vector_relations.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 2021 - 2022 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------
 
#ifndef dealii_vector_relations_h
#define dealii_vector_relations_h
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/tensor.h>
 
#include <cmath>
#include <limits>
 
DEAL_II_NAMESPACE_OPEN
 
 
namespace Physics
{
  namespace VectorRelations
  {
    template <int spacedim, typename Number>
    Number
    angle(const Tensor<1, spacedim, Number> &a,
          const Tensor<1, spacedim, Number> &b);
 
    template <int spacedim, typename Number>
    Number
    signed_angle(const Tensor<1, spacedim, Number> &a,
                 const Tensor<1, spacedim, Number> &b,
                 const Tensor<1, spacedim, Number> &axis);
  } // namespace VectorRelations
} // namespace Physics
 
 
 
#ifndef DOXYGEN
 
 
 
template <int spacedim, typename Number>
inline Number
Physics::VectorRelations::angle(const Tensor<1, spacedim, Number> &a,
                                const Tensor<1, spacedim, Number> &b)
{
  const Number a_norm = a.norm();
  const Number b_norm = b.norm();
  Assert(a_norm > 1.e-12 * b_norm && a_norm > 1.e-12 * b_norm,
         ExcMessage("Both vectors need to be non-zero!"));
 
  Number argument = (a * b) / a_norm / b_norm;
 
  // std::acos returns nan if argument is out of domain [-1,+1].
  // if argument slightly overshoots these bounds, set it to the bound.
  // allow for 8*eps as a tolerance.
  if ((1. - std::abs(argument)) < 8. * std::numeric_limits<Number>::epsilon())
    argument = std::copysign(1., argument);
 
  return std::acos(argument);
}
 
 
 
template <int spacedim, typename Number>
inline Number
Physics::VectorRelations::signed_angle(const Tensor<1, spacedim, Number> &a,
                                       const Tensor<1, spacedim, Number> &b,
                                       const Tensor<1, spacedim, Number> &axis)
{
  Assert(spacedim == 3,
         ExcMessage("This function can only be used with spacedim==3!"));
 
  Assert(std::abs(axis.norm() - 1.) < 1.e-12,
         ExcMessage("The axial vector is not a unit vector."));
  Assert(std::abs(axis * a) < 1.e-12 * a.norm() &&
           std::abs(axis * b) < 1.e-12 * b.norm(),
         ExcMessage("The vectors are not perpendicular to the axial vector."));
 
  const Number dot = a * b;
  const Number det = axis * cross_product_3d(a, b);
 
  return std::atan2(det, dot);
}
 
 
 
#endif // DOXYGEN
 
DEAL_II_NAMESPACE_CLOSE
 
#endif