eigen/test/geo_homogeneous.cpp

// 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));
}

EIGEN_DECLARE_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>()));
  }
}