test/geo_parametrizedline.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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>

template <typename LineType>
void parametrizedline(const LineType &_line) {
  /* this test covers the following files:
     ParametrizedLine.h
  */
  using std::abs;
  const Index dim = _line.dim();
  typedef typename LineType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, LineType::AmbientDimAtCompileTime, 1> VectorType;
  typedef Hyperplane<Scalar, LineType::AmbientDimAtCompileTime> HyperplaneType;
  typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, HyperplaneType::AmbientDimAtCompileTime> MatrixType;

  VectorType p0 = VectorType::Random(dim);
  VectorType p1 = VectorType::Random(dim);

  VectorType d0 = VectorType::Random(dim).normalized();

  LineType l0(p0, d0);

  Scalar s0 = internal::random<Scalar>();
  Scalar s1 = abs(internal::random<Scalar>());

  VERIFY_IS_MUCH_SMALLER_THAN(l0.distance(p0), RealScalar(1));
  VERIFY_IS_MUCH_SMALLER_THAN(l0.distance(p0 + s0 * d0), RealScalar(1));
  VERIFY_IS_APPROX((l0.projection(p1) - p1).norm(), l0.distance(p1));
  VERIFY_IS_MUCH_SMALLER_THAN(l0.distance(l0.projection(p1)), RealScalar(1));
  VERIFY_IS_APPROX(Scalar(l0.distance((p0 + s0 * d0) + d0.unitOrthogonal() * s1)), s1);

  // casting
  const int Dim = LineType::AmbientDimAtCompileTime;
  typedef typename GetDifferentType<Scalar>::type OtherScalar;
  ParametrizedLine<OtherScalar, Dim> hp1f = l0.template cast<OtherScalar>();
  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(), l0);
  ParametrizedLine<Scalar, Dim> hp1d = l0.template cast<Scalar>();
  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(), l0);

  // intersections
  VectorType p2 = VectorType::Random(dim);
  VectorType n2 = VectorType::Random(dim).normalized();
  HyperplaneType hp(p2, n2);
  Scalar t = l0.intersectionParameter(hp);
  VectorType pi = l0.pointAt(t);
  VERIFY_IS_MUCH_SMALLER_THAN(hp.signedDistance(pi), RealScalar(1));
  VERIFY_IS_MUCH_SMALLER_THAN(l0.distance(pi), RealScalar(1));
  VERIFY_IS_APPROX(l0.intersectionPoint(hp), pi);

  // transform
  if (!NumTraits<Scalar>::IsComplex) {
    MatrixType rot = MatrixType::Random(dim, dim).householderQr().householderQ();
    DiagonalMatrix<Scalar, LineType::AmbientDimAtCompileTime> scaling(VectorType::Random());
    Translation<Scalar, LineType::AmbientDimAtCompileTime> translation(VectorType::Random());

    while (scaling.diagonal().cwiseAbs().minCoeff() < RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();

    LineType l1 = l0;
    VectorType p3 = l0.pointAt(Scalar(1));
    VERIFY_IS_MUCH_SMALLER_THAN(l1.transform(rot).distance(rot * p3), Scalar(1));
    l1 = l0;
    VERIFY_IS_MUCH_SMALLER_THAN(l1.transform(rot, Isometry).distance(rot * p3), Scalar(1));
    l1 = l0;
    VERIFY_IS_MUCH_SMALLER_THAN(l1.transform(rot * scaling).distance((rot * scaling) * p3), Scalar(1));
    l1 = l0;
    VERIFY_IS_MUCH_SMALLER_THAN(l1.transform(rot * scaling * translation).distance((rot * scaling * translation) * p3),
                                Scalar(1));
    l1 = l0;
    VERIFY_IS_MUCH_SMALLER_THAN(l1.transform(rot * translation, Isometry).distance((rot * translation) * p3),
                                Scalar(1));
  }
}

template <typename Scalar>
void parametrizedline_alignment() {
  typedef ParametrizedLine<Scalar, 4, AutoAlign> Line4a;
  typedef ParametrizedLine<Scalar, 4, DontAlign> Line4u;

  EIGEN_ALIGN_MAX Scalar array1[16];
  EIGEN_ALIGN_MAX Scalar array2[16];
  EIGEN_ALIGN_MAX Scalar array3[16 + 1];
  Scalar *array3u = array3 + 1;

  Line4a *p1 = ::new (reinterpret_cast<void *>(array1)) Line4a;
  Line4u *p2 = ::new (reinterpret_cast<void *>(array2)) Line4u;
  Line4u *p3 = ::new (reinterpret_cast<void *>(array3u)) Line4u;

  p1->origin().setRandom();
  p1->direction().setRandom();
  *p2 = *p1;
  *p3 = *p1;

  VERIFY_IS_APPROX(p1->origin(), p2->origin());
  VERIFY_IS_APPROX(p1->origin(), p3->origin());
  VERIFY_IS_APPROX(p1->direction(), p2->direction());
  VERIFY_IS_APPROX(p1->direction(), p3->direction());
}

EIGEN_DECLARE_TEST(geo_parametrizedline) {
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(parametrizedline(ParametrizedLine<float, 2>()));
    CALL_SUBTEST_2(parametrizedline(ParametrizedLine<float, 3>()));
    CALL_SUBTEST_2(parametrizedline_alignment<float>());
    CALL_SUBTEST_3(parametrizedline(ParametrizedLine<double, 4>()));
    CALL_SUBTEST_3(parametrizedline_alignment<double>());
    CALL_SUBTEST_4(parametrizedline(ParametrizedLine<std::complex<double>, 5>()));
  }
}