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Public Member Functions | Private Member Functions | Private Attributes

FastCircle Class Reference

#include <FastCircle.h>

List of all members.

Public Member Functions

double c () const
 FastCircle (const GlobalPoint &outerHit, const GlobalPoint &middleHit, const GlobalPoint &aVertex)
 FastCircle (const GlobalPoint &outerHit, const GlobalPoint &middleHit, const GlobalPoint &aVertex, double norm)
bool isValid () const
double n1 () const
double n2 () const
double rho () const
double x0 () const
double y0 () const
 ~FastCircle ()

Private Member Functions

void createCircleParameters ()
AlgebraicVector3 transform (const GlobalPoint &aPoint) const

Private Attributes

double theC
GlobalPoint theInnerPoint
double theN1
double theN2
double theNorm
GlobalPoint theOuterPoint
double theRho
bool theValid
GlobalPoint theVertexPoint
double theX0
double theY0

Detailed Description

Calculate circle parameters (x0, y0, rho) for a circle: (x-x0)^2 + (y-y0)^2 = rho^2 in Global Cartesian Coordinates in the (x,y) plane for a given set of GlobalPoints. It is done by mapping the points onto the Riemann Sphere and fit a plane to the transformed coordinates of the points. The method is described in:

A.Strandlie, J.Wroldsen, R.Fruehwirth, B.Lillekjendlie: Particle tracks fitted on the Riemann sphere Computer Physics Communications 131 (2000) 95-108, 18 January 2000

Implementation: Matthias Winkler, 14 February 2001

This implementation is a specialized version of the general Circle class for three points.

Update 14.02.2001: For 3 Points (2 RecHits + Vertex) the plain parameters n1*x + n2*y + n3*z + c = 0 are analytically calculable. Update 14.02.2001: In the case that a circle fit is not possible (points are along a straight line) the parameters of the straight line can be used: c + n1*x + n2*y = 0

Definition at line 33 of file FastCircle.h.


Constructor & Destructor Documentation

FastCircle::FastCircle ( const GlobalPoint outerHit,
const GlobalPoint middleHit,
const GlobalPoint aVertex 
)

Definition at line 3 of file FastCircle.cc.

References createCircleParameters().

                                                   : 
  theOuterPoint(outerHit), 
  theInnerPoint(middleHit), 
  theVertexPoint(aVertex), 
  theNorm(100.), 
  theX0(0.), 
  theY0(0.), 
  theRho(0.),
  theN1(0.),
  theN2(0.),
  theC(0.),
  theValid(true) {

  createCircleParameters();
  
}
FastCircle::FastCircle ( const GlobalPoint outerHit,
const GlobalPoint middleHit,
const GlobalPoint aVertex,
double  norm 
)

Definition at line 22 of file FastCircle.cc.

References createCircleParameters().

                                    : 
  theOuterPoint(outerHit), 
  theInnerPoint(middleHit), 
  theVertexPoint(aVertex), 
  theNorm(norm), 
  theX0(0.), 
  theY0(0.), 
  theRho(0.),
  theN1(0.),
  theN2(0.),
  theC(0.),
  theValid(true) {

  createCircleParameters();
  
}
FastCircle::~FastCircle ( ) [inline]

Definition at line 46 of file FastCircle.h.

{}

Member Function Documentation

double FastCircle::c ( ) const [inline]

Definition at line 64 of file FastCircle.h.

References theC.

Referenced by createCircleParameters().

{return theC;}
void FastCircle::createCircleParameters ( ) [private]

Definition at line 42 of file FastCircle.cc.

References c(), alignCSCRings::e, mag2(), n, rho(), mathSSE::sqrt(), theC, theInnerPoint, theN1, theN2, theNorm, theOuterPoint, theRho, theValid, theVertexPoint, theX0, theY0, transform(), x, x0(), detailsBasic3DVector::y, y0(), and z.

Referenced by FastCircle().

                                        {
  
  AlgebraicVector3 x = transform(theOuterPoint);
  AlgebraicVector3 y = transform(theInnerPoint);
  AlgebraicVector3 z = transform(theVertexPoint);

  AlgebraicVector3 n;

  n[0] =   x[1]*(y[2] - z[2]) + y[1]*(z[2] - x[2]) + z[1]*(x[2] - y[2]);
  n[1] = -(x[0]*(y[2] - z[2]) + y[0]*(z[2] - x[2]) + z[0]*(x[2] - y[2]));
  n[2] =   x[0]*(y[1] - z[1]) + y[0]*(z[1] - x[1]) + z[0]*(x[1] - y[1]);

  double mag2 = n[0]*n[0]+n[1]*n[1]+n[2]*n[2];
  if (mag2 < 1.e-20) {
    theValid = false;
    return;
  }
  n.Unit(); // reduce n to a unit vector
  double  c = -(n[0]*x[0] + n[1]*x[1] + n[2]*x[2]);
  //  c = -(n[0]*y[0] + n[1]*y[1] + n[2]*y[2]);
  //  c = -(n[0]*z[0] + n[1]*z[1] + n[2]*z[2]);
  
  theN1 = n[0];
  theN2 = n[1];
  theC = c;

  if(fabs(c + n[2]) < 1.e-5) {
    // numeric limit
    // circle is more a straight line...
    theValid = false;
    return;
  }

  double x0 = -n[0] / (2.*(c + n[2]));
  double y0 = -n[1] / (2.*(c + n[2]));
  double rho = 
    sqrt((n[0]*n[0] + n[1]*n[1] - 4.*c*(c + n[2]))) / fabs(2.*(c + n[2]));
  
  theX0 = theNorm*x0;
  theY0 = theNorm*y0;
  theRho = theNorm*rho;

}
bool FastCircle::isValid ( void  ) const [inline]
double FastCircle::n1 ( ) const [inline]
double FastCircle::n2 ( ) const [inline]
double FastCircle::rho ( ) const [inline]
AlgebraicVector3 FastCircle::transform ( const GlobalPoint aPoint) const [private]

Definition at line 86 of file FastCircle.cc.

References funct::cos(), PV3DBase< T, PVType, FrameType >::perp(), PV3DBase< T, PVType, FrameType >::phi(), phi, dttmaxenums::R, funct::sin(), and theNorm.

Referenced by createCircleParameters().

                                                                      {

  AlgebraicVector3 riemannPoint;

  double R = aPoint.perp();
  R /= theNorm;
  double phi = 0.;
  if(R > 0.) phi = aPoint.phi();
 
  double fact = R/(1+R*R); // let's factorize the common factor out
  riemannPoint[0] = fact*cos(phi);
  riemannPoint[1] = fact*sin(phi);
  riemannPoint[2] = fact*R;
  
  return riemannPoint;
}
double FastCircle::x0 ( ) const [inline]
double FastCircle::y0 ( ) const [inline]

Member Data Documentation

double FastCircle::theC [private]

Definition at line 79 of file FastCircle.h.

Referenced by c(), and createCircleParameters().

Definition at line 69 of file FastCircle.h.

Referenced by createCircleParameters().

double FastCircle::theN1 [private]

Definition at line 77 of file FastCircle.h.

Referenced by createCircleParameters(), and n1().

double FastCircle::theN2 [private]

Definition at line 78 of file FastCircle.h.

Referenced by createCircleParameters(), and n2().

double FastCircle::theNorm [private]

Definition at line 71 of file FastCircle.h.

Referenced by createCircleParameters(), and transform().

Definition at line 68 of file FastCircle.h.

Referenced by createCircleParameters().

double FastCircle::theRho [private]

Definition at line 75 of file FastCircle.h.

Referenced by createCircleParameters(), and rho().

bool FastCircle::theValid [private]

Definition at line 81 of file FastCircle.h.

Referenced by createCircleParameters(), and isValid().

Definition at line 70 of file FastCircle.h.

Referenced by createCircleParameters().

double FastCircle::theX0 [private]

Definition at line 73 of file FastCircle.h.

Referenced by createCircleParameters(), and x0().

double FastCircle::theY0 [private]

Definition at line 74 of file FastCircle.h.

Referenced by createCircleParameters(), and y0().