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// -*- C++ -*-
//
// Package:     <package>
// Module:      Lpar
// 
// Description: <one line class summary>
//
// Implimentation:
//     <Notes on implimentation>
//
// Author:      KATAYAMA Nobuhiko
// Created:     Fri Feb  6 10:21:49 JST 1998
// $Id: Lpar.cxx,v 1.2 2008/06/30 08:46:52 max Exp $

#include <iostream>

// system include files
#include <cmath>
// user include files
#include "TrackUtil/Lpar.h"

//
// constants, enums and typedefs
//

//
// static data member definitions
//

//const double Lpar::BELLE_ALPHA(-333.564095);

//
// constructors and destructor
//
// Lpar::Lpar(double x1, double y1, double x2, double y2, double x3, double y3) {
//   circle(x1, y1, x2, y2, x3, y3);
// }
Lpar::Cpar::Cpar(const Lpar&l) {
  m_cu = l.kappa();
  if (l.alpha() !=0 && l.beta() !=0)
    m_fi = atan2(l.alpha(), -l.beta());
  else m_fi = 0;
  if(m_fi<0) m_fi+=2*M_PI;
  m_da = 2 * l.gamma()/ (1 + sqrt (1 + 4 * l.kappa() * l.gamma()));
  m_cfi = cos(m_fi);
  m_sfi = sin(m_fi);
}

// Lpar::Lpar( const Lpar& )
// {
// }

Lpar::~Lpar()
{
}

//
// assignment operators
//
// const Lpar& Lpar::operator=( const Lpar& )
// {
// }

//
// comparison operators
//
// bool Lpar::operator==( const Lpar& ) const
// {
// }

// bool Lpar::operator!=( const Lpar& ) const
// {
// }

//
// member functions
//
void Lpar::circle(double x1, double y1, double x2, double y2,
                  double x3, double y3) {
  double a;
  double b;
  double c;
  double delta = (x1-x2)*(y1-y3) - (y1-y2)*(x1-x3);
  if(delta==0) {
    //
    // three points are on a line.
    //
    m_kappa = 0;
    double r12sq = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2);
    if (r12sq>0) {
      double r12 = sqrt(r12sq);
      m_beta = -(x1-x2)/r12;
      m_alpha = (y1-y2)/r12;
      m_gamma = - (m_alpha*x1+m_beta*y1);
    } else {
      double r13sq = (x1-x3)*(x1-x3) + (y1-y3)*(y1-y3);
      if (r13sq>0) {
        double r13 = sqrt(r13sq);
        m_beta = -(x1-x3)/r13;
        m_alpha = (y1-y3)/r13;
        m_gamma = - (m_alpha*x3+m_beta*y3);
      } else {
        double r23sq = (x2-x3)*(x2-x3) + (y2-y3)*(y2-y3);
        if (r23sq>0) {
          double r23 = sqrt(r23sq);
          m_beta = -(x2-x3)/r23;
          m_alpha = (y2-y3)/r23;
          m_gamma = - (m_alpha*x3+m_beta*y3);
        } else {
          m_alpha = 1;
          m_beta = 0;
          m_gamma = 0;
        }
      }
    }
  } else {
    double r1sq = x1 * x1 + y1 * y1;
    double r2sq = x2 * x2 + y2 * y2;
    double r3sq = x3 * x3 + y3 * y3;
    a = 0.5 * (  (y1-y3)*(r1sq-r2sq) - (y1-y2)*(r1sq-r3sq)) / delta;
    b = 0.5 * (- (x1-x3)*(r1sq-r2sq) + (x1-x2)*(r1sq-r3sq)) / delta;
    double csq = (x1-a)*(x1-a) + (y1-b)*(y1-b);
    c = sqrt(csq);
    double csq2 = (x2-a)*(x2-a) + (y2-b)*(y2-b);
    double csq3 = (x3-a)*(x3-a) + (y3-b)*(y3-b);
    m_kappa = 1 / (2 * c);
    m_alpha = - 2 * a * m_kappa;
    m_beta = - 2 * b * m_kappa;
    m_gamma = (a*a + b*b - c*c) * m_kappa;
  }
}

HepMatrix Lpar::dldc() const
#ifdef BELLE_OPTIMIZED_RETURN
return vret(3,4);
{
#else
{
  HepMatrix vret(3,4);
#endif
  Cpar cp(*this);
  double xi = cp.xi();
  double s = cp.sfi();
  double c = cp.cfi();
  vret(1,1) = 2*cp.da()*s;
  vret(1,2) = -2*cp.da()*c;
  vret(1,3) = cp.da()*cp.da();
  vret(1,4) = 1;
  vret(2,1) = xi*c;
  vret(2,2) = xi*s;
  vret(2,3) = 0;
  vret(2,4) = 0;
  vret(3,1) = 2*cp.cu()*s;
  vret(3,2) = -2*cp.cu()*c;
  vret(3,3) = xi;
  vret(3,4) = 0;
  return vret;
}

bool Lpar::xy(double r, double &x, double &y, int dir) const {
  double t_kr2g = kr2g(r);
  double t_xi2 = xi2();
  double ro = r * r * t_xi2 - t_kr2g * t_kr2g;
  if ( ro < 0  ) return false;
  double rs = sqrt(ro);
  if(dir==0) {
    x = (- m_alpha * t_kr2g  -  m_beta * rs) / t_xi2;
    y = (- m_beta  * t_kr2g  + m_alpha * rs) / t_xi2;
  } else {
    x = (- m_alpha * t_kr2g  +  m_beta * rs) / t_xi2;
    y = (- m_beta  * t_kr2g  - m_alpha * rs) / t_xi2;
  }
  return true;
}

double Lpar::x(double r) const {
  double t_x, t_y;
  xy(r, t_x, t_y);
  return t_x;
}

double Lpar::y(double r) const {
  double t_x, t_y;
  xy(r, t_x, t_y);
  return t_y;
}

double Lpar::phi(double r,int dir) const {
  double x, y;
  if (!xy(r,x,y, dir)) return -1;
  double p = atan2(y,x);
  if (p<0) p += (2*M_PI);
  return p;
}

void Lpar::xhyh(double x, double y, double &xh, double &yh) const {
  double ddm = dr(x, y);
  if (ddm==0) {
    xh = x;
    yh = y;
    return;
  }
  double kdp1 = 1 + 2 * kappa() * ddm;
  xh = x - ddm * ( 2 * kappa() * x + alpha())/kdp1;
  yh = y - ddm * ( 2 * kappa() * y + beta())/kdp1;
}

double Lpar::s(double x, double y) const {
  double xh, yh, xx, yy;
  xhyh(x, y, xh, yh);
  double fk = fabs(kappa());
  if (fk==0) return 0;
  yy = 2 * fk * ( alpha() * yh - beta() * xh);
  xx = 2 * kappa() * ( alpha() * xh + beta() * yh ) + xi2();
  double sp = atan2(yy, xx);
  if (sp<0) sp += (2*M_PI);
  return sp / 2 / fk;
}

double Lpar::s(double r, int dir) const {
  double d0 = da();
  if (fabs(r)<fabs(d0)) return -1;
  double b = fabs(kappa()) * sqrt((r*r-d0*d0)/(1 + 2 * kappa() * d0));
  if (fabs(b)>1) return -1;
  if(dir==0)return asin(b)/fabs(kappa());
  return (M_PI-asin(b))/fabs(kappa());
}

HepVector Lpar::center() const
#ifdef BELLE_OPTIMIZED_RETURN
return v(3);
{
#else
{
  HepVector v(3);
#endif
  v(1) = xc();
  v(2) = yc();
  v(3) = 0;
  return(v);
}

int intersect(const Lpar&lp1, const Lpar&lp2, HepVector&v1, HepVector&v2) {
  HepVector cen1(lp1.center());
  HepVector cen2(lp2.center());
  double dx = cen1(1)-cen2(1);
  double dy = cen1(2)-cen2(2);
  double dc = sqrt(dx*dx+dy*dy);
  if(dc<fabs(0.5/lp1.kappa())+fabs(0.5/lp2.kappa())) {
    double a1 = std::sqrt(lp1.alpha()) + std::sqrt(lp1.beta());
    double a2 = std::sqrt(lp2.alpha()) + std::sqrt(lp2.beta());
    double a3 = lp1.alpha()*lp2.alpha() + lp1.beta()*lp2.beta();
    double det = lp1.alpha()*lp2.beta() - lp1.beta()*lp2.alpha();
    if(fabs(det)>1e-12) {
      double c1 = a2 * std::sqrt(lp1.kappa()) + a1 * std::sqrt(lp2.kappa()) -
        2.0 * a3 * lp1.kappa() * lp2.kappa();
      if(c1!=0) {
        double cinv = 1.0 / c1;
        double c2 = std::sqrt(a3) - 0.5 * (a1 + a2) - 2.0 * a3 *
          (lp1.gamma() * lp2.kappa() + lp2.gamma() * lp1.kappa());
        double c3 = a2 * std::sqrt(lp1.gamma()) + a1 * std::sqrt(lp2.gamma()) -
          2.0 * a3 * lp1.gamma() * lp2.gamma();
        double root = std::sqrt(c2) - 4.0 * c1 * c3;
        if (root>=0) {
          root = sqrt(root);
          double rad2[2];
          rad2[0] = 0.5 * cinv * (-c2 - root);
          rad2[1] = 0.5 * cinv * (-c2 + root);
          double ab1 = -(lp2.beta() * lp1.gamma() - lp1.beta() * lp2.gamma());
          double ab2 = (lp2.alpha() * lp1.gamma() - lp1.alpha() * lp2.gamma());
          double ac1 = -(lp2.beta() * lp1.kappa() - lp1.beta() * lp2.kappa());
          double ac2 = (lp2.alpha() * lp1.kappa() - lp1.alpha() * lp2.kappa());
          double dinv = 1.0 / det;
          v1(1) = dinv * (ab1 + ac1 * rad2[0]);
          v1(2) = dinv * (ab2 + ac2 * rad2[0]);
          v1(3) = 0;
          v2(1) = dinv * (ab1 + ac1 * rad2[1]);
          v2(2) = dinv * (ab2 + ac2 * rad2[1]);
          v2(3) = 0;
          double d1 = lp1.d(v1(1),v1(2));
          double d2 = lp2.d(v1(1),v1(2));
          double d3 = lp1.d(v2(1),v2(2));
          double d4 = lp2.d(v2(1),v2(2));
          double r = sqrt(rad2[0]);
          Lpar::Cpar cp1(lp1);
          Lpar::Cpar cp2(lp2);
          for(int j=0;j<2;j++) {
            double s1,s2;
            if(j==0) {
              s1 = lp1.s(v1(1),v1(2));
              s2 = lp2.s(v1(1),v1(2));
            } else {
              s1 = lp1.s(v2(1),v2(2));
              s2 = lp2.s(v2(1),v2(2));
            }
            double phi1 = cp1.fi() + 2 * cp1.cu() * s1;
            double phi2 = cp2.fi() + 2 * cp2.cu() * s2;
            double f = (1 + 2 * cp1.cu() * cp1.da()) *
              (1 + 2 * cp2.cu() * cp2.da()) * cos(cp1.fi()-cp2.fi());
            f -= 2 * (lp1.gamma() * lp2.kappa() + lp2.gamma() * lp1.kappa());
            double cosphi12 = f;
          }
          return 2;
        }
      }
    }
  }
  return 0;
}

//
// const member functions
//

//
// static member functions
//
        
std::ostream& operator<<(std::ostream &o, Lpar &s) {
  return o << " al=" << s.m_alpha << " be=" << s.m_beta
           << " ka=" << s.m_kappa << " ga=" << s.m_gamma;
}

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