//----------------------------------------------------------------------------
//  EgalTech 2014-2021
//----------------------------------------------------------------------------
// File : Triangulate.cpp       Data : 18.12.21          Versione : 2.3l
// Contenuto : Implementazione della classe Triangulate.
//
//
//
// Modifiche : 08.04.14 DS Creazione modulo.
//             23.06.14 DS Corretto errore con contorni CW.
//
//----------------------------------------------------------------------------

//--------------------------- Include ----------------------------------------
#include "stdafx.h"
#include "DllMain.h"
#include "Triangulate.h"
#include "ProjPlane.h"
#include "earcut.hpp"
#include "/EgtDev/Include/EGkSfrCreate.h"
#include "/EgtDev/Include/EGkPolyLine.h"
#include "/EgtDev/Include/EGkPlane3d.h"
#include "/EgtDev/Include/EGkStringUtils3d.h"
#include "/EgtDev/Include/EgtNumUtils.h"
#include "/EgtDev/Extern/fist/Include/api_fist.h"
#include <algorithm>

using namespace std ;

//----------------------------------------------------------------------------
enum EarStatus{ EAS_NULL = -1, EAS_NO = 0, EAS_OK = 1} ;
enum TrgType { TRG_STD = 0, TRG_CAP = 1, TRG_NEEDLE = 2} ;

//----------------------------------------------------------------------------
static bool ChangeStartPntVector( int nNewStart, PNTVECTOR& vPi) ;
static bool MakeByFist( const POLYLINEVECTOR& vPL, PNTVECTOR& vPt, INTVECTOR& vTr) ;
static bool RemoveFistInvalidTrg( PNTVECTOR& vPt, INTVECTOR& vTr) ;
static  int CalcTriangleType( const PNTVECTOR& vPt, const INTVECTOR& vTr, int nTrg) ;
static bool FindAdjacentOnLongerEdge( PNTVECTOR& vPt, INTVECTOR& vTr, int nTrgA, int&nEdgeA, int& nTrgB, int& nEdgeB) ;
static bool FlipTrg( INTVECTOR& vTr, int nTrgA, int nTrgB, int nEdgeA, int nEdgeB) ;
static bool TestAdjacentOnEdge( INTVECTOR& vTr, int nTrgA, int nEdgeA, int nTrgTest1, int nTrgTest2, int& nTrgB, int& nEdgeB) ;

//----------------------------------------------------------------------------
static bool FORCE_EARCUT_HPP = false ;
static bool FORCE_FIST = false ;

//----------------------------------------------------------------------------
// In : PolyLine
// Out : PNTVECTOR (Point3d Vector) : points of the polyline 
//       INTVECTOR (int Vector) : 3*T indices of above points for T triangles   
//----------------------------------------------------------------------------
bool
Triangulate::Make( const PolyLine& PL, PNTVECTOR& vPt, INTVECTOR& vTr)
{
  // pulisco i vettori di ritorno
   vPt.clear() ;
   vTr.clear() ;
  // verifico che la polilinea contenga almeno 4 punti (primo e ultimo coincidenti)
   if ( PL.GetPointNbr() < 4  ||  ! PL.IsClosed())
      return false ;

  // se fist ( e geometria più complessa di un quadrilatero)
   if ( FORCE_FIST  &&  PL.GetPointNbr() > 5)
      return MakeByFist( {PL}, vPt, vTr) ;

  // verifico che la polilinea sia chiusa e piana e calcolo il piano medio del poligono
   double dArea ;
   Plane3d plPlane ;
   if ( ! PL.IsClosedAndFlat( plPlane, dArea, 50 * EPS_SMALL))
      return false ;
  // determino il piano ottimale di proiezione e il relativo senso di rotazione
   bool bCCW ;
   if ( ! CalcProjPlane( plPlane.GetVersN(), m_nPlane, bCCW))
      return false ;

  // forzo esecuzione triangolazione con earcut.hpp
   if ( FORCE_EARCUT_HPP) {
      return MakeByEC_HPP( PL, bCCW, vPt, vTr) ;
   }

  // riempio il vettore con i vertici del poligono da triangolare
   vPt.reserve( PL.GetPointNbr() - 1) ;
   // salto il primo punto (coincide con l'ultimo)
   Point3d ptP ;
   if ( ! PL.GetFirstPoint( ptP))
      return false ;
   // inserisco i punti
   while ( PL.GetNextPoint( ptP))
      vPt.push_back( ptP) ;
  // se non CCW inverto il vettore dei punti
   if ( ! bCCW)
      reverse( vPt.begin(), vPt.end()) ;

  // eseguo la triangolazione
   double dMinMinAng2, dMinMinAng3 ;
   if ( ! MakeByEC2( vPt, vTr, dMinMinAng2)) {
      if ( ! MakeByEC3( vPt, vTr, dMinMinAng3)) {
         LOG_INFO( GetEGkLogger(), "Info : problems in MakeByEC23(1)")
         return MakeByEC_HPP( PL, bCCW, vPt, vTr) ;
      }
   }
   else if ( dMinMinAng2 < 5) {
      INTVECTOR vMyTr ;
      if ( MakeByEC3( vPt, vMyTr, dMinMinAng3)  &&  dMinMinAng3 > dMinMinAng2)
         vTr = vMyTr ;
   }

  // se era CW, devo invertire il senso dei triangoli
   if ( ! bCCW)
      reverse( vTr.begin(), vTr.end()) ;

   return true ;
}

//----------------------------------------------------------------------------
// In : POLYLINEVECTOR : vector of polylines, the first outer, the others inner
// Out : PNTVECTOR (Point3d Vector) : points of the polyline 
//       INTVECTOR (int Vector) : 3*T indices of above points for T triangles   
//----------------------------------------------------------------------------
bool
Triangulate::Make( const POLYLINEVECTOR& vPL, PNTVECTOR& vPt, INTVECTOR& vTr)
{
  // pulisco i vettori di ritorno
   vPt.clear() ;
   vTr.clear() ;
  // ci devono essere delle polilinee nel vettore
   if ( &vPL == nullptr  ||  vPL.empty())
      return false ;
  // se una sola polilinea mi riconduco al caso precedente
   if ( vPL.size() == 1)
      return Make( vPL[0], vPt, vTr) ;

  // se fist  
   if ( FORCE_FIST)
      return MakeByFist( vPL, vPt, vTr) ;

  // verifico che la polilinea esterna sia chiusa e piana e calcolo il piano medio del poligono
   double dArea ;
   Plane3d plExtPlane ;
   if ( ! vPL[0].IsClosedAndFlat( plExtPlane, dArea, 50 * EPS_SMALL))
      return false ;
  // determino il piano ottimale di proiezione e il relativo senso di rotazione
   bool bCCW ;
   if ( ! CalcProjPlane( plExtPlane.GetVersN(), m_nPlane, bCCW))
      return false ;
  // verifico le altre polilinee
   for ( int i = 1 ; i < int( vPL.size()) ; ++i) {
     // deve essere chiusa, giacere nello stesso piano ed essere orientata al contrario della esterna
      double dArea2 ;
      Plane3d plPlane ;
      if ( ! vPL[i].IsClosedAndFlat( plPlane, dArea2, 50 * EPS_SMALL)  ||
           ! AreOppositeVectorApprox( plExtPlane.GetVersN(), plPlane.GetVersN()))
         return false ;
   } 

  // forzo esecuzione triangolazione con earcut.hpp
   if ( FORCE_EARCUT_HPP) {
      return MakeByEC_HPP( vPL, bCCW, vPt, vTr) ;
   }

  // se non CCW inverto tutte le polilinee
   if ( ! bCCW) {
      for ( int i = 0 ; i < int( vPL.size()) ; ++i)
         const_cast<PolyLine&>(vPL[i]).Invert( true) ;
   }
  // calcolo ordine decrescente su Xmax o Ymax o Zmax secondo m_nPlane per le curve interne
   INTVECTOR vOrd ;
   bool bOk = SortInternalLoops( vPL, vOrd) ;
  // riempio il vettore con i punti dei poligoni da triangolare
   // calcolo spazio totale e spazio massimo per un percorso interno
   int nTot = vPL[0].GetPointNbr() - 1 ;
   int nMax = 0 ;
   for ( int i = 1 ; i < int( vPL.size()) ; ++i) {
      nTot += vPL[i].GetPointNbr() + 1 ;
      if ( vPL[i].GetPointNbr() > nMax)
         nMax = vPL[i].GetPointNbr() ;
   }
   // riservo spazio pari al totale dei punti (anche quelli ripetuti di chiusura che servono per i link)
   vPt.reserve( nTot) ;
   // inserisco i punti del contorno esterno (tranne il primo che coincide con l'ultimo)
   bOk = bOk && GetPntVectorFromPolyline( vPL[0], false, vPt) ;
   // ciclo sui percorsi interni ordinati secondo Xmax decrescente
   PNTVECTOR vPi ;
   vPi.reserve( nMax) ;
   for ( int i = 1 ; bOk && i < int( vPL.size()) ; ++ i) {
      // riordino il percorso per avere punto iniziale con Xmax
      if ( ! GetPntVectorFromPolyline( vPL[vOrd[i]], true, vPi)) {
         bOk = false ;
         break ;
      }
      // cerco un punto del percorso esterno visibile dal punto iniziale del precedente interno
      int nI ;
      if ( ! GetOuterPntToJoin( vPt, vPi[0], nI)) {
         bOk = false ;
         break ;
      }
      // riordino percorso esterno per avere questo punto all'inizio
      if ( ! ChangeStartPntVector( nI, vPt)) {
         bOk = false ;
         break ;
      }
      // ripeto punto iniziale
      vPt.push_back( vPt[0]) ;
      // accodo percorso interno
      for ( int j = 0 ; j < int( vPi.size()) ; ++j)
         vPt.push_back( vPi[j]) ;
      // ripeto punto iniziale di percorso interno
      vPt.push_back( vPi[0]) ;
      // cancello percorso interno
      vPi.clear() ;
   }
  // ripristino l'orientamento delle polilinee originali per il caso non CCW
   if ( ! bCCW) {
      for ( int i = 0 ; i < int( vPL.size()) ; ++i)
         const_cast<PolyLine&>(vPL[i]).Invert( true) ;
   }
   if ( ! bOk)
      return MakeByEC_HPP( vPL, bCCW, vPt, vTr) ;

  // eseguo la triangolazione
   double dMinMinAng2, dMinMinAng3 ;
   if ( ! MakeByEC2( vPt, vTr, dMinMinAng2)) {
      if ( ! MakeByEC3( vPt, vTr, dMinMinAng3)) {
         LOG_INFO( GetEGkLogger(), "Info : problems in MakeByEC23(N)")
         return MakeByEC_HPP( vPL, bCCW, vPt, vTr) ;
      }
   }
   else if ( dMinMinAng2 < 5) {
      INTVECTOR vMyTr ;
      if ( MakeByEC3( vPt, vMyTr, dMinMinAng3)  &&  dMinMinAng3 > dMinMinAng2)
         vTr = vMyTr ;
   }

  // se era CW, devo invertire il senso dei triangoli
   if ( ! bCCW)
      reverse( vTr.begin(), vTr.end()) ;

   return true ;
}

//---------------------------------------------------------------------------
bool
Triangulate::MakeAdvanced( const POLYLINEVECTOR& vPLORIG, PNTVECTOR& vPt, INTVECTOR& vTr)
{
   INTMATRIX vnPLIndMat ;
   return MakeAdvanced( vPLORIG, vPt, vTr, vnPLIndMat) ;
}

//---------------------------------------------------------------------------
bool
Triangulate::MakeAdvanced( const POLYLINEVECTOR& vPLORIG, PNTVECTOR& vPt, INTVECTOR& vTr, const INTMATRIX& vnPLIndMatPre)
{
   vPt.clear() ;
   vTr.clear() ;
  // se non ho PolyLine, allora non faccio nulla
   if ( vPLORIG.empty())
      return true ;
 
   POLYLINEVECTOR vPL ;
   Vector3d vtN ;
  // se non sono stati passate le info per ordinare le polyline allora le ordino
   INTMATRIX vnPLIndMat ;
   BOOLVECTOR vbInvert ;
   if ( vnPLIndMatPre.empty()) {
      if ( ! CalcRegionPolyLines( vPLORIG, vtN, vnPLIndMat, vbInvert))
         return false ;
      vPL = vPLORIG ;
      for ( int i = 0 ; i < int( vbInvert.size()) ; i++) {
         if ( vbInvert[i])
            vPL[i].Invert() ;      
      }
   }
   else {
     // ho già calcolato e riordinato tutto, devo solo fare una copia delle polyline
     // non serve fare le eventuali inversioni delle polyline, perché se è già stata calcolata la matrice dei chunck allora sono già state invertire
      vPL = vPLORIG ;
      vnPLIndMat = vnPLIndMatPre ;
   }
 
  // chiamo la Triangolazione per ogni riga della matrice ( quindi su ogni "Chunk")
   for ( int i = 0 ; i < int( vnPLIndMat.size()) ; ++ i) {
      PNTVECTOR vPt_tmp ; INTVECTOR vTr_tmp ;
      POLYLINEVECTOR vPL_tmp ;
      for ( int j = 0 ; j < int( vnPLIndMat[i].size()) ; ++ j)
         vPL_tmp.push_back( vPL[vnPLIndMat[i][j]]) ;
      if ( ! Make( vPL_tmp, vPt_tmp, vTr_tmp))
         return false ;
      int nSize = int( vPt.size()) ;
      for ( int p = 0 ; p < int( vPt_tmp.size()) ; ++ p)
         vPt.push_back( vPt_tmp[p]) ;
      for ( int t = 0 ; t < int( vTr_tmp.size()) ; ++ t)
         vTr.push_back( nSize + vTr_tmp[t]) ;
   }
 
   return true ;
}

//----------------------------------------------------------------------------
// Triangulate the CCW n-gon specified by the vertices vPt (Pt[n] != Pt[0])
// Ear Clipping algorithm from mapbox
//----------------------------------------------------------------------------
bool
Triangulate::MakeByEC_HPP( const PolyLine& PL, bool bCCW, PNTVECTOR& vPt, INTVECTOR& vTr)
{
  // pulisco i vettori di ritorno
   vPt.clear() ;
   vTr.clear() ;
  // riempio il vettore con i vertici del poligono da triangolare
   vPt.reserve( PL.GetPointNbr() - 1) ;
   // salto il primo punto (coincide con l'ultimo)
   Point3d ptP ;
   if ( ( bCCW  &&  ! PL.GetFirstPoint( ptP))  ||
        ( ! bCCW  &&  ! PL.GetLastPoint( ptP)))
      return false ;
   // inserisco i punti
   while ( ( bCCW  &&  PL.GetNextPoint( ptP))  ||
            ( ! bCCW  &&   PL.GetPrevPoint( ptP)))
      vPt.push_back( ptP) ;
  // Create array
   using Point = array<double, 2> ;
   vector<vector<Point>> polygon ;
  // Fill polygon structure with actual data. Any winding order works.
   // The first polyline defines the main polygon.
   polygon.resize( 1) ;
   polygon[0].reserve( vPt.size()) ;
   for ( int i = 0 ; i < int( vPt.size()) ;  ++i) {
      switch ( m_nPlane) {
      default : // PL_XY
         polygon[0].push_back( { vPt[i].x, vPt[i].y}) ;
         break ;
      case PL_YZ :
         polygon[0].push_back( { vPt[i].y, vPt[i].z}) ;
         break ;
      case PL_ZX :
         polygon[0].push_back( { vPt[i].z, vPt[i].x}) ;
         break ;
      }
   }
  // Run tessellation
   // Returns array of indices that refer to the vertices of the input polygon.
   // Three subsequent indices form a triangle. Output triangles are counterclockwise.
   vTr = mapbox::earcut<int32_t>( polygon) ;
   if ( vTr.empty()) {
      LOG_INFO( GetEGkLogger(), "Info : problems in MakeByEC_HPP(1)")
      return false ;
   }
   if ( ! bCCW)
      reverse( vTr.begin(), vTr.end()) ;
   return true ;
}

//----------------------------------------------------------------------------
bool
Triangulate::MakeByEC_HPP( const POLYLINEVECTOR& vPL, bool bCCW, PNTVECTOR& vPt, INTVECTOR& vTr)
{
  // pulisco i vettori di ritorno
   vPt.clear() ;
   vTr.clear() ;
  // Creo il vettore con i punti dei poligoni da triangolare
   // calcolo spazio totale e spazio massimo per un percorso interno
   int nTot = vPL[0].GetPointNbr() - 1 ;
   for ( int i = 1 ; i < int( vPL.size()) ; ++i)
      nTot += vPL[i].GetPointNbr() - 1 ;
   // riservo spazio pari al totale dei punti (esclusi quelli ripetuti)
   vPt.reserve( nTot) ;
  // Create array
   using Point = array<double, 2> ;
   vector<vector<Point>> polygon ;
   polygon.resize( vPL.size()) ;
  // Eseguo riempimento di vettore e array
   for ( int i = 0 ; i < int( vPL.size()) ; ++i) {
      polygon[i].reserve( vPL[i].GetPointNbr() - 1) ;
     // salto il primo punto (coincide con l'ultimo)
      Point3d ptP ;
      if ( ( bCCW  &&  ! vPL[i].GetFirstPoint( ptP))  ||
            ( ! bCCW  &&  ! vPL[i].GetLastPoint( ptP)))
         return false ;
     // inserisco i punti
      while ( ( bCCW  &&  vPL[i].GetNextPoint( ptP))  ||
              ( ! bCCW  &&   vPL[i].GetPrevPoint( ptP))) {
         vPt.push_back( ptP) ;
         switch ( m_nPlane) {
         default : // PL_XY
            polygon[i].push_back( { ptP.x, ptP.y}) ;
            break ;
         case PL_YZ :
            polygon[i].push_back( { ptP.y, ptP.z}) ;
            break ;
         case PL_ZX :
            polygon[i].push_back( { ptP.z, ptP.x}) ;
            break ;
         }
      }
   }
   // Run tessellation
   // Returns array of indices that refer to the vertices of the input polygon.
   // Three subsequent indices form a triangle. Output triangles are counterclockwise.
   vTr = mapbox::earcut<int32_t>( polygon) ;
   if ( vTr.empty()) {
      LOG_INFO( GetEGkLogger(), "Info : problems in MakeByEC_HPP(N)")
      return false ;
   }
   if ( ! bCCW)
      reverse( vTr.begin(), vTr.end()) ;
   return true ;
}

//----------------------------------------------------------------------------
// Triangulate the CCW n-gon specified by the vertices vPt (Pt[n] != Pt[0])
// Ear Clipping algorithm
//----------------------------------------------------------------------------
bool
Triangulate::MakeByEC( const PNTVECTOR& vPt, INTVECTOR& vTr)
{
  // Clear triangle vector
   vTr.clear() ;

  // At least 3 points
   int n = int( vPt.size()) ;
   if ( n < 3)
      return false ;

  // Creo il vettore degli indici del Poligono
   INTVECTOR vPol ;
   vPol.reserve( n) ;
   for ( int i = 0 ; i < n ; ++ i)
      vPol.push_back( i) ;

  // Preallocate triangle vector ( #triangles = n - 2)
   vTr.reserve( 3 * ( n - 2)) ;

  // Set up previous and next links to effectively form a double-linked vertex list
   INTVECTOR vPrev( n) ;
   INTVECTOR vNext( n) ;
   for ( int j = 0 ; j < n ; ++ j) {
      vPrev[j] = j - 1 ;
      vNext[j] = j + 1 ;
   }
   vPrev[0] = n - 1 ;
   vNext[n-1] = 0 ;

  // Start at vertex 0
   int i = 0 ;
   int nCount = n ;
  // Keep removing vertices until just a triangle left
   while ( n >= 3) {
     // To avoid infinite loop
      if ( nCount <= 0)
         return false ;
      -- nCount ;
     // Test if current vertex, v[i], is an ear
      bool bIsEar = TestTriangle( vPt, vPol, vPrev, vNext, i) ;
      bool bSave = bIsEar ;
     // Verify if triangle is null (accept to discard)
      if ( ! bIsEar) {
         if ( Collinear( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]))
            bIsEar = true ;
      }
     // If current vertex v[i] is an ear, delete it and visit the previous vertex
      if ( bIsEar) {
         // Triangle (v[prev[i]], v[i], v[next[i]]) is an ear
          if ( bSave) {
             vTr.push_back( vPol[vPrev[i]]) ;
             vTr.push_back( vPol[i]) ;
             vTr.push_back( vPol[vNext[i]]) ;
          }
         // Delete vertex v[i] by redirecting next and previous links
         // of neighboring verts past it. Decrement vertex count
          vNext[vPrev[i]] = vNext[i] ;
          vPrev[vNext[i]] = vPrev[i] ;
          n--;
         // Visit the previous vertex next
          i = vPrev[i] ;
         // Reset Count
          nCount = n ;
      }
      else {
         // Current vertex is not an ear; visit the next vertex
          i = vNext[i] ;
      }
   }

   return true ;
}

//----------------------------------------------------------------------------
// Triangulate the CCW n-gon specified by the vertices vPt (Pt[n] != Pt[0])
// Ear Clipping algorithm enhanced, choose smaller diagonal
//----------------------------------------------------------------------------
bool
Triangulate::MakeByEC2( const PNTVECTOR& vPt, INTVECTOR& vTr, double& dMinMinAng)
{
  // Clear triangle vector
   vTr.clear() ;
   dMinMinAng = ANG_STRAIGHT ;

  // At least 3 points
   int n = int( vPt.size()) ;
   if ( n < 3)
      return false ;

  // Creo il vettore degli indici del Poligono
   INTVECTOR vPol ;
   vPol.reserve( n) ;
   for ( int i = 0 ; i < n ; ++ i)
      vPol.push_back( i) ;

  // Preallocate triangle vector ( #triangles = n - 2)
   vTr.reserve( 3 * ( n - 2)) ;

  // Set up previous and next links to effectively form a double-linked vertex list
   INTVECTOR vPrev( n) ;
   INTVECTOR vNext( n) ;
   for ( int j = 0 ; j < n ; ++ j) {
      vPrev[j] = j - 1 ;
      vNext[j] = j + 1 ;
   }
   vPrev[0] = n - 1 ;
   vNext[n-1] = 0 ;

  // Prepare Ear status vector
   INTVECTOR vEar( n, EAS_NULL) ;

  // Prepare PointGrid
   if ( ! PrepareGrid( vPt, vPol, vPrev, vNext))
      return false ;

  // Start at vertex 0
   int i = 0 ;
   int nCount = n ;
  // Keep removing vertices until just a triangle left
   while ( n >= 3) {
     // To avoid infinite loop
      if ( nCount <= 0)
         return false ;
      -- nCount ;
     // Test if current vertex, v[i], is an ear
      if ( vEar[i] == EAS_NULL)
         vEar[i] = ( TestTriangle( vPt, vPol, vPrev, vNext, i) ? EAS_OK : EAS_NO) ;
      bool bIsEar = ( vEar[i] == EAS_OK) ;
      bool bSave = bIsEar ;
      if ( bIsEar) {
        // Save square distance of diagonal
         double dSqDist = SqDist(vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]]) ;
        // Start point for trials
         int j = i ;
         int k = i ;
        // Try with 19 next
         int nLimN = min( 19, n / 2) ;
         for ( int h = 0 ; h < nLimN ; ++ h) {
            j = vNext[j] ;
            double dMySqDist = SqDist( vPt[vPol[vPrev[j]]], vPt[vPol[vNext[j]]]) ;
            if ( dMySqDist < 0.9 * dSqDist) {
               if ( vEar[j] == EAS_NULL)
                  vEar[j] = ( TestTriangle( vPt, vPol, vPrev, vNext, j) ? EAS_OK : EAS_NO) ;
               if ( vEar[j] == EAS_OK) {
                  dSqDist = dMySqDist ;
                  i = j ;
               }
            }
         }
        // Try with 19 prev
         int nLimP = min( 19, n / 2) ;
         for ( int h = 0 ; h < nLimP ; ++ h) {
            k = vPrev[k] ;
            double dMySqDist = SqDist( vPt[vPol[vPrev[k]]], vPt[vPol[vNext[k]]]) ;
            if ( dMySqDist < 0.9 * dSqDist) {
               if ( vEar[k] == EAS_NULL)
                  vEar[k] = ( TestTriangle( vPt, vPol, vPrev, vNext, k) ? EAS_OK : EAS_NO) ;
               if ( vEar[k] == EAS_OK) {
                  dSqDist = dMySqDist ;
                  i = k ;
               }
            }
         }
      }
     // Verify if triangle is null (accept to discard)
      else {
         if ( Collinear( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]])  &&
              ! SameDirection( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]))
            bIsEar = true ;
      }
     // If current vertex v[i] is an ear, delete it and visit the previous vertex
      if ( bIsEar) {
        // Triangle (v[prev[i]], v[i], v[next[i]]) is an ear
         if ( bSave) {
            vTr.push_back( vPol[vPrev[i]]) ;
            vTr.push_back( vPol[i]) ;
            vTr.push_back( vPol[vNext[i]]) ;
            double dMinAng = CalcTriangleMinAngle( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]) ;
            dMinMinAng = min( dMinMinAng, dMinAng) ;
         }
        // Reset earity of diagonal endpoints
         vEar[vPrev[i]] = EAS_NULL ;
         vEar[vNext[i]] = EAS_NULL ;
        // Delete vertex v[i] by redirecting next and previous links
        // of neighboring verts past it. Decrement vertex count
         vNext[vPrev[i]] = vNext[i] ;
         vPrev[vNext[i]] = vPrev[i] ;
         -- n ;
        // Visit the previous vertex next
         i = vPrev[i] ;
        // Reset Count
         nCount = n ;
      }
      else {
         // Current vertex is not an ear; visit the next vertex
          i = vNext[i] ;
      }
   }

   return true ;
}

//----------------------------------------------------------------------------
// Triangulate the CCW n-gon specified by the vertices vPt (Pt[n] != Pt[0])
// Ear Clipping algorithm enhanced, choose max MinAng
//----------------------------------------------------------------------------
bool
Triangulate::MakeByEC3( const PNTVECTOR& vPt, INTVECTOR& vTr, double& dMinMinAng)
{
  // Clear triangle vector
   vTr.clear() ;
   dMinMinAng = ANG_STRAIGHT ;

  // At least 3 points
   int n = int( vPt.size()) ;
   if ( n < 3)
      return false ;

  // Creo il vettore degli indici del Poligono
   INTVECTOR vPol ;
   vPol.reserve( n) ;
   for ( int i = 0 ; i < n ; ++ i)
      vPol.push_back( i) ;

  // Preallocate triangle vector ( #triangles = n - 2)
   vTr.reserve( 3 * ( n - 2)) ;

  // Set up previous and next links to effectively form a double-linked vertex list
   INTVECTOR vPrev( n) ;
   INTVECTOR vNext( n) ;
   for ( int j = 0 ; j < n ; ++ j) {
      vPrev[j] = j - 1 ;
      vNext[j] = j + 1 ;
   }
   vPrev[0] = n - 1 ;
   vNext[n-1] = 0 ;

  // Prepare Ear status vector
   INTVECTOR vEar( n, EAS_NULL) ;

  // Prepare PointGrid
   if ( ! PrepareGrid( vPt, vPol, vPrev, vNext))
      return false ;

  // Start at vertex 0
   int i = 0 ;
   int nCount = n ;
  // Keep removing vertices until just a triangle left
   while ( n >= 3) {
     // To avoid infinite loop
      if ( nCount <= 0)
         return false ;
      -- nCount ;
     // Test if current vertex, v[i], is an ear
      if ( vEar[i] == EAS_NULL)
         vEar[i] = ( TestTriangle( vPt, vPol, vPrev, vNext, i) ? EAS_OK : EAS_NO) ;
      bool bIsEar = ( vEar[i] == EAS_OK) ;
      bool bSave = bIsEar ;
      double dMinAng = -1 ;
      if ( bIsEar) {
        // Square Length & MinAngle
         double dSqLen = SqDist(vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]]) ;
         dMinAng = CalcTriangleMinAngle( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]) ;
        // Start point for trials
         int j = i ;
         int k = i ;
        // Try with 29 next
         int nLimN = min( 29, n / 2) ;
         for ( int h = 0 ; h < nLimN ; ++ h) {
            j = vNext[j] ;
            double dMySqLen = SqDist( vPt[vPol[vPrev[j]]], vPt[vPol[vNext[j]]]) ;
            if ( dMySqLen < 2 * dSqLen) {
               double dMyMinAng = CalcTriangleMinAngle( vPt[vPol[vPrev[j]]], vPt[vPol[j]], vPt[vPol[vNext[j]]]) ;
               if ( dMyMinAng > 1.01 * dMinAng) {
                  if ( vEar[j] == EAS_NULL)
                     vEar[j] = ( TestTriangle( vPt, vPol, vPrev, vNext, j) ? EAS_OK : EAS_NO) ;
                  if ( vEar[j] == EAS_OK) {
                     dSqLen = dMySqLen ;
                     dMinAng = dMyMinAng ;
                     i = j ;
                  }
               }
            }
         }
        // Try with 29 prev
         int nLimP = min( 29, n / 2) ;
         for ( int h = 0 ; h < nLimP ; ++ h) {
            k = vPrev[k] ;
            double dMySqLen = SqDist( vPt[vPol[vPrev[k]]], vPt[vPol[vNext[k]]]) ;
            if ( dMySqLen < 2 * dSqLen) {
               double dMyMinAng = CalcTriangleMinAngle( vPt[vPol[vPrev[k]]], vPt[vPol[k]], vPt[vPol[vNext[k]]]) ;
               if ( dMyMinAng > 1.01 * dMinAng) {
                  if ( vEar[k] == EAS_NULL)
                     vEar[k] = ( TestTriangle( vPt, vPol, vPrev, vNext, k) ? EAS_OK : EAS_NO) ;
                  if ( vEar[k] == EAS_OK) {
                     dSqLen = dMySqLen ;
                     dMinAng = dMyMinAng ;
                     i = k ;
                  }
               }
            }
         }
      }
     // Verify if triangle is null (accept to discard)
      else {
         if ( Collinear( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]])  &&
              ! SameDirection( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]]))
            bIsEar = true ;
      }
     // If current vertex v[i] is an ear, delete it and visit the previous vertex
      if ( bIsEar) {
        // Triangle (v[prev[i]], v[i], v[next[i]]) is an ear to save
         if ( bSave) {
            vTr.push_back( vPol[vPrev[i]]) ;
            vTr.push_back( vPol[i]) ;
            vTr.push_back( vPol[vNext[i]]) ;
            dMinMinAng = min( dMinMinAng, dMinAng) ;
         }
        // Reset earity of diagonal endpoints
         vEar[vPrev[i]] = EAS_NULL ;
         vEar[vNext[i]] = EAS_NULL ;
        // Delete vertex v[i] by redirecting next and previous links
        // of neighboring verts past it. Decrement vertex count
         vNext[vPrev[i]] = vNext[i] ;
         vPrev[vNext[i]] = vPrev[i] ;
         -- n ;
        // Visit the previous vertex next
         i = vPrev[i] ;
        // Reset Count
         nCount = n ;
      }
      else {
        // Current vertex is not an ear; visit the next vertex
         i = vNext[i] ;
      }
   }

   return true ;
}

//----------------------------------------------------------------------------
bool
Triangulate::PrepareGrid( const PNTVECTOR& vPt, const INTVECTOR& vPol,
                          const INTVECTOR& vPrev, const INTVECTOR& vNext)
{
  // points number
   int n = int( vPol.size()) ;
  // overall box
   BBox3d b3All ;
   for ( int j = 0 ; j < n ; ++ j)
      b3All.Add( vPt[vPol[j]]) ;
  // grid cell dimension
   double dCellDim ;
   b3All.GetRadius( dCellDim) ;
   dCellDim *=  2 / sqrt( n) ;
  // grid 
   if ( ! m_VertGrid.Init( 2 * n, dCellDim))
      return false ;
   for ( int j = 0 ; j < n ; ++ j) {
     // insert only reflex vertex
      if ( ! TriangleIsCCW( vPt[vPol[vPrev[j]]], vPt[vPol[j]], vPt[vPol[vNext[j]]])) {
         if ( ! m_VertGrid.InsertPoint( vPt[vPol[j]], j))
            return false ;
      }
   }
   m_vVert.reserve( n / 5) ;

   return true ;
}

//----------------------------------------------------------------------------
bool
Triangulate::TestTriangle( const PNTVECTOR& vPt, const INTVECTOR& vPol,
                           const INTVECTOR& vPrev, INTVECTOR& vNext, int i)
{
  // Test if current vertex, v[i], is an ear
   bool bIsEar = true ;
  // An ear must be convex (here counterclockwise)
   if ( TriangleIsCCW( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]])  &&
        ! Collinear( vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]])) {
     // Loop over all vertices not part of the tentative ear
      BBox3d b3Tria ;
      b3Tria.Add( vPt[vPol[vPrev[i]]]) ;
      b3Tria.Add( vPt[vPol[i]]) ;
      b3Tria.Add( vPt[vPol[vNext[i]]]) ;
      // espando per compensare piccole approssimazioni
      b3Tria.Expand( 10 * EPS_SMALL) ;
      m_VertGrid.Find( b3Tria, m_vVert) ;
      for ( int j = 0 ; j < int( m_vVert.size()) ; ++ j) {
         int k = m_vVert[j] ;
         if ( k == i  ||  k == vPrev[i]  ||  k == vNext[i] )
            continue ;
        // If vertex k is on a triangle vertex
         if ( AreSamePoint( vPt[vPol[k]], vPt[vPol[vPrev[i]]])  ||  
              AreSamePoint( vPt[vPol[k]], vPt[vPol[i]])  ||
              AreSamePoint( vPt[vPol[k]], vPt[vPol[vNext[i]]])) {
           // Test previous segment with triangle diagonal
            if ( TestIntersection( vPt[vPol[vPrev[k]]], vPt[vPol[k]], vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]])) {
               bIsEar = false ;
               break ;
            }
           // Test next segment with triangle diagonal
            if ( TestIntersection( vPt[vPol[k]], vPt[vPol[vNext[k]]], vPt[vPol[vPrev[i]]], vPt[vPol[vNext[i]]])) {
               bIsEar = false ;
               break ;
            }
         }
        // If vertex k is inside the ear triangle, then this is not an ear
         else if ( TestPointInOrOnTriangle( vPt[vPol[k]], vPt[vPol[vPrev[i]]], vPt[vPol[i]], vPt[vPol[vNext[i]]])) {
            bIsEar = false ;
            break ;
         }
      }
   }
   else {
     // The ear triangle is clockwise so v[i] is not an ear
      bIsEar = false ;
   }

   return bIsEar ;
}

//----------------------------------------------------------------------------
// Ratio between Circumcircle Radius and Incircle Diameter (minimum 1 for equilateral) 
double
Triangulate::CalcTriangleAspectRatio( const Point3d& ptPa, const Point3d& ptPb, const Point3d& ptPc)
{
   double dSqDistA = SquareDist( ptPa, ptPb) ;
   double dSqDistB = SquareDist( ptPb, ptPc) ;
   double dSqDistC = SquareDist( ptPc, ptPa) ;
   double dTwoArea = abs( TwoArea( ptPa, ptPb, ptPc)) ;
   if ( dTwoArea < SQ_EPS_SMALL)
      return INFINITO ;
   else
      return ( max( { dSqDistA, dSqDistB, dSqDistC}) / dTwoArea) ;
}

//----------------------------------------------------------------------------
double
Triangulate::CalcTriangleMinAngle( const Point3d& ptPa, const Point3d& ptPb, const Point3d& ptPc)
{
   double dSqLenA = SquareDist( ptPa, ptPb) ;
   double dSqLenB = SquareDist( ptPb, ptPc) ;
   double dSqLenC = SquareDist( ptPc, ptPa) ;
   if ( dSqLenA > dSqLenB)
      swap( dSqLenA, dSqLenB) ;
   if ( dSqLenA > dSqLenC)
      swap( dSqLenA, dSqLenC) ;
   double dLenB = sqrt( dSqLenB) ;
   double dLenC = sqrt( dSqLenC) ;
   double dCosA = ( dSqLenB + dSqLenC - dSqLenA) / ( 2 * dLenB * dLenC) ;
   dCosA = Clamp( dCosA, -1., +1.) ;
   double dAngA = acos( dCosA) * RADTODEG ;
   return dAngA ;
}

//----------------------------------------------------------------------------
double
Triangulate::SquareDist( const Point3d& ptA, const Point3d& ptB)
{
   switch ( m_nPlane) {
   default : // PL_XY
      return (( ptB.x - ptA.x) * ( ptB.x - ptA.x) + ( ptB.y - ptA.y) * ( ptB.y - ptA.y)) ;
   case PL_YZ :
      return (( ptB.y - ptA.y) * ( ptB.y - ptA.y) + ( ptB.z - ptA.z) * ( ptB.z - ptA.z)) ;
   case PL_ZX :
      return (( ptB.z - ptA.z) * ( ptB.z - ptA.z) + ( ptB.x - ptA.x) * ( ptB.x - ptA.x)) ;
   }
}

//----------------------------------------------------------------------------
// Vector product is double of the area (positive if CCW)
double
Triangulate::TwoArea( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC)
{
   switch ( m_nPlane) {
   default : // PL_XY
      return ( ptB.x - ptA.x) * ( ptC.y - ptB.y) - ( ptB.y - ptA.y) * ( ptC.x - ptB.x) ;
   case PL_YZ :
      return ( ptB.y - ptA.y) * ( ptC.z - ptB.z) - ( ptB.z - ptA.z) * ( ptC.y - ptB.y) ;
   case PL_ZX :
      return ( ptB.z - ptA.z) * ( ptC.x - ptB.x) - ( ptB.x - ptA.x) * ( ptC.z - ptB.z) ;
   }
}

//----------------------------------------------------------------------------
// Distance less than tolerance
bool
Triangulate::AreSamePoint( const Point3d& ptA, const Point3d& ptB, double dToler)
{
   return ( SquareDist( ptA, ptB) < dToler * dToler) ;
}

//----------------------------------------------------------------------------
// Same Direction <--> Scalar Product Positive
bool
Triangulate::SameDirection( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC)
{
   switch ( m_nPlane) {
   default : // PL_XY
      return (( ptB.x - ptA.x) * ( ptC.x - ptB.x) + ( ptB.y - ptA.y) * ( ptC.y - ptB.y)) > 0 ;
   case PL_YZ :
      return (( ptB.y - ptA.y) * ( ptC.y - ptB.y) + ( ptB.z - ptA.z) * ( ptC.z - ptB.z)) > 0 ;
   case PL_ZX :
      return (( ptB.z - ptA.z) * ( ptC.z - ptB.z) + ( ptB.x - ptA.x) * ( ptC.x - ptB.x)) > 0 ;
   }
}

//----------------------------------------------------------------------------
// Collinear <--> Null Area
bool
Triangulate::Collinear( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC, double dToler)
{
   double dSqDistA = SquareDist( ptA, ptB) ;
   double dSqDistB = SquareDist( ptB, ptC) ;
   double dSqDistC = SquareDist( ptC, ptA) ;
   double dTwoArea = abs( TwoArea( ptA, ptB, ptC)) ;
   return ( dTwoArea * dTwoArea < dToler * dToler * max( { dSqDistA, dSqDistB, dSqDistC})) ;
}

//----------------------------------------------------------------------------
// Positive Area means A -> B -> C counterclockwise
bool
Triangulate::TriangleIsCCW( const Point3d& ptA, const Point3d& ptB, const Point3d& ptC, double dToler)
{
   return ( TwoArea( ptA, ptB, ptC) > dToler * dToler) ;
}

//----------------------------------------------------------------------------
// Proper intersection between line segments
bool
Triangulate::TestIntersection( const Point3d& ptA1, const Point3d& ptA2,
                               const Point3d& ptB1, const Point3d& ptB2)
{
  // Collinearity is not considered intersection
   if ( Collinear( ptA1, ptA2, ptB1)  ||
        Collinear( ptA1, ptA2, ptB2)  ||
        Collinear( ptB1, ptB2, ptA1)  ||
        Collinear( ptB1, ptB2, ptA2))
      return false ;
  // To intersect, the endpoints of a line segment must be on opposite side of the other line segment
   return ( TriangleIsCCW( ptA1, ptA2, ptB1) != TriangleIsCCW( ptA1, ptA2, ptB2)  &&
            TriangleIsCCW( ptB1, ptB2, ptA1) != TriangleIsCCW( ptB1, ptB2, ptA2)) ;
}

//----------------------------------------------------------------------------
// Test if point p is contained in triangle (a, b, c)
bool
Triangulate::TestPointInTriangle( const Point3d& ptP, const Point3d& ptA, const Point3d& ptB, const Point3d& ptC)
{
  // If P is on a vertex is considered outside
   if ( AreSamePoint( ptP, ptA))
      return false ;
   if ( AreSamePoint( ptP, ptB))
      return false ;
   if ( AreSamePoint( ptP, ptC))
      return false ;
  // If P is on the right of at least one edge is outside
   if ( TriangleIsCCW( ptA, ptP, ptB))
      return false ;
   if ( TriangleIsCCW( ptB, ptP, ptC))
      return false ;
   if ( TriangleIsCCW( ptC, ptP, ptA))
      return false ;
  // P is in triangle
   return true ;
}

//----------------------------------------------------------------------------
// test if point p is inside or on the border of triangle (a, b, c)
bool
Triangulate::TestPointInOrOnTriangle( const Point3d& ptP, const Point3d& ptA, const Point3d& ptB, const Point3d& ptC)
{
  // If P is on a vertex is considered inside
   if ( AreSamePoint( ptP, ptA))
      return true ;
   if ( AreSamePoint( ptP, ptB))
      return true ;
   if ( AreSamePoint( ptP, ptC))
      return true ;
  // If P is on the right of at least one edge is outside
   if ( TriangleIsCCW( ptA, ptP, ptB, EPS_SMALL))
     return false ;
   if ( TriangleIsCCW( ptB, ptP, ptC, EPS_SMALL))
     return false ;
   if ( TriangleIsCCW( ptC, ptP, ptA, EPS_SMALL))
     return false ;
   return true ;
}

//----------------------------------------------------------------------------
bool
Triangulate::SortInternalLoops( const POLYLINEVECTOR& vPL, INTVECTOR& vOrd)
{
  // riempio vettore con indice e massimo specifico per ogni loop interno
   typedef pair<int,double> INDMAX ;         // coppia indice, massimo
   typedef vector<INDMAX>   INDMAXVECTOR ;   // vettore di coppie indice, massimo
   INDMAXVECTOR vMax ;
   vMax.reserve( vPL.size()) ;
   vMax.emplace_back( 0, 0.0) ;
   for ( int i = 1 ; i < int( vPL.size()) ; ++ i) {
      BBox3d b3Loc ;
      vPL[i].GetLocalBBox( b3Loc) ;
      switch ( m_nPlane) {
      default : // PL_XY
         vMax.emplace_back( i, b3Loc.GetMax().x) ;
         break ;
      case PL_YZ :
         vMax.emplace_back( i, b3Loc.GetMax().y) ;
         break ;
      case PL_ZX :
         vMax.emplace_back( i, b3Loc.GetMax().z) ;
         break ;
      }
   }
  // ordino vettore in senso decrescente rispetto al massimo
   sort( vMax.begin() + 1, vMax.end(), 
         []( const INDMAX& a, const INDMAX& b) { return ( a.second > b.second) ; }) ;
  // copio indice nel vettore di ordine
   vOrd.reserve( vPL.size()) ;
   for ( int i = 0 ; i < int( vPL.size()) ; ++ i)
      vOrd.push_back( vMax[i].first) ;

   return true ;
}

//----------------------------------------------------------------------------
bool
Triangulate::GetPntVectorFromPolyline( const PolyLine& PL, bool bXmaxStart, PNTVECTOR& vPi)
{
  // copio i punti nel vettore (tranne il primo che coincide con l'ultimo)
   Point3d ptP ;
   if ( ! PL.GetFirstPoint( ptP))
      return false ;
   while ( PL.GetNextPoint( ptP)) {
      vPi.push_back( ptP) ;
   }
  // se non richiesto riordino per Xmax o Ymax o Zmax, ho finito
   if ( ! bXmaxStart)
      return true ;
  // determino l'indice del punto con Xmax
   int nI = - 1 ;
   double dXmax = - INFINITO ;
   for ( int i = 0 ; i < int( vPi.size()) ; ++ i) {
      switch ( m_nPlane) {
      default : // PL_XY
         if ( vPi[i].x > dXmax) {
            dXmax = vPi[i].x ;
            nI = i ;
         }
         break ;
      case PL_YZ :
         if ( vPi[i].y > dXmax) {
            dXmax = vPi[i].y ;
            nI = i ;
         }
         break ;
      case PL_ZX :
         if ( vPi[i].z > dXmax) {
            dXmax = vPi[i].z ;
            nI = i ;
         }
         break ;
      }
   }
   if ( nI == - 1)
      return false ;
  // riordino il vettore, per avere il punto con Xmax in prima posizione
   return ChangeStartPntVector( nI, vPi) ;
}

//----------------------------------------------------------------------------
bool
Triangulate::GetOuterPntToJoin( const PNTVECTOR& vPt, const Point3d& ptP, int& nI)
{
  // cerco prima intersezione del raggio dal punto con direzione X+ al contorno esterno
   nI = - 1 ;
   double dMinDist = INFINITO ;
   Point3d ptInt ;
   int nNumPt = int( vPt.size()) ;
   for ( int i = 0 ; i < nNumPt ; ++ i) {
     // indice punto precedente
      int h = ( i - 1 >= 0 ) ? i - 1 : nNumPt - 1 ;
     // indice punto successivo
      int j = ( i + 1 < nNumPt) ? i + 1 : 0 ;
     // mi metto nel piano principale
      switch ( m_nPlane) {
      default :  // PL_XY
        // se i punti coincidono
         if ( abs( vPt[i].x - ptP.x) < EPS_SMALL  &&  abs( vPt[i].y - ptP.y) < EPS_SMALL) {
            dMinDist = 0 ;
            nI = i ;
            ptInt = vPt[i] ;
         }
        // se punto esattamente sul raggio e raggio interno al settore
         else if ( vPt[i].x > ptP.x  &&  abs( vPt[i].y - ptP.y) < EPS_SMALL  &&
              PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
           // se distanza minore della minima, nuovo minimo
            if ( ( vPt[i].x - ptP.x) < dMinDist) {
               dMinDist = vPt[i].x - ptP.x ;
               nI = i ;
               ptInt = vPt[i] ;
            }
         }
        // se segmento al punto successivo che attraversa il raggio e raggio interno ovvero a sinistra ( segmento crescente in Y)
         else if ( vPt[i].y < ptP.y  &&  vPt[j].y > ptP.y) {
           // calcolo l'ascissa di intersezione
            double dCoeff = ( ptP.y - vPt[i].y) / ( vPt[j].y - vPt[i].y) ;
            double dX = vPt[i].x + ( vPt[j].x - vPt[i].x) * dCoeff ;
           // se sta sul raggio e distanza minore della minima
            if ( dX > ptP.x - EPS_SMALL  &&  ( dX - ptP.x) < dMinDist) {
               dMinDist = dX - ptP.x ;
               nI = ( vPt[i].x >= vPt[j].x) ? i : j ;
               double dZ = vPt[i].z + ( vPt[j].z - vPt[i].z) * dCoeff ;
               ptInt.Set( dX, ptP.y, dZ) ;
            }
         }
         break ;
      case PL_YZ :
        // se i punti coincidono
         if ( abs( vPt[i].y - ptP.y) < EPS_SMALL  &&  abs( vPt[i].z - ptP.z) < EPS_SMALL) {
            dMinDist = 0 ;
            nI = i ;
            ptInt = vPt[i] ;
         }
        // se punto esattamente sul raggio e raggio interno al settore
         else if ( vPt[i].y > ptP.y  &&  abs( vPt[i].z - ptP.z) < EPS_SMALL  &&
              PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
           // se distanza minore della minima, nuovo minimo
            if ( ( vPt[i].y - ptP.y) < dMinDist) {
               dMinDist = vPt[i].y - ptP.y ;
               nI = i ;
               ptInt = vPt[i] ;
            }
         }
        // se segmento al punto successivo che attraversa il raggio e raggio interno ovvero a sinistra ( segmento crescente in Y)
         else if ( vPt[i].z < ptP.z  &&  vPt[j].z > ptP.z) {
           // calcolo l'ascissa di intersezione
            double dCoeff = ( ptP.z - vPt[i].z) / ( vPt[j].z - vPt[i].z) ;
            double dY = vPt[i].y + ( vPt[j].y - vPt[i].y) * dCoeff ;
           // se sta sul raggio e distanza minore della minima
            if ( dY > ptP.y - EPS_SMALL  &&  ( dY - ptP.y) < dMinDist) {
               dMinDist = dY - ptP.y ;
               nI = ( vPt[i].y >= vPt[j].y) ? i : j ;
               double dX = vPt[i].x + ( vPt[j].x - vPt[i].x) * dCoeff ;
               ptInt.Set( dX, dY, ptP.z) ;
            }
         }
         break ;
      case PL_ZX :
        // se i punti coincidono
         if ( abs( vPt[i].z - ptP.z) < EPS_SMALL  &&  abs( vPt[i].x - ptP.x) < EPS_SMALL) {
            dMinDist = 0 ;
            nI = i ;
            ptInt = vPt[i] ;
         }
        // se punto esattamente sul raggio e raggio interno al settore
         else if ( vPt[i].z > ptP.z  &&  abs( vPt[i].x - ptP.x) < EPS_SMALL  &&
              PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
           // se distanza minore della minima, nuovo minimo
            if ( ( vPt[i].z - ptP.z) < dMinDist) {
               dMinDist = vPt[i].z - ptP.z ;
               nI = i ;
               ptInt = vPt[i] ;
            }
         }
        // se segmento al punto successivo che attraversa il raggio e raggio interno ovvero a sinistra ( segmento crescente in Y)
         else if ( vPt[i].x < ptP.x  &&  vPt[j].x > ptP.x) {
           // calcolo l'ascissa di intersezione
            double dCoeff = ( ptP.x - vPt[i].x) / ( vPt[j].x - vPt[i].x) ;
            double dZ = vPt[i].z + ( vPt[j].z - vPt[i].z) * dCoeff ;
           // se sta sul raggio e distanza minore della minima
            if ( dZ > ptP.z - EPS_SMALL  &&  ( dZ - ptP.z) < dMinDist) {
               dMinDist = dZ - ptP.z ;
               nI = ( vPt[i].z >= vPt[j].z) ? i : j ;
               double dY = vPt[i].y + ( vPt[j].y - vPt[i].y) * dCoeff ;
               ptInt.Set( ptP.x, dY, dZ) ;
            }
         }
         break ;
      }
   }
  // non ho trovato alcunchè, errore
   if ( nI == - 1)
      return false ;
  // se ho trovato un punto esatto del contorno, non devo fare altri controlli
   if ( AreSamePointApprox( ptInt, vPt[nI]))
      return true ;
  // devo ora verificare che il segmento che unisce i punti non intersechi altri lati del contorno esterno
  // altrimenti tengo il punto con raggio più vicino a X_AX o Y_AX o Z_AX secondo m_nPlane
   int nJ = nI ;
   Point3d ptPa = ptP ;
   Point3d ptPb = vPt[nI] ;
   Point3d ptPc = ptInt ;
   bool bSwap = false ;
   switch ( m_nPlane) {
   default : /* PL_XY */ bSwap = ( ptPb.y > ptPc.y) ; break ;
   case PL_YZ : bSwap = ( ptPb.z > ptPc.z) ; break ;
   case PL_ZX : bSwap = ( ptPb.x > ptPc.x) ; break ;
   }
   if ( bSwap)
      swap( ptPb, ptPc) ;
   double dMinTan = INFINITO ;
   double dMinSqDist = SQ_INFINITO ;
   for ( int i = 0 ; i < nNumPt ; ++ i) {
     // salto il punto già trovato
      if ( i == nJ)
         continue ;
     // verifico se sta nel triangolo
      if ( TestPointInTriangle( vPt[i], ptPa, ptPb, ptPc)) {
         double dTan = INFINITO ;
         switch ( m_nPlane) {
         default : /* PL_XY */ dTan = abs(vPt[i].y - ptP.y) / (vPt[i].x - ptP.x) ; break ;
         case PL_YZ : dTan = abs(vPt[i].z - ptP.z) / (vPt[i].y - ptP.y) ; break ;
         case PL_ZX : dTan = abs(vPt[i].x - ptP.x) / (vPt[i].z - ptP.z) ; break ;
         }
         if ( dTan < dMinTan + EPS_ZERO) {
           // indice punto precedente
            int h = ( i - 1 >= 0) ? i - 1 : nNumPt - 1 ;
           // indice punto successivo
            int j = ( i + 1 < nNumPt) ? i + 1 : 0 ;
           // verifico che il raggio che unisce i punti stia nel settore
            if ( PointInSector( ptP, vPt[h], vPt[i], vPt[j])) {
               double dSqDist = SqDist( vPt[i], ptP) ;
               if ( dTan < dMinTan - EPS_ZERO  ||  dSqDist < dMinSqDist) {
                  dMinTan = dTan ;
                  dMinSqDist = dSqDist ;
                  nI = i ;
               }
            }
         }
      }  
   }

   return true ;
}

//----------------------------------------------------------------------------
bool
Triangulate::PointInSector( const Point3d& ptTest, const Point3d& ptPrev, const Point3d& ptCorn, const Point3d& ptNext)
{
  // la parte valida del settore è a sinistra dei segmenti ptPrev --> ptCorn --> ptNext
  // se corner convesso
   if ( TriangleIsCCW( ptPrev, ptCorn, ptNext, 0))
      return ( TriangleIsCCW( ptPrev, ptCorn, ptTest)  &&
               TriangleIsCCW( ptTest, ptCorn, ptNext)) ;
  // altrimenti corner concavo ( reflex)
   else
      return ! ( TriangleIsCCW( ptTest, ptCorn, ptPrev, 0)  &&
                 TriangleIsCCW( ptNext, ptCorn, ptTest, 0)) ;
}

//----------------------------------------------------------------------------
bool
ChangeStartPntVector( int nNewStart, PNTVECTOR& vPi)
{
  // se il nuovo inizio coincide col vecchio, non devo fare alcunchè
   if ( nNewStart == 0)
      return true ;
  // se il nuovo indice è oltre la dimensione del vettore, errore
   if ( nNewStart >= int( vPi.size()))
      return false ;
  // ciclo di aggiustamento
   rotate( vPi.begin(), vPi.begin() + nNewStart, vPi.end()) ;
   return true ;
}



//----------------------------------------------------------------------------
// Funzioni per triangolare usando la libreria FIST 
//---------------------------------------------------------------------------- 

//----------------------------------------------------------------------------
int
CalcTriangleType( const PNTVECTOR& vPt, const INTVECTOR& vTr, int nTrg)
{
   Vector3d vtV1 = vPt[vTr[3*nTrg + 1]] - vPt[vTr[3*nTrg]] ;
   Vector3d vtV2 = vPt[vTr[3*nTrg + 2]] - vPt[vTr[3*nTrg + 1]] ;
   Vector3d vtN = vtV1 ^ vtV2 ;
   double dSqN = vtN.SqLen() ;

   double dSqLen1 = vtV1.SqLen() ;
   double dSqLen2 = vtV2.SqLen() ;
   double dSqLen3 = ( vtV1 + vtV2).SqLen() ;
  // un triangolo è invalido ( needle o cap) se viene scartato dai controlli di AddTriangle
   if ( dSqN < SQ_EPS_ZERO  ||  dSqN < SQ_EPS_TRIA_H * max( {dSqLen1, dSqLen2, dSqLen3})) {
      if ( dSqLen1 < SQ_EPS_ZERO  ||  dSqLen2 < SQ_EPS_ZERO  ||  dSqLen3 < SQ_EPS_ZERO)
         return TRG_NEEDLE ;
      else
         return TRG_CAP ;
   }
   else
      return TRG_STD ;
}

//----------------------------------------------------------------------------
bool
FlipTrg( INTVECTOR& vTr, int nTA, int nTB, int nEA, int nEB)
{
   vTr[3*nTA + nEA] = vTr[3*nTB + ( nEB + 2) % 3] ;
   vTr[3*nTB + nEB] = vTr[3*nTA + ( nEA + 2) % 3] ;
   return true ;
}

//----------------------------------------------------------------------------
bool 
TestAdjacentOnEdge( INTVECTOR& vTr, int nTA, int nEA, int nTTest1, int nTTest2, int& nTB, int& nEB) 
{
  // individuo quale triangolo tra nTTest1 e nTTest2 è quello adiacente a nTA lungo il lato nEA 
   nTB = -1 ;
   nEB = -1 ;
  // recupero i vertici di nEA
   int nV1 = vTr[3*nTA + nEA] ;
   int nV2 = vTr[3*nTA + ( nEA + 1) % 3] ;

  // verifico se è TTest1 quello adiacente
   if ( vTr[3*nTTest1] == nV2  &&  vTr[3*nTTest1+1] == nV1) {
      nEB = 0 ;
      nTB = nTTest1 ;
   } 
   else if ( vTr[3*nTTest1+1] == nV2  &&  vTr[3*nTTest1+2] == nV1) {
      nEB = 1 ;
      nTB = nTTest1 ;
   }            
   else if ( vTr[3*nTTest1] == nV1  &&  vTr[3*nTTest1+2] == nV2) {
      nEB = 2 ;
      nTB = nTTest1 ;
   }
  // verifico se è TTest2 quello adiacente
   else if ( vTr[3*nTTest2] == nV2  &&  vTr[3*nTTest2+1] == nV1) {
      nEB = 0 ;
      nTB = nTTest2 ;
   } 
   else if ( vTr[3*nTTest2+1] == nV2  &&  vTr[3*nTTest2+2] == nV1) {
      nEB = 1 ;
      nTB = nTTest2 ;
   }            
   else if ( vTr[3*nTTest2] == nV1  &&  vTr[3*nTTest2+2] == nV2) {
      nEB = 2 ;
      nTB = nTTest2 ;
   }   
   return true ;
}

//----------------------------------------------------------------------------
bool
FindAdjacentOnLongerEdge( PNTVECTOR& vPt, INTVECTOR& vTr, int nTA, int& nEA, int& nTB, int& nEB)
{
  // recupero il lato più lungo del triangolo nTA
   nEA = -1 ;
   double dMaxLen = -1 ;
   for ( int j = 0 ; j < 3 ; j++) {
      double dCurrLen = SqDist( vPt[vTr[3*nTA + j]], vPt[vTr[3*nTA + ( j+1)%3]]) ;
      if ( dCurrLen > dMaxLen) {
         dMaxLen = dCurrLen ;
         nEA = j ;
      }      
   }

  // cerco il triangolo nTB adiacente a nTA lungo nEA
   nTB = -1 ;
   nEB = -1 ;
   int nV1 = vTr[3*nTA + nEA] ;
   int nV2 = vTr[3*nTA + ( nEA + 1) % 3] ;
   int nTria = vTr.size() / 3 ;
   for ( int j = 0 ; j < nTria ; j++) {
      if ( j == nTA)
         continue ;
      if ( vTr[3*j] == nV2  &&  vTr[3*j+1] == nV1) {
         nEB = 0 ;
         nTB = j ;
         break ;
      } 
      else if ( vTr[3*j+1] == nV2  &&  vTr[3*j+2] == nV1) {
         nEB = 1 ;
         nTB = j ;
         break ;
      }            
      else if ( vTr[3*j] == nV1  &&  vTr[3*j+2] == nV2) {
         nEB = 2 ;
         nTB = j ;
         break ;
      }      
   }
   return true ;
}

//----------------------------------------------------------------------------
bool
RemoveFistInvalidTrg( PNTVECTOR& vPt, INTVECTOR& vTr) 
{
  // scorro tutti i triangoli alla ricerca di triangoli validi per FIST ma invalidi per le nostre tolleranze.
  // I triangoli invalidi possono essere di due tipologie: cap o needle.
  // I triangoli cap se eliminati danno origine a T-junctions, quindi devono essere gestiti opportunamente con dei flip.
  // I triangoli needle se eliminati non sono problematici, ma i loro vertici coincidenti vanno gestiti opportunamente nel
  // calcolo delle adiacenze dei triangoli cap.
  // TO DO da capire e gestire casi in cui flip lascia triangoli invalidi

   int nTria = int( vTr.size()) / 3 ;
   INTVECTOR vCapTria ;
   INTVECTOR vNeedleTria ;
   BOOLVECTOR vbIsValidTria( nTria, true) ;
   bool bRemovedTrg = false ;

   for ( int i = 0 ; i < nTria ; i ++) {
      int nTrgType = CalcTriangleType( vPt, vTr, i) ;
      if ( nTrgType == TRG_CAP) {
         vbIsValidTria[i] = false ;
         vCapTria.emplace_back( i) ;
      }         
      else if ( nTrgType == TRG_NEEDLE) {
         vNeedleTria.emplace_back( i) ;
      }         
   }   

  // se non ci sono triangoli cap non c'è bisogno di modifiche
   if ( vCapTria.empty())
      return true ;

  // 1) elimino i triangoli di tipo needle gestendo i vertici coincidenti
   if ( ! vNeedleTria.empty()) {
      bRemovedTrg = true ;
      for ( int i = 0 ; i < int( vNeedleTria.size()) ; i++) {
         int nT = vNeedleTria[i] ; 
         if ( vTr[3*nT] != vTr[3*nT+1]  &&  vTr[3*nT] != vTr[3*nT+2]  &&  vTr[3*nT+1] != vTr[3*nT+2]) {
           // individuo i vertici coincidenti
            int nOldId = -1 ;
            int nNewId = -1 ;
            Vector3d vtV1 = vPt[vTr[3*nT+1]] - vPt[vTr[3*nT]] ;
            if ( vtV1.SqLen() < SQ_EPS_ZERO) {
              // vertici coincidenti 0 e 1
               nOldId = vTr[3*nT] ;
               nNewId = vTr[3*nT+1] ;            
            }
            else {
               Vector3d vtV2 = vPt[vTr[3*nT+2]] - vPt[vTr[3*nT+1]] ;
               if ( vtV2.SqLen() < SQ_EPS_ZERO) {
                 // vertici coincidenti 1 e 2
                  nOldId = vTr[3*nT+1] ;
                  nNewId = vTr[3*nT+2] ;
               }
               else {
                 // vertici coincidenti 0 e 2
                  nOldId = vTr[3*nT] ;
                  nNewId = vTr[3*nT+2] ;
               }           
            }
           // aggiorno il vettore dei triangoli unificando i vertici coincidenti 
            for ( int k = 0 ; k < int( vTr.size()) ; k ++) {
               if ( vTr[k] == nOldId)
                  vTr[k] = nNewId ;        
            }
         }
        // annullo il triangolo
         vTr[3*nT] = -1 ;
         vTr[3*nT+1] = -1 ;
         vTr[3*nT+2] = -1 ;
      }  
   }

  // 2) sistemo i triangoli di tipo cap
   for ( int i = 0 ; i < int( vCapTria.size()) ; i++) {

      int nTA = vCapTria[i] ;
     // verifico se il triangolo è già stato resto valido ( da una catena)
      if ( vbIsValidTria[nTA])
         continue ;

     // trovo l'adiacenza sul suo lato più lungo
      int nEA = -1 ;
      int nEB = -1 ;
      int nTB = -1 ;
      FindAdjacentOnLongerEdge( vPt, vTr, nTA, nEA, nTB, nEB) ;

      if ( nTB == -1) {
        // se non ha un triangolo adiacente posso annullarlo
         vTr[3*nTA] = -1 ;
         vTr[3*nTA+1] = -1 ;
         vTr[3*nTA+2] = -1 ;
         vbIsValidTria[nTA] = true ;
         bRemovedTrg = true ;
         continue ;
      }
      else if ( vbIsValidTria[nTB]) {
        // se è adiacente è valido, eseguo il flip
         FlipTrg( vTr, nTA, nTB, nEA, nEB) ;
         vbIsValidTria[nTA] = true ;
      }
      else {
        // se adiacente è invalido, individuo una catena di triangoli invalidi da risolvere non appena si indentifica
        // adiacenza con triangolo valido
         INTVECTOR vChain, vChainEdges ;
         vChain.emplace_back( nTA) ;
         vChainEdges.emplace_back( nEA) ;
         int nTCurr = nTB ;
         int nEOther ;
         while ( nTCurr != -1  &&  ! vbIsValidTria[nTCurr]) {

           // calcolo il successivo
            int nTOther, nECurr ;
            FindAdjacentOnLongerEdge( vPt, vTr, nTCurr, nECurr, nTOther, nEOther) ;

            if ( nTOther == vChain.back()) {
              // se ho trovato un'adiacenza ambigua ( ovvero due triangoli invalidi adiacenti sui loro lati più lunghi)
              // flip dei due triangoli per modificare il lato più lungo e togliere adiacenza ambigua
               FlipTrg( vTr, nTCurr, nTOther, nECurr, nEOther) ;
               if ( vChain.size() > 1) {
                  vChain.pop_back() ;
                  vChainEdges.pop_back() ;
                 // individuo il nuovo adiacente all'ultimo triangolo della catena tra i due appena flippati
                  TestAdjacentOnEdge( vTr, vChain.back(), vChainEdges.back(), nTCurr, nTOther, nTB, nEB) ;
                  nTOther = nTB ;
               }
            }
            else {
               vChain.emplace_back( nTCurr) ;
               vChainEdges.emplace_back( nECurr) ;
            }
           // aggiorno per iterazione successiva
            nTCurr = nTOther ;           
         }

        // se la catena termina su triangolo nullo, annullo tutti i triangoli della catena
         if ( nTCurr == -1) {
            bRemovedTrg = true ;
            for ( int k = 0 ; k < int( vChain.size()) ; k++) {
               if ( vbIsValidTria[vChain[k]])
                  continue ;
               vTr[3*vChain[k]] = -1 ;
               vTr[3*vChain[k] + 1] = -1 ;
               vTr[3*vChain[k] + 2] = -1 ;
               vbIsValidTria[vChain[k]] = true ;
            }
         }
        // se catena termina su un triangolo valido, applico il flip a cascata a partire dall'ultimo triangolo invalido
         else {            
            FlipTrg( vTr, vChain.back(), nTCurr, vChainEdges.back(), nEOther) ;
            vbIsValidTria[vChain.back()] = true ;
            int nTrgTest1 = vChain.back() ;
            int nTrgTest2 = nTCurr ;
            for ( int j = int( vChain.size()-2) ; j >= 0 ; j--) {
              // triangolo corrente
               int nTA = vChain[j] ;
               if ( vbIsValidTria[nTA])
                  continue ;
               int nEA = vChainEdges[j] ;
              // devo trovare il nuovo adiacente dopo il flip dei successivi nella catena
               TestAdjacentOnEdge( vTr, nTA, nEA, nTrgTest1, nTrgTest2, nTB, nEB) ;
              // flip per rendere valido il triangolo corrente 
               FlipTrg( vTr, nTA, nTB, nEA, nEB) ;
               vbIsValidTria[nTA] = true ;
              // aggiorno i trg di test per lo step successivo 
               nTrgTest1 = nTA ;
               nTrgTest2 = nTB ;
            }
         }
      }
   }

  // se sono stati annullati dei triangoli, li rimuovo dal vettore
   if ( bRemovedTrg) {
      INTVECTOR vTrTmp ;
      vTrTmp.reserve( vTr.size()) ;
      for ( int i = 0 ; i < int( vTr.size()) ; i++)
         if ( vTr[i] != -1)
            vTrTmp.emplace_back( vTr[i]) ;
      swap( vTr, vTrTmp) ;
   }

   return true ;
}

//----------------------------------------------------------------------------
bool
MakeByFist( const POLYLINEVECTOR& vPL, PNTVECTOR& vPt, INTVECTOR& vTr) 
{
  // opzioni di triangolazione
   rt_options rt_opt ;
   InitDefaults( &rt_opt) ;
   rt_opt.ears_top = false ;
   rt_opt.ears_random = false ;
   rt_opt.ears_sorted = true ;
   rt_opt.ears_fancy = true ;

  // creo oggetto di fist per triangolazione
   global_struct fist ;
   InitGlobalStruct( &fist, &rt_opt, true) ;

  // allocazione ottimizzata degli array di fist
   int nLoops = int( vPL.size()) ;
   int nVertices = 0 ;
   for ( int i = 0 ; i < nLoops ; i ++)
      nVertices += ( vPL[i].GetPointNbr() - 1) ;
   OptimizeMemoryAllocation( &fist, nLoops, nVertices) ;

  // assegno i dati a fist
   for ( int i = 0 ; i < nLoops ; i ++) {   
     // salvo i vertici saltando il primo punto ( coincide con l'ultimo)
      Point3d pt ;
      if ( ! vPL[i].GetFirstPoint( pt))
         return false ;
      while ( vPL[i].GetNextPoint( pt))
         StoreVertex( &fist.c_vertex, pt.x, pt.y, pt.z) ;
     // salvo il loop
      int nPoints = vPL[i].GetPointNbr() ;
      AddLoopInFace( &fist, nLoops - 1, i == 0, nPoints - 1) ;
   }
   StoreGroupNumber( &fist.c_list, &fist.c_vertex) ;

  // eseguo triangolazione
   Triangulate( &fist) ;

  // recupero i vertici da fist
   vPt.reserve( fist.c_vertex.num_vertices) ;
   for ( int i = 0 ; i < fist.c_vertex.num_vertices ; i ++)
      vPt.emplace_back( fist.c_vertex.vertices[i].x, fist.c_vertex.vertices[i].y, fist.c_vertex.vertices[i].z) ;
 
  // recupero i triangoli da fist 
   vTr.reserve( 3 * fist.c_vertex.num_triangles) ; 
   for ( int i = 0 ; i < fist.c_vertex.num_triangles ; i ++) {
      vTr.emplace_back( fist.c_vertex.triangles[i].v1) ;
      vTr.emplace_back( fist.c_vertex.triangles[i].v2) ;
      vTr.emplace_back( fist.c_vertex.triangles[i].v3) ;
   }

  // rimuovo eventuali triangoli validi per fist ma invalidi per le nostre tolleranze
   RemoveFistInvalidTrg( vPt, vTr) ;   

  // chiudo fist e dealloco la sua memoria
   FIST_TerminateProgram( &fist) ;

   return true ;
}