1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_ORTHOMETHODS_H
12#define EIGEN_ORTHOMETHODS_H
13
14namespace Eigen {
15
16/** \geometry_module
17  *
18  * \returns the cross product of \c *this and \a other
19  *
20  * Here is a very good explanation of cross-product: http://xkcd.com/199/
21  * \sa MatrixBase::cross3()
22  */
23template<typename Derived>
24template<typename OtherDerived>
25inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
26MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
27{
28  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
29  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
30
31  // Note that there is no need for an expression here since the compiler
32  // optimize such a small temporary very well (even within a complex expression)
33  typename internal::nested<Derived,2>::type lhs(derived());
34  typename internal::nested<OtherDerived,2>::type rhs(other.derived());
35  return typename cross_product_return_type<OtherDerived>::type(
36    numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
37    numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
38    numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
39  );
40}
41
42namespace internal {
43
44template< int Arch,typename VectorLhs,typename VectorRhs,
45          typename Scalar = typename VectorLhs::Scalar,
46          bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
47struct cross3_impl {
48  static inline typename internal::plain_matrix_type<VectorLhs>::type
49  run(const VectorLhs& lhs, const VectorRhs& rhs)
50  {
51    return typename internal::plain_matrix_type<VectorLhs>::type(
52      numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
53      numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
54      numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
55      0
56    );
57  }
58};
59
60}
61
62/** \geometry_module
63  *
64  * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
65  *
66  * The size of \c *this and \a other must be four. This function is especially useful
67  * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
68  *
69  * \sa MatrixBase::cross()
70  */
71template<typename Derived>
72template<typename OtherDerived>
73inline typename MatrixBase<Derived>::PlainObject
74MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
75{
76  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
77  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
78
79  typedef typename internal::nested<Derived,2>::type DerivedNested;
80  typedef typename internal::nested<OtherDerived,2>::type OtherDerivedNested;
81  DerivedNested lhs(derived());
82  OtherDerivedNested rhs(other.derived());
83
84  return internal::cross3_impl<Architecture::Target,
85                        typename internal::remove_all<DerivedNested>::type,
86                        typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
87}
88
89/** \returns a matrix expression of the cross product of each column or row
90  * of the referenced expression with the \a other vector.
91  *
92  * The referenced matrix must have one dimension equal to 3.
93  * The result matrix has the same dimensions than the referenced one.
94  *
95  * \geometry_module
96  *
97  * \sa MatrixBase::cross() */
98template<typename ExpressionType, int Direction>
99template<typename OtherDerived>
100const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
101VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
102{
103  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
104  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
105    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
106
107  CrossReturnType res(_expression().rows(),_expression().cols());
108  if(Direction==Vertical)
109  {
110    eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
111    res.row(0) = (_expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1)).conjugate();
112    res.row(1) = (_expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2)).conjugate();
113    res.row(2) = (_expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0)).conjugate();
114  }
115  else
116  {
117    eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
118    res.col(0) = (_expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1)).conjugate();
119    res.col(1) = (_expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2)).conjugate();
120    res.col(2) = (_expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0)).conjugate();
121  }
122  return res;
123}
124
125namespace internal {
126
127template<typename Derived, int Size = Derived::SizeAtCompileTime>
128struct unitOrthogonal_selector
129{
130  typedef typename plain_matrix_type<Derived>::type VectorType;
131  typedef typename traits<Derived>::Scalar Scalar;
132  typedef typename NumTraits<Scalar>::Real RealScalar;
133  typedef typename Derived::Index Index;
134  typedef Matrix<Scalar,2,1> Vector2;
135  static inline VectorType run(const Derived& src)
136  {
137    VectorType perp = VectorType::Zero(src.size());
138    Index maxi = 0;
139    Index sndi = 0;
140    src.cwiseAbs().maxCoeff(&maxi);
141    if (maxi==0)
142      sndi = 1;
143    RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
144    perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
145    perp.coeffRef(sndi) =  numext::conj(src.coeff(maxi)) * invnm;
146
147    return perp;
148   }
149};
150
151template<typename Derived>
152struct unitOrthogonal_selector<Derived,3>
153{
154  typedef typename plain_matrix_type<Derived>::type VectorType;
155  typedef typename traits<Derived>::Scalar Scalar;
156  typedef typename NumTraits<Scalar>::Real RealScalar;
157  static inline VectorType run(const Derived& src)
158  {
159    VectorType perp;
160    /* Let us compute the crossed product of *this with a vector
161     * that is not too close to being colinear to *this.
162     */
163
164    /* unless the x and y coords are both close to zero, we can
165     * simply take ( -y, x, 0 ) and normalize it.
166     */
167    if((!isMuchSmallerThan(src.x(), src.z()))
168    || (!isMuchSmallerThan(src.y(), src.z())))
169    {
170      RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
171      perp.coeffRef(0) = -numext::conj(src.y())*invnm;
172      perp.coeffRef(1) = numext::conj(src.x())*invnm;
173      perp.coeffRef(2) = 0;
174    }
175    /* if both x and y are close to zero, then the vector is close
176     * to the z-axis, so it's far from colinear to the x-axis for instance.
177     * So we take the crossed product with (1,0,0) and normalize it.
178     */
179    else
180    {
181      RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
182      perp.coeffRef(0) = 0;
183      perp.coeffRef(1) = -numext::conj(src.z())*invnm;
184      perp.coeffRef(2) = numext::conj(src.y())*invnm;
185    }
186
187    return perp;
188   }
189};
190
191template<typename Derived>
192struct unitOrthogonal_selector<Derived,2>
193{
194  typedef typename plain_matrix_type<Derived>::type VectorType;
195  static inline VectorType run(const Derived& src)
196  { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
197};
198
199} // end namespace internal
200
201/** \returns a unit vector which is orthogonal to \c *this
202  *
203  * The size of \c *this must be at least 2. If the size is exactly 2,
204  * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
205  *
206  * \sa cross()
207  */
208template<typename Derived>
209typename MatrixBase<Derived>::PlainObject
210MatrixBase<Derived>::unitOrthogonal() const
211{
212  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
213  return internal::unitOrthogonal_selector<Derived>::run(derived());
214}
215
216} // end namespace Eigen
217
218#endif // EIGEN_ORTHOMETHODS_H
219