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
14 namespace 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 */
23 template<typename Derived>
24 template<typename OtherDerived>
25 inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
cross(const MatrixBase<OtherDerived> & other)26 MatrixBase<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
42 namespace internal {
43
44 template< int Arch,typename VectorLhs,typename VectorRhs,
45 typename Scalar = typename VectorLhs::Scalar,
46 bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
47 struct cross3_impl {
48 static inline typename internal::plain_matrix_type<VectorLhs>::type
runcross3_impl49 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 */
71 template<typename Derived>
72 template<typename OtherDerived>
73 inline typename MatrixBase<Derived>::PlainObject
cross3(const MatrixBase<OtherDerived> & other)74 MatrixBase<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() */
98 template<typename ExpressionType, int Direction>
99 template<typename OtherDerived>
100 const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
cross(const MatrixBase<OtherDerived> & other)101 VectorwiseOp<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
125 namespace internal {
126
127 template<typename Derived, int Size = Derived::SizeAtCompileTime>
128 struct 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;
rununitOrthogonal_selector135 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
151 template<typename Derived>
152 struct 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
191 template<typename Derived>
192 struct 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 */
208 template<typename Derived>
209 typename MatrixBase<Derived>::PlainObject
210 MatrixBase<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