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// test file for HSO3.hpp and HSO4.hpp
// (C) Copyright Hubert Holin 2001.
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
#include <iostream>
#include <boost/math/quaternion.hpp>
#include "HSO3.hpp"
#include "HSO4.hpp"
const int number_of_intervals = 5;
const float pi = ::std::atan(1.0f)*4;
void test_SO3();
void test_SO4();
int main()
{
test_SO3();
test_SO4();
::std::cout << "That's all folks!" << ::std::endl;
}
//
// Test of quaternion and R^3 rotation relationship
//
void test_SO3_spherical()
{
::std::cout << "Testing spherical:" << ::std::endl;
::std::cout << ::std::endl;
const float rho = 1.0f;
float theta;
float phi1;
float phi2;
for (int idxphi2 = 0; idxphi2 <= number_of_intervals; idxphi2++)
{
phi2 = (-pi/2)+(idxphi2*pi)/number_of_intervals;
for (int idxphi1 = 0; idxphi1 <= number_of_intervals; idxphi1++)
{
phi1 = (-pi/2)+(idxphi1*pi)/number_of_intervals;
for (int idxtheta = 0; idxtheta <= number_of_intervals; idxtheta++)
{
theta = -pi+(idxtheta*(2*pi))/number_of_intervals;
::std::cout << "theta = " << theta << " ; ";
::std::cout << "phi1 = " << phi1 << " ; ";
::std::cout << "phi2 = " << phi2;
::std::cout << ::std::endl;
::boost::math::quaternion<float> q = ::boost::math::spherical(rho, theta, phi1, phi2);
::std::cout << "q = " << q << ::std::endl;
R3_matrix<float> rot = quaternion_to_R3_rotation(q);
::std::cout << "rot = ";
::std::cout << "\t" << rot.a11 << "\t" << rot.a12 << "\t" << rot.a13 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a21 << "\t" << rot.a22 << "\t" << rot.a23 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a31 << "\t" << rot.a32 << "\t" << rot.a33 << ::std::endl;
::boost::math::quaternion<float> p = R3_rotation_to_quaternion(rot, &q);
::std::cout << "p = " << p << ::std::endl;
::std::cout << "round trip discrepancy: " << ::boost::math::abs(q-p) << ::std::endl;
::std::cout << ::std::endl;
}
}
}
::std::cout << ::std::endl;
}
void test_SO3_semipolar()
{
::std::cout << "Testing semipolar:" << ::std::endl;
::std::cout << ::std::endl;
const float rho = 1.0f;
float alpha;
float theta1;
float theta2;
for (int idxalpha = 0; idxalpha <= number_of_intervals; idxalpha++)
{
alpha = (idxalpha*(pi/2))/number_of_intervals;
for (int idxtheta1 = 0; idxtheta1 <= number_of_intervals; idxtheta1++)
{
theta1 = -pi+(idxtheta1*(2*pi))/number_of_intervals;
for (int idxtheta2 = 0; idxtheta2 <= number_of_intervals; idxtheta2++)
{
theta2 = -pi+(idxtheta2*(2*pi))/number_of_intervals;
::std::cout << "alpha = " << alpha << " ; ";
::std::cout << "theta1 = " << theta1 << " ; ";
::std::cout << "theta2 = " << theta2;
::std::cout << ::std::endl;
::boost::math::quaternion<float> q = ::boost::math::semipolar(rho, alpha, theta1, theta2);
::std::cout << "q = " << q << ::std::endl;
R3_matrix<float> rot = quaternion_to_R3_rotation(q);
::std::cout << "rot = ";
::std::cout << "\t" << rot.a11 << "\t" << rot.a12 << "\t" << rot.a13 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a21 << "\t" << rot.a22 << "\t" << rot.a23 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a31 << "\t" << rot.a32 << "\t" << rot.a33 << ::std::endl;
::boost::math::quaternion<float> p = R3_rotation_to_quaternion(rot, &q);
::std::cout << "p = " << p << ::std::endl;
::std::cout << "round trip discrepancy: " << ::boost::math::abs(q-p) << ::std::endl;
::std::cout << ::std::endl;
}
}
}
::std::cout << ::std::endl;
}
void test_SO3_multipolar()
{
::std::cout << "Testing multipolar:" << ::std::endl;
::std::cout << ::std::endl;
float rho1;
float rho2;
float theta1;
float theta2;
for (int idxrho = 0; idxrho <= number_of_intervals; idxrho++)
{
rho1 = (idxrho*1.0f)/number_of_intervals;
rho2 = ::std::sqrt(1.0f-rho1*rho1);
for (int idxtheta1 = 0; idxtheta1 <= number_of_intervals; idxtheta1++)
{
theta1 = -pi+(idxtheta1*(2*pi))/number_of_intervals;
for (int idxtheta2 = 0; idxtheta2 <= number_of_intervals; idxtheta2++)
{
theta2 = -pi+(idxtheta2*(2*pi))/number_of_intervals;
::std::cout << "rho1 = " << rho1 << " ; ";
::std::cout << "theta1 = " << theta1 << " ; ";
::std::cout << "theta2 = " << theta2;
::std::cout << ::std::endl;
::boost::math::quaternion<float> q = ::boost::math::multipolar(rho1, theta1, rho2, theta2);
::std::cout << "q = " << q << ::std::endl;
R3_matrix<float> rot = quaternion_to_R3_rotation(q);
::std::cout << "rot = ";
::std::cout << "\t" << rot.a11 << "\t" << rot.a12 << "\t" << rot.a13 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a21 << "\t" << rot.a22 << "\t" << rot.a23 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a31 << "\t" << rot.a32 << "\t" << rot.a33 << ::std::endl;
::boost::math::quaternion<float> p = R3_rotation_to_quaternion(rot, &q);
::std::cout << "p = " << p << ::std::endl;
::std::cout << "round trip discrepancy: " << ::boost::math::abs(q-p) << ::std::endl;
::std::cout << ::std::endl;
}
}
}
::std::cout << ::std::endl;
}
void test_SO3_cylindrospherical()
{
::std::cout << "Testing cylindrospherical:" << ::std::endl;
::std::cout << ::std::endl;
float t;
float radius;
float longitude;
float latitude;
for (int idxt = 0; idxt <= number_of_intervals; idxt++)
{
t = -1.0f+(idxt*2.0f)/number_of_intervals;
radius = ::std::sqrt(1.0f-t*t);
for (int idxlatitude = 0; idxlatitude <= number_of_intervals; idxlatitude++)
{
latitude = (-pi/2)+(idxlatitude*pi)/number_of_intervals;
for (int idxlongitude = 0; idxlongitude <= number_of_intervals; idxlongitude++)
{
longitude = -pi+(idxlongitude*(2*pi))/number_of_intervals;
::std::cout << "t = " << t << " ; ";
::std::cout << "longitude = " << longitude;
::std::cout << "latitude = " << latitude;
::std::cout << ::std::endl;
::boost::math::quaternion<float> q = ::boost::math::cylindrospherical(t, radius, longitude, latitude);
::std::cout << "q = " << q << ::std::endl;
R3_matrix<float> rot = quaternion_to_R3_rotation(q);
::std::cout << "rot = ";
::std::cout << "\t" << rot.a11 << "\t" << rot.a12 << "\t" << rot.a13 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a21 << "\t" << rot.a22 << "\t" << rot.a23 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a31 << "\t" << rot.a32 << "\t" << rot.a33 << ::std::endl;
::boost::math::quaternion<float> p = R3_rotation_to_quaternion(rot, &q);
::std::cout << "p = " << p << ::std::endl;
::std::cout << "round trip discrepancy: " << ::boost::math::abs(q-p) << ::std::endl;
::std::cout << ::std::endl;
}
}
}
::std::cout << ::std::endl;
}
void test_SO3_cylindrical()
{
::std::cout << "Testing cylindrical:" << ::std::endl;
::std::cout << ::std::endl;
float r;
float angle;
float h1;
float h2;
for (int idxh2 = 0; idxh2 <= number_of_intervals; idxh2++)
{
h2 = -1.0f+(idxh2*2.0f)/number_of_intervals;
for (int idxh1 = 0; idxh1 <= number_of_intervals; idxh1++)
{
h1 = ::std::sqrt(1.0f-h2*h2)*(-1.0f+(idxh2*2.0f)/number_of_intervals);
r = ::std::sqrt(1.0f-h1*h1-h2*h2);
for (int idxangle = 0; idxangle <= number_of_intervals; idxangle++)
{
angle = -pi+(idxangle*(2*pi))/number_of_intervals;
::std::cout << "angle = " << angle << " ; ";
::std::cout << "h1 = " << h1;
::std::cout << "h2 = " << h2;
::std::cout << ::std::endl;
::boost::math::quaternion<float> q = ::boost::math::cylindrical(r, angle, h1, h2);
::std::cout << "q = " << q << ::std::endl;
R3_matrix<float> rot = quaternion_to_R3_rotation(q);
::std::cout << "rot = ";
::std::cout << "\t" << rot.a11 << "\t" << rot.a12 << "\t" << rot.a13 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a21 << "\t" << rot.a22 << "\t" << rot.a23 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a31 << "\t" << rot.a32 << "\t" << rot.a33 << ::std::endl;
::boost::math::quaternion<float> p = R3_rotation_to_quaternion(rot, &q);
::std::cout << "p = " << p << ::std::endl;
::std::cout << "round trip discrepancy: " << ::boost::math::abs(q-p) << ::std::endl;
::std::cout << ::std::endl;
}
}
}
::std::cout << ::std::endl;
}
void test_SO3()
{
::std::cout << "Testing SO3:" << ::std::endl;
::std::cout << ::std::endl;
test_SO3_spherical();
test_SO3_semipolar();
test_SO3_multipolar();
test_SO3_cylindrospherical();
test_SO3_cylindrical();
}
//
// Test of quaternion and R^4 rotation relationship
//
void test_SO4_spherical()
{
::std::cout << "Testing spherical:" << ::std::endl;
::std::cout << ::std::endl;
const float rho1 = 1.0f;
const float rho2 = 1.0f;
float theta1;
float phi11;
float phi21;
float theta2;
float phi12;
float phi22;
for (int idxphi21 = 0; idxphi21 <= number_of_intervals; idxphi21++)
{
phi21 = (-pi/2)+(idxphi21*pi)/number_of_intervals;
for (int idxphi22 = 0; idxphi22 <= number_of_intervals; idxphi22++)
{
phi22 = (-pi/2)+(idxphi22*pi)/number_of_intervals;
for (int idxphi11 = 0; idxphi11 <= number_of_intervals; idxphi11++)
{
phi11 = (-pi/2)+(idxphi11*pi)/number_of_intervals;
for (int idxphi12 = 0; idxphi12 <= number_of_intervals; idxphi12++)
{
phi12 = (-pi/2)+(idxphi12*pi)/number_of_intervals;
for (int idxtheta1 = 0; idxtheta1 <= number_of_intervals; idxtheta1++)
{
theta1 = -pi+(idxtheta1*(2*pi))/number_of_intervals;
for (int idxtheta2 = 0; idxtheta2 <= number_of_intervals; idxtheta2++)
{
theta2 = -pi+(idxtheta2*(2*pi))/number_of_intervals;
::std::cout << "theta1 = " << theta1 << " ; ";
::std::cout << "phi11 = " << phi11 << " ; ";
::std::cout << "phi21 = " << phi21;
::std::cout << "theta2 = " << theta2 << " ; ";
::std::cout << "phi12 = " << phi12 << " ; ";
::std::cout << "phi22 = " << phi22;
::std::cout << ::std::endl;
::boost::math::quaternion<float> p1 = ::boost::math::spherical(rho1, theta1, phi11, phi21);
::std::cout << "p1 = " << p1 << ::std::endl;
::boost::math::quaternion<float> q1 = ::boost::math::spherical(rho2, theta2, phi12, phi22);
::std::cout << "q1 = " << q1 << ::std::endl;
::std::pair< ::boost::math::quaternion<float> , ::boost::math::quaternion<float> > pq1 =
::std::make_pair(p1,q1);
R4_matrix<float> rot = quaternions_to_R4_rotation(pq1);
::std::cout << "rot = ";
::std::cout << "\t" << rot.a11 << "\t" << rot.a12 << "\t" << rot.a13 << "\t" << rot.a14 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a21 << "\t" << rot.a22 << "\t" << rot.a23 << "\t" << rot.a24 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a31 << "\t" << rot.a32 << "\t" << rot.a33 << "\t" << rot.a34 << ::std::endl;
::std::cout << "\t";
::std::cout << "\t" << rot.a41 << "\t" << rot.a42 << "\t" << rot.a43 << "\t" << rot.a44 << ::std::endl;
::std::pair< ::boost::math::quaternion<float> , ::boost::math::quaternion<float> > pq2 =
R4_rotation_to_quaternions(rot, &pq1);
::std::cout << "p1 = " << pq2.first << ::std::endl;
::std::cout << "p2 = " << pq2.second << ::std::endl;
::std::cout << "round trip discrepancy: " << ::std::sqrt(::boost::math::norm(pq1.first-pq2.first)+::boost::math::norm(pq1.second-pq2.second)) << ::std::endl;
::std::cout << ::std::endl;
}
}
}
}
}
}
::std::cout << ::std::endl;
}
void test_SO4()
{
::std::cout << "Testing SO4:" << ::std::endl;
::std::cout << ::std::endl;
test_SO4_spherical();
}
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