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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 EIGEN_STRONG_INLINE
31 : : typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
32 : : #else
33 : : typename MatrixBase<Derived>::PlainObject
34 : : #endif
35 : 18302 : 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 : 18302 : typename internal::nested_eval<Derived,2>::type lhs(derived());
43 : 18302 : typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
44 : : return typename cross_product_return_type<OtherDerived>::type(
45 : 18302 : numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
46 : 18302 : numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
47 : 36604 : numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
48 : 36604 : );
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
58 : : 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
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
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
148 : : 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
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