1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <[email protected]>
5 // Copyright (C) 2006-2008 Benoit Jacob <[email protected]>
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 \ingroup 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 *
22 * With complex numbers, the cross product is implemented as
23 * \f$ (\mathbf{a}+i\mathbf{b}) \times (\mathbf{c}+i\mathbf{d}) = (\mathbf{a} \times \mathbf{c} - \mathbf{b} \times \mathbf{d}) - i(\mathbf{a} \times \mathbf{d} - \mathbf{b} \times \mathbf{c})\f$
24 *
25 * \sa MatrixBase::cross3()
26 */
27 template<typename Derived>
28 template<typename OtherDerived>
29 #ifndef EIGEN_PARSED_BY_DOXYGEN
30 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
31 typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
32 #else
33 typename MatrixBase<Derived>::PlainObject
34 #endif
cross(const MatrixBase<OtherDerived> & other)35 MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
36 {
37 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
38 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
39
40 // Note that there is no need for an expression here since the compiler
41 // optimize such a small temporary very well (even within a complex expression)
42 typename internal::nested_eval<Derived,2>::type lhs(derived());
43 typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
44 return typename cross_product_return_type<OtherDerived>::type(
45 numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
46 numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
47 numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
48 );
49 }
50
51 namespace internal {
52
53 template< int Arch,typename VectorLhs,typename VectorRhs,
54 typename Scalar = typename VectorLhs::Scalar,
55 bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
56 struct cross3_impl {
57 EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
runcross3_impl58 run(const VectorLhs& lhs, const VectorRhs& rhs)
59 {
60 return typename internal::plain_matrix_type<VectorLhs>::type(
61 numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
62 numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
63 numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
64 0
65 );
66 }
67 };
68
69 }
70
71 /** \geometry_module \ingroup Geometry_Module
72 *
73 * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
74 *
75 * The size of \c *this and \a other must be four. This function is especially useful
76 * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
77 *
78 * \sa MatrixBase::cross()
79 */
80 template<typename Derived>
81 template<typename OtherDerived>
82 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
cross3(const MatrixBase<OtherDerived> & other)83 MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
84 {
85 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
86 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
87
88 typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
89 typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
90 DerivedNested lhs(derived());
91 OtherDerivedNested rhs(other.derived());
92
93 return internal::cross3_impl<Architecture::Target,
94 typename internal::remove_all<DerivedNested>::type,
95 typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
96 }
97
98 /** \geometry_module \ingroup Geometry_Module
99 *
100 * \returns a matrix expression of the cross product of each column or row
101 * of the referenced expression with the \a other vector.
102 *
103 * The referenced matrix must have one dimension equal to 3.
104 * The result matrix has the same dimensions than the referenced one.
105 *
106 * \sa MatrixBase::cross() */
107 template<typename ExpressionType, int Direction>
108 template<typename OtherDerived>
109 EIGEN_DEVICE_FUNC
110 const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
cross(const MatrixBase<OtherDerived> & other)111 VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
112 {
113 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
114 EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
115 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
116
117 typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
118 typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
119
120 CrossReturnType res(_expression().rows(),_expression().cols());
121 if(Direction==Vertical)
122 {
123 eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
124 res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
125 res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
126 res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
127 }
128 else
129 {
130 eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
131 res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
132 res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
133 res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
134 }
135 return res;
136 }
137
138 namespace internal {
139
140 template<typename Derived, int Size = Derived::SizeAtCompileTime>
141 struct unitOrthogonal_selector
142 {
143 typedef typename plain_matrix_type<Derived>::type VectorType;
144 typedef typename traits<Derived>::Scalar Scalar;
145 typedef typename NumTraits<Scalar>::Real RealScalar;
146 typedef Matrix<Scalar,2,1> Vector2;
147 EIGEN_DEVICE_FUNC
rununitOrthogonal_selector148 static inline VectorType run(const Derived& src)
149 {
150 VectorType perp = VectorType::Zero(src.size());
151 Index maxi = 0;
152 Index sndi = 0;
153 src.cwiseAbs().maxCoeff(&maxi);
154 if (maxi==0)
155 sndi = 1;
156 RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
157 perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
158 perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
159
160 return perp;
161 }
162 };
163
164 template<typename Derived>
165 struct unitOrthogonal_selector<Derived,3>
166 {
167 typedef typename plain_matrix_type<Derived>::type VectorType;
168 typedef typename traits<Derived>::Scalar Scalar;
169 typedef typename NumTraits<Scalar>::Real RealScalar;
170 EIGEN_DEVICE_FUNC
171 static inline VectorType run(const Derived& src)
172 {
173 VectorType perp;
174 /* Let us compute the crossed product of *this with a vector
175 * that is not too close to being colinear to *this.
176 */
177
178 /* unless the x and y coords are both close to zero, we can
179 * simply take ( -y, x, 0 ) and normalize it.
180 */
181 if((!isMuchSmallerThan(src.x(), src.z()))
182 || (!isMuchSmallerThan(src.y(), src.z())))
183 {
184 RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
185 perp.coeffRef(0) = -numext::conj(src.y())*invnm;
186 perp.coeffRef(1) = numext::conj(src.x())*invnm;
187 perp.coeffRef(2) = 0;
188 }
189 /* if both x and y are close to zero, then the vector is close
190 * to the z-axis, so it's far from colinear to the x-axis for instance.
191 * So we take the crossed product with (1,0,0) and normalize it.
192 */
193 else
194 {
195 RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
196 perp.coeffRef(0) = 0;
197 perp.coeffRef(1) = -numext::conj(src.z())*invnm;
198 perp.coeffRef(2) = numext::conj(src.y())*invnm;
199 }
200
201 return perp;
202 }
203 };
204
205 template<typename Derived>
206 struct unitOrthogonal_selector<Derived,2>
207 {
208 typedef typename plain_matrix_type<Derived>::type VectorType;
209 EIGEN_DEVICE_FUNC
210 static inline VectorType run(const Derived& src)
211 { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
212 };
213
214 } // end namespace internal
215
216 /** \geometry_module \ingroup Geometry_Module
217 *
218 * \returns a unit vector which is orthogonal to \c *this
219 *
220 * The size of \c *this must be at least 2. If the size is exactly 2,
221 * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
222 *
223 * \sa cross()
224 */
225 template<typename Derived>
226 EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
227 MatrixBase<Derived>::unitOrthogonal() const
228 {
229 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
230 return internal::unitOrthogonal_selector<Derived>::run(derived());
231 }
232
233 } // end namespace Eigen
234
235 #endif // EIGEN_ORTHOMETHODS_H
236