text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.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/QR>
  
  #include<iostream>
  using namespace std;
  
  template<typename T> EIGEN_DONT_INLINE
  void kill_extra_precision(T& x) { eigen_assert((void*)(&x) != (void*)0); }
  
  
  template<typename BoxType> void alignedbox(const BoxType& _box)
  {
    /* this test covers the following files:
       AlignedBox.h
    */
    typedef typename BoxType::Index Index;  
    typedef typename BoxType::Scalar Scalar;
    typedef typename NumTraits<Scalar>::Real RealScalar;
    typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
  
    const Index dim = _box.dim();
  
    VectorType p0 = VectorType::Random(dim);
    VectorType p1 = VectorType::Random(dim);
    while( p1 == p0 ){
        p1 =  VectorType::Random(dim); }
    RealScalar s1 = internal::random<RealScalar>(0,1);
  
    BoxType b0(dim);
    BoxType b1(VectorType::Random(dim),VectorType::Random(dim));
    BoxType b2;
    
    kill_extra_precision(b1);
    kill_extra_precision(p0);
    kill_extra_precision(p1);
  
    b0.extend(p0);
    b0.extend(p1);
    VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));
    VERIFY(b0.contains(b0.center()));
    VERIFY_IS_APPROX(b0.center(),(p0+p1)/Scalar(2));
  
    (b2 = b0).extend(b1);
    VERIFY(b2.contains(b0));
    VERIFY(b2.contains(b1));
    VERIFY_IS_APPROX(b2.clamp(b0), b0);
  
    // intersection
    BoxType box1(VectorType::Random(dim));
    box1.extend(VectorType::Random(dim));
    BoxType box2(VectorType::Random(dim));
    box2.extend(VectorType::Random(dim));
  
    VERIFY(box1.intersects(box2) == !box1.intersection(box2).isEmpty()); 
  
    // alignment -- make sure there is no memory alignment assertion
    BoxType *bp0 = new BoxType(dim);
    BoxType *bp1 = new BoxType(dim);
    bp0->extend(*bp1);
    delete bp0;
    delete bp1;
  
    // sampling
    for( int i=0; i<10; ++i )
    {
        VectorType r = b0.sample();
        VERIFY(b0.contains(r));
    }
  
  }
  
  
  
  template<typename BoxType>
  void alignedboxCastTests(const BoxType& _box)
  {
    // casting  
    typedef typename BoxType::Index Index;
    typedef typename BoxType::Scalar Scalar;
    typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
  
    const Index dim = _box.dim();
  
    VectorType p0 = VectorType::Random(dim);
    VectorType p1 = VectorType::Random(dim);
  
    BoxType b0(dim);
  
    b0.extend(p0);
    b0.extend(p1);
  
    const int Dim = BoxType::AmbientDimAtCompileTime;
    typedef typename GetDifferentType<Scalar>::type OtherScalar;
    AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();
    VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);
    AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();
    VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
  }
  
  
  void specificTest1()
  {
      Vector2f m; m << -1.0f, -2.0f;
      Vector2f M; M <<  1.0f,  5.0f;
  
      typedef AlignedBox2f  BoxType;
      BoxType box( m, M );
  
      Vector2f sides = M-m;
      VERIFY_IS_APPROX(sides, box.sizes() );
      VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
      VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
      VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
  
      VERIFY_IS_APPROX( 14.0f, box.volume() );
      VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() );
      VERIFY_IS_APPROX( std::sqrt( 53.0f ), box.diagonal().norm() );
  
      VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );
      VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) );
      Vector2f bottomRight; bottomRight << M[0], m[1];
      Vector2f topLeft; topLeft << m[0], M[1];
      VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) );
      VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) );
  }
  
  
  void specificTest2()
  {
      Vector3i m; m << -1, -2, 0;
      Vector3i M; M <<  1,  5, 3;
  
      typedef AlignedBox3i  BoxType;
      BoxType box( m, M );
  
      Vector3i sides = M-m;
      VERIFY_IS_APPROX(sides, box.sizes() );
      VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
      VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
      VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
  
      VERIFY_IS_APPROX( 42, box.volume() );
      VERIFY_IS_APPROX( 62, box.diagonal().squaredNorm() );
  
      VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeftFloor ) );
      VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) );
      Vector3i bottomRightFloor; bottomRightFloor << M[0], m[1], m[2];
      Vector3i topLeftFloor; topLeftFloor << m[0], M[1], m[2];
      VERIFY_IS_APPROX( bottomRightFloor, box.corner( BoxType::BottomRightFloor ) );
      VERIFY_IS_APPROX( topLeftFloor, box.corner( BoxType::TopLeftFloor ) );
  }
  
  
  void test_geo_alignedbox()
  {
    for(int i = 0; i < g_repeat; i++)
    {
      CALL_SUBTEST_1( alignedbox(AlignedBox2f()) );
      CALL_SUBTEST_2( alignedboxCastTests(AlignedBox2f()) );
  
      CALL_SUBTEST_3( alignedbox(AlignedBox3f()) );
      CALL_SUBTEST_4( alignedboxCastTests(AlignedBox3f()) );
  
      CALL_SUBTEST_5( alignedbox(AlignedBox4d()) );
      CALL_SUBTEST_6( alignedboxCastTests(AlignedBox4d()) );
  
      CALL_SUBTEST_7( alignedbox(AlignedBox1d()) );
      CALL_SUBTEST_8( alignedboxCastTests(AlignedBox1d()) );
  
      CALL_SUBTEST_9( alignedbox(AlignedBox1i()) );
      CALL_SUBTEST_10( alignedbox(AlignedBox2i()) );
      CALL_SUBTEST_11( alignedbox(AlignedBox3i()) );
  
      CALL_SUBTEST_14( alignedbox(AlignedBox<double,Dynamic>(4)) );
    }
    CALL_SUBTEST_12( specificTest1() );
    CALL_SUBTEST_13( specificTest2() );
  }
  