AnglesUtil.h

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#ifndef INC_ANGLESUTIL
#define INC_ANGLESUTIL
// File: AnglesUtil.hpp
//
// Purpose:  Provide useful functions for calculating angles and eta
//
// Created:   4-NOV-1998  Serban Protopopescu
// History:   replaced old KinemUtil
// Modified:  23-July-2000 Add rapidity calculation
//            14-Aug-2003 converted all functions to double precision
// Dependencies (#includes)
 
#include <cmath>
#include <cstdlib>
 
namespace kinem {
  const double PI = 2.0 * acos(0.);
  const double TWOPI = 2.0 * PI;
  const float ETA_LIMIT = 15.0;
  const float EPSILON = 1.E-10;
 
  //  calculate phi from x, y
  inline double phi(double x, double y);
  //  calculate phi for a line defined by xy1 and xy2 (xy2-xy1)
  inline double phi(double xy1[2], double xy2[2]);
  inline double phi(float xy1[2], float xy2[2]);
 
  //  calculate theta from x, y, z
  inline double theta(double x, double y, double z);
  //  calculate theta for a line defined by xyz1 and xyz2 (xyz2-xyz1)
  inline double theta(double xyz1[3], double xyz2[3]);
  inline double theta(float xyz1[3], float xyz2[3]);
  //  calculate theta from eta
  inline double theta(double etap);
 
  //  calculate eta from x, y, z (return also theta)
  inline double eta(double x, double y, double z);
  //  calculate eta for a line defined by xyz1 and xyz2 (xyz2-xyz1)
  inline double eta(double xyz1[3], double xyz2[3]);
  inline double eta(float xyz1[3], float xyz2[3]);
  //  calculate eta from theta
  inline double eta(double th);
 
  // calculate rapidity from E, pz
  inline double y(double E, double pz);
 
  //  calculate phi1-phi2 keeping value between 0 and pi
  inline double delta_phi(double ph11, double phi2);
  // calculate phi1-phi2 keeping value between -pi and pi
  inline double signed_delta_phi(double ph11, double phi2);
  // calculate eta1 - eta2
  inline double delta_eta(double eta1, double eta2);
 
  //  calculate deltaR
  inline double delta_R(double eta1, double phi1, double eta2, double phi2);
 
  //  calculate unit vectors given two points
  inline void uvectors(double u[3], double xyz1[3], double xyz2[3]);
  inline void uvectors(float u[3], float xyz1[3], float xyz2[3]);
 
  inline double tanl_from_theta(double theta);
  inline double theta_from_tanl(double tanl);
}  // namespace kinem
 
inline double kinem::phi(double x, double y) {
  double PHI = atan2(y, x);
  return (PHI >= 0) ? PHI : kinem::TWOPI + PHI;
}
 
inline double kinem::phi(float xy1[2], float xy2[2]) {
  double dxy1[2] = {xy1[0], xy1[1]};
  double dxy2[2] = {xy2[0], xy2[1]};
  return phi(dxy1, dxy2);
}
 
inline double kinem::phi(double xy1[2], double xy2[2]) {
  double x = xy2[0] - xy1[0];
  double y = xy2[1] - xy1[1];
  return phi(x, y);
}
 
inline double kinem::delta_phi(double phi1, double phi2) {
  double PHI = fabs(phi1 - phi2);
  return (PHI <= PI) ? PHI : kinem::TWOPI - PHI;
}
 
inline double kinem::delta_eta(double eta1, double eta2) { return eta1 - eta2; }
 
inline double kinem::signed_delta_phi(double phi1, double phi2) {
  double phia = phi1;
  if (phi1 > PI)
    phia = phi1 - kinem::TWOPI;
  double phib = phi2;
  if (phi2 > PI)
    phib = phi2 - kinem::TWOPI;
  double dphi = phia - phib;
  if (dphi > PI)
    dphi -= kinem::TWOPI;
  if (dphi < -PI)
    dphi += kinem::TWOPI;
  return dphi;
}
 
inline double kinem::delta_R(double eta1, double phi1, double eta2, double phi2) {
  double deta = eta1 - eta2;
  double dphi = kinem::delta_phi(phi1, phi2);
  return sqrt(deta * deta + dphi * dphi);
}
 
inline double kinem::theta(double xyz1[3], double xyz2[3]) {
  double x = xyz2[0] - xyz1[0];
  double y = xyz2[1] - xyz1[1];
  double z = xyz2[2] - xyz1[2];
  return theta(x, y, z);
}
 
inline double kinem::theta(float xyz1[3], float xyz2[3]) {
  double dxyz1[3] = {xyz1[0], xyz1[1], xyz1[2]};
  double dxyz2[3] = {xyz2[0], xyz2[1], xyz2[2]};
  return theta(dxyz1, dxyz2);
}
 
inline double kinem::theta(double x, double y, double z) { return atan2(sqrt(x * x + y * y), z); }
 
inline double kinem::theta(double etap) { return 2.0 * atan(exp(-etap)); }
 
inline double kinem::eta(double xyz1[3], double xyz2[3]) {
  double x = xyz2[0] - xyz1[0];
  double y = xyz2[1] - xyz1[1];
  double z = xyz2[2] - xyz1[2];
  return eta(x, y, z);
}
 
inline double kinem::eta(float xyz1[3], float xyz2[3]) {
  double dxyz1[3] = {xyz1[0], xyz1[1], xyz1[2]};
  double dxyz2[3] = {xyz2[0], xyz2[1], xyz2[2]};
  return eta(dxyz1, dxyz2);
}
 
inline double kinem::eta(double x, double y, double z) {
  return 0.5 * log((sqrt(x * x + y * y + z * z) + z + EPSILON) / (sqrt(x * x + y * y + z * z) - z + EPSILON));
}
 
inline double kinem::eta(double th) {
  if (th == 0)
    return ETA_LIMIT;
  if (th >= PI - 0.0001)
    return -ETA_LIMIT;
  return -log(tan(th / 2.0));
}
 
inline double kinem::y(double E, double pz) { return 0.5 * log((E + pz + EPSILON) / (E - pz + EPSILON)); }
 
inline void kinem::uvectors(double u[3], double xyz1[3], double xyz2[3]) {
  double xdiff = xyz2[0] - xyz1[0];
  double ydiff = xyz2[1] - xyz1[1];
  double zdiff = xyz2[2] - xyz1[2];
  double s = sqrt(xdiff * xdiff + ydiff * ydiff + zdiff * zdiff);
  if (s > 0) {
    u[0] = xdiff / s;
    u[1] = ydiff / s;
    u[2] = zdiff / s;
  } else {
    u[0] = 0;
    u[1] = 0;
    u[2] = 0;
  }
}
 
inline void kinem::uvectors(float u[3], float xyz1[3], float xyz2[3]) {
  double du[3];
  double dxyz1[3] = {xyz1[0], xyz1[1], xyz1[2]};
  double dxyz2[3] = {xyz2[0], xyz2[1], xyz2[2]};
  uvectors(du, dxyz1, dxyz2);
  u[0] = du[0];
  u[1] = du[1];
  u[2] = du[2];
}
 
inline double kinem::tanl_from_theta(double theta) { return tan(PI / 2.0 - theta); }
 
inline double kinem::theta_from_tanl(double tanl) { return PI / 2.0 - atan(tanl); }
 
#endif  // INC_ANGLESUTIL