libgetfem++-dev 4.2.1~beta1~svn4482~dfsg-2build1 / usr / include / getfem / getfem_mesher.h

/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2004-2012 Julien Pommier, Yves Renard
 
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/**@file getfem_mesher.h
   @author  Julien Pommier <Julien.Pommier@insa-toulouse.fr>, Yves Renard <Yves.Renard@insa-lyon.fr>
   @date May 1, 2004.
   @brief a broken mesher.
*/

#ifndef GETFEM_MESHER_H__
#define GETFEM_MESHER_H__


#include "getfem_mesh.h"
#include "gmm/gmm_condition_number.h"
#include "bgeot_comma_init.h"
#include "gmm/gmm_solver_bfgs.h"
#include "getfem_export.h"
#include "bgeot_kdtree.h"
#include <typeinfo>

namespace getfem {

  class mesher_virtual_function {
  public:
    virtual scalar_type operator()(const base_node &P) const = 0;
    virtual ~mesher_virtual_function() {}
  };

  class mvf_constant : public mesher_virtual_function {
    scalar_type c;
  public: 
    mvf_constant(scalar_type c_) : c(c_) {}
    scalar_type operator()(const base_node &) const { return c; }
  };

  // Signed distance definition. Should not be a real signed distance but
  // should satisfy that dist(P) is less than the euclidean distance from
  // P to the boundary and more than 1/sqrt(N) time this distance.

#define SEPS 1e-8

  class mesher_signed_distance : public mesher_virtual_function {
  protected:
    mutable size_type id;
  public:
    mesher_signed_distance() : id(size_type(-1)) {}
    virtual bool bounding_box(base_node &bmin, base_node &bmax) const = 0;
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector &bv) const = 0;
    virtual scalar_type grad(const base_node &P,
			     base_small_vector &G) const = 0;
    virtual void hess(const base_node &P, base_matrix &H) const = 0;
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const=0;
    virtual scalar_type operator()(const base_node &P) const  = 0;
  };

  class mesher_half_space : public mesher_signed_distance {
    base_node x0; base_small_vector n; scalar_type xon;
  public:
    mesher_half_space(const base_node &x0_, const base_small_vector &n_)
      : x0(x0_), n(n_)
    { n /= gmm::vect_norm2(n); xon = gmm::vect_sp(x0, n); }
    bool bounding_box(base_node &, base_node &) const
    { return false; }
    virtual scalar_type operator()(const base_node &P) const
    { return xon - gmm::vect_sp(P,n); }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector &bv) const {
      scalar_type d = xon - gmm::vect_sp(P,n);
      bv[id] = (gmm::abs(d) < SEPS);
      return d;
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      id = list.size(); list.push_back(this);
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      G = n; G *= scalar_type(-1); 
      return xon - gmm::vect_sp(P,n);
    }
    void hess(const base_node &P, base_matrix &H) const {
      gmm::resize(H, P.size(), P.size()); gmm::clear(H);
    }

  };

  class mesher_level_set : public mesher_signed_distance {
    bgeot::base_poly base;
    mutable std::vector<base_poly> gradient;
    mutable std::vector<base_poly> hessian;
    const fem<base_poly> *pf;
    mutable int initialized;
    scalar_type shift_ls;     // for the computation of a gap on a level_set.
  public:
    bool is_initialized(void) const { return initialized; }
    mesher_level_set() : initialized(0) {}
    template <typename VECT>
    mesher_level_set(pfem pf_, const VECT &coeff_,
		     scalar_type shift_ls_ = scalar_type(0)) {
      shift_ls = shift_ls_; init_base(pf_, coeff_);
      if (shift_ls != scalar_type(0)) {
	base_node P(pf->dim()); base_small_vector G(pf->dim());
	grad(P, G);
	shift_ls *= gmm::vect_norm2(G);
      }
    }
    template <typename VECT> void init_base(pfem pf_, const VECT &coeff_);
    void init_grad(void) const;
    void init_hess(void) const;

    bool bounding_box(base_node &, base_node &) const
    { return false; }
    virtual scalar_type operator()(const base_node &P) const
    {  return bgeot::to_scalar(base.eval(P.begin())) + shift_ls; }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector &bv) const
    { scalar_type d = (*this)(P); bv[id] = (gmm::abs(d) < SEPS); return d; }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      id = list.size(); list.push_back(this);
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const;
    void hess(const base_node &P, base_matrix &H) const;
  };

  template <typename VECT> 
  void mesher_level_set::init_base(pfem pf_, const VECT &coeff_) {
    std::vector<scalar_type> coeff(coeff_.begin(), coeff_.end());
    GMM_ASSERT1(gmm::vect_norm2(coeff) != 0, "level is zero!");
    pf = dynamic_cast<const fem<base_poly>* > (pf_.get());
    GMM_ASSERT1(pf, "PK fem are required for level set (got "
		<< typeid(pf_).name() << ")");
    base = base_poly(pf->base()[0].dim(), pf->base()[0].degree());
    for (unsigned i=0; i < pf->nb_base(0); ++i) {
      base += pf->base()[i] * coeff[i];
    }
    initialized = 0; 
  }




  class mesher_ball : public mesher_signed_distance {
    base_node x0; scalar_type R;
  public:
    mesher_ball(base_node x0_, scalar_type R_) : x0(x0_), R(R_) {}
    bool bounding_box(base_node &bmin, base_node &bmax) const { 
      bmin = bmax = x0; 
      for (size_type i=0; i < x0.size(); ++i) { bmin[i] -= R; bmax[i] += R; }
      return true;
    }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector &bv) const {
      scalar_type d = gmm::vect_dist2(P,x0)-R;
      bv[id] = (gmm::abs(d) < SEPS);
      return d;
    }
    virtual scalar_type operator()(const base_node &P) const
    { return gmm::vect_dist2(P,x0)-R; }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      id = list.size(); list.push_back(this);
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      G = P; G -= x0;
      scalar_type e= gmm::vect_norm2(G), d = e - R;
      while (e == scalar_type(0))
	{ gmm::fill_random(G); e = gmm::vect_norm2(G); }
      G /= e;
      return d;
    }
    void hess(const base_node &, base_matrix &) const {
      GMM_ASSERT1(false, "Sorry, to be done");
    }
  };

  class mesher_rectangle : public mesher_signed_distance {
    // ajouter une rotation rigide et translation ..
    base_node rmin, rmax;
    std::vector<mesher_half_space> hfs;
  public:
    mesher_rectangle(base_node rmin_, base_node rmax_)
      : rmin(rmin_), rmax(rmax_) {
      base_node n(rmin_.size());
      for (unsigned k = 0; k < rmin.size(); ++k) {
	n[k] = 1.0;
	hfs.push_back(mesher_half_space(rmin, n));
	n[k] = -1.0;
	hfs.push_back(mesher_half_space(rmax, n));
	n[k] = 0.0;
      }
    }
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      bmin = rmin; bmax = rmax;
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const {
      size_type N = rmin.size();
      scalar_type d = rmin[0] - P[0];
      for (size_type i=0; i < N; ++i) {
	d = std::max(d, rmin[i] - P[i]);
	d = std::max(d, P[i] - rmax[i]);
      }
      return d;
    }

    virtual scalar_type operator()(const base_node &P, dal::bit_vector &bv)
      const {
      scalar_type d = this->operator()(P);
      if (gmm::abs(d) < SEPS)
	for (int k = 0; k < 2*rmin.size(); ++k) hfs[k](P, bv);
      return d;
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      unsigned i = 0; scalar_type di = hfs[i](P);
      for (int k = 1; k < 2*rmin.size(); ++k) {
	scalar_type dk = hfs[k](P);
	if (dk > di) { i = k; di = dk; }
      }
      return hfs[i].grad(P, G);
    }
    void hess(const base_node &P, base_matrix &H) const {
      gmm::resize(H, P.size(), P.size()); gmm::clear(H);
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      for (int k = 0; k < 2*rmin.size(); ++k)
	hfs[k].register_constraints(list);
    }
  };


  class mesher_simplex_ref : public mesher_signed_distance {
    // ajouter une rotation rigide, homothetie,  et translation ..
    std::vector<mesher_half_space> hfs;
    unsigned N;
    base_node org;
  public:
    mesher_simplex_ref(unsigned N_) : N(N_) {
      base_node no(N);
      org = no;
      for (unsigned k = 0; k < N; ++k) {
	no[k] = scalar_type(1);
	hfs.push_back(mesher_half_space(org, no));
	no[k] = scalar_type(0);
      }
      std::fill(org.begin(), org.end(), scalar_type(1)/scalar_type(N));
      no = -org;
      hfs.push_back(mesher_half_space(org, no));
    }
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      bmin.resize(N); bmax.resize(N);
      std::fill(bmin.begin(), bmin.end(), scalar_type(0));
      std::fill(bmax.begin(), bmax.end(), scalar_type(1));
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const {
      scalar_type d = - P[0];
      for (size_type i=1; i < N; ++i) d = std::max(d, - P[i]);
      d = std::max(d, gmm::vect_sp(P - org, org) / gmm::vect_norm2(org));
      return d;
    }

    virtual scalar_type operator()(const base_node &P, dal::bit_vector &bv)
      const {
      scalar_type d = this->operator()(P);
      if (gmm::abs(d) < SEPS) for (unsigned k = 0; k < N+1; ++k) hfs[k](P, bv);
      return d;
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      unsigned i = 0; scalar_type di = hfs[i](P);
      for (unsigned k = 1; k < N+1; ++k) {
	scalar_type dk = hfs[k](P);
	if (dk > di) { i = k; di = dk; }
      }
      return hfs[i].grad(P, G);
    }
    void hess(const base_node &P, base_matrix &H) const {
      gmm::resize(H, P.size(), P.size()); gmm::clear(H);
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const
    { for (unsigned k = 0; k < N+1; ++k) hfs[k].register_constraints(list); }
  };

  class mesher_prism_ref : public mesher_signed_distance {
    // ajouter une rotation rigide, homothetie,  et translation ..
    std::vector<mesher_half_space> hfs;
    unsigned N;
    base_node org;
  public:
    mesher_prism_ref(unsigned N_) : N(N_) {
      base_node no(N);
      org = no;
      for (unsigned k = 0; k < N; ++k) {
	no[k] = scalar_type(1);
	hfs.push_back(mesher_half_space(org, no));
	no[k] = scalar_type(0);
      }
      no[N-1] = -scalar_type(1);
      org[N-1] = scalar_type(1);
      hfs.push_back(mesher_half_space(org, no));
      std::fill(org.begin(), org.end(), scalar_type(1)/scalar_type(N));
      org[N-1] = scalar_type(0);
      no = -org;
      hfs.push_back(mesher_half_space(org, no));
      
    }
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      bmin.resize(N); bmax.resize(N);
      std::fill(bmin.begin(), bmin.end(), scalar_type(0));
      std::fill(bmax.begin(), bmax.end(), scalar_type(1));
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const {
      scalar_type d = - P[0];
      for (size_type i=1; i < N; ++i) d = std::max(d, - P[i]);
      d = std::max(d, P[N-1] - scalar_type(1));
      d = std::max(d, gmm::vect_sp(P - org, org) / gmm::vect_norm2(org));
      return d;
    }

    virtual scalar_type operator()(const base_node &P, dal::bit_vector &bv)
      const {
      scalar_type d = this->operator()(P);
      if (gmm::abs(d) < SEPS) for (unsigned k = 0; k < N+2; ++k) hfs[k](P, bv);
      return d;
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      unsigned i = 0; scalar_type di = hfs[i](P);
      for (unsigned k = 1; k < N+2; ++k) {
	scalar_type dk = hfs[k](P);
	if (dk > di) { i = k; di = dk; }
      }
      return hfs[i].grad(P, G);
    }
    void hess(const base_node &P, base_matrix &H) const {
      gmm::resize(H, P.size(), P.size()); gmm::clear(H);
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const
    { for (unsigned k = 0; k < N+2; ++k) hfs[k].register_constraints(list); }
  };


  // Rem : It would be better for the convergence of Newton's methods to
  //       take somthing more smooth than min. for instance tthe square root
  //       of positive parts or negative parts depending on the position of
  //       point (in or out the domain).

  extern const mesher_half_space void_signed_distance;

  class mesher_union : public mesher_signed_distance {
    std::vector<const mesher_signed_distance *> dists;
    mutable std::vector<scalar_type> vd;
    mutable bool isin;
    bool with_min;
  public:
    mesher_union(const std::vector<const mesher_signed_distance *>
			&dists_) : dists(dists_) 
    { vd.resize(dists.size()); }

    mesher_union(const mesher_signed_distance &a_,
		 const mesher_signed_distance &b_,
		 const mesher_signed_distance &c_ = void_signed_distance,
		 const mesher_signed_distance &d_ = void_signed_distance,
		 const mesher_signed_distance &e_ = void_signed_distance,
		 const mesher_signed_distance &f_ = void_signed_distance,
		 const mesher_signed_distance &g_ = void_signed_distance,
		 const mesher_signed_distance &h_ = void_signed_distance,
		 const mesher_signed_distance &i_ = void_signed_distance,
		 const mesher_signed_distance &j_ = void_signed_distance,
		 const mesher_signed_distance &k_ = void_signed_distance,
		 const mesher_signed_distance &l_ = void_signed_distance,
		 const mesher_signed_distance &m_ = void_signed_distance,
		 const mesher_signed_distance &n_ = void_signed_distance,
		 const mesher_signed_distance &o_ = void_signed_distance,
		 const mesher_signed_distance &p_ = void_signed_distance,
		 const mesher_signed_distance &q_ = void_signed_distance,
		 const mesher_signed_distance &r_ = void_signed_distance,
		 const mesher_signed_distance &s_ = void_signed_distance,
		 const mesher_signed_distance &t_ = void_signed_distance) {
      dists.push_back(&a_); dists.push_back(&b_);
      size_type nb = 2; with_min = true;
      if (&c_ != &void_signed_distance) { dists.push_back(&c_); ++nb; }
      if (&d_ != &void_signed_distance) { dists.push_back(&d_); ++nb; }
      if (&e_ != &void_signed_distance) { dists.push_back(&e_); ++nb; }
      if (&f_ != &void_signed_distance) { dists.push_back(&f_); ++nb; }
      if (&g_ != &void_signed_distance) { dists.push_back(&g_); ++nb; }
      if (&h_ != &void_signed_distance) { dists.push_back(&h_); ++nb; }
      if (&i_ != &void_signed_distance) { dists.push_back(&i_); ++nb; }
      if (&j_ != &void_signed_distance) { dists.push_back(&j_); ++nb; }
      if (&k_ != &void_signed_distance) { dists.push_back(&k_); ++nb; }
      if (&l_ != &void_signed_distance) { dists.push_back(&l_); ++nb; }
      if (&m_ != &void_signed_distance) { dists.push_back(&m_); ++nb; }
      if (&n_ != &void_signed_distance) { dists.push_back(&n_); ++nb; }
      if (&o_ != &void_signed_distance) { dists.push_back(&o_); ++nb; }
      if (&p_ != &void_signed_distance) { dists.push_back(&p_); ++nb; }
      if (&q_ != &void_signed_distance) { dists.push_back(&q_); ++nb; }
      if (&r_ != &void_signed_distance) { dists.push_back(&r_); ++nb; }
      if (&s_ != &void_signed_distance) { dists.push_back(&s_); ++nb; }
      if (&t_ != &void_signed_distance) { dists.push_back(&t_); ++nb; }
      vd.resize(nb);
    }
    
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      base_node bmin2, bmax2;
      bool b = dists[0]->bounding_box(bmin, bmax);
      if (!b) return false;
      for (size_type k = 1; k < dists.size(); ++k) {
	b = dists[k]->bounding_box(bmin2, bmax2);
	if (!b) return false;
	for (unsigned i=0; i < bmin.size(); ++i) { 
	  bmin[i] = std::min(bmin[i],bmin2[i]);
	  bmax[i] = std::max(bmax[i],bmax2[i]);
	}
      }
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const {
      scalar_type d, f(0), g(1);
      if (with_min) {
	d = (*(dists[0]))(P);
	for (size_type k = 1; k < dists.size(); ++k)
	  d = std::min(d, (*(dists[k]))(P));
      }
      else { // essai raté ...
	isin = false;
	for (size_type k = 0; k < dists.size(); ++k) {
	  vd[k] = (*(dists[k]))(P);
	  if (vd[k] <= scalar_type(0)) isin = true;
	  f += gmm::sqr(gmm::neg(vd[k]));
	  g *= gmm::pos(vd[k]);
	}
	d = isin ? -gmm::sqrt(f)
	  : pow(g, scalar_type(1) / scalar_type(dists.size()));
      }
      return d;
    }
    scalar_type operator()(const base_node &P, dal::bit_vector &bv) const {
      if (with_min) {
	scalar_type d = vd[0] = (*(dists[0]))(P);
	bool ok = (d > -SEPS);
	for (size_type k = 1; k < dists.size(); ++k) {
	  vd[k] = (*(dists[k]))(P); if (vd[k] <= -SEPS) ok = false;
	  d = std::min(d,vd[k]);
	}
	for (size_type k = 0; ok && k < dists.size(); ++k) {
	  if (vd[k] < SEPS) (*(dists[k]))(P, bv);
	}
	return d;
      }
      else { // essai raté ...
	vd[0] = (*(dists[0]))(P);
	bool ok = (vd[0] > -SEPS);
	for (size_type k = 1; k < dists.size(); ++k) {
	  vd[k] = (*(dists[k]))(P); if (vd[k] <= -SEPS) ok = false;
	}
	for (size_type k = 0; ok && k < dists.size(); ++k) {
	  if (vd[k] < SEPS) (*(dists[k]))(P, bv);
	}
	return operator()(P);
      }
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      for (size_type k = 0; k < dists.size(); ++k)
	dists[k]->register_constraints(list); 
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      scalar_type d;
      if (with_min /* || gmm::abs(d) < SEPS*/) {
	d = (*(dists[0]))(P);
	size_type i = 0;
	for (size_type k = 1; k < dists.size(); ++k) {
	  scalar_type d2 = (*(dists[k]))(P);
	  if (d2 < d) { d = d2; i = k; }
	}
	return dists[i]->grad(P, G);
      }
      else { // essai raté ...
	d = operator()(P);
	base_small_vector Gloc;
	for (size_type k = 0; k < dists.size(); ++k) {
	  dists[k]->grad(P, Gloc);
	  if (isin) 
	    Gloc *= -gmm::neg(vd[k]);
	  else 
	    Gloc *= pow(d, scalar_type(dists.size())) / vd[k];
	  if (!k) G = Gloc; else G += Gloc;
	}
	if (isin)
	  G *= scalar_type(1) / d;
	else
	  G /= pow(d, scalar_type(dists.size()-1)) * scalar_type(dists.size());
	return d;
      }
    }
    void hess(const base_node &P, base_matrix &H) const {
      scalar_type d = (*(dists[0]))(P);
      if (with_min || gmm::abs(d) < SEPS) {
	size_type i = 0;
	for (size_type k = 1; k < dists.size(); ++k) {
	  scalar_type d2 = (*(dists[k]))(P);
	  if (d2 < d) { d = d2; i = k; }
	}
	dists[i]->hess(P, H);
      }
      else {
	GMM_ASSERT1(false, "Sorry, to e done");
      }
    }
  };

  class mesher_intersection : public mesher_signed_distance {
    std::vector<const mesher_signed_distance *> dists;
    mutable std::vector<scalar_type> vd;

    // const mesher_signed_distance &a, &b;
  public:
    
    mesher_intersection(const std::vector<const mesher_signed_distance *>
			&dists_) : dists(dists_) 
    { vd.resize(dists.size()); }
    
    mesher_intersection(const mesher_signed_distance &a_,
		 const mesher_signed_distance &b_,
		 const mesher_signed_distance &c_ = void_signed_distance,
		 const mesher_signed_distance &d_ = void_signed_distance,
		 const mesher_signed_distance &e_ = void_signed_distance,
		 const mesher_signed_distance &f_ = void_signed_distance,
		 const mesher_signed_distance &g_ = void_signed_distance,
		 const mesher_signed_distance &h_ = void_signed_distance,
		 const mesher_signed_distance &i_ = void_signed_distance,
		 const mesher_signed_distance &j_ = void_signed_distance,
		 const mesher_signed_distance &k_ = void_signed_distance,
		 const mesher_signed_distance &l_ = void_signed_distance,
		 const mesher_signed_distance &m_ = void_signed_distance,
		 const mesher_signed_distance &n_ = void_signed_distance,
		 const mesher_signed_distance &o_ = void_signed_distance,
		 const mesher_signed_distance &p_ = void_signed_distance,
		 const mesher_signed_distance &q_ = void_signed_distance,
		 const mesher_signed_distance &r_ = void_signed_distance,
		 const mesher_signed_distance &s_ = void_signed_distance,
		 const mesher_signed_distance &t_ = void_signed_distance) {
      dists.push_back(&a_); dists.push_back(&b_);
      size_type nb = 2;
      if (&c_ != &void_signed_distance) { dists.push_back(&c_); ++nb; }
      if (&d_ != &void_signed_distance) { dists.push_back(&d_); ++nb; }
      if (&e_ != &void_signed_distance) { dists.push_back(&e_); ++nb; }
      if (&f_ != &void_signed_distance) { dists.push_back(&f_); ++nb; }
      if (&g_ != &void_signed_distance) { dists.push_back(&g_); ++nb; }
      if (&h_ != &void_signed_distance) { dists.push_back(&h_); ++nb; }
      if (&i_ != &void_signed_distance) { dists.push_back(&i_); ++nb; }
      if (&j_ != &void_signed_distance) { dists.push_back(&j_); ++nb; }
      if (&k_ != &void_signed_distance) { dists.push_back(&k_); ++nb; }
      if (&l_ != &void_signed_distance) { dists.push_back(&l_); ++nb; }
      if (&m_ != &void_signed_distance) { dists.push_back(&m_); ++nb; }
      if (&n_ != &void_signed_distance) { dists.push_back(&n_); ++nb; }
      if (&o_ != &void_signed_distance) { dists.push_back(&o_); ++nb; }
      if (&p_ != &void_signed_distance) { dists.push_back(&p_); ++nb; }
      if (&q_ != &void_signed_distance) { dists.push_back(&q_); ++nb; }
      if (&r_ != &void_signed_distance) { dists.push_back(&r_); ++nb; }
      if (&s_ != &void_signed_distance) { dists.push_back(&s_); ++nb; }
      if (&t_ != &void_signed_distance) { dists.push_back(&t_); ++nb; }
      vd.resize(nb);
    }
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      base_node bmin2, bmax2;
      bool first;
      bool b = dists[0]->bounding_box(bmin, bmax); first = !b;
      for (size_type k = 1; k < dists.size(); ++k) {
	bool bb = dists[k]->bounding_box(bmin2, bmax2);
	for (unsigned i=0; i < bmin.size() && bb && !first; ++i) { 
	  bmin[i] = std::max(bmin[i],bmin2[i]);
	  bmax[i] = std::max(std::min(bmax[i],bmax2[i]), bmin[i]);
	}
	if (first && bb) { bmin = bmin2; bmax = bmax2; first = false; }
	b = b || bb;
      }
      return b;
    }
    virtual scalar_type operator()(const base_node &P) const {
      scalar_type d = (*(dists[0]))(P);
      for (size_type k = 1; k < dists.size(); ++k)
	d = std::max(d, (*(dists[k]))(P));
      return d;

    }
    scalar_type operator()(const base_node &P, dal::bit_vector &bv) const {
      scalar_type d = vd[0] = (*(dists[0]))(P);
      bool ok = (d < SEPS);
      for (size_type k = 1; k < dists.size(); ++k) {
	vd[k] = (*(dists[k]))(P); if (vd[k] >= SEPS) ok = false;
	d = std::min(d,vd[k]);
      }
      for (size_type k = 0; ok && k < dists.size(); ++k) {
	if (vd[k] > -SEPS) (*(dists[k]))(P, bv);
      }
      return d;
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      for (size_type k = 0; k < dists.size(); ++k) {
	dists[k]->register_constraints(list); 
      }
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      scalar_type d = (*(dists[0]))(P);
      size_type i = 0;
      for (size_type k = 1; k < dists.size(); ++k) {
	scalar_type d2 = (*(dists[k]))(P);
	if (d2 > d) { d = d2; i = k; }
      }
      return dists[i]->grad(P, G);
    }
    void hess(const base_node &P, base_matrix &H) const {
      scalar_type d = (*(dists[0]))(P);
      size_type i = 0;
      for (size_type k = 1; k < dists.size(); ++k) {
	scalar_type d2 = (*(dists[k]))(P);
	if (d2 > d) { d = d2; i = k; }
      }
      dists[i]->hess(P, H);
    }
  };

  class mesher_setminus : public mesher_signed_distance {
    const mesher_signed_distance &a, &b;
  public:
    mesher_setminus(const mesher_signed_distance& a_,
		    const mesher_signed_distance &b_) : a(a_), b(b_) {}
    bool bounding_box(base_node &bmin, base_node &bmax) const
    { return a.bounding_box(bmin,bmax); }
    scalar_type operator()(const base_node &P, dal::bit_vector &bv) const {
      scalar_type da = a(P), db = -b(P);
      if (da < SEPS && db < SEPS) {
	if (da > -SEPS) a(P, bv);
	if (db > -SEPS) b(P, bv);
      }
      return std::max(da, db);
    }
    scalar_type operator()(const base_node &P) const
    { return std::max(a(P),-b(P)); }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      a.register_constraints(list); b.register_constraints(list);
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      scalar_type da = a(P), db = -b(P);
      if (da > db) return a.grad(P, G);
      else { b.grad(P, G); G *= scalar_type(-1); return db; }
    }
    void hess(const base_node &P, base_matrix &H) const {
      scalar_type da = a(P), db = -b(P);
      if (da > db) a.hess(P, H);
      else { b.hess(P, H); gmm::scale(H, scalar_type(-1)); }
    }

  };
  

  class mesher_tube : public mesher_signed_distance {
    base_node x0; base_node n; scalar_type R;
  public:
      mesher_tube(base_node x0_, base_node n_, scalar_type R_)
	: x0(x0_), n(n_), R(R_)
    { n /= gmm::vect_norm2(n); }
    bool bounding_box(base_node &, base_node &) const
    { return false; }
    virtual scalar_type operator()(const base_node &P) const {
      base_node v(P); v -= x0;
      gmm::add(gmm::scaled(n, -gmm::vect_sp(v, n)), v);
      return gmm::vect_norm2(v) - R;
    }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector &bv) const {
      scalar_type d = (*this)(P);
      bv[id] = (gmm::abs(d) < SEPS);
      return d;
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      id = list.size(); list.push_back(this);
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      G = P; G -= x0;
      gmm::add(gmm::scaled(n, -gmm::vect_sp(G, n)), G);
      scalar_type e = gmm::vect_norm2(G), d = e - R;
      while (e == scalar_type(0)) {
	gmm::fill_random(G);
	gmm::add(gmm::scaled(n, -gmm::vect_sp(G, n)), G);
	e = gmm::vect_norm2(G);
      }
      G /= e;
      return d;
    }
    void hess(const base_node &, base_matrix &) const {
      GMM_ASSERT1(false, "Sorry, to be done");
    }
  };

  class mesher_cylinder : public mesher_signed_distance {
    base_node x0; base_small_vector n;
    scalar_type L, R;
    mesher_tube t;
    mesher_half_space p1, p2;
    mesher_intersection i1;
  public:
    mesher_cylinder(const base_node &c, const base_small_vector &no,
		    scalar_type L_, scalar_type R_)
      : x0(c), n(no/gmm::vect_norm2(no)), L(L_), R(R_), t(x0, n, R),
	p1(x0, n), p2(x0+n*L, -1.0 * n), i1(p1, p2, t) {}
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      base_node x1(x0+n*L);
      bmin = bmax = x0;
      for (unsigned i = 0; i < gmm::vect_size(x0); ++i) {
	bmin[i] = std::min(x0[i], x1[i]) - R;
	bmax[i] = std::max(x0[i], x1[i]) + R;
      }
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const { return i1(P); }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector& bv) const
    { return i1(P, bv); }
    scalar_type grad(const base_node &P, base_small_vector &G) const
      { return i1.grad(P, G); }
    void hess(const base_node &, base_matrix &) const {
      GMM_ASSERT1(false, "Sorry, to be done");
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const
    { i1.register_constraints(list); }
  };



  class mesher_infinite_cone : public mesher_signed_distance {
    // uses the true distance to a cone.
    base_node x0; base_node n; scalar_type alpha;
  public:
      mesher_infinite_cone(base_node x0_, base_node n_, scalar_type alpha_)
	: x0(x0_), n(n_), alpha(alpha_)
    { n /= gmm::vect_norm2(n); }
    bool bounding_box(base_node &, base_node &) const
    { return false; }
    virtual scalar_type operator()(const base_node &P) const {
      base_node v(P); v -= x0;
      scalar_type v_n = gmm::vect_sp(v, n);
      gmm::add(gmm::scaled(n, -v_n), v);
      return gmm::vect_norm2(v) * cos(alpha) - gmm::abs(v_n) * sin(alpha);
    }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector &bv) const {
      scalar_type d = (*this)(P);
      bv[id] = (gmm::abs(d) < SEPS);
      return d;
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const {
      id = list.size(); list.push_back(this);
    }
    scalar_type grad(const base_node &P, base_small_vector &v) const {
      v = P; v -= x0;
      scalar_type v_n = gmm::vect_sp(v, n);
      gmm::add(gmm::scaled(n, -v_n), v);
      scalar_type no = gmm::vect_norm2(v);
      scalar_type d = no * cos(alpha) - gmm::abs(v_n) * sin(alpha);
      while (no ==  scalar_type(0)) {
	gmm::fill_random(v);
	gmm::add(gmm::scaled(n, -gmm::vect_sp(v, n)), v);
	no = gmm::vect_norm2(v);
      }
      v *= cos(alpha) / no;
      v -= (sin(alpha) * gmm::sgn(v_n)) * n;
      return d;
    }
    void hess(const base_node &, base_matrix &) const {
      GMM_ASSERT1(false, "Sorry, to be done");
    }
  };

  class mesher_cone : public mesher_signed_distance {
    base_node x0; base_small_vector n;
    scalar_type L, alpha;
    mesher_infinite_cone t;
    mesher_half_space p1, p2;
    mesher_intersection i1;
  public:
    mesher_cone(const base_node &c, const base_small_vector &no,
		    scalar_type L_, scalar_type alpha_)
      : x0(c), n(no/gmm::vect_norm2(no)), L(L_), alpha(alpha_),
	t(x0, n, alpha), p1(x0, n), p2(x0+n*L, -1.0 * n), i1(p1, p2, t) {}
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      base_node x1(x0+n*L);
      scalar_type R = L * sin(alpha);
      bmin = bmax = x0;
      for (unsigned i = 0; i < gmm::vect_size(x0); ++i) {
	bmin[i] = std::min(x0[i], x1[i]) - R;
	bmax[i] = std::max(x0[i], x1[i]) + R;
      }
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const { return i1(P); }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector& bv) const
    { return i1(P, bv); }
    scalar_type grad(const base_node &P, base_small_vector &G) const
      { return i1.grad(P, G); }
    void hess(const base_node &, base_matrix &) const {
      GMM_ASSERT1(false, "Sorry, to be done");
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const
    { i1.register_constraints(list); }
  };

  class mesher_ellipse : public mesher_signed_distance {
    base_node x0; base_small_vector n, t;
    scalar_type r, R, a;
  public:
    mesher_ellipse(const base_node &center, const base_small_vector &no,
		    scalar_type r_, scalar_type R_)
      : x0(center), n(no/gmm::vect_norm2(no)), r(r_), R(R_) {
      t[0] = -n[1]; t[1] = n[0];
      if (R < r) { std::swap(r, R); std::swap(n, t); }
      a = sqrt(R*R - r*r);
    }
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      bmin = bmax = x0;
      for (unsigned i = 0; i < 2; ++i) { bmin[i] -= R; bmax[i] += R; }
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const { 
      base_small_vector v(P); v -= x0;
      scalar_type vt = gmm::vect_sp(v, t);
      vt = std::max(-a, std::min(a, vt));
      base_node x1 = x0 + t*vt;
      base_small_vector v1(P); v1 -= x1;
      scalar_type v1n = gmm::vect_sp(v1, n), v1t = gmm::vect_sp(v1, t);
      scalar_type x1n = gmm::vect_sp(x1, n), x1t = gmm::vect_sp(x1, t);
      scalar_type ea = v1n*v1n / (r*r) + v1t * v1t / (R*R);
      scalar_type eb = 2. * (x1n*v1n / (r*r) + x1t*v1t / (R*R));
      scalar_type ec = x1n*x1n / (r*r) + x1t * x1t / (R*R);

      scalar_type delta = eb*eb - 4 * ea * ec;
      assert(delta >= 0);
      scalar_type lambda = (-eb + sqrt(delta)) / (2. * ea);
      return (1.-lambda)*gmm::vect_norm2(v1);
    }
    virtual scalar_type operator()(const base_node &P,
				   dal::bit_vector& bv) const {
      scalar_type d = this->operator()(P);
      bv[id] = (gmm::abs(d) < SEPS);
      return d;
    }
    scalar_type grad(const base_node &, base_small_vector &) const
    { GMM_ASSERT1(false, "Sorry, to be done"); return 0.; }
    void hess(const base_node &, base_matrix &) const {
      GMM_ASSERT1(false, "Sorry, to be done");
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>& list) const
    { id = list.size(); list.push_back(this); }
  };


  class mesher_torus : public mesher_signed_distance { // to be done
    // ajouter une rotation rigide et translation ..
    scalar_type R, r;
  public:
    mesher_torus(scalar_type RR, scalar_type rr) : R(RR), r(rr) {}
    bool bounding_box(base_node &bmin, base_node &bmax) const {
      bmin = base_node(3); bmax = base_node(3);
      bmin[0] = bmin[1] = -R-r; bmin[2] = -r;
      bmax[0] = bmax[1] = +R+r; bmax[2] = +r;
      return true;
    }
    virtual scalar_type operator()(const base_node &P) const {
      scalar_type x = P[0], y = P[1], z = P[2], c = sqrt(x*x + y*y);
      return (c == 0.) ? R - r : sqrt(gmm::sqr(c-R) + z*z) - r;
    }
    virtual scalar_type operator()(const base_node &P, dal::bit_vector&bv)
      const {
      scalar_type d = this->operator()(P);
      bv[id] = (gmm::abs(d) < SEPS);
      return d;
    }
    scalar_type grad(const base_node &P, base_small_vector &G) const {
      G.resize(3);
      scalar_type x = P[0], y = P[1], z = P[2], c = sqrt(x*x + y*y), d(0);
      if (c == 0.) {
	d = R - r;
	gmm::fill_random(G); G[2] = 0.0; G /= gmm::vect_norm2(G);
      }
      else {
	scalar_type w = 1. - R / c, e = sqrt(gmm::sqr(c-R) + z*z);
	d = e - r;
	if (e == 0.) {
	  gmm::fill_random(G); G[0] = x; G[1] = y; G /= gmm::vect_norm2(G);
	}
	else {
	  G[0] = x * w / e; G[1] = y * w / e; G[2] = z / e;
	}
      }
      return d;
    }
    void hess(const base_node &, base_matrix &) const {
      GMM_ASSERT1(false, "Sorry, to be done");
    }
    virtual void register_constraints(std::vector<const
				      mesher_signed_distance*>&list) const
    { id = list.size(); list.push_back(this); }
  };


  

  // interface with qhull
  void delaunay(const std::vector<base_node> &pts,
		gmm::dense_matrix<size_type>& simplexes);

  
  // mesher
  void build_mesh(mesh &m, const mesher_signed_distance& dist_,
		  scalar_type h0, const std::vector<base_node> &fixed_points
		  = std::vector<base_node>(), size_type K = 1, int noise = -1,
		  size_type iter_max = 500, int prefind = 1,
		  scalar_type dist_point_hull = 4,
		  scalar_type boundary_threshold_flatness = 0.11);

  // exported functions
  bool try_projection(const mesher_signed_distance& dist, base_node &X,
		      bool on_surface = false);
  bool pure_multi_constraint_projection
  (const std::vector<const mesher_signed_distance*> &list_constraints,
   base_node &X, const dal::bit_vector &cts);
  scalar_type curvature_radius_estimate(const mesher_signed_distance &dist,
					base_node X, bool proj = false);
  scalar_type min_curvature_radius_estimate
  (const std::vector<const mesher_signed_distance*> &list_constraints,
   const base_node &X, const dal::bit_vector &cts, size_type hide_first = 0);

}

#endif /* GETFEM_MESHER_H__ */