361 lines
10 KiB
C++
361 lines
10 KiB
C++
/**
|
|
* @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); }
|
|
/* ************************************************************************* */
|
|
|