+ gp_XYZ yAxis;
+ for ( i = 0; i < _simplices.size(); ++i )
+ {
+ yAxis = vecs[i];
+ if ( yAxis.SquareModulus() > tol )
+ break;
+ }
+ gp_XYZ xAxis = yAxis ^ zAxis;
+ // SMESH_TNodeXYZ p0( _simplices[0]._nPrev );
+ // const double tol = 1e-6 * ( p0.Distance( _simplices[1]._nPrev ) +
+ // p0.Distance( _simplices[2]._nPrev ));
+ // gp_XYZ center = smoothLaplacian();
+ // gp_XYZ xAxis, yAxis, zAxis;
+ // for ( i = 0; i < _simplices.size(); ++i )
+ // {
+ // xAxis = SMESH_TNodeXYZ( _simplices[i]._nPrev ) - center;
+ // if ( xAxis.SquareModulus() > tol*tol )
+ // break;
+ // }
+ // for ( i = 1; i < _simplices.size(); ++i )
+ // {
+ // yAxis = SMESH_TNodeXYZ( _simplices[i]._nPrev ) - center;
+ // zAxis = xAxis ^ yAxis;
+ // if ( zAxis.SquareModulus() > tol*tol )
+ // break;
+ // }
+ // if ( i == _simplices.size() ) return newPos;
+
+ yAxis = zAxis ^ xAxis;
+ xAxis /= xAxis.Modulus();
+ yAxis /= yAxis.Modulus();
+
+ // get half-planes of _simplices
+
+ vector< _halfPlane > halfPlns( _simplices.size() );
+ int nbHP = 0;
+ for ( size_t i = 0; i < _simplices.size(); ++i )
+ {
+ gp_XYZ OP1 = SMESH_TNodeXYZ( _simplices[i]._nPrev ) - center;
+ gp_XYZ OP2 = SMESH_TNodeXYZ( _simplices[i]._nNext ) - center;
+ gp_XY p1( OP1 * xAxis, OP1 * yAxis );
+ gp_XY p2( OP2 * xAxis, OP2 * yAxis );
+ gp_XY vec12 = p2 - p1;
+ double dist12 = vec12.Modulus();
+ if ( dist12 < tol )
+ continue;
+ vec12 /= dist12;
+ halfPlns[ nbHP ]._pos = p1;
+ halfPlns[ nbHP ]._dir = vec12;
+ halfPlns[ nbHP ]._inNorm.SetCoord( -vec12.Y(), vec12.X() );
+ ++nbHP;
+ }
+
+ // intersect boundaries of half-planes, define state of intersection points
+ // in relation to all half-planes and calculate internal point of a 2D polygon
+
+ double sumLen = 0;
+ gp_XY newPos2D (0,0);
+
+ enum { UNDEF = -1, NOT_OUT, IS_OUT, NO_INT };
+ typedef std::pair< gp_XY, int > TIntPntState; // coord and isOut state
+ TIntPntState undefIPS( gp_XY(1e100,1e100), UNDEF );
+
+ vector< vector< TIntPntState > > allIntPnts( nbHP );
+ for ( int iHP1 = 0; iHP1 < nbHP; ++iHP1 )
+ {
+ vector< TIntPntState > & intPnts1 = allIntPnts[ iHP1 ];
+ if ( intPnts1.empty() ) intPnts1.resize( nbHP, undefIPS );
+
+ int iPrev = SMESH_MesherHelper::WrapIndex( iHP1 - 1, nbHP );
+ int iNext = SMESH_MesherHelper::WrapIndex( iHP1 + 1, nbHP );
+
+ int nbNotOut = 0;
+ const gp_XY* segEnds[2] = { 0, 0 }; // NOT_OUT points
+
+ for ( int iHP2 = 0; iHP2 < nbHP; ++iHP2 )
+ {
+ if ( iHP1 == iHP2 ) continue;
+
+ TIntPntState & ips1 = intPnts1[ iHP2 ];
+ if ( ips1.second == UNDEF )
+ {
+ // find an intersection point of boundaries of iHP1 and iHP2
+
+ if ( iHP2 == iPrev ) // intersection with neighbors is known
+ ips1.first = halfPlns[ iHP1 ]._pos;
+ else if ( iHP2 == iNext )
+ ips1.first = halfPlns[ iHP2 ]._pos;
+ else if ( !halfPlns[ iHP1 ].FindInterestion( halfPlns[ iHP2 ], ips1.first ))
+ ips1.second = NO_INT;
+
+ // classify the found intersection point
+ if ( ips1.second != NO_INT )
+ {
+ ips1.second = NOT_OUT;
+ for ( int i = 0; i < nbHP && ips1.second == NOT_OUT; ++i )
+ if ( i != iHP1 && i != iHP2 &&
+ halfPlns[ i ].IsOut( ips1.first, tol ))
+ ips1.second = IS_OUT;
+ }
+ vector< TIntPntState > & intPnts2 = allIntPnts[ iHP2 ];
+ if ( intPnts2.empty() ) intPnts2.resize( nbHP, undefIPS );
+ TIntPntState & ips2 = intPnts2[ iHP1 ];
+ ips2 = ips1;
+ }
+ if ( ips1.second == NOT_OUT )
+ {
+ ++nbNotOut;
+ segEnds[ bool(segEnds[0]) ] = & ips1.first;
+ }
+ }
+
+ // find a NOT_OUT segment of boundary which is located between
+ // two NOT_OUT int points
+
+ if ( nbNotOut < 2 )
+ continue; // no such a segment
+
+ if ( nbNotOut > 2 )
+ {
+ // sort points along the boundary
+ map< double, TIntPntState* > ipsByParam;
+ for ( int iHP2 = 0; iHP2 < nbHP; ++iHP2 )
+ {
+ TIntPntState & ips1 = intPnts1[ iHP2 ];
+ if ( ips1.second != NO_INT )
+ {
+ gp_XY op = ips1.first - halfPlns[ iHP1 ]._pos;
+ double param = op * halfPlns[ iHP1 ]._dir;
+ ipsByParam.insert( make_pair( param, & ips1 ));
+ }
+ }
+ // look for two neighboring NOT_OUT points
+ nbNotOut = 0;
+ map< double, TIntPntState* >::iterator u2ips = ipsByParam.begin();
+ for ( ; u2ips != ipsByParam.end(); ++u2ips )
+ {
+ TIntPntState & ips1 = *(u2ips->second);
+ if ( ips1.second == NOT_OUT )
+ segEnds[ bool( nbNotOut++ ) ] = & ips1.first;
+ else if ( nbNotOut >= 2 )
+ break;
+ else
+ nbNotOut = 0;
+ }
+ }
+
+ if ( nbNotOut >= 2 )
+ {
+ double len = ( *segEnds[0] - *segEnds[1] ).Modulus();
+ sumLen += len;
+
+ newPos2D += 0.5 * len * ( *segEnds[0] + *segEnds[1] );
+ }
+ }
+
+ if ( sumLen > 0 )
+ {
+ newPos2D /= sumLen;
+ newPos = center + xAxis * newPos2D.X() + yAxis * newPos2D.Y();
+ }
+ else
+ {
+ newPos = center;
+ }
+
+ return newPos;