/*
 * Project: MoleCuilder
 * Description: creates and alters molecular systems
 * Copyright (C)  2014 Frederik Heber. All rights reserved.
 * 
 *
 *   This file is part of MoleCuilder.
 *
 *    MoleCuilder is free software: you can redistribute it and/or modify
 *    it under the terms of the GNU General Public License as published by
 *    the Free Software Foundation, either version 2 of the License, or
 *    (at your option) any later version.
 *
 *    MoleCuilder is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU General Public License for more details.
 *
 *    You should have received a copy of the GNU General Public License
 *    along with MoleCuilder.  If not, see <http://www.gnu.org/licenses/>.
 */

/*
 * SphericalPointDistributionUnitTest.cpp
 *
 *  Created on: May 29, 2014
 *      Author: heber
 */

// include config.h
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

using namespace std;

#include <cppunit/CompilerOutputter.h>
#include <cppunit/extensions/TestFactoryRegistry.h>
#include <cppunit/ui/text/TestRunner.h>

// include headers that implement a archive in simple text format
#include <boost/archive/text_oarchive.hpp>
#include <boost/archive/text_iarchive.hpp>

#include "SphericalPointDistributionUnitTest.hpp"

#include <boost/assign.hpp>
#include <boost/math/quaternion.hpp>

#include "CodePatterns/Assert.hpp"
#include "CodePatterns/Log.hpp"

#include "LinearAlgebra/Line.hpp"

#include "Fragmentation/Exporters/SphericalPointDistribution.hpp"

#include "LinearAlgebra/Line.hpp"

#ifdef HAVE_TESTRUNNER
#include "UnitTestMain.hpp"
#endif /*HAVE_TESTRUNNER*/

using namespace boost::assign;

/********************************************** Test classes **************************************/

// Registers the fixture into the 'registry'
CPPUNIT_TEST_SUITE_REGISTRATION( SphericalPointDistributionTest );


void SphericalPointDistributionTest::setUp()
{
  // failing asserts should be thrown
  ASSERT_DO(Assert::Throw);

  setVerbosity(6);
}


void SphericalPointDistributionTest::tearDown()
{
}


/** UnitTest for matchSphericalPointDistributions() with two points
 */
void SphericalPointDistributionTest::matchSphericalPointDistributionsTest_2()
{
  SphericalPointDistribution SPD(1.);
  // test with one point, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(Vector(1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<2>();
    SphericalPointDistribution::Polygon_t expected;
    expected += Vector(-1.,0.,0.);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip of axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,1.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<2>();
    SphericalPointDistribution::Polygon_t expected;
    expected += Vector(0.,-1.,0.);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip to another axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,0.,-1.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<2>();
    SphericalPointDistribution::Polygon_t expected;
    expected += Vector(0.,0.,1.);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<2>();
    SphericalPointDistribution::Polygon_t expected;
    expected += RotationAxis.rotateVector(Vector(-1.,0.,0.), 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }
}

void perturbPolygon(
    SphericalPointDistribution::WeightedPolygon_t &_polygon,
    double _amplitude
    )
{
  for (SphericalPointDistribution::WeightedPolygon_t::iterator iter = _polygon.begin();
      iter != _polygon.end(); ++iter) {
    Vector perturber;
    perturber.GetOneNormalVector(iter->first);
    perturber.Scale(_amplitude);
    iter->first = iter->first + perturber;
    (iter->first).Normalize();
  }
}

static
bool areEqualToWithinBounds(
    const SphericalPointDistribution::Polygon_t &_polygon,
    const SphericalPointDistribution::Polygon_t &_otherpolygon,
    double _amplitude
    )
{
  // same size?
  if (_polygon.size() != _otherpolygon.size())
    return false;
  // same points ? We just check witrh trivial mapping, nothing fancy ...
  bool status = true;
  SphericalPointDistribution::Polygon_t::const_iterator iter = _polygon.begin();
  SphericalPointDistribution::Polygon_t::const_iterator otheriter = _otherpolygon.begin();
  for (; iter != _polygon.end(); ++iter, ++otheriter) {
    status &= (*iter - *otheriter).Norm() < _amplitude;
  }
  return status;
}

/** UnitTest for areEqualToWithinBounds()
 */
void SphericalPointDistributionTest::areEqualToWithinBoundsTest()
{
  // test with no points
  {
    SphericalPointDistribution::Polygon_t polygon;
    SphericalPointDistribution::Polygon_t expected = polygon;
    CPPUNIT_ASSERT( areEqualToWithinBounds(polygon, expected, std::numeric_limits<double>::epsilon()*1e2) );
  }
  // test with one point
  {
    SphericalPointDistribution::Polygon_t polygon;
    polygon += Vector(1.,0.,0.);
    SphericalPointDistribution::Polygon_t expected = polygon;
    CPPUNIT_ASSERT( areEqualToWithinBounds(polygon, expected, std::numeric_limits<double>::epsilon()*1e2) );
  }
  // test with two points
  {
    SphericalPointDistribution::Polygon_t polygon;
    polygon += Vector(1.,0.,0.);
    polygon += Vector(0.,1.,0.);
    SphericalPointDistribution::Polygon_t expected = polygon;
    CPPUNIT_ASSERT( areEqualToWithinBounds(polygon, expected, std::numeric_limits<double>::epsilon()*1e2) );
  }

  // test with two points in different order: THIS GOES WRONG: We only check trivially
  {
    SphericalPointDistribution::Polygon_t polygon;
    polygon += Vector(1.,0.,0.);
    polygon += Vector(0.,1.,0.);
    SphericalPointDistribution::Polygon_t expected;
    expected += Vector(0.,1.,0.);
    expected += Vector(1.,0.,0.);
    CPPUNIT_ASSERT( !areEqualToWithinBounds(polygon, expected, std::numeric_limits<double>::epsilon()*1e2) );
  }

  // test with two different points
  {
    SphericalPointDistribution::Polygon_t polygon;
    polygon += Vector(1.,0.,0.);
    polygon += Vector(0.,1.,0.);
    SphericalPointDistribution::Polygon_t expected;
    expected += Vector(1.01,0.,0.);
    expected += Vector(0.,1.,0.);
    CPPUNIT_ASSERT( areEqualToWithinBounds(polygon, expected, 0.05) );
    CPPUNIT_ASSERT( !areEqualToWithinBounds(polygon, expected, 0.005) );
  }

  // test with different number of points
  {
    SphericalPointDistribution::Polygon_t polygon;
    polygon += Vector(1.,0.,0.);
    polygon += Vector(0.,1.,0.);
    SphericalPointDistribution::Polygon_t expected;
    expected += Vector(0.,1.,0.);
    CPPUNIT_ASSERT( !areEqualToWithinBounds(polygon, expected, 0.05) );
  }
}


/** UnitTest for matchSphericalPointDistributions() with three points
 */
void SphericalPointDistributionTest::matchSphericalPointDistributionsTest_3()
{
  SphericalPointDistribution SPD(1.);

  // test with one point, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<3>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip of x and y axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,1.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<3>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter) {
      std::swap((*iter)[0], (*iter)[1]);
      (*iter)[0] *= -1.;
    }
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with two points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-0.5, sqrt(3)*0.5,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<3>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with two points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-0.5, sqrt(3)*0.5,0.), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<3>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with three points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-0.5, sqrt(3)*0.5,0.), 1);
    polygon += std::make_pair( Vector(-0.5, -sqrt(3)*0.5,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<3>();
    SphericalPointDistribution::Polygon_t expected; // empty cause none are vacant
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }


  // test with three points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-0.5, sqrt(3)*0.5,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-0.5, -sqrt(3)*0.5,0.), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<3>();
    SphericalPointDistribution::Polygon_t expected; // empty cause none are vacant
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }
}

/** UnitTest for matchSphericalPointDistributions() with four points
 */
void SphericalPointDistributionTest::matchSphericalPointDistributionsTest_4()
{
  SphericalPointDistribution SPD(1.);

  // test with one point, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<4>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip of axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,1.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<4>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter) {
      std::swap((*iter)[0], (*iter)[1]);
      (*iter)[0] *= -1.;
    }
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with two points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1./3.0, 2.0*M_SQRT2/3.0,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<4>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with two points, matching trivially, also with slightly perturbed
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1./3.0, 2.0*M_SQRT2/3.0,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<4>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with two points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1./3.0, 2.0*M_SQRT2/3.0,0.), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<4>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with three points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1./3.0, 2.0*M_SQRT2/3.0,0.), 1);
    polygon += std::make_pair( Vector(-1./3.0, -M_SQRT2/3.0, M_SQRT2/sqrt(3)), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<4>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with three points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1./3.0, 2.0*M_SQRT2/3.0,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1./3.0, -M_SQRT2/3.0, M_SQRT2/sqrt(3)), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<4>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }
}

/** UnitTest for matchSphericalPointDistributions() with five points
 */
void SphericalPointDistributionTest::matchSphericalPointDistributionsTest_5()
{
  SphericalPointDistribution SPD(1.);

  // test with one point, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<5>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip of axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,1.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<5>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter) {
      std::swap((*iter)[0], (*iter)[1]);
      (*iter)[0] *= -1.;
    }
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with two points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<5>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with two points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180.*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1.,0.,0.), 47.6/180.*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<5>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180.*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    // the three remaining points sit on a plane that may be rotated arbitrarily
    // so we cannot simply check for equality between expected and remaining
    // hence, we just check that they are orthogonal to the first two points
    CPPUNIT_ASSERT_EQUAL( expected.size(), remaining.size() );
    for (SphericalPointDistribution::WeightedPolygon_t::const_iterator fixiter = polygon.begin();
        fixiter != polygon.end(); ++fixiter) {
      for (SphericalPointDistribution::Polygon_t::const_iterator iter = remaining.begin();
          iter != remaining.end(); ++iter) {
        CPPUNIT_ASSERT( (fixiter->first).IsNormalTo(*iter) );
      }
    }
  }

  // test with three points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1., 0.0, 0.0), 1);
    polygon += std::make_pair( Vector(0.0, 1., 0.0), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<5>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with three points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1., 0.0, 0.0), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(0.0, 1., 0.0), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<5>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }
}

/** UnitTest for matchSphericalPointDistributions() with six points
 */
void SphericalPointDistributionTest::matchSphericalPointDistributionsTest_6()
{
  SphericalPointDistribution SPD(1.);

  // test with one point, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<6>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip of axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,1.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<6>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter) {
      std::swap((*iter)[0], (*iter)[1]);
      (*iter)[0] *= -1.;
    }
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with two points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<6>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second spoint
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with two points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1.,0.,0.), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<6>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second spoint
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    // the four remaining points sit on a plane that may have been rotated arbitrarily
    // so we cannot simply check for equality between expected and remaining
    // hence, we just check that they are orthogonal to the first two points
    CPPUNIT_ASSERT_EQUAL( expected.size(), remaining.size() );
    for (SphericalPointDistribution::WeightedPolygon_t::const_iterator fixiter = polygon.begin();
        fixiter != polygon.end(); ++fixiter) {
      for (SphericalPointDistribution::Polygon_t::const_iterator iter = remaining.begin();
          iter != remaining.end(); ++iter) {
        CPPUNIT_ASSERT( (fixiter->first).IsNormalTo(*iter) );
      }
    }
  }

  // test with three points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1., 0.0, 0.0), 1);
    polygon += std::make_pair( Vector(0.0, 1., 0.0), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<6>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with three points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1., 0.0, 0.0), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(0.0, 1., 0.0), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<6>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }
}

/** UnitTest for matchSphericalPointDistributions() with seven points
 */
void SphericalPointDistributionTest::matchSphericalPointDistributionsTest_7()
{
  SphericalPointDistribution SPD(1.);

  // test with one point, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<7>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip of axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,1.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<7>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter) {
      std::swap((*iter)[0], (*iter)[1]);
      (*iter)[0] *= -1.;
    }
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with two points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<7>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with two points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1.,0.,0.), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<7>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    // the five remaining points sit on a plane that may have been rotated arbitrarily
    // so we cannot simply check for equality between expected and remaining
    // hence, we just check that they are orthogonal to the first two points
    CPPUNIT_ASSERT_EQUAL( expected.size(), remaining.size() );
    for (SphericalPointDistribution::WeightedPolygon_t::const_iterator fixiter = polygon.begin();
        fixiter != polygon.end(); ++fixiter) {
      for (SphericalPointDistribution::Polygon_t::const_iterator iter = remaining.begin();
          iter != remaining.end(); ++iter) {
        CPPUNIT_ASSERT( (fixiter->first).IsNormalTo(*iter) );
      }
    }
  }

  // test with three points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1., 0.0, 0.0), 1);
    polygon += std::make_pair( Vector(0.0, 1., 0.0), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<7>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with three points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1., 0.0, 0.0), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(0.0, 1., 0.0), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<7>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }
}

/** UnitTest for matchSphericalPointDistributions() with eight points
 */
void SphericalPointDistributionTest::matchSphericalPointDistributionsTest_8()
{
  SphericalPointDistribution SPD(1.);

  // test with one point, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<8>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with one point, just a flip of axis
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(0.,1.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<8>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter) {
      std::swap((*iter)[0], (*iter)[1]);
      (*iter)[0] *= -1.;
    }
   SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
  }

  // test with two points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1.,0.,0.), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<8>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with two points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1.,0.,0.), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<8>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    // the six remaining points sit on two planes that may have been rotated arbitrarily
    // so we cannot simply check for equality between expected and remaining
    // hence, we just check that they are orthogonal to the first two points
    CPPUNIT_ASSERT_EQUAL( expected.size(), remaining.size() );
    for (SphericalPointDistribution::WeightedPolygon_t::const_iterator fixiter = polygon.begin();
        fixiter != polygon.end(); ++fixiter) {
      SphericalPointDistribution::Polygon_t::const_iterator expectiter = expected.begin();
      SphericalPointDistribution::Polygon_t::const_iterator remainiter = remaining.begin();
      for (;remainiter != remaining.end(); ++expectiter, ++remainiter) {
        // check that points in expected/remaining have same angle to the given ones
//        CPPUNIT_ASSERT_EQUAL( (*expectiter).Angle(*fixiter), (*remainiter).Angle(*fixiter) );
        CPPUNIT_ASSERT( fabs( (*expectiter).Angle(fixiter->first) - (*remainiter).Angle(fixiter->first) )
            < std::numeric_limits<double>::epsilon()*1e4 );
      }
    }
  }

  // test with three points, matching trivially
  {
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair( Vector(1.,0.,0.), 1);
    polygon += std::make_pair( Vector(-1., 0.0, 0.0), 1);
    polygon += std::make_pair( Vector(-1./3.0, 2.0*M_SQRT2/3.0, 0.0), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<8>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }

  // test with three points, full rotation
  {
    Line RotationAxis(zeroVec, Vector(0.2, 0.43, 0.6893248));
    SphericalPointDistribution::WeightedPolygon_t polygon;
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(1.,0.,0.), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1., 0.0, 0.0), 47.6/180*M_PI), 1);
    polygon += std::make_pair(RotationAxis.rotateVector(Vector(-1./3.0, 2.0*M_SQRT2/3.0, 0.0), 47.6/180*M_PI), 1);
    SphericalPointDistribution::Polygon_t newpolygon =
        SPD.get<8>();
    SphericalPointDistribution::Polygon_t expected = newpolygon;
    expected.pop_front(); // remove first point
    expected.pop_front(); // remove second point
    expected.pop_front(); // remove third point
    for (SphericalPointDistribution::Polygon_t::iterator iter = expected.begin();
        iter != expected.end(); ++iter)
      *iter = RotationAxis.rotateVector(*iter, 47.6/180*M_PI);
    SphericalPointDistribution::Polygon_t remaining =
        SphericalPointDistribution::matchSphericalPointDistributions(
            polygon,
            newpolygon);
    CPPUNIT_ASSERT_EQUAL( expected, remaining );
    // also slightly perturbed
    const double amplitude = 0.05;
    perturbPolygon(polygon, amplitude);
    CPPUNIT_ASSERT( areEqualToWithinBounds(expected, remaining, amplitude) );
  }
}