test/geo_quaternion.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Geometry>
#include <Eigen/LU>
#include <Eigen/SVD>
#include "AnnoyingScalar.h"

template <typename T>
T bounded_acos(T v) {
  using std::acos;
  using std::max;
  using std::min;
  return acos((max)(T(-1), (min)(v, T(1))));
}

template <typename QuatType>
void check_slerp(const QuatType& q0, const QuatType& q1) {
  using std::abs;
  typedef typename QuatType::Scalar Scalar;
  typedef AngleAxis<Scalar> AA;

  Scalar largeEps = test_precision<Scalar>();

  Scalar theta_tot = AA(q1 * q0.inverse()).angle();
  if (theta_tot > Scalar(EIGEN_PI)) theta_tot = Scalar(2.) * Scalar(EIGEN_PI) - theta_tot;
  for (Scalar t = 0; t <= Scalar(1.001); t += Scalar(0.1)) {
    QuatType q = q0.slerp(t, q1);
    Scalar theta = AA(q * q0.inverse()).angle();
    VERIFY(abs(q.norm() - 1) < largeEps);
    if (theta_tot == 0)
      VERIFY(theta_tot == 0);
    else
      VERIFY(abs(theta - t * theta_tot) < largeEps);
  }
}

template <typename Scalar, int Options>
void quaternion(void) {
  /* this test covers the following files:
     Quaternion.h
  */
  using std::abs;
  typedef Matrix<Scalar, 3, 1> Vector3;
  typedef Matrix<Scalar, 3, 3> Matrix3;
  typedef Quaternion<Scalar, Options> Quaternionx;
  typedef AngleAxis<Scalar> AngleAxisx;

  Scalar largeEps = test_precision<Scalar>();
  if (internal::is_same<Scalar, float>::value) largeEps = Scalar(1e-3);

  Scalar eps = internal::random<Scalar>() * Scalar(1e-2);

  Vector3 v0 = Vector3::Random(), v1 = Vector3::Random(), v2 = Vector3::Random(), v3 = Vector3::Random();

  Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)),
         b = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));

  // Quaternion: Identity(), setIdentity();
  Quaternionx q1, q2;
  q2.setIdentity();
  VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
  q1.coeffs().setRandom();
  VERIFY_IS_APPROX(q1.coeffs(), (q1 * q2).coeffs());

#ifndef EIGEN_NO_IO
  // Printing
  std::ostringstream ss;
  ss << q2;
  VERIFY(ss.str() == "0i + 0j + 0k + 1");
#endif

  // concatenation
  q1 *= q2;

  q1 = AngleAxisx(a, v0.normalized());
  q2 = AngleAxisx(a, v1.normalized());

  // angular distance
  Scalar refangle = abs(AngleAxisx(q1.inverse() * q2).angle());
  if (refangle > Scalar(EIGEN_PI)) refangle = Scalar(2) * Scalar(EIGEN_PI) - refangle;

  if ((q1.coeffs() - q2.coeffs()).norm() > Scalar(10) * largeEps) {
    VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));
  }

  // Action on vector by the q v q* formula
  VERIFY_IS_APPROX(q1 * v2, (q1 * Quaternionx(Scalar(0), v2) * q1.inverse()).vec());
  VERIFY_IS_APPROX(q1.inverse() * v2, (q1.inverse() * Quaternionx(Scalar(0), v2) * q1).vec());

  // rotation matrix conversion
  VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
  VERIFY_IS_APPROX(q1 * q2 * v2, q1.toRotationMatrix() * q2.toRotationMatrix() * v2);

  VERIFY((q2 * q1).isApprox(q1 * q2, largeEps) ||
         !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));

  q2 = q1.toRotationMatrix();
  VERIFY_IS_APPROX(q1 * v1, q2 * v1);

  Matrix3 rot1(q1);
  VERIFY_IS_APPROX(q1 * v1, rot1 * v1);
  Quaternionx q3(rot1.transpose() * rot1);
  VERIFY_IS_APPROX(q3 * v1, v1);

  // angle-axis conversion
  AngleAxisx aa = AngleAxisx(q1);
  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);

  // Do not execute the test if the rotation angle is almost zero, or
  // the rotation axis and v1 are almost parallel.
  if (abs(aa.angle()) > Scalar(5) * test_precision<Scalar>() && (aa.axis() - v1.normalized()).norm() < Scalar(1.99) &&
      (aa.axis() + v1.normalized()).norm() < Scalar(1.99)) {
    VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle() * 2, aa.axis())) * v1);
  }

  // from two vector creation
  VERIFY_IS_APPROX(v2.normalized(), (q2.setFromTwoVectors(v1, v2) * v1).normalized());
  VERIFY_IS_APPROX(v1.normalized(), (q2.setFromTwoVectors(v1, v1) * v1).normalized());
  VERIFY_IS_APPROX(-v1.normalized(), (q2.setFromTwoVectors(v1, -v1) * v1).normalized());
  if (internal::is_same<Scalar, double>::value) {
    v3 = (v1.array() + eps).matrix();
    VERIFY_IS_APPROX(v3.normalized(), (q2.setFromTwoVectors(v1, v3) * v1).normalized());
    VERIFY_IS_APPROX(-v3.normalized(), (q2.setFromTwoVectors(v1, -v3) * v1).normalized());
  }

  // from two vector creation static function
  VERIFY_IS_APPROX(v2.normalized(), (Quaternionx::FromTwoVectors(v1, v2) * v1).normalized());
  VERIFY_IS_APPROX(v1.normalized(), (Quaternionx::FromTwoVectors(v1, v1) * v1).normalized());
  VERIFY_IS_APPROX(-v1.normalized(), (Quaternionx::FromTwoVectors(v1, -v1) * v1).normalized());
  if (internal::is_same<Scalar, double>::value) {
    v3 = (v1.array() + eps).matrix();
    VERIFY_IS_APPROX(v3.normalized(), (Quaternionx::FromTwoVectors(v1, v3) * v1).normalized());
    VERIFY_IS_APPROX(-v3.normalized(), (Quaternionx::FromTwoVectors(v1, -v3) * v1).normalized());
  }

  // inverse and conjugate
  VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
  VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);

  // test casting
  Quaternion<float> q1f = q1.template cast<float>();
  VERIFY_IS_APPROX(q1f.template cast<Scalar>(), q1);
  Quaternion<double> q1d = q1.template cast<double>();
  VERIFY_IS_APPROX(q1d.template cast<Scalar>(), q1);

  // test bug 369 - improper alignment.
  Quaternionx* q = new Quaternionx;
  delete q;

  q1 = Quaternionx::UnitRandom();
  q2 = Quaternionx::UnitRandom();
  check_slerp(q1, q2);

  q1 = AngleAxisx(b, v1.normalized());
  q2 = AngleAxisx(b + Scalar(EIGEN_PI), v1.normalized());
  check_slerp(q1, q2);

  q1 = AngleAxisx(b, v1.normalized());
  q2 = AngleAxisx(-b, -v1.normalized());
  check_slerp(q1, q2);

  q1 = Quaternionx::UnitRandom();
  q2.coeffs() = -q1.coeffs();
  check_slerp(q1, q2);
}

template <typename Scalar>
void mapQuaternion(void) {
  typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
  typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;
  typedef Map<Quaternion<Scalar> > MQuaternionUA;
  typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
  typedef Quaternion<Scalar> Quaternionx;
  typedef Matrix<Scalar, 3, 1> Vector3;
  typedef AngleAxis<Scalar> AngleAxisx;

  Vector3 v0 = Vector3::Random(), v1 = Vector3::Random();
  Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));

  EIGEN_ALIGN_MAX Scalar array1[4];
  EIGEN_ALIGN_MAX Scalar array2[4];
  EIGEN_ALIGN_MAX Scalar array3[4 + 1];
  Scalar* array3unaligned = array3 + 1;

  MQuaternionA mq1(array1);
  MCQuaternionA mcq1(array1);
  MQuaternionA mq2(array2);
  MQuaternionUA mq3(array3unaligned);
  MCQuaternionUA mcq3(array3unaligned);

  //  std::cerr << array1 << " " << array2 << " " << array3 << "\n";
  mq1 = AngleAxisx(a, v0.normalized());
  mq2 = mq1;
  mq3 = mq1;

  Quaternionx q1 = mq1;
  Quaternionx q2 = mq2;
  Quaternionx q3 = mq3;
  Quaternionx q4 = MCQuaternionUA(array3unaligned);

  VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());
  VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());
  VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());

  VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);
  VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);

  VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);
  VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);

  VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);
  VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);

  VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);
  VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);

  VERIFY_IS_APPROX(mq1 * mq2, q1 * q2);
  VERIFY_IS_APPROX(mq3 * mq2, q3 * q2);
  VERIFY_IS_APPROX(mcq1 * mq2, q1 * q2);
  VERIFY_IS_APPROX(mcq3 * mq2, q3 * q2);

  // Bug 1461, compilation issue with Map<const Quat>::w(), and other reference/constness checks:
  VERIFY_IS_APPROX(mcq3.coeffs().x() + mcq3.coeffs().y() + mcq3.coeffs().z() + mcq3.coeffs().w(), mcq3.coeffs().sum());
  VERIFY_IS_APPROX(mcq3.x() + mcq3.y() + mcq3.z() + mcq3.w(), mcq3.coeffs().sum());
  mq3.w() = 1;
  const Quaternionx& cq3(q3);
  VERIFY(&cq3.x() == &q3.x());
  const MQuaternionUA& cmq3(mq3);
  VERIFY(&cmq3.x() == &mq3.x());
  // FIXME the following should be ok. The problem is that currently the LValueBit flag
  // is used to determine whether we can return a coeff by reference or not, which is not enough for Map<const ...>.
  // const MCQuaternionUA& cmcq3(mcq3);
  // VERIFY( &cmcq3.x() == &mcq3.x() );

  // test cast
  {
    Quaternion<float> q1f = mq1.template cast<float>();
    VERIFY_IS_APPROX(q1f.template cast<Scalar>(), mq1);
    Quaternion<double> q1d = mq1.template cast<double>();
    VERIFY_IS_APPROX(q1d.template cast<Scalar>(), mq1);
  }
}

template <typename Scalar>
void quaternionAlignment(void) {
  typedef Quaternion<Scalar, AutoAlign> QuaternionA;
  typedef Quaternion<Scalar, DontAlign> QuaternionUA;

  EIGEN_ALIGN_MAX Scalar array1[4];
  EIGEN_ALIGN_MAX Scalar array2[4];
  EIGEN_ALIGN_MAX Scalar array3[4 + 1];
  Scalar* arrayunaligned = array3 + 1;

  QuaternionA* q1 = ::new (reinterpret_cast<void*>(array1)) QuaternionA;
  QuaternionUA* q2 = ::new (reinterpret_cast<void*>(array2)) QuaternionUA;
  QuaternionUA* q3 = ::new (reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;

  q1->coeffs().setRandom();
  *q2 = *q1;
  *q3 = *q1;

  VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());
  VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());
}

template <typename PlainObjectType>
void check_const_correctness(const PlainObjectType&) {
  // there's a lot that we can't test here while still having this test compile!
  // the only possible approach would be to run a script trying to compile stuff and checking that it fails.
  // CMake can help with that.

  // verify that map-to-const don't have LvalueBit
  typedef std::add_const_t<PlainObjectType> ConstPlainObjectType;
  VERIFY(!(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit));
  VERIFY(!(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit));
  VERIFY(!(Map<ConstPlainObjectType>::Flags & LvalueBit));
  VERIFY(!(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit));
}

// Regression for bug 1573
struct MovableClass {
  // The following line is a workaround for gcc 4.7 and 4.8 (see bug 1573 comments).
  static_assert(std::is_nothrow_move_constructible<Quaternionf>::value, "");
  MovableClass() = default;
  MovableClass(const MovableClass&) = default;
  MovableClass(MovableClass&&) noexcept = default;
  MovableClass& operator=(const MovableClass&) = default;
  MovableClass& operator=(MovableClass&&) = default;
  Quaternionf m_quat;
};

EIGEN_DECLARE_TEST(geo_quaternion) {
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1((quaternion<float, AutoAlign>()));
    CALL_SUBTEST_1(check_const_correctness(Quaternionf()));
    CALL_SUBTEST_1((quaternion<float, DontAlign>()));
    CALL_SUBTEST_1((quaternionAlignment<float>()));
    CALL_SUBTEST_1(mapQuaternion<float>());

    CALL_SUBTEST_2((quaternion<double, AutoAlign>()));
    CALL_SUBTEST_2(check_const_correctness(Quaterniond()));
    CALL_SUBTEST_2((quaternion<double, DontAlign>()));
    CALL_SUBTEST_2((quaternionAlignment<double>()));
    CALL_SUBTEST_2(mapQuaternion<double>());

#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
    AnnoyingScalar::dont_throw = true;
#endif
    CALL_SUBTEST_3((quaternion<AnnoyingScalar, AutoAlign>()));
  }
}