Changeset b67d89 for src/Fragmentation/Exporters/SphericalPointDistribution.cpp

Timestamp:

Sep 12, 2016, 11:48:34 PM (8 years ago)

Author:

Frederik Heber <heber@…>

Branches:

Action_Thermostats, Add_AtomRandomPerturbation, Add_FitFragmentPartialChargesAction, Add_RotateAroundBondAction, Add_SelectAtomByNameAction, Adding_Graph_to_ChangeBondActions, Adding_MD_integration_tests, Adding_StructOpt_integration_tests, Automaking_mpqc_open, AutomationFragmentation_failures, Candidate_v1.5.4, Candidate_v1.6.0, Candidate_v1.6.1, ChangeBugEmailaddress, ChangingTestPorts, ChemicalSpaceEvaluator, Combining_Subpackages, Debian_Package_split, Debian_package_split_molecuildergui_only, Disabling_MemDebug, Docu_Python_wait, EmpiricalPotential_contain_HomologyGraph, EmpiricalPotential_contain_HomologyGraph_documentation, Enable_parallel_make_install, Enhance_userguide, Enhanced_StructuralOptimization, Enhanced_StructuralOptimization_continued, Example_ManyWaysToTranslateAtom, Exclude_Hydrogens_annealWithBondGraph, FitPartialCharges_GlobalError, Fix_ChargeSampling_PBC, Fix_ChronosMutex, Fix_FitPartialCharges, Fix_FitPotential_needs_atomicnumbers, Fix_ForceAnnealing, Fix_IndependentFragmentGrids, Fix_ParseParticles, Fix_ParseParticles_split_forward_backward_Actions, Fix_StatusMsg, Fix_StepWorldTime_single_argument, Fix_Verbose_Codepatterns, ForceAnnealing_goodresults, ForceAnnealing_oldresults, ForceAnnealing_tocheck, ForceAnnealing_with_BondGraph, ForceAnnealing_with_BondGraph_continued, ForceAnnealing_with_BondGraph_continued_betteresults, ForceAnnealing_with_BondGraph_contraction-expansion, GeometryObjects, Gui_displays_atomic_force_velocity, IndependentFragmentGrids, IndependentFragmentGrids_IndividualZeroInstances, IndependentFragmentGrids_IntegrationTest, IndependentFragmentGrids_Sole_NN_Calculation, JobMarket_RobustOnKillsSegFaults, JobMarket_StableWorkerPool, JobMarket_unresolvable_hostname_fix, ODR_violation_mpqc_open, PartialCharges_OrthogonalSummation, PythonUI_with_named_parameters, QtGui_reactivate_TimeChanged_changes, Recreated_GuiChecks, RotateToPrincipalAxisSystem_UndoRedo, SaturateAtoms_findBestMatching, StoppableMakroAction, Subpackage_CodePatterns, Subpackage_JobMarket, Subpackage_LinearAlgebra, Subpackage_levmar, Subpackage_mpqc_open, Subpackage_vmg, ThirdParty_MPQC_rebuilt_buildsystem, TrajectoryDependenant_MaxOrder, TremoloParser_IncreasedPrecision, TremoloParser_MultipleTimesteps, Ubuntu_1604_changes, stable

Children:

2199c2

Parents:

158ecb

git-author:

Frederik Heber <heber@…> (06/12/14 07:23:12)

git-committer:

Frederik Heber <heber@…> (09/12/16 23:48:34)

Message:

Using the idea of three points giving a triangle to find rotation axis.

• we calculate the center of either triangle and rotate the center of the ideal point distribution to match the one from the given points.
• next we have the triangles normals as axis, take the first matching point and rotate align it.
• we have to deal with a lot of special cases: What if only zero, one, or two points are given ...
• in general we assume that the triangle lies relatively flat on the sphere's surface but what if the origin is in the triangle plane or even the calculated center is at the origin ...
• TESTS: SphericalPointDistributionUnitTest working again, regression tests FragmentMolecule-cylces and StoreSaturatedFragment working.

File:

• src/Fragmentation/Exporters/SphericalPointDistribution.cpp (modified) (9 diffs)

src/Fragmentation/Exporters/SphericalPointDistribution.cpp

@@ -53 +53 @@
 
 #include "LinearAlgebra/Line.hpp"
+#include "LinearAlgebra/Plane.hpp"
 #include "LinearAlgebra/RealSpaceMatrix.hpp"
 #include "LinearAlgebra/Vector.hpp"
 
-typedef std::list<unsigned int> IndexList_t;
-typedef std::vector<unsigned int> IndexArray_t;
-typedef std::vector<Vector> VectorArray_t;
+// static entities
+const double SphericalPointDistribution::SQRT_3(sqrt(3.0));
+const double SphericalPointDistribution::warn_amplitude = 1e-2;
+
 typedef std::vector<double> DistanceArray_t;
 
-// static instances
-const double SphericalPointDistribution::SQRT_3(sqrt(3.0));
-
+inline
 DistanceArray_t calculatePairwiseDistances(
-    const std::vector<Vector> &_returnpolygon,
-    const IndexList_t &_indices
+    const std::vector<Vector> &_points,
+    const SphericalPointDistribution::IndexList_t &_indices
     )
 {
   DistanceArray_t result;
-  for (IndexList_t::const_iterator firstiter = _indices.begin();
+  for (SphericalPointDistribution::IndexList_t::const_iterator firstiter = _indices.begin();
       firstiter != _indices.end(); ++firstiter) {
-    for (IndexList_t::const_iterator seconditer = firstiter;
+    for (SphericalPointDistribution::IndexList_t::const_iterator seconditer = firstiter;
         seconditer != _indices.end(); ++seconditer) {
       if (firstiter == seconditer)
         continue;
-      const double distance = (_returnpolygon[*firstiter] - _returnpolygon[*seconditer]).NormSquared();
+      const double distance = (_points[*firstiter] - _points[*seconditer]).NormSquared();
       result.push_back(distance);
     }
@@ -101 +101 @@
  * \return pair with L1 and squared L2 error
  */
-std::pair<double, double> calculateErrorOfMatching(
+std::pair<double, double> SphericalPointDistribution::calculateErrorOfMatching(
     const std::vector<Vector> &_old,
     const std::vector<Vector> &_new,
@@ -138 +138 @@
 }
 
-SphericalPointDistribution::Polygon_t removeMatchingPoints(
+SphericalPointDistribution::Polygon_t SphericalPointDistribution::removeMatchingPoints(
     const VectorArray_t &_points,
     const IndexList_t &_matchingindices
@@ -163 +163 @@
 }
 
-struct MatchingControlStructure {
-  bool foundflag;
-  double bestL2;
-  IndexList_t bestmatching;
-  VectorArray_t oldreturnpolygon;
-  VectorArray_t newreturnpolygon;
-};
-
 /** Recursive function to go through all possible matchings.
  *
@@ -178 +170 @@
  * \param _matchingsize
  */
-void recurseMatchings(
+void SphericalPointDistribution::recurseMatchings(
     MatchingControlStructure &_MCS,
     IndexList_t &_matching,
@@ -215 +207 @@
       // calculate errors
       std::pair<double, double> errors = calculateErrorOfMatching(
-          _MCS.oldreturnpolygon, _MCS.newreturnpolygon, _matching);
+          _MCS.oldpoints, _MCS.newpoints, _matching);
       if (errors.first < L1THRESHOLD) {
         _MCS.bestmatching = _matching;
@@ -227 +219 @@
 }
 
-/** Rotates a given polygon around x, y, and z axis by the given angles.
- *
- * \param _polygon polygon whose points to rotate
- * \param _q quaternion specifying the rotation of the coordinate system
+/** Decides by an orthonormal third vector whether the sign of the rotation
+ * angle should be negative or positive.
+ *
+ * \return -1 or 1
  */
-SphericalPointDistribution::Polygon_t rotatePolygon(
+inline
+double determineSignOfRotation(
+    const Vector &_oldPosition,
+    const Vector &_newPosition,
+    const Vector &_RotationAxis
+    )
+{
+  Vector dreiBein(_oldPosition);
+  dreiBein.VectorProduct(_RotationAxis);
+  dreiBein.Normalize();
+  const double sign =
+      (dreiBein.ScalarProduct(_newPosition) < 0.) ? -1. : +1.;
+  LOG(6, "DEBUG: oldCenter on plane is " << _oldPosition
+      << ", newCenter in plane is " << _newPosition
+      << ", and dreiBein is " << dreiBein);
+  return sign;
+}
+
+/** Finds combinatorially the best matching between points in \a _polygon
+ * and \a _newpolygon.
+ *
+ * We find the matching with the smallest L2 error, where we break when we stumble
+ * upon a matching with zero error.
+ *
+ * \sa recurseMatchings() for going through all matchings
+ *
+ * \param _polygon here, we have indices 0,1,2,...
+ * \param _newpolygon and here we need to find the correct indices
+ * \return list of indices: first in \a _polygon goes to first index for \a _newpolygon
+ */
+SphericalPointDistribution::IndexList_t SphericalPointDistribution::findBestMatching(
     const SphericalPointDistribution::Polygon_t &_polygon,
-    const boost::math::quaternion<double> &_q)
-{
-  SphericalPointDistribution::Polygon_t rotated_polygon = _polygon;
-  boost::math::quaternion<double> q_inverse =
-      boost::math::conj(_q)/(boost::math::norm(_q));
-
-  // apply rotation angles
-  for (SphericalPointDistribution::Polygon_t::iterator iter = rotated_polygon.begin();
-      iter != rotated_polygon.end(); ++iter) {
-    Vector &current = *iter;
-    boost::math::quaternion<double> p(0, current[0], current[1], current[2]);
-    p = _q * p * q_inverse;
-    LOG(5, "DEBUG: Rotated point is " << p);
-    // i have no idea why but first component comes up with wrong sign
-    current[0] = -p.R_component_2();
-    current[1] = p.R_component_3();
-    current[2] = p.R_component_4();
-  }
-
-  return rotated_polygon;
+    const SphericalPointDistribution::Polygon_t &_newpolygon
+    )
+{
+  MatchingControlStructure MCS;
+  MCS.foundflag = false;
+  MCS.bestL2 = std::numeric_limits<double>::max();
+  MCS.oldpoints.insert(MCS.oldpoints.begin(), _polygon.begin(),_polygon.end() );
+  MCS.newpoints.insert(MCS.newpoints.begin(), _newpolygon.begin(),_newpolygon.end() );
+
+  // search for bestmatching combinatorially
+  {
+    // translate polygon into vector to enable index addressing
+    IndexList_t indices(_newpolygon.size());
+    std::generate(indices.begin(), indices.end(), UniqueNumber);
+    IndexList_t matching;
+
+    // walk through all matchings
+    const unsigned int matchingsize = _polygon.size();
+    ASSERT( matchingsize <= indices.size(),
+        "SphericalPointDistribution::matchSphericalPointDistributions() - not enough new points to choose for matching to old ones.");
+    recurseMatchings(MCS, matching, indices, matchingsize);
+  }
+  return MCS.bestmatching;
+}
+
+inline
+Vector calculateCenter(
+    const SphericalPointDistribution::VectorArray_t &_positions,
+    const SphericalPointDistribution::IndexList_t &_indices)
+{
+  Vector Center;
+  Center.Zero();
+  for (SphericalPointDistribution::IndexList_t::const_iterator iter = _indices.begin();
+      iter != _indices.end(); ++iter)
+    Center += _positions[*iter];
+  if (!_indices.empty())
+    Center *= 1./(double)_indices.size();
+
+  return Center;
+}
+
+inline
+void calculateOldAndNewCenters(
+    Vector &_oldCenter,
+    Vector &_newCenter,
+    const SphericalPointDistribution::VectorArray_t &_referencepositions,
+    const SphericalPointDistribution::VectorArray_t &_currentpositions,
+    const SphericalPointDistribution::IndexList_t &_bestmatching)
+{
+  const size_t NumberIds = std::min(_bestmatching.size(), (size_t)3);
+  SphericalPointDistribution::IndexList_t continuousIds(NumberIds, -1);
+  std::generate(continuousIds.begin(), continuousIds.end(), UniqueNumber);
+  _oldCenter = calculateCenter(_referencepositions, continuousIds);
+  // C++11 defines a copy_n function ...
+  SphericalPointDistribution::IndexList_t::const_iterator enditer = _bestmatching.begin();
+  std::advance(enditer, NumberIds);
+  SphericalPointDistribution::IndexList_t firstbestmatchingIds(NumberIds, -1);
+  std::copy(_bestmatching.begin(), enditer, firstbestmatchingIds.begin());
+  _newCenter = calculateCenter( _currentpositions, firstbestmatchingIds);
+}
+
+SphericalPointDistribution::Rotation_t SphericalPointDistribution::findPlaneAligningRotation(
+    const VectorArray_t &_referencepositions,
+    const VectorArray_t &_currentpositions,
+    const IndexList_t &_bestmatching
+    )
+{
+#ifndef NDEBUG
+  bool dontcheck = false;
+#endif
+  // initialize to no rotation
+  Rotation_t Rotation;
+  Rotation.first.Zero();
+  Rotation.first[0] = 1.;
+  Rotation.second = 0.;
+
+  // calculate center of triangle/line/point consisting of first points of matching
+  Vector oldCenter;
+  Vector newCenter;
+  calculateOldAndNewCenters(
+      oldCenter, newCenter,
+      _referencepositions, _currentpositions, _bestmatching);
+
+  if ((!oldCenter.IsZero()) && (!newCenter.IsZero())) {
+    LOG(4, "DEBUG: oldCenter is " << oldCenter << ", newCenter is " << newCenter);
+    oldCenter.Normalize();
+    newCenter.Normalize();
+    if (!oldCenter.IsEqualTo(newCenter)) {
+      // calculate rotation axis and angle
+      Rotation.first = oldCenter;
+      Rotation.first.VectorProduct(newCenter);
+      Rotation.second = oldCenter.Angle(newCenter); // /(M_PI/2.);
+    } else {
+      // no rotation required anymore
+    }
+  } else {
+    LOG(4, "DEBUG: oldCenter is " << oldCenter << ", newCenter is " << newCenter);
+    if ((oldCenter.IsZero()) && (newCenter.IsZero())) {
+      // either oldCenter or newCenter (or both) is directly at origin
+      if (_bestmatching.size() == 2) {
+        // line case
+        Vector oldPosition = _currentpositions[*_bestmatching.begin()];
+        Vector newPosition = _referencepositions[0];
+        // check whether we need to rotate at all
+        if (!oldPosition.IsEqualTo(newPosition)) {
+          Rotation.first = oldPosition;
+          Rotation.first.VectorProduct(newPosition);
+          // orientation will fix the sign here eventually
+          Rotation.second = oldPosition.Angle(newPosition);
+        } else {
+          // no rotation required anymore
+        }
+      } else {
+        // triangle case
+        // both triangles/planes have same center, hence get axis by
+        // VectorProduct of Normals
+        Plane newplane(_referencepositions[0], _referencepositions[1], _referencepositions[2]);
+        VectorArray_t vectors;
+        for (IndexList_t::const_iterator iter = _bestmatching.begin();
+            iter != _bestmatching.end(); ++iter)
+          vectors.push_back(_currentpositions[*iter]);
+        Plane oldplane(vectors[0], vectors[1], vectors[2]);
+        Vector oldPosition = oldplane.getNormal();
+        Vector newPosition = newplane.getNormal();
+        // check whether we need to rotate at all
+        if (!oldPosition.IsEqualTo(newPosition)) {
+          Rotation.first = oldPosition;
+          Rotation.first.VectorProduct(newPosition);
+          Rotation.first.Normalize();
+
+          // construct reference vector to determine direction of rotation
+          const double sign = determineSignOfRotation(oldPosition, newPosition, Rotation.first);
+          Rotation.second = sign * oldPosition.Angle(newPosition);
+          LOG(5, "DEBUG: Rotating plane normals by " << Rotation.second
+              << " around axis " << Rotation.first);
+        } else {
+          // else do nothing
+        }
+      }
+    } else {
+      // TODO: we can't do anything here, but this case needs to be dealt with when
+      // we have no ideal geometries anymore
+      if ((oldCenter-newCenter).Norm() > warn_amplitude)
+        ELOG(2, "oldCenter is " << oldCenter << ", yet newCenter is " << newCenter);
+#ifndef NDEBUG
+      // else they are considered close enough
+      dontcheck = true;
+#endif
+    }
+  }
+
+#ifndef NDEBUG
+  // check: rotation brings newCenter onto oldCenter position
+  if (!dontcheck) {
+    Line Axis(zeroVec, Rotation.first);
+    Vector test = Axis.rotateVector(newCenter, Rotation.second);
+    LOG(4, "CHECK: rotated newCenter is " << test
+        << ", oldCenter is " << oldCenter);
+    ASSERT( (test - oldCenter).NormSquared() < std::numeric_limits<double>::epsilon()*1e4,
+        "matchSphericalPointDistributions() - rotation does not work as expected by "
+        +toString((test - oldCenter).NormSquared())+".");
+  }
+#endif
+
+  return Rotation;
+}
+
+SphericalPointDistribution::Rotation_t SphericalPointDistribution::findPointAligningRotation(
+    const VectorArray_t &remainingold,
+    const VectorArray_t &remainingnew,
+    const IndexList_t &_bestmatching)
+{
+  // initialize rotation to zero
+  Rotation_t Rotation;
+  Rotation.first.Zero();
+  Rotation.first[0] = 1.;
+  Rotation.second = 0.;
+
+  // recalculate center
+  Vector oldCenter;
+  Vector newCenter;
+  calculateOldAndNewCenters(
+      oldCenter, newCenter,
+      remainingold, remainingnew, _bestmatching);
+
+  Vector oldPosition = remainingnew[*_bestmatching.begin()];
+  Vector newPosition = remainingold[0];
+  LOG(6, "DEBUG: oldPosition is " << oldPosition << " and newPosition is " << newPosition);
+  if (!oldPosition.IsEqualTo(newPosition)) {
+    if ((!oldCenter.IsZero()) && (!newCenter.IsZero())) {
+      oldCenter.Normalize();  // note weighted sum of normalized weight is not normalized
+      Rotation.first = oldCenter;
+      LOG(6, "DEBUG: Picking normalized oldCenter as Rotation.first " << oldCenter);
+      oldPosition.ProjectOntoPlane(Rotation.first);
+      newPosition.ProjectOntoPlane(Rotation.first);
+      LOG(6, "DEBUG: Positions after projection are " << oldPosition << " and " << newPosition);
+    } else {
+      if (_bestmatching.size() == 2) {
+        // line situation
+        try {
+          Plane oldplane(oldPosition, oldCenter, newPosition);
+          Rotation.first = oldplane.getNormal();
+          LOG(6, "DEBUG: Plane is " << oldplane << " and normal is " << Rotation.first);
+        } catch (LinearDependenceException &e) {
+          LOG(6, "DEBUG: Vectors defining plane are linearly dependent.");
+          // oldPosition and newPosition are on a line, just flip when not equal
+          if (!oldPosition.IsEqualTo(newPosition)) {
+            Rotation.first.Zero();
+            Rotation.first.GetOneNormalVector(oldPosition);
+            LOG(6, "DEBUG: For flipping we use Rotation.first " << Rotation.first);
+            assert( Rotation.first.ScalarProduct(oldPosition) < std::numeric_limits<double>::epsilon()*1e4);
+  //              Rotation.second = M_PI;
+          } else {
+            LOG(6, "DEBUG: oldPosition and newPosition are equivalent.");
+          }
+        }
+      } else {
+        // triangle situation
+        Plane oldplane(remainingold[0], remainingold[1], remainingold[2]);
+        Rotation.first = oldplane.getNormal();
+        LOG(6, "DEBUG: oldPlane is " << oldplane << " and normal is " << Rotation.first);
+        oldPosition.ProjectOntoPlane(Rotation.first);
+        LOG(6, "DEBUG: Positions after projection are " << oldPosition << " and " << newPosition);
+      }
+    }
+    // construct reference vector to determine direction of rotation
+    const double sign = determineSignOfRotation(oldPosition, newPosition, Rotation.first);
+    Rotation.second = sign * oldPosition.Angle(newPosition);
+  } else {
+    LOG(6, "DEBUG: oldPosition and newPosition are equivalent, hence no orientating rotation.");
+  }
+
+  return Rotation;
 }
 
@@ -269 +504 @@
       << " with new polygon " << _newpolygon);
 
+  if (_polygon.size() == _newpolygon.size()) {
+    // same number of points desired as are present? Do nothing
+    LOG(2, "INFO: There are no vacant points to return.");
+    return remainingreturnpolygon;
+  }
+
   if (_polygon.size() > 0) {
-    MatchingControlStructure MCS;
-    MCS.foundflag = false;
-    MCS.bestL2 = std::numeric_limits<double>::max();
-    MCS.oldreturnpolygon.insert(MCS.oldreturnpolygon.begin(), _polygon.begin(),_polygon.end() );
-    MCS.newreturnpolygon.insert(MCS.newreturnpolygon.begin(), _newpolygon.begin(),_newpolygon.end() );
-
-    // search for bestmatching combinatorially
+    IndexList_t bestmatching = findBestMatching(_polygon, _newpolygon);
+    LOG(2, "INFO: Best matching is " << bestmatching);
+
+    // determine rotation angles to align the two point distributions with
+    // respect to bestmatching:
+    // we use the center between the three first matching points
+    /// the first rotation brings these two centers to coincide
+    VectorArray_t rotated_newpolygon = remainingnew;
     {
-      // translate polygon into vector to enable index addressing
-      IndexList_t indices(_newpolygon.size());
-      std::generate(indices.begin(), indices.end(), UniqueNumber);
-      IndexList_t matching;
-
-      // walk through all matchings
-      const unsigned int matchingsize = _polygon.size();
-      ASSERT( matchingsize <= indices.size(),
-          "SphericalPointDistribution::matchSphericalPointDistributions() - not enough new returnpolygon to choose for matching to old ones.");
-      recurseMatchings(MCS, matching, indices, matchingsize);
-    }
-    LOG(2, "INFO: Best matching is " << MCS.bestmatching);
-
-    // determine rotation angles to align the two point distributions with
-    // respect to bestmatching
-    VectorArray_t rotated_newpolygon = remainingnew;
-    Vector oldCenter;
-    {
-      // calculate center of triangle/line/point consisting of first points of matching
-      Vector newCenter;
-      IndexList_t::const_iterator iter = MCS.bestmatching.begin();
-      unsigned int i = 0;
-      for (; (i<3) && (i<MCS.bestmatching.size()); ++i, ++iter) {
-        oldCenter += remainingold[i];
-        newCenter += remainingnew[*iter];
-      }
-      oldCenter *= 1./(double)i;
-      newCenter *= 1./(double)i;
-      LOG(4, "DEBUG: oldCenter is " << oldCenter << ", newCenter is " << newCenter);
-
-      if ((oldCenter - newCenter).NormSquared() > std::numeric_limits<double>::epsilon()*1e4) {
-        // setup quaternion
-        Vector RotationAxis = oldCenter;
-        RotationAxis.VectorProduct(newCenter);
-        Line Axis(zeroVec, RotationAxis);
-        RotationAxis.Normalize();
-        const double RotationAngle = oldCenter.Angle(newCenter); // /(M_PI/2.);
-        LOG(5, "DEBUG: Rotate coordinate system by " << RotationAngle
-            << " around axis " << RotationAxis);
-
-        // apply rotation angles
-        for (VectorArray_t::iterator iter = rotated_newpolygon.begin();
-            iter != rotated_newpolygon.end(); ++iter) {
-          Vector &current = *iter;
-          LOG(5, "DEBUG: Original point is " << current);
-          current =  Axis.rotateVector(current, RotationAngle);
-          LOG(5, "DEBUG: Rotated point is " << current);
+      Rotation_t Rotation = findPlaneAligningRotation(
+          remainingold,
+          remainingnew,
+          bestmatching);
+      LOG(5, "DEBUG: Rotating coordinate system by " << Rotation.second
+          << " around axis " << Rotation.first);
+      Line Axis(zeroVec, Rotation.first);
+
+      // apply rotation angle to bring newCenter to oldCenter
+      for (VectorArray_t::iterator iter = rotated_newpolygon.begin();
+          iter != rotated_newpolygon.end(); ++iter) {
+        Vector &current = *iter;
+        LOG(6, "DEBUG: Original point is " << current);
+        current =  Axis.rotateVector(current, Rotation.second);
+        LOG(6, "DEBUG: Rotated point is " << current);
+      }
+
+#ifndef NDEBUG
+      // check: rotated "newCenter" should now equal oldCenter
+      {
+        Vector oldCenter;
+        Vector rotatednewCenter;
+        calculateOldAndNewCenters(
+            oldCenter, rotatednewCenter,
+            remainingold, rotated_newpolygon, bestmatching);
+        // NOTE: Center must not necessarily lie on the sphere with norm 1, hence, we
+        // have to normalize it just as before, as oldCenter and newCenter lengths may differ.
+        if ((!oldCenter.IsZero()) && (!rotatednewCenter.IsZero())) {
+          oldCenter.Normalize();
+          rotatednewCenter.Normalize();
+          LOG(4, "CHECK: rotatednewCenter is " << rotatednewCenter
+              << ", oldCenter is " << oldCenter);
+          ASSERT( (rotatednewCenter - oldCenter).NormSquared() < std::numeric_limits<double>::epsilon()*1e4,
+              "matchSphericalPointDistributions() - rotation does not work as expected by "
+              +toString((rotatednewCenter - oldCenter).NormSquared())+".");
         }
       }
-    }
-    // rotate triangle/line/point around itself to match orientation
-    if (MCS.bestmatching.size() > 1) {
-      if (oldCenter.NormSquared() > std::numeric_limits<double>::epsilon()*1e4) {
-        // construct RotationAxis and two points on its plane, defining the angle
-        const Line RotationAxis(zeroVec, oldCenter);
-        Vector oldPosition(rotated_newpolygon[*MCS.bestmatching.begin()]);
-        oldPosition.ProjectOntoPlane(RotationAxis.getDirection());
-        Vector newPosition(remainingold[*MCS.bestmatching.begin()]);
-        newPosition.ProjectOntoPlane(RotationAxis.getDirection());
-
-        // construct reference vector to determine direction of rotation
-        Vector dreiBein(oldPosition);
-        dreiBein.VectorProduct(oldCenter);
-        dreiBein.Normalize();
-        const double sign =
-            (dreiBein.ScalarProduct(newPosition) < 0.) ? -1. : +1.;
-        LOG(6, "DEBUG: oldCenter on plane is " << oldPosition
-            << ", newCenter in plane is " << newPosition
-            << ", and dreiBein is " << dreiBein);
-        const double RotationAngle = sign * oldPosition.Angle(newPosition);
-        LOG(5, "DEBUG: Rotating around self is " << RotationAngle
-            << " around axis " << RotationAxis);
+#endif
+    }
+    /// the second (orientation) rotation aligns the planes such that the
+    /// points themselves coincide
+    if (bestmatching.size() > 1) {
+      Rotation_t Rotation = findPointAligningRotation(
+          remainingold,
+          rotated_newpolygon,
+          bestmatching);
+
+      // construct RotationAxis and two points on its plane, defining the angle
+      Rotation.first.Normalize();
+      const Line RotationAxis(zeroVec, Rotation.first);
+
+      LOG(5, "DEBUG: Rotating around self is " << Rotation.second
+          << " around axis " << RotationAxis);
 
 #ifndef NDEBUG
-        // check: first bestmatching in rotated_newpolygon and remainingnew
-        // should now equal
-        {
-          const IndexList_t::const_iterator iter = MCS.bestmatching.begin();
-          Vector rotatednew = RotationAxis.rotateVector(
-              rotated_newpolygon[*iter],
-              RotationAngle);
-          LOG(4, "CHECK: rotated first new bestmatching is " << rotatednew
-              << " while old was " << remainingold[*iter]);
-          ASSERT( (rotatednew - remainingold[*iter]).Norm()
-              < std::numeric_limits<double>::epsilon()*1e4,
-              "matchSphericalPointDistributions() - orientation rotation does not work as expected.");
-        }
+      // check: first bestmatching in rotated_newpolygon and remainingnew
+      // should now equal
+      {
+        const IndexList_t::const_iterator iter = bestmatching.begin();
+        Vector rotatednew = RotationAxis.rotateVector(
+            rotated_newpolygon[*iter],
+            Rotation.second);
+        LOG(4, "CHECK: rotated first new bestmatching is " << rotatednew
+            << " while old was " << remainingold[0]);
+        ASSERT( (rotatednew - remainingold[0]).Norm() < warn_amplitude,
+            "matchSphericalPointDistributions() - orientation rotation ends up off by more than "
+            +toString(warn_amplitude)+".");
+      }
 #endif
 
-        for (VectorArray_t::iterator iter = rotated_newpolygon.begin();
-            iter != rotated_newpolygon.end(); ++iter) {
-          Vector &current = *iter;
-          LOG(6, "DEBUG: Original point is " << current);
-          current = RotationAxis.rotateVector(current, RotationAngle);
-          LOG(6, "DEBUG: Rotated point is " << current);
-        }
+      for (VectorArray_t::iterator iter = rotated_newpolygon.begin();
+          iter != rotated_newpolygon.end(); ++iter) {
+        Vector &current = *iter;
+        LOG(6, "DEBUG: Original point is " << current);
+        current = RotationAxis.rotateVector(current, Rotation.second);
+        LOG(6, "DEBUG: Rotated point is " << current);
       }
     }
@@ -379 +601 @@
     // remove all points in matching and return remaining ones
     SphericalPointDistribution::Polygon_t remainingpoints =
-        removeMatchingPoints(rotated_newpolygon, MCS.bestmatching);
+        removeMatchingPoints(rotated_newpolygon, bestmatching);
     LOG(2, "INFO: Remaining points are " << remainingpoints);
     return remainingpoints;