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NaturalCurve.H

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#ifndef _NATURALCURVE_H
#define _NATURALCURVE_H

#include <Frenet.H>
#include <Model.H>

namespace xchen 
{
  class NaturalCurve : public Model
  {
  public:
      typedef double (*KapaFun)(double);
      typedef double (*TauFun)(double);

  public:      
      NaturalCurve(KapaFun kapa, TauFun tau, const Frame& f=Frame(), double stp=0.01);
      void Generate(double stepsize = 0.01);

  private:
      vector<Frenet> frenets;
      double step;
      KapaFun k;
      TauFun t;

      bool stop() const { return frenets.size() > 9000; }
  };

  inline NaturalCurve :: NaturalCurve(KapaFun kapa, TauFun tau, const Frame& f, double stp) : k(kapa), t(tau), step(0) 
  { 
    Frenet frt(f, k(0), t(0));

    double 
      diag = sqrt( t(0) * t(0) + k(0) * k(0) ),
      cn =  k(0) / diag, 
      sn = t(0) / diag, 
      cn2 = k(0) * k(0) / (t(0) * t(0) + k(0) * k(0)),
      r = cn2 / k(0);

    frt.f1 = dVector3D( cn, 0, sn );
    frt.f3 = dVector3D( -sn, 0, cn );
    frt.pos[1] -= r;
      
    frenets.push_back( frt ); 
    Generate(stp); 
  }

  inline void NaturalCurve :: Generate(double stepsize)
  {
    if(step != stepsize)
      frenets.erase(frenets.begin()+1, frenets.end());

    frenets.reserve(9100);

    step = stepsize;
 
    double s = step * (frenets.size()-1);
      
    cout << "in generating\n";
      
    for(int i=0; !stop(); i++)
    {
      Frenet& prev_frt = frenets.back();
      frenets.push_back( prev_frt );
      Frenet& cur_frt = frenets.back();

      cur_frt.pos += prev_frt.f1 * step;

      cur_frt.f1 += prev_frt.f2 * prev_frt.k * step;
      cur_frt.f3 -= prev_frt.f2 * prev_frt.t * step;
      cur_frt.f2 += (-prev_frt.f1 * prev_frt.k + prev_frt.f3 * prev_frt.t) * step;

      s += step;
      cur_frt.k = k(s);
      cur_frt.t = t(s);

      if( !(i%5) )
      {
        cur_frt.f1.Normalize();
        cur_frt.f2.Normalize();
        cur_frt.f3.Normalize();
      }

      if(i>9000)                                                             
        cout << "frenets.max_size() is " <<  frenets.max_size() << endl;
    }
    cout << "generating done\n";
  }
      
}

#endif

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