Visual Servoing Platform  version 3.6.1 under development (2024-05-27)
testRotation.cpp

Test theta.u and quaternion multiplication.

/****************************************************************************
*
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* it under the terms of the GNU General Public License as published by
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*
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* Campus Universitaire de Beaulieu
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* WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* Description:
* Test theta.u and quaternion multiplication.
*/
#include <visp3/core/vpConfig.h>
#ifdef VISP_HAVE_CATCH2
#include <visp3/core/vpThetaUVector.h>
#include <visp3/core/vpUniRand.h>
#define CATCH_CONFIG_RUNNER
#include <catch.hpp>
namespace
{
vpThetaUVector generateThetaU(vpUniRand &rng)
{
vpMath::rad(rng.uniform(-180.0, 180.0)) *
vpColVector({ rng.uniform(-1.0, 1.0), rng.uniform(-1.0, 1.0), rng.uniform(-1.0, 1.0) }).normalize());
}
vpQuaternionVector generateQuat(vpUniRand &rng)
{
const double angle = vpMath::rad(rng.uniform(-180.0, 180.0));
const double ctheta = std::cos(angle);
const double stheta = std::sin(angle);
const double ax = rng.uniform(-1.0, 1.0);
const double ay = rng.uniform(-1.0, 1.0);
const double az = rng.uniform(-1.0, 1.0);
return vpQuaternionVector(stheta * ax, stheta * ay, stheta * az, ctheta);
}
} // namespace
bool test(const std::string &s, const vpArray2D<double> &v, const std::vector<double> &bench)
{
std::cout << s << "(" << v.getRows() << "," << v.getCols() << ") = [" << v << "]" << std::endl;
if (bench.size() != v.size()) {
std::cout << "Test fails: bad size wrt bench" << std::endl;
return false;
}
for (unsigned int i = 0; i < v.size(); i++) {
if (std::fabs(v.data[i] - bench[i]) > std::fabs(v.data[i]) * std::numeric_limits<double>::epsilon()) {
std::cout << "Test fails: bad content" << std::endl;
return false;
}
}
return true;
}
bool test(const std::string &s, const vpArray2D<double> &v, const vpColVector &bench)
{
std::cout << s << "(" << v.getRows() << "," << v.getCols() << ") = [" << v << "]" << std::endl;
if (bench.size() != v.size()) {
std::cout << "Test fails: bad size wrt bench" << std::endl;
return false;
}
for (unsigned int i = 0; i < v.size(); i++) {
if (std::fabs(v.data[i] - bench[i]) > std::fabs(v.data[i]) * std::numeric_limits<double>::epsilon()) {
std::cout << "Test fails: bad content" << std::endl;
return false;
}
}
return true;
}
bool test(const std::string &s, const vpRotationVector &v, const double &bench)
{
std::cout << s << "(" << v.getRows() << "," << v.getCols() << ") = [" << v << "]" << std::endl;
for (unsigned int i = 0; i < v.size(); i++) {
if (std::fabs(v[i] - bench) > std::fabs(v[i]) * std::numeric_limits<double>::epsilon()) {
std::cout << "Test fails: bad content" << std::endl;
return false;
}
}
return true;
}
bool test_matrix_equal(const vpHomogeneousMatrix &M1, const vpHomogeneousMatrix &M2, double epsilon = 1e-10)
{
for (unsigned int i = 0; i < 4; i++) {
for (unsigned int j = 0; j < 4; j++) {
if (!vpMath::equal(M1[i][j], M2[i][j], epsilon)) {
return false;
}
}
}
return true;
}
TEST_CASE("Common rotation operations", "[rotation]")
{
SECTION("Theta u initialization")
{
std::vector<double> bench1(3, vpMath::rad(10));
vpColVector bench3(3, vpMath::rad(10));
CHECK(test("r1", r1, bench1));
bench1.clear();
bench1 = r1.toStdVector();
CHECK(test("r1", r1, bench1));
r1.build(bench3);
CHECK(test("r1", r1, bench3));
vpThetaUVector r2 = r1;
CHECK(test("r2", r2, bench1));
CHECK(r2.data != r1.data);
CHECK(test("r2", r2, vpMath::rad(10)));
r3 = vpMath::rad(10);
CHECK(test("r3", r3, bench1));
for (unsigned int i = 0; i < r3.size(); i++) {
CHECK(std::fabs(r3[i] - bench1[i]) < std::fabs(r3[i]) * std::numeric_limits<double>::epsilon());
}
const vpColVector r4 = 0.5 * r1;
std::vector<double> bench2(3, vpMath::rad(5));
CHECK(test("r4", r4, bench2));
const vpThetaUVector r5(r3);
CHECK(test("r5", r5, bench1));
}
SECTION("Rxyz initialization")
{
std::vector<double> bench1(3, vpMath::rad(10));
vpColVector bench3(3, vpMath::rad(10));
CHECK(test("r1", r1, bench1));
bench1.clear();
bench1 = r1.toStdVector();
CHECK(test("r1", r1, bench1));
r1.build(bench3);
CHECK(test("r1", r1, bench3));
vpRxyzVector r2 = r1;
CHECK(test("r2", r2, bench1));
CHECK(test("r2", r2, vpMath::rad(10)));
r3 = vpMath::rad(10);
CHECK(test("r3", r3, bench1));
for (unsigned int i = 0; i < r3.size(); i++) {
CHECK(std::fabs(r3[i] - bench1[i]) <= std::fabs(r3[i]) * std::numeric_limits<double>::epsilon());
}
vpColVector r4 = 0.5 * r1;
std::vector<double> bench2(3, vpMath::rad(5));
CHECK(test("r4", r4, bench2));
vpRxyzVector r5(r3);
CHECK(test("r5", r5, bench1));
}
SECTION("rzyx initialization")
{
std::vector<double> bench1(3, vpMath::rad(10));
vpColVector bench3(3, vpMath::rad(10));
CHECK(test("r1", r1, bench1));
bench1.clear();
bench1 = r1.toStdVector();
CHECK(test("r1", r1, bench1));
r1.build(bench3);
CHECK(test("r1", r1, bench3));
vpRzyxVector r2 = r1;
CHECK(test("r2", r2, bench1));
CHECK(test("r2", r2, vpMath::rad(10)));
r3 = vpMath::rad(10);
CHECK(test("r3", r3, bench1));
for (unsigned int i = 0; i < r3.size(); i++) {
CHECK(std::fabs(r3[i] - bench1[i]) <= std::fabs(r3[i]) * std::numeric_limits<double>::epsilon());
}
vpColVector r4 = 0.5 * r1;
std::vector<double> bench2(3, vpMath::rad(5));
CHECK(test("r4", r4, bench2));
vpRzyxVector r5(r3);
CHECK(test("r5", r5, bench1));
}
SECTION("rzyz initialiation")
{
std::vector<double> bench1(3, vpMath::rad(10));
vpColVector bench3(3, vpMath::rad(10));
CHECK(test("r1", r1, bench1));
bench1.clear();
bench1 = r1.toStdVector();
CHECK(test("r1", r1, bench1));
r1.build(bench3);
CHECK(test("r1", r1, bench3));
vpRzyzVector r2 = r1;
CHECK(test("r2", r2, bench1));
CHECK(test("r2", r2, vpMath::rad(10)));
r3 = vpMath::rad(10);
CHECK(test("r3", r3, bench1));
for (unsigned int i = 0; i < r3.size(); i++) {
CHECK(std::fabs(r3[i] - bench1[i]) <= std::fabs(r3[i]) * std::numeric_limits<double>::epsilon());
}
vpColVector r4 = 0.5 * r1;
std::vector<double> bench2(3, vpMath::rad(5));
CHECK(test("r4", r4, bench2));
vpRzyzVector r5(r3);
CHECK(test("r5", r5, bench1));
}
SECTION("Test quaternion initialization", "[quaternion]")
{
std::vector<double> bench1(4, vpMath::rad(10));
vpColVector bench3(4, vpMath::rad(10));
CHECK(test("r1", r1, bench1));
bench1.clear();
bench1 = r1.toStdVector();
CHECK(test("r1", r1, bench1));
r1.build(bench3);
CHECK(test("r1", r1, bench3));
CHECK(test("r2", r2, bench1));
CHECK(test("r2", r2, vpMath::rad(10)));
CHECK(test("r3", r3, bench1));
for (unsigned int i = 0; i < r3.size(); i++) {
CHECK(std::fabs(r3[i] - bench1[i]) <= std::fabs(r3[i]) * std::numeric_limits<double>::epsilon());
}
vpColVector r4 = 0.5 * r1;
std::vector<double> bench2(4, vpMath::rad(5));
CHECK(test("r4", r4, bench2));
CHECK(test("r5", r5, bench1));
}
SECTION("Conversions")
{
for (int i = -10; i < 10; i++) {
for (int j = -10; j < 10; j++) {
vpThetaUVector tu(vpMath::rad(90 + i), vpMath::rad(170 + j), vpMath::rad(45));
tu.build(vpRotationMatrix(tu)); // put some coherence into rotation convention
std::cout << "Initialization " << std::endl;
double theta;
tu.extract(theta, u);
std::cout << "theta=" << vpMath::deg(theta) << std::endl;
std::cout << "u=" << u << std::endl;
std::cout << "From vpThetaUVector to vpRotationMatrix " << std::endl;
R.build(tu);
std::cout << "Matrix R";
CHECK(R.isARotationMatrix());
std::cout << R << std::endl;
std::cout << "From vpRotationMatrix to vpQuaternionVector " << std::endl;
CHECK(q.magnitude() == Approx(1.0).margin(1e-4));
std::cout << q << std::endl;
R.build(q);
CHECK(R.isARotationMatrix());
std::cout << "From vpQuaternionVector to vpRotationMatrix " << std::endl;
std::cout << "From vpRotationMatrix to vpRxyzVector " << std::endl;
vpRxyzVector RxyzbuildR(R);
std::cout << RxyzbuildR << std::endl;
std::cout << "From vpRxyzVector to vpThetaUVector " << std::endl;
std::cout << " use From vpRxyzVector to vpRotationMatrix " << std::endl;
std::cout << " use From vpRotationMatrix to vpThetaUVector " << std::endl;
vpThetaUVector tubuildEu;
tubuildEu.build(R);
std::cout << std::endl;
std::cout << "result : should equivalent to the first one " << std::endl;
double theta2;
tubuildEu.extract(theta2, u2);
std::cout << "theta=" << vpMath::deg(theta2) << std::endl;
std::cout << "u=" << u2 << std::endl;
CHECK(vpMath::abs(theta2 - theta) < std::numeric_limits<double>::epsilon() * 1e10);
CHECK(vpMath::abs(u[0] - u2[0]) < std::numeric_limits<double>::epsilon() * 1e10);
CHECK(vpMath::abs(u[1] - u2[1]) < std::numeric_limits<double>::epsilon() * 1e10);
CHECK(vpMath::abs(u[2] - u2[2]) < std::numeric_limits<double>::epsilon() * 1e10);
}
}
SECTION("Conversion from and to rzyz vector")
{
std::cout << "Initialization vpRzyzVector " << std::endl;
std::cout << rzyz << std::endl;
std::cout << "From vpRzyzVector to vpRotationMatrix " << std::endl;
R.build(rzyz);
CHECK(R.isARotationMatrix());
std::cout << "From vpRotationMatrix to vpRzyzVector " << std::endl;
vpRzyzVector rzyz_final;
rzyz_final.build(R);
CHECK(test("rzyz", rzyz_final, vpColVector(rzyz)));
std::cout << rzyz_final << std::endl;
}
SECTION("Conversion from and to rzyx vector")
{
std::cout << "Initialization vpRzyxVector " << std::endl;
std::cout << rzyx << std::endl;
std::cout << "From vpRzyxVector to vpRotationMatrix " << std::endl;
R.build(rzyx);
CHECK(R.isARotationMatrix());
std::cout << R << std::endl;
std::cout << "From vpRotationMatrix to vpRzyxVector " << std::endl;
vpRzyxVector rzyx_final;
rzyx_final.build(R);
bool ret = test("rzyx", rzyx_final, vpColVector(rzyx));
if (ret == false) {
// Euler angle representation is not unique
std::cout << "Rzyx vector differ. Test rotation matrix..." << std::endl;
vpRotationMatrix RR(rzyx_final);
if (R == RR) {
std::cout << "Rzyx vector differ but rotation matrix is valid" << std::endl;
ret = true;
}
}
CHECK(ret);
std::cout << rzyx_final << std::endl;
}
}
SECTION("Rotation matrix extraction from homogeneous matrix and multiplication")
{
// Test rotation_matrix * homogeneous_matrix
vpHomogeneousMatrix _1_M_2_truth;
_1_M_2_truth[0][0] = 0.9835;
_1_M_2_truth[0][1] = -0.0581;
_1_M_2_truth[0][2] = 0.1716;
_1_M_2_truth[0][3] = 0;
_1_M_2_truth[1][0] = -0.0489;
_1_M_2_truth[1][1] = -0.9972;
_1_M_2_truth[1][2] = -0.0571;
_1_M_2_truth[1][3] = 0;
_1_M_2_truth[2][0] = 0.1744;
_1_M_2_truth[2][1] = 0.0478;
_1_M_2_truth[2][2] = -0.9835;
_1_M_2_truth[2][3] = 0;
_2_M_3_[0][0] = 0.9835;
_2_M_3_[0][1] = -0.0581;
_2_M_3_[0][2] = 0.1716;
_2_M_3_[0][3] = 0.0072;
_2_M_3_[1][0] = -0.0489;
_2_M_3_[1][1] = -0.9972;
_2_M_3_[1][2] = -0.0571;
_2_M_3_[1][3] = 0.0352;
_2_M_3_[2][0] = 0.1744;
_2_M_3_[2][1] = 0.0478;
_2_M_3_[2][2] = -0.9835;
_2_M_3_[2][3] = 0.9470;
vpRotationMatrix _1_R_2_ = _1_M_2_truth.getRotationMatrix();
vpHomogeneousMatrix _1_M_3_(_1_R_2_* _2_M_3_);
vpHomogeneousMatrix _1_M_3_truth(_1_M_2_truth * _2_M_3_);
CHECK(test_matrix_equal(_1_M_3_, _1_M_3_truth));
}
}
TEST_CASE("Theta u multiplication", "[theta.u]")
{
const int nTrials = 100;
const uint64_t seed = 0x123456789;
vpUniRand rng(seed);
for (int iter = 0; iter < nTrials; iter++) {
const vpThetaUVector tu0 = generateThetaU(rng);
const vpThetaUVector tu1 = generateThetaU(rng);
const vpRotationMatrix c1Rc2(tu0);
const vpRotationMatrix c2Rc3(tu1);
const vpRotationMatrix c1Rc3_ref = c1Rc2 * c2Rc3;
const vpThetaUVector c1_tu_c3 = tu0 * tu1;
// two rotation vectors can represent the same rotation,
// that is why we compare the rotation matrices
const vpRotationMatrix c1Rc3(c1_tu_c3);
const double tolerance = 1e-9;
for (unsigned int i = 0; i < 3; i++) {
for (unsigned int j = 0; j < 3; j++) {
CHECK(c1Rc3_ref[i][j] == Approx(c1Rc3[i][j]).epsilon(0).margin(tolerance));
}
}
}
}
TEST_CASE("Quaternion multiplication", "[quaternion]")
{
const int nTrials = 100;
const uint64_t seed = 0x123456789;
vpUniRand rng(seed);
for (int iter = 0; iter < nTrials; iter++) {
const vpQuaternionVector q0 = generateQuat(rng);
const vpQuaternionVector q1 = generateQuat(rng);
const vpRotationMatrix c1Rc2(q0);
const vpRotationMatrix c2Rc3(q1);
const vpRotationMatrix c1Rc3_ref = c1Rc2 * c2Rc3;
const vpQuaternionVector c1_q_c3 = q0 * q1;
// two quaternions of opposite sign can represent the same rotation,
// that is why we compare the rotation matrices
const vpRotationMatrix c1Rc3(c1_q_c3);
const double tolerance = 1e-9;
for (unsigned int i = 0; i < 3; i++) {
for (unsigned int j = 0; j < 3; j++) {
CHECK(c1Rc3_ref[i][j] == Approx(c1Rc3[i][j]).epsilon(0).margin(tolerance));
}
}
}
}
int main(int argc, char *argv[])
{
Catch::Session session; // There must be exactly one instance
// Let Catch (using Clara) parse the command line
session.applyCommandLine(argc, argv);
int numFailed = session.run();
// numFailed is clamped to 255 as some unices only use the lower 8 bits.
// This clamping has already been applied, so just return it here
// You can also do any post run clean-up here
return numFailed;
}
#else
#include <iostream>
int main() { return EXIT_SUCCESS; }
#endif
unsigned int getCols() const
Definition: vpArray2D.h:329
Type * data
Address of the first element of the data array.
Definition: vpArray2D.h:139
unsigned int size() const
Return the number of elements of the 2D array.
Definition: vpArray2D.h:341
unsigned int getRows() const
Definition: vpArray2D.h:339
Implementation of column vector and the associated operations.
Definition: vpColVector.h:163
vpColVector extract(unsigned int r, unsigned int colsize) const
Definition: vpColVector.h:369
Implementation of an homogeneous matrix and operations on such kind of matrices.
vpRotationMatrix getRotationMatrix() const
static double rad(double deg)
Definition: vpMath.h:127
static Type abs(const Type &x)
Definition: vpMath.h:267
static bool equal(double x, double y, double threshold=0.001)
Definition: vpMath.h:454
static double deg(double rad)
Definition: vpMath.h:117
Implementation of a rotation vector as quaternion angle minimal representation.
void set(double x, double y, double z, double w)
Implementation of a rotation matrix and operations on such kind of matrices.
vpRotationMatrix & build(const vpHomogeneousMatrix &M)
bool isARotationMatrix(double threshold=1e-6) const
Implementation of a generic rotation vector.
Implementation of a rotation vector as Euler angle minimal representation.
Definition: vpRxyzVector.h:177
Implementation of a rotation vector as Euler angle minimal representation.
Definition: vpRzyxVector.h:178
vpRzyxVector & build(const vpRotationMatrix &R)
Implementation of a rotation vector as Euler angle minimal representation.
Definition: vpRzyzVector.h:176
vpRzyzVector & build(const vpRotationMatrix &R)
Implementation of a rotation vector as axis-angle minimal representation.
vpThetaUVector & build(const vpHomogeneousMatrix &M)
void extract(double &theta, vpColVector &u) const
Class for generating random numbers with uniform probability density.
Definition: vpUniRand.h:123
int uniform(int a, int b)
Definition: vpUniRand.cpp:159