AxisAngle.cxx

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// @(#)root/mathcore:$Id$
// Authors: W. Brown, M. Fischler, L. Moneta    2005
 
/**********************************************************************
 *                                                                    *
 * Copyright (c) 2005 , LCG ROOT FNAL MathLib Team                    *
 *                                                                    *
 *                                                                    *
 **********************************************************************/
 
// Header file for class AxisAngle, a rotation in 3 dimensions
// represented by its axis and angle of rotation
//
// Created by: Mark Fischler Tues July 5  2005
//
#include "MathX/GenVectorX/AxisAngle.h"
 
#include <cmath>
#include <algorithm>
 
#include "MathX/GenVectorX/Cartesian3D.h"
#include "MathX/GenVectorX/DisplacementVector3D.h"
#include "MathX/GenVectorX/Rotation3D.h"
 
#include "MathX/GenVectorX/AccHeaders.h"
 
#include "MathX/GenVectorX/MathHeaders.h"
 
namespace ROOT {
 
namespace ROOT_MATH_ARCH {
 
// ========== Constructors and Assignment =====================
 
void AxisAngle::RectifyAngle()
{
   // Note: We could require the angle to be in [0,pi) since we
   //       can represent negative angles by flipping the axis.
   //       We choose not to do this.
 
   if (fAngle <= Pi() && fAngle > -Pi())
      return;
 
   if (fAngle > 0) {
      int n = static_cast<int>((fAngle + Pi()) / (2 * Pi()));
      fAngle -= 2 * Pi() * n;
   } else {
      int n = static_cast<int>(-(fAngle - Pi()) / (2 * Pi()));
      fAngle += 2 * Pi() * n;
   }
} // RectifyAngle()
 
void AxisAngle::Rectify()
{
   // The two conditions are that the angle is in (-pi, pi] and
   // the axis is a unit vector.
 
   Scalar r2 = fAxis.Mag2();
   if (r2 == 0) {
      fAxis.SetCoordinates(0, 0, 1);
      fAngle = 0;
      return;
   }
   fAxis *= (1.0 / r2);
   RectifyAngle();
} // Rectify()
 
// ======== Transformation to other Rotation Forms ==================
 
enum ERotation3DMatrixIndex {
   kXX = 0,
   kXY = 1,
   kXZ = 2,
   kYX = 3,
   kYY = 4,
   kYZ = 5,
   kZX = 6,
   kZY = 7,
   kZZ = 8
};
 
// ========== Operations =====================
 
DisplacementVector3D<Cartesian3D<double>> AxisAngle::operator()(const XYZVector &v) const
{
   Scalar c = math_cos(fAngle);
   Scalar s = math_sin(fAngle);
   Scalar p = fAxis.Dot(v) * (1 - c);
   return DisplacementVector3D<Cartesian3D<double>>(
      c * v.X() + p * fAxis.X() + s * (fAxis.Y() * v.Z() - fAxis.Z() * v.Y()),
      c * v.Y() + p * fAxis.Y() + s * (fAxis.Z() * v.X() - fAxis.X() * v.Z()),
      c * v.Z() + p * fAxis.Z() + s * (fAxis.X() * v.Y() - fAxis.Y() * v.X()));
}
 
#if !defined(ROOT_MATH_SYCL) && !defined(ROOT_MATH_CUDA)
// ========== I/O =====================
 
std::ostream &operator<<(std::ostream &os, const AxisAngle &a)
{
   // TODO - this will need changing for machine-readable issues
   //        and even the human readable form may need formatting improvements
   os << "\n" << a.Axis() << "  " << a.Angle() << "\n";
   return os;
}
#endif
 
} // namespace ROOT_MATH_ARCH
} // namespace ROOT