OrthoMethods.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_ORTHOMETHODS_H
00012 #define EIGEN_ORTHOMETHODS_H
00013 
00014 namespace Eigen { 
00015 
00016 /** \geometry_module
00017   *
00018   * \returns the cross product of \c *this and \a other
00019   *
00020   * Here is a very good explanation of cross-product: http://xkcd.com/199/
00021   * \sa MatrixBase::cross3()
00022   */
00023 template<typename Derived>
00024 template<typename OtherDerived>
00025 inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
00026 MatrixBase<Derived>::cross (const MatrixBase<OtherDerived>& other) const
00027 {
00028   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
00029   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
00030 
00031   // Note that there is no need for an expression here since the compiler
00032   // optimize such a small temporary very well (even within a complex expression)
00033   typename internal::nested<Derived,2>::type lhs(derived());
00034   typename internal::nested<OtherDerived,2>::type rhs(other.derived());
00035   return typename cross_product_return_type<OtherDerived>::type(
00036     numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
00037     numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
00038     numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
00039   );
00040 }
00041 
00042 namespace internal {
00043 
00044 template< int Arch,typename VectorLhs,typename VectorRhs,
00045           typename Scalar = typename VectorLhs::Scalar,
00046           bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
00047 struct cross3_impl {
00048   static inline typename internal::plain_matrix_type<VectorLhs>::type
00049   run(const VectorLhs& lhs, const VectorRhs& rhs)
00050   {
00051     return typename internal::plain_matrix_type<VectorLhs>::type(
00052       numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
00053       numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
00054       numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
00055       0
00056     );
00057   }
00058 };
00059 
00060 }
00061 
00062 /** \geometry_module
00063   *
00064   * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
00065   *
00066   * The size of \c *this and \a other must be four. This function is especially useful
00067   * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
00068   *
00069   * \sa MatrixBase::cross()
00070   */
00071 template<typename Derived>
00072 template<typename OtherDerived>
00073 inline typename MatrixBase<Derived>::PlainObject
00074 MatrixBase<Derived>::cross3 (const MatrixBase<OtherDerived>& other) const
00075 {
00076   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
00077   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
00078 
00079   typedef typename internal::nested<Derived,2>::type DerivedNested;
00080   typedef typename internal::nested<OtherDerived,2>::type OtherDerivedNested;
00081   DerivedNested lhs(derived());
00082   OtherDerivedNested rhs(other.derived());
00083 
00084   return internal::cross3_impl<Architecture::Target,
00085                         typename internal::remove_all<DerivedNested>::type,
00086                         typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
00087 }
00088 
00089 /** \returns a matrix expression of the cross product of each column or row
00090   * of the referenced expression with the \a other vector.
00091   *
00092   * The referenced matrix must have one dimension equal to 3.
00093   * The result matrix has the same dimensions than the referenced one.
00094   *
00095   * \geometry_module
00096   *
00097   * \sa MatrixBase::cross() */
00098 template<typename ExpressionType, int Direction>
00099 template<typename OtherDerived>
00100 const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
00101 VectorwiseOp<ExpressionType,Direction>::cross (const MatrixBase<OtherDerived>& other) const
00102 {
00103   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
00104   EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
00105     YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
00106 
00107   CrossReturnType res(_expression().rows(),_expression().cols());
00108   if(Direction==Vertical)
00109   {
00110     eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
00111     res.row(0) = (_expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1)).conjugate();
00112     res.row(1) = (_expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2)).conjugate();
00113     res.row(2) = (_expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0)).conjugate();
00114   }
00115   else
00116   {
00117     eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
00118     res.col(0) = (_expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1)).conjugate();
00119     res.col(1) = (_expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2)).conjugate();
00120     res.col(2) = (_expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0)).conjugate();
00121   }
00122   return res;
00123 }
00124 
00125 namespace internal {
00126 
00127 template<typename Derived, int Size = Derived::SizeAtCompileTime>
00128 struct unitOrthogonal_selector
00129 {
00130   typedef typename plain_matrix_type<Derived>::type VectorType;
00131   typedef typename traits<Derived>::Scalar Scalar;
00132   typedef typename NumTraits<Scalar>::Real RealScalar;
00133   typedef typename Derived::Index Index;
00134   typedef Matrix<Scalar,2,1> Vector2;
00135   static inline VectorType run(const Derived& src)
00136   {
00137     VectorType perp = VectorType::Zero(src.size());
00138     Index maxi = 0;
00139     Index sndi = 0;
00140     src.cwiseAbs().maxCoeff(&maxi);
00141     if (maxi==0)
00142       sndi = 1;
00143     RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
00144     perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
00145     perp.coeffRef(sndi) =  numext::conj(src.coeff(maxi)) * invnm;
00146 
00147     return perp;
00148    }
00149 };
00150 
00151 template<typename Derived>
00152 struct unitOrthogonal_selector<Derived,3>
00153 {
00154   typedef typename plain_matrix_type<Derived>::type VectorType;
00155   typedef typename traits<Derived>::Scalar Scalar;
00156   typedef typename NumTraits<Scalar>::Real RealScalar;
00157   static inline VectorType run(const Derived& src)
00158   {
00159     VectorType perp;
00160     /* Let us compute the crossed product of *this with a vector
00161      * that is not too close to being colinear to *this.
00162      */
00163 
00164     /* unless the x and y coords are both close to zero, we can
00165      * simply take ( -y, x, 0 ) and normalize it.
00166      */
00167     if((!isMuchSmallerThan(src.x(), src.z()))
00168     || (!isMuchSmallerThan(src.y(), src.z())))
00169     {
00170       RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
00171       perp.coeffRef(0) = -numext::conj(src.y())*invnm;
00172       perp.coeffRef(1) = numext::conj(src.x())*invnm;
00173       perp.coeffRef(2) = 0;
00174     }
00175     /* if both x and y are close to zero, then the vector is close
00176      * to the z-axis, so it's far from colinear to the x-axis for instance.
00177      * So we take the crossed product with (1,0,0) and normalize it.
00178      */
00179     else
00180     {
00181       RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
00182       perp.coeffRef(0) = 0;
00183       perp.coeffRef(1) = -numext::conj(src.z())*invnm;
00184       perp.coeffRef(2) = numext::conj(src.y())*invnm;
00185     }
00186 
00187     return perp;
00188    }
00189 };
00190 
00191 template<typename Derived>
00192 struct unitOrthogonal_selector<Derived,2>
00193 {
00194   typedef typename plain_matrix_type<Derived>::type VectorType;
00195   static inline VectorType run(const Derived& src)
00196   { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
00197 };
00198 
00199 } // end namespace internal
00200 
00201 /** \returns a unit vector which is orthogonal to \c *this
00202   *
00203   * The size of \c *this must be at least 2. If the size is exactly 2,
00204   * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
00205   *
00206   * \sa cross()
00207   */
00208 template<typename Derived>
00209 typename MatrixBase<Derived>::PlainObject
00210 MatrixBase<Derived>::unitOrthogonal () const
00211 {
00212   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
00213   return internal::unitOrthogonal_selector<Derived>::run(derived());
00214 }
00215 
00216 } // end namespace Eigen
00217 
00218 #endif // EIGEN_ORTHOMETHODS_H