Reference documentation for deal.II version 9.4.1
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vector_relations.h
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1// ---------------------------------------------------------------------
2//
3// Copyright (C) 2021 by the deal.II authors
4//
5// This file is part of the deal.II library.
6//
7// The deal.II library is free software; you can use it, redistribute
8// it, and/or modify it under the terms of the GNU Lesser General
10// version 2.1 of the License, or (at your option) any later version.
11// The full text of the license can be found in the file LICENSE.md at
12// the top level directory of deal.II.
13//
14// ---------------------------------------------------------------------
15
16#ifndef dealii_vector_relations_h
17#define dealii_vector_relations_h
18
19#include <deal.II/base/config.h>
20
21#include <deal.II/base/tensor.h>
22
23#include <cmath>
24
26
27
28namespace Physics
29{
33 namespace VectorRelations
34 {
44 template <int spacedim, typename Number>
45 Number
48
76 template <int spacedim, typename Number>
77 Number
80 const Tensor<1, spacedim, Number> &axis);
81 } // namespace VectorRelations
82} // namespace Physics
83
84
85
86#ifndef DOXYGEN
87
88
89
90template <int spacedim, typename Number>
91inline Number
94{
95 const Number a_norm = a.norm();
96 const Number b_norm = b.norm();
97 Assert(a_norm > 1.e-12 * b_norm && a_norm > 1.e-12 * b_norm,
98 ExcMessage("Both vectors need to be non-zero!"));
99
100 Number argument = (a * b) / a_norm / b_norm;
101
102 // std::acos returns nan if argument is out of domain [-1,+1].
103 // if argument slightly overshoots these bounds, set it to the bound.
104 // allow for 8*eps as a tolerance.
105 if ((1. - std::abs(argument)) < 8. * std::numeric_limits<Number>::epsilon())
106 argument = std::copysign(1., argument);
107
108 return std::acos(argument);
109}
110
111
112
113template <int spacedim, typename Number>
114inline Number
117 const Tensor<1, spacedim, Number> &axis)
118{
119 Assert(spacedim == 3,
120 ExcMessage("This function can only be used with spacedim==3!"));
121
122 Assert(std::abs(axis.norm() - 1.) < 1.e-12,
123 ExcMessage("The axial vector is not a unit vector."));
124 Assert(std::abs(axis * a) < 1.e-12 * a.norm() &&
125 std::abs(axis * b) < 1.e-12 * b.norm(),
126 ExcMessage("The vectors are not perpendicular to the axial vector."));
127
128 const Number dot = a * b;
129 const Number det = axis * cross_product_3d(a, b);
130
131 return std::atan2(det, dot);
132}
133
134
135
136#endif // DOXYGEN
137
139
140#endif
Definition: tensor.h:503
numbers::NumberTraits< Number >::real_type norm() const
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:442
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:443
#define Assert(cond, exc)
Definition: exceptions.h:1473
static ::ExceptionBase & ExcMessage(std::string arg1)
SymmetricTensor< 2, dim, Number > b(const Tensor< 2, dim, Number > &F)
Number signed_angle(const Tensor< 1, spacedim, Number > &a, const Tensor< 1, spacedim, Number > &b, const Tensor< 1, spacedim, Number > &axis)
Number angle(const Tensor< 1, spacedim, Number > &a, const Tensor< 1, spacedim, Number > &b)
::VectorizedArray< Number, width > abs(const ::VectorizedArray< Number, width > &)
constexpr Tensor< 1, dim, typename ProductType< Number1, Number2 >::type > cross_product_3d(const Tensor< 1, dim, Number1 > &src1, const Tensor< 1, dim, Number2 > &src2)
Definition: tensor.h:2660