SundanceCurveIntegralCalc.cpp

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/*
 * SundanceCurveIntagralCalc.cpp
 *
 *  Created on: Sep 2, 2010
 *      Author: benk
 */

#include "SundanceCurveIntegralCalc.hpp"
#include "SundanceOut.hpp"
#include "PlayaTabs.hpp"
#include "SundanceCellJacobianBatch.hpp"
#include "SundancePolygon2D.hpp"
#include "SundancePolygonQuadrature.hpp"
#include "SundanceSurf3DCalc.hpp"
#include "SundanceSurfQuadrature.hpp"

using namespace Sundance;

CurveIntegralCalc::CurveIntegralCalc() {
  //nothing to do
}

void CurveIntegralCalc::getCurveQuadPoints(CellType  maxCellType ,
                 int maxCellLID ,
                 const Mesh& mesh ,
                 const ParametrizedCurve& paramCurve,
                 const QuadratureFamily& quad ,
                 Array<Point>& curvePoints ,
                 Array<Point>& curveDerivs ,
                 Array<Point>& curveNormals ){

  int verb = 0;
  Tabs tabs;

    // get all the points from the maxDimCell
  int nr_point = mesh.numFacets( mesh.spatialDim() , 0 , 0);
  Array<Point> maxCellsPoints(nr_point);
  int tmp_i , point_LID;

  SUNDANCE_MSG3(verb, tabs << "CurveIntegralCalc::getCurveQuadPoints nr points per cell: " << nr_point)
  for (int jj = 0 ; jj < nr_point ; jj++){
    point_LID = mesh.facetLID( mesh.spatialDim() , maxCellLID , 0 , jj , tmp_i );
    maxCellsPoints[jj] = mesh.nodePosition(point_LID);
    SUNDANCE_MSG3(verb, tabs << " max cell point p[" << jj << "]:"<< maxCellsPoints[jj]);
  }

  // if we have a polygon in 2D then use specialized curve integrals
  if (usePolygoneCurveQuadrature( maxCellType , mesh , paramCurve)){
    // specialized curve integral
    CurveIntegralCalc::getCurveQuadPoints_polygon( maxCellLID , maxCellType , mesh , maxCellsPoints , paramCurve,
                    quad , curvePoints , curveDerivs , curveNormals);
  } else {
    // general curve integral
    if ( use3DSurfQuadrature( maxCellType , mesh ) ){
      CurveIntegralCalc::getSurfQuadPoints(maxCellLID , maxCellType , mesh , maxCellsPoints , paramCurve,
          quad , curvePoints , curveDerivs , curveNormals);
       //CurveIntegralCalc::getCurveQuadPoints_line( maxCellLID , maxCellType , mesh , maxCellsPoints , paramCurve,
        //                quad , curvePoints , curveDerivs , curveNormals);
    } else {
        CurveIntegralCalc::getCurveQuadPoints_line( maxCellLID , maxCellType , mesh , maxCellsPoints , paramCurve,
                  quad , curvePoints , curveDerivs , curveNormals);
    }
  }

}

void CurveIntegralCalc::getCurveQuadPoints_line(
                                   int  maxCellLID ,
                                   CellType  maxCellType ,
                                   const Mesh& mesh ,
                                   const Array<Point>& cellPoints,
                   const ParametrizedCurve& paramCurve,
                   const QuadratureFamily& quad ,
                   Array<Point>& curvePoints ,
                   Array<Point>& curveDerivs ,
                   Array<Point>& curveNormals ){

  int verb = 0;
  Tabs tabs;

    // select the dimension of the curve
  switch (paramCurve.getCurveDim()){
    case 1: {

      SUNDANCE_MSG3(verb, tabs << "CurveIntegralCalc::getCurveQuadPoints_line, curve has ONE dimnesion")
      // 1D curve integral in 2D or 3D

      // first determine the two intersection points with the edges
      Point startPoint(0.0,0.0);
      Point endPoint(0.0,0.0);
        int nrPoints , total_points = 0 ;

      switch (maxCellType){
        case QuadCell:{
          // loop over each edge and detect intersection point
          // there can be only one
          TEUCHOS_TEST_FOR_EXCEPTION( cellPoints.size() != 4 ,
              std::runtime_error ," CurveIntegralCalc::getCurveQuadPoints , QuadCell must have 4 points" );
        SUNDANCE_MSG3(verb, tabs << "CurveIntegralCalc::getCurveQuadPoints_line, on QuadCell")
          Array<Point> result(0);
          int edegIndex[4][2] = { {0,1} , {0,2} , {1,3} , {2,3} };

          // loop over the edges
          for (int jj = 0 ; jj < 4 ; jj++ ){
          paramCurve.returnIntersectPoints(cellPoints[edegIndex[jj][0]], cellPoints[edegIndex[jj][1]], nrPoints , result);
          // test if we have intersection point
            if (nrPoints == 1){
              if (total_points == 0) startPoint = result[0];
              else endPoint = result[0];
              SUNDANCE_MSG3(verb, tabs << "found Int. point:" << result[0]);
            total_points += nrPoints;
            }
          SUNDANCE_MSG3(verb, tabs << "ind:" << jj << ", nr Int points :" << nrPoints
              << " , start:" << startPoint << ", end:"<< endPoint);
          // if we have more than one intersection point then just ignore that edge
          TEUCHOS_TEST_FOR_EXCEPTION( nrPoints > 1 ,
              std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints , QuadCell one edge " << jj << " , can have only one intersection point"
              << " edgeP0:" << cellPoints[edegIndex[jj][0]] << " edgeP1:" << cellPoints[edegIndex[jj][1]] );
          }
          // test if we have too much intersection points
          TEUCHOS_TEST_FOR_EXCEPTION( total_points > 2 ,std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints total_points > 2 : " << total_points );
        SUNDANCE_MSG3(verb, tabs << "CurveIntegralCalc::getCurveQuadPoints_line, end finding intersection points")
        } break;
        case TriangleCell:{
          TEUCHOS_TEST_FOR_EXCEPTION( cellPoints.size() != 3 , std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints , TriangleCell must have 3 points" );
          Array<Point> result;
          int edegIndex[3][2] = { {0,1} , {0,2} , {1,2} };

          // loop over the edges
          for (int jj = 0 ; jj < 3 ; jj++ ){
          paramCurve.returnIntersectPoints(cellPoints[edegIndex[jj][0]], cellPoints[edegIndex[jj][1]], nrPoints , result);
          // test if we have intersection point
            if (nrPoints == 1){
              if (total_points == 0) startPoint = result[0];
              else endPoint = result[0];
              SUNDANCE_MSG3(verb, tabs << "found Int. point:" << result[0]);
            total_points += nrPoints;
            }
            // if we have more than one intersection point then just ignore that edge
            TEUCHOS_TEST_FOR_EXCEPTION( nrPoints > 1 ,
              std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints , TriangleCell one edge " << jj << " , can have only one intersection point"
              << " edgeP0:" << cellPoints[edegIndex[jj][0]] << " edgeP1:" << cellPoints[edegIndex[jj][1]] );
          }
          // test if we have too much intersection points
          TEUCHOS_TEST_FOR_EXCEPTION( total_points > 2 ,std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints total_points > 2 : " << total_points );
        } break;
        default : {
          TEUCHOS_TEST_FOR_EXCEPTION( true , std::runtime_error , "CurveIntegralCalc::getCurveQuadPoints , Unknown Cell in 2D" );
        }
      }
      // test for to many intersection points
      TEUCHOS_TEST_FOR_EXCEPTION( total_points > 2 ,std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints , no much intersection points: " << total_points);

      // -> having the intersection points now we have to determine the:
      // quad points and the gradients at the points(which norm will be in the integration)
      // and the normalized normal vector (normalized since we need the sin and cos for Nitsche )
      // -> as a very simple approach we consider the curve as a line between intersection points "startPoint -> endPoint"

      // in the X direction the line should always have increasing values
      if (startPoint[0] > endPoint[0]){
        Point tmp = startPoint;
        startPoint = endPoint;
        endPoint = tmp;
      }
      SUNDANCE_MSG3(verb, tabs << "start end and points , start:" << startPoint << ", end:"<< endPoint)

      // get the quadrature points for the line
      Array<Point> quadPoints;
      Array<double> quadWeights;
      quad.getPoints( LineCell , quadPoints , quadWeights );
      int nr_quad_points = quadPoints.size();

      // The intersection points , we distribute the points along the line
      curvePoints.resize(nr_quad_points);
      SUNDANCE_MSG3(verb, tabs << " setting reference quadrature points" );
      for (int ii = 0 ; ii < nr_quad_points ; ii++) {
        SUNDANCE_MSG3(verb, tabs << " nr:" << ii << " Line quad point:" << quadPoints[ii] << ", line:" << (endPoint - startPoint));
        curvePoints[ii] = startPoint + quadPoints[ii][0]*(endPoint - startPoint);

        // we transform the intersection points to the reference cell
        // this should work for unstructured case
        // - get the Jacobian of the cells
        // - get the inverse of this Jacobian
        // - apply this Jacobian to the physical points (pos0 = (0,0))of the cell

        Array<int> cellLID(1); cellLID[0] = maxCellLID;
          CellJacobianBatch JBatch;
          JBatch.resize(1, 2, 2);
        mesh.getJacobians(2, cellLID , JBatch);
        double pointc[2] = { curvePoints[ii][0] - cellPoints[0][0] , curvePoints[ii][1] - cellPoints[0][1]};
        JBatch.applyInvJ(0, pointc , 1 , false);
        curvePoints[ii][0] = pointc[0];
        curvePoints[ii][1] = pointc[1];

        SUNDANCE_MSG3(verb, tabs << " quad point nr:" << ii << " = " << curvePoints[ii]);
      }


      // The derivatives at points, for this simple method are simple and constant over the whole quadrature
      curveDerivs.resize(nr_quad_points);
      Point dist_point(endPoint[0] - startPoint[0] , endPoint[1] - startPoint[1]);
      SUNDANCE_MSG3(verb, tabs << " setting derivative values points" );
      for (int ii = 0 ; ii < nr_quad_points ; ii++) {
        curveDerivs[ii] = endPoint - startPoint;
        SUNDANCE_MSG3(verb, tabs << " curve Derivatives point nr:" << ii << " = " << curveDerivs[ii]);
      }


      // calculate the norms to the curve
      curveNormals.resize(nr_quad_points);

      // this is a shorter variant
      SUNDANCE_MSG3(verb, tabs << " setting normal values at points" );
      for (int ii = 0 ; ii < nr_quad_points ; ii++) {
        Point norm_vec = Point(-curveDerivs[ii][1], curveDerivs[ii][0]);
        norm_vec = norm_vec / ::sqrt(norm_vec*norm_vec);
        double relative_length = 1e-2 * ::sqrt((endPoint - startPoint)*(endPoint - startPoint));
        if ( paramCurve.curveEquation( startPoint + relative_length*norm_vec ) > 0 ) {
          curveNormals[ii] = -norm_vec;
        }
        else {
          curveNormals[ii] = norm_vec;
        }
        SUNDANCE_MSG3(verb, tabs << " curve Normals point nr:" << ii << " = " << curveNormals[ii]);
      }


    } break;

//========================== END 1D curve in 2D context ==========================



    case 2: {
// ====================2D curve integral in 3D context =============================

      // take the intersection with each edge,
      // from these intersection points construct one 3D (convex) polygon (from triangle to hexadron)
      //  - maybe divide the polygons into many triangles
      // map the quadrature points somehow inside this surface

      // here we consider a simple surface, as it is in bilinear interpolation
      Tabs tabs;
      switch (maxCellType){
        case BrickCell:{
          int edegIndex[12][2] = { {0,1} , {0,2} , {0,4} , {1,3} , {1,5} , {2,3} , {2,6} , {3,7} ,
                               {4,5} , {4,6} , {5,7} , {6,7} };
          int faceEdges[6][4]  = { {0,1,3,5} , {0,2,4,8} , {1,2,6,9} , {3,4,7,10} , {5,6,7,11} , {8,9,10,11} };
          // loop over the edges
          int t_inters_points = 0;
          int nrPoints = 0;
          Array<Point> edgeIntersectPoint(t_inters_points);
          Array<int> edgeIndex(t_inters_points);
          Array<int> edgePointI(12,-1);

          // loop over the edges and get the intersection points
          for (int jj = 0 ; jj < 12 ; jj++ ){
            Array<Point> result(0);
          paramCurve.returnIntersectPoints(cellPoints[edegIndex[jj][0]], cellPoints[edegIndex[jj][1]], nrPoints , result);
          // test if we have intersection point
            if (nrPoints > 0){
              edgeIntersectPoint.resize( t_inters_points + 1 );
              edgeIndex.resize( t_inters_points + 1 );
              edgeIntersectPoint[t_inters_points] = result[0];
              edgeIndex[t_inters_points] = jj;
              edgePointI[jj] = t_inters_points;
              SUNDANCE_MSG3(verb, tabs << "found Int. point [" << t_inters_points <<"]=" << result[0]);
              t_inters_points++;
            }
          SUNDANCE_MSG3(verb, tabs << "ind:" << jj << ", nr Int points :" << nrPoints );
          TEUCHOS_TEST_FOR_EXCEPTION( nrPoints > 1 ,
              std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints , QuadCell one edge " << jj << " , can have only one intersection point" );
          } // getting intersection points


          // -------- get the point which is nearest to the other points ---------
          Array<double> totDist(t_inters_points);
          // calculate the distance from each point to each point
          SUNDANCE_MSG3(verb, tabs << " Calculating distances ");
          for (int i = 0 ; i < t_inters_points ; i++){
            double sum = 0.0;
            for (int j = 0 ; j < t_inters_points ; j++){
              sum = sum + ::sqrt(edgeIntersectPoint[i]*edgeIntersectPoint[j]);
            }
            totDist[i] = sum;
          }
          // find the point which is mostly in the middle
          int minIndex = 0;
          for (int i = 1 ; i < t_inters_points ; i++){
            if (totDist[i] < totDist[minIndex]) minIndex = i;
          }
          SUNDANCE_MSG3(verb, tabs << " minIndex = " << minIndex );


          // --------- discover the polygon and the triangles-----------
          // todo: what if there is no or only too few intersection points
          int intersTriangleInd = 0;
          int nrTriangles = t_inters_points-2;
          Array<int> triangles(3*nrTriangles,-1);
          Array<double> triangle_area(nrTriangles,0.0);
          double total_area = 0.0;
          SUNDANCE_MSG3(verb, tabs << " nrTriangles = " << nrTriangles );
          int intPointProc = -1;
          int intPointProc_lastNeigh = -1;

// -------------------------------------
          // get one neighboring intersection point of the "minIndex", this will be the starting direction of the polygon
          for (int jj = 0 ; jj < 6 ; jj++ )
          {
            int nrIpointPerFace = 0;
            int firstPI = -1 , secondPI = -1;
            // loop over each edge in one face
            for (int ii = 0 ; ii < 4 ; ii++){
              // if this edge has one intersection point
              if ( edgePointI[faceEdges[jj][ii]] >= 0){
                if (nrIpointPerFace > 0){
                  secondPI = edgePointI[faceEdges[jj][ii]];
                }else{
                  firstPI = edgePointI[faceEdges[jj][ii]];
                }
                TEUCHOS_TEST_FOR_EXCEPTION( nrIpointPerFace > 2 , std::runtime_error,"getCurveQuadPoints , nrIpointPerFace > 2 , " << nrIpointPerFace );
                nrIpointPerFace++;
              }
            }
            TEUCHOS_TEST_FOR_EXCEPTION( nrIpointPerFace == 1 , std::runtime_error,"getCurveQuadPoints , nrIpointPerFace == 1 , " << nrIpointPerFace );
            // Found the first neighboring point of "minIndex"
            if (( nrIpointPerFace > 1) && ((minIndex == firstPI) || (minIndex == secondPI) )){
                SUNDANCE_MSG3(verb, tabs << " Found  starting line:" << firstPI << " -> " << secondPI);
                intPointProc_lastNeigh = minIndex;
                if (minIndex == firstPI){
                  intPointProc = secondPI;
                }else{
                  intPointProc = firstPI;
                }
                // once we found then break the current for loop
                break;
            }
          }
          TEUCHOS_TEST_FOR_EXCEPTION( intPointProc < 0 , std::runtime_error,"getCurveQuadPoints , intPointProc < 0 , " << intPointProc );
          // store this as act. point and get the next one(which is not neighbor to "minIndex") which is not the one which we already had
            // here we create all triangles, by traversing the polygon in one direction, so that the mapping will be continous
            for (int pI = 0 ; pI < nrTriangles; pI++)
            {
              // for each new
            for (int jj = 0 ; jj < 6 ; jj++ )
            {
              int nrIpointPerFace = 0;
              int firstPI = -1 , secondPI = -1;
              // loop over each edge in one face
              for (int ii = 0 ; ii < 4 ; ii++){
                // if this edge has one intersection point
                if ( edgePointI[faceEdges[jj][ii]] >= 0){
                  if (nrIpointPerFace > 0){
                    secondPI = edgePointI[faceEdges[jj][ii]];
                  }else{
                    firstPI = edgePointI[faceEdges[jj][ii]];
                  }
                  TEUCHOS_TEST_FOR_EXCEPTION( nrIpointPerFace > 2 , std::runtime_error,"getCurveQuadPoints , nrIpointPerFace > 2 , " << nrIpointPerFace );
                  nrIpointPerFace++;
                }
              }
              TEUCHOS_TEST_FOR_EXCEPTION( nrIpointPerFace == 1 , std::runtime_error,"getCurveQuadPoints , nrIpointPerFace == 1 , " << nrIpointPerFace );
              // condition to find the neighbor of "intPointProc" but not the one which has been already found
              if (( nrIpointPerFace > 1) && ((intPointProc == firstPI) || (intPointProc == secondPI))
                  && ((intPointProc_lastNeigh != firstPI) && (intPointProc_lastNeigh != secondPI)))
              {
                  SUNDANCE_MSG3(verb, tabs << " Found next line:" << firstPI << " -> " << secondPI);
                  if (intPointProc == firstPI){
                    intPointProc = secondPI;
                    intPointProc_lastNeigh = firstPI;
                  }else{
                    intPointProc = firstPI;
                    intPointProc_lastNeigh = secondPI;
                  }
                  // add triangle
                  triangles[intersTriangleInd] = minIndex;
                  triangles[intersTriangleInd+1] = intPointProc_lastNeigh;
                  triangles[intersTriangleInd+2] = intPointProc;
                  SUNDANCE_MSG3(verb, tabs << " Found triangle:" << minIndex << " , " << firstPI << " , " << secondPI);
                  Point v1 = edgeIntersectPoint[firstPI] - edgeIntersectPoint[minIndex];
                  Point v2 = edgeIntersectPoint[secondPI] - edgeIntersectPoint[minIndex];
                  Point areaV = cross(v1,v2);
                  SUNDANCE_MSG3(verb, tabs << " TriangINdex = " << intersTriangleInd << " , area = " << ::sqrt(areaV*areaV));
                  triangle_area[ intersTriangleInd/3 ] = ::sqrt(areaV*areaV) / (double)2.0 ; // div by 2 to get the are of the triangle
                  total_area = total_area + triangle_area[ intersTriangleInd/3 ];
                  intersTriangleInd = intersTriangleInd + 3;
                  // once we found the next triangle then break the current for loop
                  break;
              }
            }
          }
// ---------------------------
          SUNDANCE_MSG3(verb, tabs << " END Found triangle  total_area=" << total_area);


          // if we have only 1 triangle (3 intersection points) then add to the longest edge one middle point
          // so that we will have at least 2 triangles
          if (t_inters_points < 4){
            // 0,1,2
            SUNDANCE_MSG3(verb, tabs << " Add one additional point to have at least 2 triangles ");
            int longEdI1 = -1 , longEdI2 = -1;
            for (int ii = 0 ; ii < t_inters_points ; ii++)
              if ( (ii != minIndex) ){
                longEdI1 = ii;
                break;
              }
            for (int ii = 0 ; ii < t_inters_points ; ii++)
              if ( (ii != minIndex) && (ii != longEdI1) ){
                longEdI2 = ii;
                break;
              }
            TEUCHOS_TEST_FOR_EXCEPTION( (longEdI1 < 0)||(longEdI2 < 0), std::runtime_error," (longEdI1 < 0)||(longEdI2 < 0):" << longEdI1 << "," <<longEdI2);

            //add the middle point
            edgeIntersectPoint.resize(t_inters_points+1);
            edgeIntersectPoint[t_inters_points] = edgeIntersectPoint[longEdI1]/2.0 + edgeIntersectPoint[longEdI2]/2.0;

            int new_p = t_inters_points;
            t_inters_points += 1;
            nrTriangles += 1;

            // we'll have two new triangles
            triangles.resize(3*(nrTriangles));
            triangles[0] = minIndex;
            triangles[1] = longEdI1;
            triangles[2] = new_p;
            triangles[3] = minIndex;
            triangles[4] = new_p;
            triangles[5] = longEdI2;
                    // the are will be half of the original one
            triangle_area[0] = triangle_area[0] / 2.0;
            triangle_area.resize(2);
            triangle_area[1] = triangle_area[0];
          }

          // now map the quadrature points to the real cell (triangles)
        Array<Point> quadPoints;
        Array<double> quadWeights;
        quad.getPoints( QuadCell , quadPoints , quadWeights );
        int nr_quad_points = quadPoints.size();

        // --------- the quadrature points per cell ------------
        curvePoints.resize(nr_quad_points);
        Array<int> triangleInd(nr_quad_points,-1);
        SUNDANCE_MSG3(verb, tabs << " setting reference quadrature points" );
        for (int ii = 0 ; ii < nr_quad_points ; ii++) {
          //SUNDANCE_MSG3(verb, tabs << " nr:" << ii << " Quad quad point:" << quadPoints[ii] << ", line:" << (endPoint - startPoint));
          int tInd = -1;
          Point tmp(0.0,0.0,0.0);
          get3DRealCoordsOnSurf( quadPoints[ii] , cellPoints , triangles ,
                  nrTriangles , edgeIntersectPoint, tInd , tmp );
          triangleInd[ii] = tInd;
          curvePoints[ii] = tmp;
          //set the real quad points
          SUNDANCE_MSG3(verb, tabs << " quad point nr:" << ii << " = " << curvePoints[ii]);
        }

        // ------- The derivatives at points, for this simple method are simple and constant over the whole quadrature -----
        curveDerivs.resize(nr_quad_points);
        SUNDANCE_MSG3(verb, tabs << " setting surface values points" );
        for (int ii = 0 ; ii < nr_quad_points ; ii++) {
          // set the vector according to formula (only the vector noem will be taken in account)
          int tInd = triangleInd[ii] ;
          curveDerivs[ii] = Point( nrTriangles*triangle_area[tInd] , 0.0, 0.0 );
          //curveDerivs[ii] = Point( total_area , 0.0, 0.0 ); //total_area
          SUNDANCE_MSG3(verb, tabs << " curve Derivatives point nr:" << ii << " = " << curveDerivs[ii]);
        }


        // calculate the norms to the curve
        curveNormals.resize(nr_quad_points);
        SUNDANCE_MSG3(verb, tabs << " setting normal values at points" );
        for (int ii = 0 ; ii < nr_quad_points ; ii++) {
          int tInd = triangleInd[ii];
          // get the normal to the triangle
            Point norm_vec = cross( edgeIntersectPoint[triangles[3*tInd+1]] - edgeIntersectPoint[triangles[3*tInd]] ,
                edgeIntersectPoint[triangles[3*tInd+2]] - edgeIntersectPoint[triangles[3*tInd]]);
            double relative_length = 1e-2 * ::sqrt(norm_vec*norm_vec);
            norm_vec = norm_vec / ::sqrt(norm_vec*norm_vec);
            if ( paramCurve.curveEquation( edgeIntersectPoint[triangles[3*tInd]] + relative_length*norm_vec ) > 0 ) {
              curveNormals[ii] = -norm_vec;
            }
            else {
              curveNormals[ii] = norm_vec;
            }
            SUNDANCE_MSG3(verb, tabs << " curve Normals point nr:" << ii << " = " << curveNormals[ii]);
        }

                break;
        } // ----------- end brick cell --------------
        case TetCell:{
          // todo: later when this will be needed
          TEUCHOS_TEST_FOR_EXCEPTION( true, std::runtime_error,"CurveIntagralCalc::getCurveQuadPoints , not implemented for " << maxCellType );
          break;
        }
        default:{
          TEUCHOS_TEST_FOR_EXCEPTION( true, std::runtime_error,"CurveIntagralCalc::getCurveQuadPoints , not implemented for " << maxCellType );
        }
      }
      SUNDANCE_MSG3(verb, tabs << " END CurveIntagralCalc::getCurveQuadPoints");
    } break;

//========================== END 2D curve in 3D context ==========================

    default: {
        // throw exception
    TEUCHOS_TEST_FOR_EXCEPTION( true, std::runtime_error,"CurveIntagralCalc::getCurveQuadPoints , curve dimension must be 1 or two ");
    }
  }
}


void CurveIntegralCalc::get3DRealCoordsOnSurf(const Point &refP ,
    const Array<Point>& cellPoints,
        const Array<int> &triangles ,
        const int nrTriag ,
        const Array<Point> edgeIntersectPoint,
        int &triagIndex ,
        Point &realPoint){

  Tabs tabs;
  int verb = 0;
  realPoint[0] = 0.0; realPoint[1] = 0.0; realPoint[2] = 0.0;
  SUNDANCE_MSG3(verb, tabs << " start get3DRealCoordsOnSurf refP="<<refP );
  Point v1;
  Point v2;
  // these matrixes were calculated in octave
  double case1[2][4] = {{1 ,-1  ,0   ,1},{ 1 , 0 ,  -1  , 1}};
  double case2[3][4] = {{1 ,-2, 0, 2} , { 2 , -2, -1, 2},{ 1 , 0, -1, 1}};
  double case3[4][4] = {{1, -2,0 , 2} , { 2 , -2, -1,2},{ 2, -1,-2, 2},{ 2 ,0, -2,  1}};
  double *refInv = 0;
  switch (nrTriag){
    case 2:{
      if (refP[0] >= refP[1]){ // first triangle
        triagIndex = 0; v1 = Point(1.0,0.0); v2 = Point(1.0,1.0);
      }else{// second triangle
        triagIndex = 1; v1 = Point(1.0,1.0); v2 = Point(0.0,1.0);
      }
      refInv = case1[triagIndex];
      break;
    }
    case 3:{
      if (refP[0] >= 2*refP[1]){ // first triangle
        triagIndex = 0; v1 = Point(1.0,0.0); v2 = Point(1.0,0.5);
      }else if ((refP[0] <= 2*refP[1]) && (refP[0] >= refP[1])){ // second triangle
        triagIndex = 1; v1 = Point(1.0,0.5); v2 = Point(1.0,1.0);
      }else{ // third triangle
        triagIndex = 2; v1 = Point(1.0,1.0); v2 = Point(0.0,1.0);
      }
      refInv = case2[triagIndex];
      break;
    }
    case 4:{
      if (refP[0] >= 2*refP[1]){ // first triangle
        triagIndex = 0; v1 = Point(1.0,0.0); v2 = Point(1.0,0.5);
      }else if ((refP[0] <= 2*refP[1]) && (refP[0] >= refP[1])){// second triangle
        triagIndex = 1; v1 = Point(1.0,0.5); v2 = Point(1.0,1.0);
      }else if ((refP[0] <= refP[1]) && (2*refP[0] >= refP[1])){// third triangle
        triagIndex = 2; v1 = Point(1.0,1.0); v2 = Point(0.5,1.0);
      }else{ // fourth triangle
        triagIndex = 3;v1 = Point(0.5,1.0); v2 = Point(0.0,1.0);
      }
      refInv = case3[triagIndex];
      break;
    }
    default:{
      TEUCHOS_TEST_FOR_EXCEPTION( true, std::runtime_error,"get3DRealCoordsOnSurf , too many triangles " << nrTriag);
    }
  }
  // get the three points of the triangle
  Point p0 = edgeIntersectPoint[triangles[3*triagIndex]];
  Point p1 = edgeIntersectPoint[triangles[3*triagIndex+1]];
  Point p2 = edgeIntersectPoint[triangles[3*triagIndex+2]];
  SUNDANCE_MSG3(verb, tabs << "get3DRealCoordsOnSurf p0="<<p0<<" , p1="<<p1<<" , p2="<<p2);
  SUNDANCE_MSG3(verb, tabs << "get3DRealCoordsOnSurf v1=" << v1 << " , v2=" << v2 << " , triagIndex=" << triagIndex);

  // transfor to the reference 2D coordinates
  double ref_x = refInv[0] * refP[0] + refInv[1]*refP[1];
  double ref_y = refInv[2] * refP[0] + refInv[3]*refP[1];
  SUNDANCE_MSG3(verb, tabs << " after traf to ref_x ="<<ref_x<<" , ref_y="<<ref_y );

  // transform from 2D ref to 3D triangle real coordinate
  realPoint = p0 + ref_x*(p1-p0) + ref_y*(p2-p0);
  SUNDANCE_MSG3(verb, tabs << " end get3DRealCoordsOnSurf , realPoint="<<realPoint );
  SUNDANCE_MSG3(verb, tabs << " end get3DRealCoordsOnSurf cellPoints[0]="<<cellPoints[0]<<" , cellPoints[7]="<<cellPoints[7] );

  // transform the point in real coordinates back to reference 3D coordinates
  // this works only for cubes (structured)
  realPoint[0] = (realPoint[0] - cellPoints[0][0]) / (cellPoints[7][0] - cellPoints[0][0]);
  realPoint[1] = (realPoint[1] - cellPoints[0][1]) / (cellPoints[7][1] - cellPoints[0][1]);
  realPoint[2] = (realPoint[2] - cellPoints[0][2]) / (cellPoints[7][2] - cellPoints[0][2]);
  SUNDANCE_MSG3(verb, tabs << " end get3DRealCoordsOnSurf triagIndex="<<triagIndex<<" , realPoint="<<realPoint );

}


bool CurveIntegralCalc::usePolygoneCurveQuadrature(
    const CellType& cellType ,
    const Mesh& mesh ,
    const ParametrizedCurve& paramCurve){

  // Maximal cell type
  CellType maxCellType = mesh.cellType(mesh.spatialDim());

  switch (maxCellType)
  {
  // We have a triangle based mesh
  case TriangleCell:
  {
    switch (cellType)
    {
    case TriangleCell:
    { break; }
    default: {}
    }
    break;
  }
  case QuadCell:
  {
    switch(cellType)
    {
    case QuadCell:
    {
      // this works only in 2D for polygons, it is important that we ask the underlying object and not the object itself
      const Polygon2D* poly = dynamic_cast<const Polygon2D* > ( paramCurve.ptr().get()->getUnderlyingCurveObj() );
      if ( poly != 0 ){
        return true;
      }
      break;
    }
    default: {}
    }
    break;
  }
  default: { }
  }
  //
  return false;
}


void CurveIntegralCalc::getCurveQuadPoints_polygon(
                               int  maxCellLID ,
                               CellType  maxCellType ,
                               const Mesh& mesh ,
                               const Array<Point>& cellPoints,
                 const ParametrizedCurve& paramCurve,
                 const QuadratureFamily& quad ,
                 Array<Point>& curvePoints ,
                 Array<Point>& curveDerivs ,
                 Array<Point>& curveNormals ) {

  // this works only in 2D for polygons, it is important that we ask the underlying object and not the object itself
  const Polygon2D* polygon = dynamic_cast<const Polygon2D* > ( paramCurve.ptr().get()->getUnderlyingCurveObj() );
  if ( (polygon == 0) || (maxCellType != QuadCell) ) {
    TEUCHOS_TEST_FOR_EXCEPTION( true , std::runtime_error , " getCurveQuadPoints_polygon , paramCurve must be a Polygon and the cell must be a quad" );
    return;
  }

  // the algorithm is to create separate line segments
  //(P1,P2,d1),(P2,P3,d2),(P4,P5,d3) ... d1,d2,d3 are normalized lengths
  // see these line segments as one continuous line and maps the quadrature points on the segments

  Array<Point> allIntPoints(0);
  Array<int> allIntPointsEdge(0);
  Array<Point> allPolygonPoints(0);
  int nrPoints , total_points , polyNrPoint ;
  Tabs tabs;
  int verb = 0;
  double eps = 1e-14;

  SUNDANCE_MSG3(verb, " ---------- START METHOD -----------  ");

  //
  switch (maxCellType){
    case QuadCell:{
      // loop over each edge and detect intersection point
      // there can be only one
    TEUCHOS_TEST_FOR_EXCEPTION( cellPoints.size() != 4 ,
          std::runtime_error ," CurveIntegralCalc::getCurveQuadPoints , QuadCell must have 4 points" );
    //SUNDANCE_MSG3(verb, tabs << "CurveIntegralCalc::getCurveQuadPoints_line, on QuadCell")
      Array<Point> result(5);
      int edegIndex[4][2] = { {0,1} , {0,2} , {1,3} , {2,3} };
      bool pointExists;

      total_points = 0;
      // loop over the edges
      for (int jj = 0 ; jj < 4 ; jj++ ){
      paramCurve.returnIntersectPoints(cellPoints[edegIndex[jj][0]], cellPoints[edegIndex[jj][1]], nrPoints , result);
      // add the intersection points to the list of intersection points
        for (int ptmp = 0 ; ptmp < nrPoints ; ptmp++){
          pointExists = false;
          //SUNDANCE_MSG3(verb, tabs << "getCurveQuadPoints_line  INVESTIGATE Intersect point:" << result[ptmp]);
          for (int tmp_r = 0 ; tmp_r < total_points ; tmp_r++){
            Point tmpPoint = result[ptmp];
            tmpPoint = tmpPoint - allIntPoints[tmp_r];
            if ( ::sqrt(tmpPoint * tmpPoint) < eps ) pointExists = true;
          }
          // add only if this point does not exist in the list
          if (!pointExists){
            //SUNDANCE_MSG3(verb, tabs << "getCurveQuadPoints_line  ADD  Intersect point:" << result[ptmp]);
            allIntPoints.resize( total_points + 1 );
            allIntPointsEdge.resize( total_points + 1 );
            allIntPoints[total_points] = result[ptmp];
            allIntPointsEdge[total_points] = jj;
            total_points = total_points + 1;
          }
        }
      }
      // test if we have too much intersection points
    //SUNDANCE_MSG3(verb, tabs << "CurveIntegralCalc::getCurveQuadPoints_line, end finding intersection points")
     } break;
     case TriangleCell:{
      TEUCHOS_TEST_FOR_EXCEPTION( true , std::runtime_error , " CurveIntegralCalc::getCurveQuadPoints_polygon , TriangleCell not implemented yet" );
     } break;
     default : {
      TEUCHOS_TEST_FOR_EXCEPTION( true , std::runtime_error , "CurveIntegralCalc::getCurveQuadPoints_polygon , Unknown Cell in 2D" );
   }
  }

  // now we have all the intersection points which are not the same (duplicates are eliminated)
  // we get the points from the polygon
  polygon->getCellsPolygonesPoint( maxCellLID ,allPolygonPoints);
  polyNrPoint = allPolygonPoints.size();

  // now we should merge the intersection points and the points from the polygon
  // into a line segments

  nrPoints = polyNrPoint + total_points;
  Array<Point> segmentStart(0);
  Array<Point> segmentEnd(0);
  int segmentNr = 0 , flagMode , edgeActual = 0;
  Array<bool> usedIntPoint( total_points , false );

  // todo:
  if (total_points < 2) {
    std::cout << "total_points = " << total_points << " , P0:" << allIntPoints[0] << std::endl;
  }
  if (total_points == 3) {
    std::cout << "total_points = " << total_points << "P0:" << allIntPoints[0] <<
        " , P1:" << allIntPoints[1] << " , P2:" << allIntPoints[2] << std::endl;
    total_points = 2;
  }
  if (total_points > 4) {
    std::cout << "total_points = " << total_points << "P0:" << allIntPoints[0] << " , P1:" << allIntPoints[1]
           << " , P2:" << allIntPoints[2] << " , P3:" << allIntPoints[3] << std::endl;
    total_points = 4;
  }

  TEUCHOS_TEST_FOR_EXCEPTION( (total_points != 2) && (total_points != 4) , std::runtime_error , "nr Intersect point can be eighter 2 or 4 but is " << total_points);

  // ---- create total_points/2 different segments ----
  flagMode = 0;
  for (int intP = 0 ; intP < total_points ; intP++ ){
    if (flagMode == 0){
      // get a point which is not used
      int Pind = -1;
      for (int stmp = 0 ; stmp < total_points ; stmp++){
        // this point was not used then take it
        if (!usedIntPoint[stmp]) { Pind = stmp; break;}
      }
      //SUNDANCE_MSG3(verb, tabs << "getCurveQuadPoints_line flag mode 0 , found Index Pind:" << Pind << " , start:"<<allIntPoints[Pind]);
      segmentStart.resize( segmentNr + 1);
      segmentEnd.resize( segmentNr + 1 );
      edgeActual = allIntPointsEdge[Pind];
      segmentStart[ segmentNr ] = allIntPoints[Pind];
      usedIntPoint[ Pind ] = true;
      flagMode = 1;
    } else {
      // here we have a start point we are looking for an end of the segment line
      double dist = 1e+100;
      int Pind = -1;
      for (int stmp = 0 ; stmp < total_points ; stmp++){
        // the condition when to test one intersection point
        if ( !usedIntPoint[stmp] && ( (edgeActual != allIntPointsEdge[stmp]) || total_points < 3 ) ){
          Point tmpPointC = (segmentStart[segmentNr] - allIntPoints[stmp]);
          double thisDist = ::sqrt(tmpPointC*tmpPointC);
          if ( thisDist < dist ) {
            dist = thisDist;
            Pind = stmp;
          }
        }
      }
      //SUNDANCE_MSG3(verb, tabs << "getCurveQuadPoints_line flag mode 1 , found Index Pind:" << Pind << " , end:"<<allIntPoints[Pind]);
      segmentEnd[ segmentNr ] = allIntPoints[Pind];
      usedIntPoint[ Pind ] = true;
      flagMode = 0;
      segmentNr = segmentNr + 1;
    }
  }

  // ---- at this point we have the start and end points of the segments
  // ---- now we should insert the polygon points
  for (int polyPoint = 0 ; polyPoint < polyNrPoint ; polyPoint++ ){
    // find the line segment which will be split
    double totalDist = 1e+100;
    int segInd = -1;
    for (int pl = 0; pl < segmentNr ; pl++ ){
      Point d1p = segmentStart[pl] - allPolygonPoints[polyPoint];
      double d1 = ::sqrt(d1p*d1p);
      Point d2p = segmentEnd[pl] - allPolygonPoints[polyPoint];
      double d2 = ::sqrt(d2p*d2p);
      Point dist_prev = segmentEnd[pl] - segmentStart[pl];
      double d_p = ::sqrt(dist_prev*dist_prev);
      //SUNDANCE_MSG3(verb, tabs << " Probe actual segment START :" << segmentStart[pl] << " , END:" << segmentEnd[pl] );
      //SUNDANCE_MSG3(verb, tabs << " Probe actual point to pl:" << pl << " actual dist:" << (d1+d2-d_p) << " , totalDist:" << totalDist);
      // test if this is the shortest segment till now where to insert the polygon point
      if ( (d1 + d2 - d_p < totalDist) && (d1 > eps) && (d2 > eps) ) {
        totalDist = d1 + d2 - d_p;
        segInd = pl;
      }
    }

    //SUNDANCE_MSG3(verb, tabs << " Add polygon point to segInd:" << segInd << " , polyPoint:" << polyPoint
    //    << " , allPolygonPoints[polyPoint]:" << allPolygonPoints[polyPoint]);
    // if the point is already in or no segment found
    if ( segInd < 0) continue;

    // "segInd" shows the segment which should be split
    segmentStart.resize( segmentNr + 1);
    segmentEnd.resize( segmentNr + 1 );
    // enlarge first the vector
    for (int tmpP = segmentNr-1; tmpP >= segInd ; tmpP--){
      segmentStart[tmpP+1] = segmentStart[tmpP];
      segmentEnd[tmpP+1] = segmentEnd[tmpP];
    }

    // insert the new line segment
    segmentEnd[segInd] = allPolygonPoints[polyPoint];
    segmentStart[segInd+1] = allPolygonPoints[polyPoint];
    segmentNr = segmentNr + 1;
  }

  // --- now we have all line segments now calculate each length
  Array<double> segmentLengthRel(0);
  Array<double> segmentStartLengthRel(0);
  segmentLengthRel.resize(segmentNr);
  segmentStartLengthRel.resize(segmentNr);

  // calculate the length of each line, so that we can find
  double totalLength = 0.0 , actLen = 0.0;
  for (int seg = 0 ; seg < segmentNr ; seg++){
    totalLength = totalLength + ::sqrt( (segmentEnd[seg]-segmentStart[seg])*(segmentEnd[seg]-segmentStart[seg]) );
    //SUNDANCE_MSG3(verb, tabs << " total length seg:" << seg << " , totalLength = " << totalLength);
    //SUNDANCE_MSG3(verb, tabs << "  segmentStart[seg] = " << segmentStart[seg] <<" segmentEnd[seg]:" << segmentEnd[seg] );
  }

    // update the lengths of each segment
  for (int seg = 0 ; seg < segmentNr ; seg++){
    double thisLength = ::sqrt( (segmentEnd[seg]-segmentStart[seg])*(segmentEnd[seg]-segmentStart[seg]) );
    segmentLengthRel[seg] = thisLength/totalLength;
    segmentStartLengthRel[seg] = actLen/totalLength;
    //SUNDANCE_MSG3(verb, tabs << " Absolute length seg:" << seg << " , segmentLengthRel[seg] = " << segmentLengthRel[seg]
    //                                << " , segmentStartLengthRel[seg]=" << segmentStartLengthRel[seg]);
    //SUNDANCE_MSG3( verb , tabs << " segmentStart[seg]: " << segmentStart[seg] << " , segmentEnd[seg]:" << segmentEnd[seg]);
    actLen = actLen + thisLength;
  }

  //try to convert the quadrature to a polygon curve integral class
  // this quadrature class is special for polygon curve integrals
  const PolygonQuadrature* polyquad = dynamic_cast<const PolygonQuadrature*> (quad.ptr().get());
  if ( polyquad == 0 ) {
    TEUCHOS_TEST_FOR_EXCEPTION( true , std::runtime_error ,
      " getCurveQuadPoints_polygon , Quadrature for a polygon curve must be PolygonQuadrature" );
    return;
  }

  // get the quadrature points for line segments
  Array<Point> quadPoints;
  Array<double> quadWeights;
  polyquad->getPoints( LineCell , quadPoints , quadWeights );
  int nr_quad_points = quadPoints.size();
  Point endPoint , startPoint;
  int maxLineSegments = PolygonQuadrature::getNrMaxLinePerCell();
  Array<int> cellLID(1); cellLID[0] = maxCellLID;
  CellJacobianBatch JBatch;
  JBatch.resize(1, 2, 2);
  mesh.getJacobians(2, cellLID , JBatch);

  TEUCHOS_TEST_FOR_EXCEPTION( maxLineSegments < segmentNr , std::runtime_error , " getCurveQuadPoints_polygon , nr of polygon lines inside one cell too high" <<
              " Use PolygonQuadrature::getNrMaxLinePerCell(" << segmentNr << ") , now it is only: " << maxLineSegments );

  // ---- at this stage we have the line segments,
  // we just need to map the quadrature points to the line and calculate the normal vector
  curvePoints.resize(nr_quad_points);
  curveDerivs.resize(nr_quad_points);
  curveNormals.resize(nr_quad_points);

  // get the line segment which contains this quadrature point
  int ii = 0;
  for (int seg = 0; seg < segmentNr ; seg++ )
  {
    // the start and end points of the line segment
    startPoint = segmentStart[seg];
    endPoint = segmentEnd[seg];

    // the calculation of the normal vector is usual, we look to the middle of the segment and see if it is inside or outside
    // since this is a polygon this must be determined
    Point curvderi = endPoint - startPoint;
    Point norm_vec = Point( -curvderi[1] , curvderi[0] );
    norm_vec = norm_vec / ::sqrt(norm_vec*norm_vec);
    double relative_length = 1e-2 * ::sqrt(curvderi*curvderi);
    bool invNormVect = false;
    // this segment must be a line, and we test which part is inside
    if ( paramCurve.curveEquation( (0.5*endPoint + 0.5*startPoint) + relative_length*norm_vec ) > 0 ) {
      invNormVect = true;
    }
    else {
      invNormVect = false;
    }

    // loop over each quadrature point for one line segment
    for (int pointNr = 0 ; pointNr < nr_quad_points/maxLineSegments ; pointNr++ , ii++ )
    {
      // now we have
      //SUNDANCE_MSG3(verb, tabs << "pointNr:" << pointNr << " , nr:" << ii << " Line quad point:" << quadPoints[ii] << ", line:" << (endPoint - startPoint)
      //  << " , segmentsLength: " << segmentStartLengthRel[seg] );
      //SUNDANCE_MSG3(verb, tabs << " nr:" << ii << " startPoint:" <<  startPoint << " , endPoint:" <<  endPoint );
      // here we map the quadrature point on the line segment
      curvePoints[ii] = startPoint + quadPoints[ii][0]*(endPoint - startPoint);

      // here we transform the real coordinate back to the
      double pointc[2] = { curvePoints[ii][0] - cellPoints[0][0] , curvePoints[ii][1] - cellPoints[0][1] };
      JBatch.applyInvJ(0, pointc , 1 , false);
      curvePoints[ii][0] = pointc[0];
      curvePoints[ii][1] = pointc[1];
      //SUNDANCE_MSG3(verb, tabs << " quad point nr:" << ii << " = " << curvePoints[ii]);

      // the derivative we calculate by simply take the total length
      // in the curve integral we use only the norm of this point
      curveDerivs[ii] = Point( segmentLengthRel[seg]*totalLength*((double)maxLineSegments) , 0.0 );
      //SUNDANCE_MSG3(verb, tabs << " curve Derivatives point nr:" << ii << " = " << curveDerivs[ii]);

      // set the normal vector
      if ( invNormVect ) {
        curveNormals[ii] = -norm_vec;
      }
      else {
        curveNormals[ii] = norm_vec;
      }
      //SUNDANCE_MSG3(verb, tabs << " curve Normals point nr:" << ii << " = " << curveNormals[ii]);
    }
  }

  // for the rest of the points just set zero values , these point should not have influence
  for  ( ; ii < nr_quad_points ; ii++ ){
    curvePoints[ii] = Point( 0.0 , 0.0 );
    curveDerivs[ii] = Point( 0.0 , 0.0 );
    curveNormals[ii] = Point( 0.0 , 0.0 );
  }

  SUNDANCE_MSG3(verb, " ---------- END METHOD -----------  ");
}


void CurveIntegralCalc::getSurfQuadPoints(
                               int  maxCellLID ,
                               CellType  maxCellType ,
                               const Mesh& mesh ,
                               const Array<Point>& cellPoints,
                 const ParametrizedCurve& paramCurve,
                 const QuadratureFamily& quad ,
                 Array<Point>& curvePoints ,
                 Array<Point>& curveDerivs ,
                 Array<Point>& curveNormals ) {

  const SurfQuadrature* surfquad = dynamic_cast<const SurfQuadrature*> (quad.ptr().get());
  if ( surfquad == 0 ) {
    TEUCHOS_TEST_FOR_EXCEPTION( true , std::runtime_error ,
      " getSurfQuadPoints , Surface Quadrature for a 3D must be SurfQuadrature" );
    return;
  }

  Array<Point> quadPoints;
  Array<double> quadWeights;
  surfquad->getPoints( TriangleCell , quadPoints , quadWeights );
  int nr_quad_points = quadPoints.size();
  int maxTriangles = SurfQuadrature::getNrMaxTrianglePerCell();
  int nrQuadPointPerTriag = nr_quad_points/maxTriangles;
  int verb = 0;
  curvePoints.resize(nr_quad_points);
  curveDerivs.resize(nr_quad_points);
  curveNormals.resize(nr_quad_points);

  Array<Point> intersectPoints;
  Array<int> edgeIndex;
  Array<int> triangleIndex;
    // the results in this form will be in physical coordinates
  SundanceSurf3DCalc::getCurveQuadPoints( maxCellType , maxCellLID , mesh , paramCurve, cellPoints,
             intersectPoints ,  edgeIndex , triangleIndex );

  int  nr_triag = triangleIndex.size()/3  ,  qind = 0;
  double totalArea = 0.0 , area;
  // first compute the total area of all triangles
  for (int t = 0 ; t < nr_triag ; t++){
    // for each triangle
    Point p0 = intersectPoints[triangleIndex[3*t]];
    Point p1 = intersectPoints[triangleIndex[3*t + 1]];
    Point p2 = intersectPoints[triangleIndex[3*t + 2]];
    Point n = cross(p1-p0,p2-p0);
    totalArea = totalArea + ::sqrt(n*n);
  }


  SUNDANCE_MSG3(verb, " nr_triag = " << nr_triag);
  // for each resulted triangles compute the quadrature points and the normal
  for (int t = 0 ; t < nr_triag ; t++){
    // for each triangle
    Point p0 = intersectPoints[triangleIndex[3*t]];
    Point p1 = intersectPoints[triangleIndex[3*t + 1]];
    Point p2 = intersectPoints[triangleIndex[3*t + 2]];

    Point n = cross(p1-p0,p2-p0);
    // calculate area
    area = ::sqrt(n*n); // / 2.0; -> no division by two
    // invert the normal vector if necessary
    if ( paramCurve.curveEquation( p0 + 5e-3*n ) > 0 ) { n = (-1)*n; }
    n = (1/::sqrt(n*n))*n; // normalize the normal vector

    // for each quadrature point on this triangle
    //SUNDANCE_MSG3(verb, " p0 = " << p0 << " , p1 = " << p1 << " , p2 = " << p2 );
    //SUNDANCE_MSG3(verb, " area = " << area << " , n = " << n );
    for (int q = 0 ; q < nrQuadPointPerTriag ; q++ , qind++){
      // this is the point in real coordinates
      Point pTmp = p0 + quadPoints[qind][0] * (p1-p0) + quadPoints[qind][1] * (p2-p0);
      //SUNDANCE_MSG3(verb, "REAL curvePoints["<<qind<<"]=" << pTmp );
      // here we transform it to reference coordinates
      curvePoints[qind] = Point( (pTmp[0] -  cellPoints[0][0])/(cellPoints[7][0] - cellPoints[0][0]),
                             (pTmp[1] -  cellPoints[0][1])/(cellPoints[7][1] - cellPoints[0][1]),
                             (pTmp[2] -  cellPoints[0][2])/(cellPoints[7][2] - cellPoints[0][2]) );
      //SUNDANCE_MSG3(verb, "REF curvePoints["<<qind<<"]=" << curvePoints[qind] );
      curveDerivs[qind] = Point( area * ((double)maxTriangles) , 0.0 , 0.0 );
      curveNormals[qind] = n;
    }
  }

  // the rest of the quadrature points we set to zero
  for ( ; qind < nr_quad_points ; qind++){
    curvePoints[qind] = Point( 0 , 0 , 0 );
    curveDerivs[qind] = Point( 0 , 0 , 0 );
    curveNormals[qind] = Point( 0 , 0 , 0 );
  }
  SUNDANCE_MSG3(verb, " ---------- END METHOD -----------  ");
}