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 \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 inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
31 #else
32 inline typename MatrixBase<Derived>::PlainObject
33 #endif
cross(const MatrixBase<OtherDerived> & other)34 MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
35 {
36 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
37 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
38
39 // Note that there is no need for an expression here since the compiler
40 // optimize such a small temporary very well (even within a complex expression)
41 typename internal::nested_eval<Derived,2>::type lhs(derived());
42 typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
43 return typename cross_product_return_type<OtherDerived>::type(
44 numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
45 numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
46 numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
47 );
48 }
49
50 namespace internal {
51
52 template< int Arch,typename VectorLhs,typename VectorRhs,
53 typename Scalar = typename VectorLhs::Scalar,
54 bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
55 struct cross3_impl {
56 EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
runcross3_impl57 run(const VectorLhs& lhs, const VectorRhs& rhs)
58 {
59 return typename internal::plain_matrix_type<VectorLhs>::type(
60 numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
61 numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
62 numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
63 0
64 );
65 }
66 };
67
68 }
69
70 /** \geometry_module \ingroup Geometry_Module
71 *
72 * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
73 *
74 * The size of \c *this and \a other must be four. This function is especially useful
75 * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
76 *
77 * \sa MatrixBase::cross()
78 */
79 template<typename Derived>
80 template<typename OtherDerived>
81 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
cross3(const MatrixBase<OtherDerived> & other)82 MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
83 {
84 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
85 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
86
87 typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
88 typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
89 DerivedNested lhs(derived());
90 OtherDerivedNested rhs(other.derived());
91
92 return internal::cross3_impl<Architecture::Target,
93 typename internal::remove_all<DerivedNested>::type,
94 typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
95 }
96
97 /** \geometry_module \ingroup Geometry_Module
98 *
99 * \returns a matrix expression of the cross product of each column or row
100 * of the referenced expression with the \a other vector.
101 *
102 * The referenced matrix must have one dimension equal to 3.
103 * The result matrix has the same dimensions than the referenced one.
104 *
105 * \sa MatrixBase::cross() */
106 template<typename ExpressionType, int Direction>
107 template<typename OtherDerived>
108 EIGEN_DEVICE_FUNC
109 const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
cross(const MatrixBase<OtherDerived> & other)110 VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
111 {
112 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
113 EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
114 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
115
116 typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
117 typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
118
119 CrossReturnType res(_expression().rows(),_expression().cols());
120 if(Direction==Vertical)
121 {
122 eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
123 res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
124 res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
125 res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
126 }
127 else
128 {
129 eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
130 res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
131 res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
132 res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
133 }
134 return res;
135 }
136
137 namespace internal {
138
139 template<typename Derived, int Size = Derived::SizeAtCompileTime>
140 struct unitOrthogonal_selector
141 {
142 typedef typename plain_matrix_type<Derived>::type VectorType;
143 typedef typename traits<Derived>::Scalar Scalar;
144 typedef typename NumTraits<Scalar>::Real RealScalar;
145 typedef Matrix<Scalar,2,1> Vector2;
146 EIGEN_DEVICE_FUNC
rununitOrthogonal_selector147 static inline VectorType run(const Derived& src)
148 {
149 VectorType perp = VectorType::Zero(src.size());
150 Index maxi = 0;
151 Index sndi = 0;
152 src.cwiseAbs().maxCoeff(&maxi);
153 if (maxi==0)
154 sndi = 1;
155 RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
156 perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
157 perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
158
159 return perp;
160 }
161 };
162
163 template<typename Derived>
164 struct unitOrthogonal_selector<Derived,3>
165 {
166 typedef typename plain_matrix_type<Derived>::type VectorType;
167 typedef typename traits<Derived>::Scalar Scalar;
168 typedef typename NumTraits<Scalar>::Real RealScalar;
169 EIGEN_DEVICE_FUNC
170 static inline VectorType run(const Derived& src)
171 {
172 VectorType perp;
173 /* Let us compute the crossed product of *this with a vector
174 * that is not too close to being colinear to *this.
175 */
176
177 /* unless the x and y coords are both close to zero, we can
178 * simply take ( -y, x, 0 ) and normalize it.
179 */
180 if((!isMuchSmallerThan(src.x(), src.z()))
181 || (!isMuchSmallerThan(src.y(), src.z())))
182 {
183 RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
184 perp.coeffRef(0) = -numext::conj(src.y())*invnm;
185 perp.coeffRef(1) = numext::conj(src.x())*invnm;
186 perp.coeffRef(2) = 0;
187 }
188 /* if both x and y are close to zero, then the vector is close
189 * to the z-axis, so it's far from colinear to the x-axis for instance.
190 * So we take the crossed product with (1,0,0) and normalize it.
191 */
192 else
193 {
194 RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
195 perp.coeffRef(0) = 0;
196 perp.coeffRef(1) = -numext::conj(src.z())*invnm;
197 perp.coeffRef(2) = numext::conj(src.y())*invnm;
198 }
199
200 return perp;
201 }
202 };
203
204 template<typename Derived>
205 struct unitOrthogonal_selector<Derived,2>
206 {
207 typedef typename plain_matrix_type<Derived>::type VectorType;
208 EIGEN_DEVICE_FUNC
209 static inline VectorType run(const Derived& src)
210 { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
211 };
212
213 } // end namespace internal
214
215 /** \geometry_module \ingroup Geometry_Module
216 *
217 * \returns a unit vector which is orthogonal to \c *this
218 *
219 * The size of \c *this must be at least 2. If the size is exactly 2,
220 * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
221 *
222 * \sa cross()
223 */
224 template<typename Derived>
225 EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
226 MatrixBase<Derived>::unitOrthogonal() const
227 {
228 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
229 return internal::unitOrthogonal_selector<Derived>::run(derived());
230 }
231
232 } // end namespace Eigen
233
234 #endif // EIGEN_ORTHOMETHODS_H
235