plugin/seq/ClosePoints.cpp

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/* This file is part of FreeFEM.                                            */
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/* FreeFEM is free software: you can redistribute it and/or modify          */
/* it under the terms of the GNU Lesser General Public License as           */
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/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the            */
/* GNU Lesser General Public License for more details.                      */
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// SUMMARY : ...
// LICENSE : LGPLv3
// ORG     : LJLL Universite Pierre et Marie Curie, Paris, FRANCE
// AUTHORS : ...
// E-MAIL  : ...

/* clang-format off */
//ff-c++-LIBRARY-dep: [flann]
//ff-c++-cpp-dep:
/* clang-format on */

#include <ff++.hpp>
#include <AFunction_ext.hpp>
using namespace Fem2D;

static bool debug = false;

class R2close {
 public:
  double *data;    // minimal points+ delta
  typedef double *Point;
  int n, nx, offset;
  Point *P;
  const double EPSILON;
  double x0, y0, x1, y1, coef;    // boundin box
  R2close( ) : data(0), n(0), nx(1000000), P(new Point[nx]), EPSILON(1e-6), offset(0) {
    InitialiserListe( );
  }

  R2close(double *dd, int mx, double eps = 1e-6, int offsett = 1)
    : data(dd), n(0), nx(mx), P(new Point[nx]), EPSILON(eps), offset(offsett) {
    InitialiserListe( );
  }

  Point operator[](int i) const { return P[i]; }

  int N, m;     // le nombre de code = ncase()%n
  int *head;    // pointeur tableau de dimension  m    contenant les tete de liste pour chaque code
  int *next;    // pointeur tableau de dimension nx donnant le point suivant de mÍme code
  static const int NotaPoint = -1;
  void InitialiserListe( ) {
    if (data) {
      x0 = data[0];
      y0 = data[1];
      x1 = data[2];
      y1 = data[3];
    } else {
      x0 = 0;
      y0 = 1;
      x1 = 0;
      y1 = 1;
    }

    coef = 1. / max(x1 - x0, y1 - y0);
    if (verbosity > 10) {
      cout << "     bounding box ClosePoints  Pmin=[" << x0 << ", " << y0 << "], Pmax=[ " << x1
           << " " << y1 << "] "
           << "eps= " << EPSILON << endl;
    }

    N = max(sqrt(nx), 10.);
    m = max(nx / 10, 100);
    next = new int[nx];
    head = new int[m];

    for (int i = 0; i < m; ++i) {
      head[i] = NotaPoint;
    }
  }

  int AddSimple(double *p) {
    double x = p[0], y = p[offset];

    assert(n < nx);
    P[n] = p;

    int k = ncase(x, y) % m;
    assert(k >= 0);
    next[n] = head[k];
    head[k] = n;
    if (debug) {
      cout << "  AddSimple " << n << " <- " << k << " / " << x << " " << y << " / " << offset
           << endl;
    }

    return n++;
  }

 private:
  Point *Exist(double *p) const {
    double x = p[0], y = p[offset];

    for (int i = 0; i < n; ++i) {
      if (Equivalent(x, y, P[i])) {
        return P + i;
      }
    }

    return 0;
  }

 public:
  bool Equivalent(double x0, double y0, const Point Q) const {
    return ((x0 - Q[0]) * (x0 - Q[0]) + (y0 - Q[offset]) * (y0 - Q[offset])) < EPSILON * EPSILON;
  }

  Point *Exist(double x, double y, int k) const {
    for (int i = head[k % m]; i != NotaPoint; i = next[i]) {
      if (Equivalent(x, y, P[i])) {
        return P + i;
      }
    }

    return 0;
  }

  int Add(double *p) {
    Point *q = Exist(p);

    if (q) {
      return q - P;    // numero du point
    } else {
      return AddSimple(p);
    }
  }

  int FindAll(double x, double y, int *p) {
    int nbp = 0;

    if (debug) {
      cout << " Find " << x << " " << y << " " << EPSILON << " " << ncase(x, y) << ": ";
    }

    double eps = EPSILON / 2;
    Point *q = 0;
    int kk[9] = {}, k = 0, nc;

    for (int i = -1; i < 2; ++i) {
      for (int j = -1; j < 2; ++j) {
        nc = ncase(x + eps * i, y + eps * j);
        if (nc >= 0) {
          for (int i = 0; i < k; ++i) {    // remove double cas e..
            if (kk[i] == nc) {
              nc = -1;
              break;
            }
          }
        }

        if (nc >= 0) {
          kk[k++] = nc;
        }
      }
    }

    if (k > 4) {
      cout << "   ClosePoints: FindAll Bug ??? : " << k << " : ";

      for (int i = 0; i < k; ++i) {
        cout << " " << kk[i];
      }

      cout << endl;
    }

    assert(k <= 4);

    for (int i = 0; i < k; ++i) {
      int k = kk[i];

      for (int i = head[k % m]; i != NotaPoint; i = next[i]) {
        if (Equivalent(x, y, P[i])) {
          p[nbp++] = i;
        }
      }
    }

    return nbp;
  }

  Point *Find(double x, double y) {
    if (debug) {
      cout << " Find " << x << " " << y << " " << EPSILON << " " << ncase(x, y) << ": ";
    }

    // double x = p[0], y=p[offset];
    double eps = EPSILON / 2;
    Point *q = 0;
    int kk[9] = {}, k = 0, nc;

    for (int i = -1; i < 2; ++i) {
      for (int j = -1; j < 2; ++j) {
        nc = ncase(x + eps * i, y + eps * j);
        // cout <<x+eps*i << " " << y+eps*j << " " << nc << " . ";
        if (nc >= 0) {
          for (int i = 0; i < k; ++i) {    // remove double cas e..
            if (kk[i] == nc) {
              nc = -1;
              break;
            }
          }
        }

        if (nc >= 0) {
          kk[k++] = nc;
        }
      }
    }

    if (k > 4) {
      cout << "   ClosePoints: Bug ??? : " << k << " : ";

      for (int i = 0; i < k; ++i) {
        cout << " " << kk[i];
      }

      cout << endl;
    }

    assert(k <= 4);

    for (int i = 0; i < k; ++i) {
      q = Exist(x, y, kk[i]);
      if (debug) {
        cout << " " << kk[i];
      }

      if (q) {
        break;
      }
    }

    if (debug) {
      cout << " q= " << q << endl;
    }

    if (q) {
      return q;    // numero du point
    } else {
      return 0;
    }
  }

  Point *Find(double *p) { return Find(*p, *(p + offset)); }

  int AddOpt(double *p) {
    Point *q = Find(p);

    if (q) {
      return q - P;    // numero du point
    } else {
      return AddSimple(p);
    }
  }

  long ncase(double x, double y) {
    if (x < x0 || x >= x1 || y < y0 || y >= y1) {
      return -1;    // dehors
    } else {
      return long((x - x0) / EPSILON / 2) +
             long((y - y0) / EPSILON / 2) * N;    // indice de la case contenant (x,y).
    }
  }

  ~R2close( ) {
    delete[] P;
    delete[] head;
    delete[] next;
  }

  // pas de copie de  cette structure

 private:
  R2close(const R2close &);
  R2close &operator=(const R2close &);
};

double dist2(int n, double *p, double *q) {
  double s = 0;

  for (int i = 0; i < n; ++n) {
    s += (q[i] - p[i]) * (q[i] - p[i]);
  }

  return s;
}

long Hcode(int n, double eps, double *p, double *p0);

KN< long > *CloseTo2(Stack stack, double const &eps, KNM_< double > const &P,
                     KNM_< double > const &Q) {
  long Pm0 = P.M( );
  long Qm0 = Q.M( );
  int po10 = P.step * P.shapei.step;
  double x0 = P(0, ':').min( );
  double y0 = P(1, ':').min( );
  double x1 = P(0, ':').max( );
  double y1 = P(1, ':').max( );

  // add cc
  double dd = max(x1 - x0, y1 - y0) * 0.01;

  if (dd == 0) {
    dd = max(abs(x0), abs(y0)) * 1e-8;
  }

  if (dd == 0) {
    dd = 1e-8;
  }

  double data[] = {x0 - dd, y0 - dd, x1 + dd, y1 + dd};
  R2close S(data, Pm0, eps, po10);

  for (int i = 0; i < Pm0; ++i) {
    if (verbosity > 19) {
      cout << i << " :: " << P(0, i) << " " << P(1, i) << endl;
    }

    S.AddSimple(&P(0, i));
  }

  KN< long > *pr = new KN< long >(Qm0);

  for (int i = 0; i < Qm0; ++i) {
    R2close::Point *p = S.Find(Q(0, i), Q(1, i));
    if (p) {
      (*pr)[i] = p - S.P;
    } else {
      (*pr)[i] = -1;
    }
  }

  return Add2StackOfPtr2FreeRC(stack, pr);
}

KN< long > *CloseTo2t(Stack stack, double const &eps, KNM_< double > const &P,
                      KNM_< double > const &Q) {
  return CloseTo2(stack, eps, P.t( ), Q.t( ));
}

KN< long > *CloseTo(Stack stack, double const &eps, KNM_< double > const &P,
                    KNM< double > *const &q, bool tq, bool inv = 0) {
  long n0 = P.N( );
  long m0 = P.M( );

  if (verbosity > 2) {
    cout << " -ClosePoints Size array;   n0 " << n0 << " m0 " << m0 << endl;
  }

  ffassert(n0 == 2);
  KNM< double > &Qo = *q;
  double *p0 = &(P(0, 0));
  int offset10 = P.step * P.shapei.step;
  int offset01 = P.step * P.shapej.step;
  if (verbosity > 10) {
    cout << "     offset of 0 1 :  " << offset01 << endl;
    cout << "     offset of 1 0 :  " << offset10 << endl;
  }

  // MeshPoint &mp = *MeshPointStack(stack);	// the struct to get x, y, normal, value
  double x0 = P(0, ':').min( );
  double y0 = P(1, ':').min( );
  double x1 = P(0, ':').max( );
  double y1 = P(1, ':').max( );

  // add cc
  double dd = max(x1 - x0, y1 - y0) * 0.01;
  double data[] = {x0 - dd, y0 - dd, x1 + dd, y1 + dd};
  KN< long > *pr = 0;
  if (inv) {
    pr = new KN< long >(m0);
  }

  R2close S(data, m0, eps, offset10);

  for (int i = 0; i < m0; ++i) {
    if (verbosity > 19) {
      cout << i << " :: " << P(0, i) << " " << P(1, i) << endl;
    }

    int j = S.AddOpt(&P(0, i));
    if (pr) {
      (*pr)[i] = j;
    }
  }

  if (pr == 0) {
    pr = new KN< long >(S.n);
  }

  if (q) {
    if (tq) {
      Qo.resize(S.n, n0);
    } else {
      Qo.resize(n0, S.n);
    }

    KNM_< double > Q(tq ? Qo.t( ) : Qo);

    for (int i = 0; i < S.n; ++i) {
      double *pi = S[i];
      if (!inv) {
        (*pr)[i] = (pi - p0) / offset01;
      }

      for (int j = 0; j < n0; ++j) {
        Q(j, i) = pi[j * offset10];
      }
    }
  } else if (!inv) {
    for (int i = 0; i < S.n; ++i) {
      double *pi = S[i];
      (*pr)[i] = (pi - p0) / offset01;
    }
  }

  if (verbosity > 2) {
    cout << "  - ClosePoint: nb of common points " << m0 - S.n;
  }

  return Add2StackOfPtr2FreeRC(stack, pr);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, KNM< double > *const &p,
                    KNM< double > *const &q) {
  KNM_< double > P(*p);
  return CloseTo(stack, eps, P, q, false, inv);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, Transpose< KNM< double > * > const &p,
                    KNM< double > *const &q) {
  KNM_< double > P(p.t->t( ));
  return CloseTo(stack, eps, P, q, false, inv);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, Transpose< KNM< double > * > const &p,
                    Transpose< KNM< double > * > const &q) {
  KNM_< double > P(p.t->t( ));
  return CloseTo(stack, eps, P, q, true, inv);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, KNM< double > *const &p,
                    Transpose< KNM< double > * > const &q) {
  KNM_< double > P(*p);
  return CloseTo(stack, eps, P, q.t, true, inv);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, KNM< double > *const &p) {
  KNM_< double > P(*p);
  return CloseTo(stack, eps, P, 0, false, inv);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, KNM_< double > const &p) {
  KNM_< double > P(p);
  if (verbosity > 5) {
    cout << " CloseTo KNM_ " << P.N( ) << " " << P.M( ) << endl;
  }

  return CloseTo(stack, eps, P, 0, false, inv);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, Transpose< KNM< double > * > const &p) {
  KNM_< double > P(p.t->t( ));
  return CloseTo(stack, eps, P, 0, false, inv);
}

template< bool inv >
KN< long > *CloseTo(Stack stack, double const &eps, pmesh const &pTh, KNM< double > *const &pq) {
  ffassert(pTh && pq);
  const Mesh &Th = *pTh;
  const KNM< double > Q = *pq;
  int np = Q.N( );
  assert(Q.M( ) >= 2);
  KN< long > *pr = new KN< long >(inv ? Th.nv : np);
  KN< int > b(Th.nv);
  b = 0;

  for (int i = 0; i < Th.nv; i++) {
    if (Th(i).lab != 0) {
      b[i] = 1;
    }
  }

  for (int i = 0; i < Th.neb; i++) {
    b[Th(Th.bedges[i][0])] = 1;
    b[Th(Th.bedges[i][1])] = 1;
  }

  *pr = -1L;
  R2 Pmin, Pmax;
  Th.BoundingBox(Pmin, Pmax);
  int nv = b.sum( );
  if (verbosity > 9) {
    cout << " Th.nv " << Th.nv << " " << nv << "/ " << Pmin << " " << Pmax << endl;
  }

  FQuadTree *quadtree =
    new FQuadTree(pTh, Pmin, Pmax, nv);    // put all the old vertices in the quadtree

  // copy of the old vertices
  for (int i = 0; i < Th.nv; i++) {
    if (b[i]) {
      cout << i << " " << Th.vertices[i] << endl;
      quadtree->Add(Th.vertices[i]);
    }
  }

  cout << " After quadterr" << endl;

  for (int j = 0; j < np; ++j) {
    R2 P(Q(j, 0), Q(j, 1));
    Vertex *pV = quadtree->ToClose(P, eps);
    if (pV) {
      pV = quadtree->NearestVertex(P);
      long k = Th(pV);
      if (inv) {
        (*pr)[k] = j;
      } else {
        (*pr)[j] = k;
      }
    }
  }

  delete quadtree;

  return Add2StackOfPtr2FreeRC(stack, pr);
}

bool InterAB_Disq(R2 A, R2 B, R2 C, double r) {
  double ACB = det(A, C, B);

  if (ACB < 0) {
    return false;
  }

  R2 AB(A, B);
  R2 AC(A, C), CB(C, B);
  double LAB = AB.norme( );
  double H = ACB / 4 / LAB;
  if (H > r) {
    return false;
  }

  double AC2 = AC.norme2( ), r2 = r * r;
  if (AC2 < r2) {
    return true;
  }

  double CB2 = CB.norme2( );
  if (CB2 < r2) {
    return true;
  }

  double ABAC = (AB, AC), ABCB = (AB, CB);
  return ABAC > 0 && ABCB > 0;
}

void Add(KN< long > &I, int i) {
  int n = I.N( );
  int m = -I[n - 1];

  if (m <= 0) {
    m = n;
    n = m * 2;
    I.resize(n);
    I[n - 1] = -m - 1;
  } else {
    --m;
  }

  if (debug) {
    cout << " add " << m << " " << i << " " << n << endl;
  }

  I[m] = i;
  if (m < n - 1) {
    --I[n - 1];
  }
}

void Clean(KN< long > &I) {
  int n = I.N( );
  int m = -I[n - 1];

  if (m >= 0) {
    I.resize(m - 1);
  }
}

long Voisinage(KNM_< double > const &P, KNM_< double > const &Q, double const &eps,
               KN< KN< long > > *const &IJ) {
  debug = (verbosity > 999);
  int np = P.N( );
  int nq = Q.N( );
  int mp = P.M( );
  int mq = Q.M( );
  double *p = &P(0, 0);
  int offset01 = P.step * P.shapej.step;
  int offset10 = P.step * P.shapei.step;
  ffassert(mp == 2);
  ffassert(mq == 2);
  KN< int > lp(np);

  IJ->resize(nq);

  for (int i = 0; i < nq; i++) {
    (*IJ)[i].resize(2);
    (*IJ)[i][0] = -1;
    (*IJ)[i][1] = -1;
  }

  if (verbosity > 99) {
    cout << " offset01 " << offset01 << " " << offset10 << " p" << p << " " << np << " " << P.M( )
         << endl;
  }

  // store - the size in last value of IJ[i][j]
  double data[4];
  data[0] = data[2] = p[0];
  data[1] = data[3] = p[offset01];

  for (int i = 0, k = 0; i < np; ++i, k += offset10) {
    data[0] = min(data[0], p[k]);
    data[2] = max(data[2], p[k]);
    data[1] = min(data[1], p[k + offset01]);
    data[3] = max(data[3], p[k + offset01]);
  }

  double eps2 = eps + eps;
  data[0] -= eps2;
  data[2] += eps2;
  data[1] -= eps2;
  data[3] += eps2;

  R2close SP(data, np, eps, offset01);

  for (int i = 0; i < np; ++i) {
    SP.AddSimple(&P(i, 0));
  }

  for (int j = 0; j < nq; ++j) {
    int nlp = SP.FindAll(Q(j, 0), Q(j, 1), lp);

    for (int k = 0; k < nlp; ++k) {
      int i = lp[k];
      if (verbosity > 99) {
        cout << " Add to i=" << i << " -> j " << j << endl;
      }

      Add((*IJ)[i], j);
    }
  }

  for (int j = 0; j < nq; ++j) {
    Clean((*IJ)[j]);
  }

  debug = 0;
  return 0;
}

#ifdef WITH_flann
#include <flann/flann.hpp>
long ff_flann_search(KNM_< double > const &P, KNM_< double > const &Q, double const &eps,
                     KN< KN< long > > *const &pIJ) {
  KN< KN< long > > &IJ = *pIJ;
  int mp = P.M( );
  int mq = Q.M( );
  int np = P.N( );
  int nq = Q.N( );
  double *p = &P(0, 0);
  double *q = &Q(0, 0);
  int offset01 = P.step * P.shapej.step;
  int offset10 = P.step * P.shapei.step;
  int qoffset01 = Q.step * Q.shapej.step;
  int qoffset10 = Q.step * Q.shapei.step;

  cout << np << " " << nq << " po 01,10 =:" << offset01 << ", " << offset10 << ", " << &P(0, 1) - p
       << " qo 01,10 =:" << qoffset01 << ", " << qoffset10 << ", " << &Q(0, 1) - q << endl;
  cout << np << " " << mp << endl;
  cout << nq << " " << mq << endl;

  ffassert(mp == mq && offset10 == 1 && qoffset10 == 1);

  IJ.resize(nq);
  flann::Matrix< double > dataset(p, np, mp);
  flann::Matrix< double > query(q, nq, mq);
  std::vector< std::vector< int > > indices;
  std::vector< std::vector< double > > dists;
  flann::SearchParams params(128);
  params.eps = eps;
  flann::Index< flann::L2< double > > index(dataset, flann::KDTreeIndexParams(4));
  index.buildIndex( );
  index.radiusSearch(query, indices, dists, eps, params);

  for (int j = 0; j < indices.size( ); ++j) {
    IJ[j].resize(indices[j].size( ));

    for (int k = 0; k < indices[j].size( ); ++k) {
      IJ[j][k] = indices[j][k];
    }
  }

  for (int j = 0; j < indices.size( ); ++j) {
    int k = j * mq;
    cout << j << " [ " << q[k] << " " << q[k + 1] << "] : ";

    for (int k = 0; k < indices[j].size( ); ++k) {
      cout << indices[j][k] << " " << dists[j][k] << ", ";
    }

    cout << endl;
  }

  return 0;
}

#endif
using bamg::BinaryRand;
int WalkInTriangle(const Mesh &Th, int it, double *lambda, R2 PF) {
  const Triangle &T(Th[it]);
  const R2 Q[3] = {(const R2)T[0], (const R2)T[1], (const R2)T[2]};

  R2 P = lambda[0] * Q[0] + lambda[1] * Q[1] + lambda[2] * Q[2];

  //  couleur(15);MoveTo( P); LineTo( PF);
  R l[3];
  l[0] = Area2(PF, Q[1], Q[2]);
  l[1] = Area2(Q[0], PF, Q[2]);
  l[2] = Area2(Q[0], Q[1], PF);
  R Det = l[0] + l[1] + l[2];
  l[0] /= Det;
  l[1] /= Det;
  l[2] /= Det;
  const R eps = 1e-5;
  int neg[3], k = 0;
  int kk = -1;
  if (l[0] > -eps && l[1] > -eps && l[2] > -eps) {

    lambda[0] = l[0];
    lambda[1] = l[1];
    lambda[2] = l[2];
  } else {

    if (l[0] < eps && lambda[0] != l[0]) neg[k++] = 0;
    if (l[1] < eps && lambda[1] != l[1]) neg[k++] = 1;
    if (l[2] < eps && lambda[2] != l[2]) neg[k++] = 2;
    R eps1 = T.area * 1.e-5;

    if (k == 2)    // 2
    {
      // let j be the vertex beetween the 2 edges
      int j = 3 - neg[0] - neg[1];
      R S = Area2(P, PF, Q[j]);

      if (S > eps1)
        kk = (j + 1) % 3;
      else if (S < -eps1)
        kk = (j + 2) % 3;
      else if (BinaryRand( ))
        kk = (j + 1) % 3;
      else
        kk = (j + 2) % 3;

    } else if (k == 1)
      kk = neg[0];
    if (kk >= 0) {
      R d = lambda[kk] - l[kk];

      throwassert(d);
      R coef = lambda[kk] / d;
      R coef1 = 1 - coef;
      lambda[0] = lambda[0] * coef1 + coef * l[0];
      lambda[1] = lambda[1] * coef1 + coef * l[1];
      lambda[2] = lambda[2] * coef1 + coef * l[2];
      lambda[kk] = 0;
    }
  }
  int jj = 0;
  R lmx = lambda[0];
  if (lmx < lambda[1]) jj = 1, lmx = lambda[1];
  if (lmx < lambda[2]) jj = 2, lmx = lambda[2];
  if (lambda[0] < 0) lambda[jj] += lambda[0], lambda[0] = 0;
  if (lambda[1] < 0) lambda[jj] += lambda[1], lambda[1] = 0;
  if (lambda[2] < 0) lambda[jj] += lambda[2], lambda[2] = 0;
  return kk;
}
BoundaryEdge *Cut(const Mesh &Th, R2 P, R2 &PF) {
  R2 PHat;
  bool outside;
  R l[3];
  const Triangle *K = Th.Find(P, PHat, outside);
  ffassert(!outside);
  int it = Th(K);
  PHat.toBary(l);
  int k = 0;
  int j;
  while ((j = WalkInTriangle(Th, it, l, PF)) >= 0) {
    int jj = j;
    throwassert(l[j] == 0);
    R a = l[(j + 1) % 3], b = l[(j + 2) % 3];
    int itt = Th.ElementAdj(it, j);
    if (itt == it || itt < 0) {
      PF = Th[it](R2(l + 1));    // point de sortie
      int i1 = Th(it, (jj + 1) % 3), i2 = Th(it, (jj + 2) % 3);
      return Th.TheBoundaryEdge(i1, i2);
    }
    it = itt;
    l[j] = 0;
    l[(j + 1) % 3] = b;
    l[(j + 2) % 3] = a;
    ffassert(k++ < 1000);
  }
  return 0;
}
long BorderIntersect(pmesh const &pTh, KN_< double > const &IX, KN_< double > const &IY,
                     KN_< double > const &OX, KN_< double > const &OY, KN_< long > const &cL) {
  const Mesh &Th = *pTh;
  KN_< double > ox = OX, oy = OY;
  KN_< long > L = cL;
  int np = IX.N( );
  ffassert(OX.N( ) == np && OY.N( ) == np && IY.N( ) == np && cL.N( ) == np);    //  verif taille
  long ni = 0;
  for (int i = 0; i < np; ++i) {
    R2 P(IX[i], IY[i]);
    R2 Q(OX[i], OY[i]);
    BoundaryEdge *e = Cut(Th, P, Q);

    if (e) {
      L[i] = e->lab;
      OX[i] = Q.x, OY[i] = Q.y;
    } else
      L[i] = notaregion;
  }
  return ni;
}

static void init( ) {
#ifdef WITH_flann
  Global.Add("radiusSearch", "(",
             new OneOperator4_< long, KNM_< double >, KNM_< double >, double, KN< KN< long > > * >(
               ff_flann_search));
#endif
  Global.Add("Voisinage", "(",
             new OneOperator4_< long, KNM_< double >, KNM_< double >, double, KN< KN< long > > * >(
               Voisinage));
  Global.Add("neighborhood", "(",
             new OneOperator4_< long, KNM_< double >, KNM_< double >, double, KN< KN< long > > * >(
               Voisinage));
  Global.Add("ClosePoints2", "(",
             new OneOperator3s_< KN< long > *, double, KNM_< double >, KNM_< double > >(CloseTo2));

  // numbering ..
  Global.Add("ClosePoints", "(",
             new OneOperator2s_< KN< long > *, double, KNM_< double > >(CloseTo< false >));
  Global.Add("ClosePoints", "(",
             new OneOperator3s_< KN< long > *, double, pmesh, KNM< double > * >(CloseTo< false >));
  Global.Add("ClosePoints1", "(",
             new OneOperator2s_< KN< long > *, double, KNM_< double > >(CloseTo< true >));
  Global.Add("ClosePoints1", "(",
             new OneOperator3s_< KN< long > *, double, pmesh, KNM< double > * >(CloseTo< true >));
  Global.Add("BorderIntersect", "(",
             new OneOperator6_< long, pmesh, KN_< double >, KN_< double >, KN_< double >,
                                KN_< double >, KN_< long > >(BorderIntersect));
}

LOADFUNC(init);