// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

#include "main.h"
#include <Eigen/Geometry>

template<typename Scalar> void geometry(void)
{
  /* this test covers the following files:
     Cross.h Quaternion.h, Transform.cpp
  */

  typedef Matrix<Scalar,3,3> Matrix3;
  typedef Matrix<Scalar,4,4> Matrix4;
  typedef Matrix<Scalar,3,1> Vector3;
  typedef Matrix<Scalar,4,1> Vector4;
  typedef Quaternion<Scalar> Quaternion;

  Quaternion q1, q2;
  Vector3 v0 = Vector3::random(),
    v1 = Vector3::random(),
    v2 = Vector3::random();

  Scalar a;

  q1.fromAngleAxis(ei_random<Scalar>(-M_PI, M_PI), v0.normalized());
  q2.fromAngleAxis(ei_random<Scalar>(-M_PI, M_PI), v1.normalized());

  // rotation matrix conversion
//   VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
//   VERIFY_IS_APPROX(q1 * q2 * v2,
//     q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
//   VERIFY_IS_NOT_APPROX(q2 * q1 * v2,
//     q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
//   q2.fromRotationMatrix(q1.toRotationMatrix());
//   VERIFY_IS_APPROX(q1*v1,q2*v1);
//
//   // Euler angle conversion
//   VERIFY_IS_APPROX(q2.fromEulerAngles(q1.toEulerAngles()) * v1, q1 * v1);
//   v2 = q2.toEulerAngles();
//   VERIFY_IS_APPROX(q2.fromEulerAngles(v2).toEulerAngles(), v2);
//   VERIFY_IS_NOT_APPROX(q2.fromEulerAngles(v2.cwiseProduct(Vector3(0.2,-0.2,1))).toEulerAngles(), v2);
//
//   // angle-axis conversion
//   q1.toAngleAxis(a, v2);
//   VERIFY_IS_APPROX(q1 * v1, q2.fromAngleAxis(a,v2) * v1);
//   VERIFY_IS_NOT_APPROX(q1 * v1, q2.fromAngleAxis(2*a,v2) * v1);
//
//   // from two vector creation
//   VERIFY_IS_APPROX(v2.normalized(),(q2.fromTwoVectors(v1,v2)*v1).normalized());
//   VERIFY_IS_APPROX(v2.normalized(),(q2.fromTwoVectors(v1,v2)*v1).normalized());
//
//   // inverse and conjugate
//   VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
//   VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);

  // cross product
  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
  Matrix3 m;
  m << v0.normalized(),
      (v0.cross(v1)).normalized(),
      (v0.cross(v1).cross(v0)).normalized();
  VERIFY(m.isOrtho());

  // Transform
  // TODO complete the tests !
  typedef Transform<Scalar,2> Transform2;
  typedef Transform<Scalar,3> Transform3;

  a = 0;
  while (ei_abs(a)<0.1)
    a = ei_random<Scalar>(-0.4*M_PI, 0.4*M_PI);
  q1.fromAngleAxis(a, v0.normalized());
  Transform3 t0, t1, t2;
  t0.setIdentity();
  t0.affine() = q1.toRotationMatrix();
  t1.setIdentity();
  t1.affine() = q1.toRotationMatrix();

  v0 << 50, 2, 1;//= Vector3::random().cwiseProduct(Vector3(10,2,0.5));
  t0.scale(v0);
  t1.prescale(v0);

  VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
  VERIFY_IS_NOT_APPROX((t1 * Vector3(1,0,0)).norm(), v0.x());

  t0.setIdentity();
  t1.setIdentity();
  v1 << 1, 2, 3;
  t0.affine() = q1.toRotationMatrix();
  t0.pretranslate(v0);
  t0.scale(v1);
  t1.affine() = q1.conjugate().toRotationMatrix();
  t1.prescale(v1.cwiseInverse());
  t1.translate(-v0);

  VERIFY((t0.matrix() * t1.matrix()).isIdentity());
}

void test_geometry()
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( geometry<float>() );
//     CALL_SUBTEST( geometry<double>() );
  }
}