text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 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>
  
  template<typename Scalar,int Size> void homogeneous(void)
  {
    /* this test covers the following files:
       Homogeneous.h
    */
  
    typedef Matrix<Scalar,Size,Size> MatrixType;
    typedef Matrix<Scalar,Size,1, ColMajor> VectorType;
  
    typedef Matrix<Scalar,Size+1,Size> HMatrixType;
    typedef Matrix<Scalar,Size+1,1> HVectorType;
  
    typedef Matrix<Scalar,Size,Size+1>   T1MatrixType;
    typedef Matrix<Scalar,Size+1,Size+1> T2MatrixType;
    typedef Matrix<Scalar,Size+1,Size> T3MatrixType;
  
    VectorType v0 = VectorType::Random(),
               ones = VectorType::Ones();
  
    HVectorType hv0 = HVectorType::Random();
  
    MatrixType m0 = MatrixType::Random();
  
    HMatrixType hm0 = HMatrixType::Random();
  
    hv0 << v0, 1;
    VERIFY_IS_APPROX(v0.homogeneous(), hv0);
    VERIFY_IS_APPROX(v0, hv0.hnormalized());
    
    VERIFY_IS_APPROX(v0.homogeneous().sum(), hv0.sum());
    VERIFY_IS_APPROX(v0.homogeneous().minCoeff(), hv0.minCoeff());
    VERIFY_IS_APPROX(v0.homogeneous().maxCoeff(), hv0.maxCoeff());
  
    hm0 << m0, ones.transpose();
    VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0);
    VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
    hm0.row(Size-1).setRandom();
    for(int j=0; j<Size; ++j)
      m0.col(j) = hm0.col(j).head(Size) / hm0(Size,j);
    VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
  
    T1MatrixType t1 = T1MatrixType::Random();
    VERIFY_IS_APPROX(t1 * (v0.homogeneous().eval()), t1 * v0.homogeneous());
    VERIFY_IS_APPROX(t1 * (m0.colwise().homogeneous().eval()), t1 * m0.colwise().homogeneous());
  
    T2MatrixType t2 = T2MatrixType::Random();
    VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());
    VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());
    VERIFY_IS_APPROX(t2 * (v0.homogeneous().asDiagonal()), t2 * hv0.asDiagonal());
    VERIFY_IS_APPROX((v0.homogeneous().asDiagonal()) * t2, hv0.asDiagonal() * t2);
  
    VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,
                      v0.transpose().rowwise().homogeneous() * t2);
    VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t2,
                      m0.transpose().rowwise().homogeneous() * t2);
  
    T3MatrixType t3 = T3MatrixType::Random();
    VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t3,
                      v0.transpose().rowwise().homogeneous() * t3);
    VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t3,
                      m0.transpose().rowwise().homogeneous() * t3);
  
    // test product with a Transform object
    Transform<Scalar, Size, Affine> aff;
    Transform<Scalar, Size, AffineCompact> caff;
    Transform<Scalar, Size, Projective> proj;
    Matrix<Scalar, Size, Dynamic>   pts;
    Matrix<Scalar, Size+1, Dynamic> pts1, pts2;
  
    aff.affine().setRandom();
    proj = caff = aff;
    pts.setRandom(Size,internal::random<int>(1,20));
    
    pts1 = pts.colwise().homogeneous();
    VERIFY_IS_APPROX(aff  * pts.colwise().homogeneous(), (aff  * pts1).colwise().hnormalized());
    VERIFY_IS_APPROX(caff * pts.colwise().homogeneous(), (caff * pts1).colwise().hnormalized());
    VERIFY_IS_APPROX(proj * pts.colwise().homogeneous(), (proj * pts1));
  
    VERIFY_IS_APPROX((aff  * pts1).colwise().hnormalized(),  aff  * pts);
    VERIFY_IS_APPROX((caff * pts1).colwise().hnormalized(), caff * pts);
    
    pts2 = pts1;
    pts2.row(Size).setRandom();
    VERIFY_IS_APPROX((aff  * pts2).colwise().hnormalized(), aff  * pts2.colwise().hnormalized());
    VERIFY_IS_APPROX((caff * pts2).colwise().hnormalized(), caff * pts2.colwise().hnormalized());
    VERIFY_IS_APPROX((proj * pts2).colwise().hnormalized(), (proj * pts2.colwise().hnormalized().colwise().homogeneous()).colwise().hnormalized());
    
    // Test combination of homogeneous
    
    VERIFY_IS_APPROX( (t2 * v0.homogeneous()).hnormalized(),
                         (t2.template topLeftCorner<Size,Size>() * v0 + t2.template topRightCorner<Size,1>())
                       / ((t2.template bottomLeftCorner<1,Size>()*v0).value() + t2(Size,Size)) );
    
    VERIFY_IS_APPROX( (t2 * pts.colwise().homogeneous()).colwise().hnormalized(),
                      (Matrix<Scalar, Size+1, Dynamic>(t2 * pts1).colwise().hnormalized()) );
    
    VERIFY_IS_APPROX( (t2 .lazyProduct( v0.homogeneous() )).hnormalized(), (t2 * v0.homogeneous()).hnormalized() );
    VERIFY_IS_APPROX( (t2 .lazyProduct  ( pts.colwise().homogeneous() )).colwise().hnormalized(), (t2 * pts1).colwise().hnormalized() );
    
    VERIFY_IS_APPROX( (v0.transpose().homogeneous() .lazyProduct( t2 )).hnormalized(), (v0.transpose().homogeneous()*t2).hnormalized() );
    VERIFY_IS_APPROX( (pts.transpose().rowwise().homogeneous() .lazyProduct( t2 )).rowwise().hnormalized(), (pts1.transpose()*t2).rowwise().hnormalized() );
  
    VERIFY_IS_APPROX( (t2.template triangularView<Lower>() * v0.homogeneous()).eval(), (t2.template triangularView<Lower>()*hv0) );
  }
  
  void test_geo_homogeneous()
  {
    for(int i = 0; i < g_repeat; i++) {
      CALL_SUBTEST_1(( homogeneous<float,1>() ));
      CALL_SUBTEST_2(( homogeneous<double,3>() ));
      CALL_SUBTEST_3(( homogeneous<double,8>() ));
    }
  }
  