CircleEq< T > Class Template Reference

#include <CircleEq.h>

Public Member Functions
constexpr std::pair< T, T >	center () const
	CircleEq ()
constexpr	CircleEq (T x1, T y1, T x2, T y2, T x3, T y3)
constexpr void	compute (T x1, T y1, T x2, T y2, T x3, T y3)
constexpr std::pair< T, T >	cosdir () const
constexpr std::pair< T, T >	cosdir (T x, T y) const
constexpr auto	curvature () const
constexpr T	dca (T x, T y) const
constexpr T	dca0 () const
constexpr auto	radius () const

Public Attributes
T	m_alpha = 0
T	m_beta = 0
T	m_c = 0
T	m_xp = 0
T	m_yp = 0

Detailed Description

template<typename T>
class CircleEq< T >

| 1) circle is parameterized as: | | C*[(X-Xp)**2+(Y-Yp)**2] - 2*alpha*(X-Xp) - 2*beta*(Y-Yp) = 0 | | Xp,Yp is a point on the track; | | C = 1/r0 is the curvature ( sign of C is charge of particle ); | | alpha & beta are the direction cosines of the radial vector at Xp,Yp | | i.e. alpha = C*(X0-Xp), | | beta = C*(Y0-Yp), |

where center of circle is at X0,Y0.
Slope dy/dx of tangent at Xp,Yp is -alpha/beta.
2) the z dimension of the helix is parameterized by gamma = dZ/dSperp
this is also the tangent of the pitch angle of the helix.
with this parameterization, (alpha,beta,gamma) rotate like a vector.
3) For tracks going inward at (Xp,Yp), C, alpha, beta, and gamma change sign

|

Definition at line 24 of file CircleEq.h.

Constructor & Destructor Documentation

CircleEq() [1/2]

template<typename T>

CircleEq< T >::CircleEq ( )

inline

Definition at line 26 of file CircleEq.h.

{}

CircleEq() [2/2]

template<typename T>

constexpr CircleEq< T >::CircleEq ( T  x1, T  y1, T  x2, T  y2, T  x3, T  y3  )

inline

Definition at line 28 of file CircleEq.h.

References CircleEq< T >::compute(), testProducerWithPsetDescEmpty_cfi::x1, testProducerWithPsetDescEmpty_cfi::x2, testProducerWithPsetDescEmpty_cfi::y1, and testProducerWithPsetDescEmpty_cfi::y2.

{ compute(x1, y1, x2, y2, x3, y3); }

Member Function Documentation

center()

template<typename T>

constexpr std::pair<T, T> CircleEq< T >::center ( ) const

inline

Definition at line 58 of file CircleEq.h.

References CircleEq< T >::m_alpha, CircleEq< T >::m_beta, CircleEq< T >::m_c, CircleEq< T >::m_xp, and CircleEq< T >::m_yp.

{ return std::make_pair(m_xp + m_alpha / m_c, m_yp + m_beta / m_c); }

compute()

template<typename T >

constexpr void CircleEq< T >::compute	(	T	x1,
		T	y1,
		T	x2,
		T	y2,
		T	x3,
		T	y3
	)

Definition at line 70 of file CircleEq.h.

References funct::abs(), hgcalPlots::ct, EgammaValidation_cff::num, cmsswSequenceInfo::seq, mathSSE::sqrt(), testProducerWithPsetDescEmpty_cfi::x1, testProducerWithPsetDescEmpty_cfi::x2, testProducerWithPsetDescEmpty_cfi::y1, and testProducerWithPsetDescEmpty_cfi::y2.

Referenced by CircleEq< T >::CircleEq().

                                                                      {
  bool noflip = std::abs(x3 - x1) < std::abs(y3 - y1);

  auto x1p = noflip ? x1 - x2 : y1 - y2;
  auto y1p = noflip ? y1 - y2 : x1 - x2;
  auto d12 = x1p * x1p + y1p * y1p;
  auto x3p = noflip ? x3 - x2 : y3 - y2;
  auto y3p = noflip ? y3 - y2 : x3 - x2;
  auto d32 = x3p * x3p + y3p * y3p;

  auto num = x1p * y3p - y1p * x3p;  // num also gives correct sign for CT
  auto det = d12 * y3p - d32 * y1p;

  auto st2 = (d12 * x3p - d32 * x1p);
  auto seq = det * det + st2 * st2;
  auto al2 = T(1.) / std::sqrt(seq);
  auto be2 = -st2 * al2;
  auto ct = T(2.) * num * al2;
  al2 *= det;

  m_xp = x2;
  m_yp = y2;
  m_c = noflip ? ct : -ct;
  m_alpha = noflip ? al2 : -be2;
  m_beta = noflip ? be2 : -al2;
}

cosdir() [1/2]

template<typename T>

constexpr std::pair<T, T> CircleEq< T >::cosdir ( ) const

inline

Definition at line 50 of file CircleEq.h.

References CircleEq< T >::m_alpha, and CircleEq< T >::m_beta.

{ return std::make_pair(m_alpha, m_beta); }

cosdir() [2/2]

template<typename T>

constexpr std::pair<T, T> CircleEq< T >::cosdir ( T  x, T  y  ) const

inline

Definition at line 53 of file CircleEq.h.

References CircleEq< T >::m_alpha, CircleEq< T >::m_beta, CircleEq< T >::m_c, CircleEq< T >::m_xp, CircleEq< T >::m_yp, x, and y.

                                                 {
    return std::make_pair(m_alpha - m_c * (x - m_xp), m_beta - m_c * (y - m_yp));
  }

curvature()

template<typename T>

constexpr auto CircleEq< T >::curvature ( ) const

inline

Definition at line 47 of file CircleEq.h.

References CircleEq< T >::m_c.

{ return m_c; }

dca()

template<typename T>

constexpr T CircleEq< T >::dca ( T  x, T  y  ) const

inline

Definition at line 40 of file CircleEq.h.

References CircleEq< T >::m_alpha, CircleEq< T >::m_beta, CircleEq< T >::m_c, CircleEq< T >::m_xp, CircleEq< T >::m_yp, mathSSE::sqrt(), x, and y.

                                  {
    x = m_c * (m_xp - x) + m_alpha;
    y = m_c * (m_yp - y) + m_beta;
    return std::sqrt(x * x + y * y) - T(1);
  }

dca0()

template<typename T>

constexpr T CircleEq< T >::dca0 ( ) const

inline

Definition at line 33 of file CircleEq.h.

References CircleEq< T >::m_alpha, CircleEq< T >::m_beta, CircleEq< T >::m_c, CircleEq< T >::m_xp, CircleEq< T >::m_yp, mathSSE::sqrt(), x, and y.

                           {
    auto x = m_c * m_xp + m_alpha;
    auto y = m_c * m_yp + m_beta;
    return std::sqrt(x * x + y * y) - T(1);
  }

radius()

template<typename T>

constexpr auto CircleEq< T >::radius ( void  ) const

inline

Definition at line 60 of file CircleEq.h.

References CircleEq< T >::m_c.

{ return T(1) / m_c; }

Member Data Documentation

m_alpha

template<typename T>

T CircleEq< T >::m_alpha = 0

Definition at line 65 of file CircleEq.h.

Referenced by CircleEq< T >::center(), CircleEq< T >::cosdir(), CircleEq< T >::dca(), and CircleEq< T >::dca0().

m_beta

template<typename T>

T CircleEq< T >::m_beta = 0

Definition at line 66 of file CircleEq.h.

Referenced by CircleEq< T >::center(), CircleEq< T >::cosdir(), CircleEq< T >::dca(), and CircleEq< T >::dca0().

m_c

template<typename T>

T CircleEq< T >::m_c = 0

Definition at line 64 of file CircleEq.h.

Referenced by CircleEq< T >::center(), CircleEq< T >::cosdir(), CircleEq< T >::curvature(), CircleEq< T >::dca(), CircleEq< T >::dca0(), and CircleEq< T >::radius().

m_xp

template<typename T>

T CircleEq< T >::m_xp = 0

Definition at line 62 of file CircleEq.h.

Referenced by CircleEq< T >::center(), CircleEq< T >::cosdir(), CircleEq< T >::dca(), and CircleEq< T >::dca0().

m_yp

template<typename T>

T CircleEq< T >::m_yp = 0

Definition at line 63 of file CircleEq.h.

Referenced by CircleEq< T >::center(), CircleEq< T >::cosdir(), CircleEq< T >::dca(), and CircleEq< T >::dca0().