CircleCenterXY.h

/**************************************************************************
 * basf2 (Belle II Analysis Software Framework)                           *
 * Author: The Belle II Collaboration                                     *
 *                                                                        *
 * See git log for contributors and copyright holders.                    *
 * This file is licensed under LGPL-3.0, see LICENSE.md.                  *
 **************************************************************************/
 
#pragma once
 
#include <tracking/trackFindingVXD/filterMap/filterFramework/SelectionVariable.h>
#include <framework/geometry/B2Vector3.h>
#include <framework/core/FrameworkExceptions.h>
 
#define CIRCLECENTERXY_NAME CircleCenterXY
 
namespace Belle2 {

  template <typename PointType >
  class CIRCLECENTERXY_NAME : public SelectionVariable< PointType, 3, B2Vector3D > {
  public:
    BELLE2_DEFINE_EXCEPTION(Straight_Line, "The hits are on a straight Line (or indistinguishably near to being on it).");

    PUT_NAME_FUNCTION(CIRCLECENTERXY_NAME);

    static B2Vector3D value(const PointType& a, const PointType& b, const PointType& c)
    {
      // calculates the intersection point using Cramer's rule.
      // x_1+s*n_1==x_2+t*n_2 --> n_1 *s - n_2 *t == x_2 - x_1 --> http://en.wikipedia.org/wiki/Cramer%27s_rule
      double inX = b.X() - c.X(); // x value of the normal vector of the inner segment (b-c)
      double inY = b.Y() - c.Y(); // y value of the normal vector of the inner segment (b-c)
      double outX = a.X() - b.X(); // x value of the normal vector of the outer segment (a-b)
      double outY = a.Y() - b.Y(); // y value of the normal vector of the outer segment (a-b)
 
      //searching solution for Ax = b, aij are the matrix elements of A, bi are elements of b
      double a11 = inY;
      double a12 = -inX;
      double a21 = -outY;
      double a22 = outX;
      double b1 = b.X() + outX * 0.5 - (c.X() + inX * 0.5);
      double b2 = b.Y() + outY * 0.5 - (c.Y() + inY * 0.5);
 
      if (a11 * a22 == a12 * a21) { throw Straight_Line(); }
 
      double s = (b1 * a22 - b2 * a21) / (a11 * a22 - a12 * a21); //the determinant is zero if the three hits are on a line in (x,y).
 
      return B2Vector3D(c.X() + inX * 0.5 + s * inY, c.Y() + inY * 0.5 - s * inX, 0.);
    }
 
 
 
  };

}