate2)
{
  Matrix computed = Drotate2(R);
  Matrix numerical = numericalDerivative22(rotate,R,P);
  CHECK(assert_equal(numerical,computed,error));
}

/* ************************************************************************* */
TEST( Rot3, unrotate)
{
  Point3 w = R*P;
  CHECK(assert_equal(unrotate(R,w),P));
}

/* ************************************************************************* */
// unrotate derivatives

TEST( Rot3, Dunrotate1)
{
  Matrix computed = Dunrotate1(R, P);
  Matrix numerical = numericalDerivative21(unrotate,R,P);
  CHECK(assert_equal(numerical,computed,error));
}

TEST( Rot3, Dunrotate2_DNunrotate2)
{
  Matrix computed = Dunrotate2(R);
  Matrix numerical = numericalDerivative22(unrotate,R,P);
  CHECK(assert_equal(numerical,computed,error));
}

/* ************************************************************************* */
TEST( Rot3, compose )
{
	Rot3 R1 = rodriguez(0.1, 0.2, 0.3);
	Rot3 R2 = rodriguez(0.2, 0.3, 0.5);

	Rot3 expected = R1*R2;
	Rot3 actual = compose(R1, R2);
	CHECK(assert_equal(expected,actual));

	Matrix numericalH1 = numericalDerivative21<Rot3,Rot3,Rot3>(compose, R1, R2, 1e-5);
	Matrix actualH1 = Dcompose1(R1, R2);
	CHECK(assert_equal(numericalH1,actualH1));

	Matrix actualH2 = Dcompose2(R1, R2);
	Matrix numericalH2 = numericalDerivative22<Rot3,Rot3,Rot3>(compose, R1, R2, 1e-5);
	CHECK(assert_equal(numericalH2,actualH2));
}

/* ************************************************************************* */
TEST( Rot3, between )
{
	Rot3 R = rodriguez(0.1, 0.4, 0.2);
	Rot3 origin;
	CHECK(assert_equal(R, between(origin,R)));
	CHECK(assert_equal(inverse(R), between(R,origin)));

	Rot3 R1 = rodriguez(0.1, 0.2, 0.3);
	Rot3 R2 = rodriguez(0.2, 0.3, 0.5);

	Rot3 expected = R2*inverse(R1);
	Rot3 actual = between(R1, R2);
	CHECK(assert_equal(expected,actual));

	Matrix numericalH1 = numericalDerivative21(between<Rot3> , R1, R2, 1e-5);
	Matrix actualH1 = Dbetween1(R1, R2);
	CHECK(assert_equal(numericalH1,actualH1));

	Matrix actualH2 = Dbetween2(R1, R2);
	Matrix numericalH2 = numericalDerivative22(between<Rot3> , R1, R2, 1e-5);
	CHECK(assert_equal(numericalH2,actualH2));
}

/* ************************************************************************* */
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)));
}

/* ************************************************************************* */
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(eye(3),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_(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_(3,0.1,0.2,0.3),Rot3::ypr(0.1,0.2,0.3).ypr()));

  // Try ypr for pure yaw-pitch-roll matrices
  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),Rot3::pitch(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
	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));
}

/* ************************************************************************* */
int main(){ TestResult tr; return TestRegistry::runAllTests(tr); }
/* ************************************************************************* */