Function homogeneous

test/geo_homogeneous.cpp:13–116

#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,