eigen/Eigen/src/Geometry/OrthoMethods.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

#ifndef EIGEN_CROSS_H
#define EIGEN_CROSS_H

/** \geometry_module
  * \returns the cross product of \c *this and \a other */
template<typename Derived>
template<typename OtherDerived>
inline typename ei_eval<Derived>::type
MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
{
  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3);
  
  // Note that there is no need for an expression here since the compiler
  // optimize such a small temporary very well (even within a complex expression)
  const typename ei_nested<Derived,2>::type lhs(derived());
  const typename ei_nested<OtherDerived,2>::type rhs(other.derived());
  return typename ei_eval<Derived>::type(
    lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1),
    lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2),
    lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)
  );
}

template<typename Derived, int Size = Derived::SizeAtCompileTime>
struct ei_perpendicular_selector
{
  typedef typename ei_eval<Derived>::type VectorType;
  typedef typename ei_traits<Derived>::Scalar Scalar;
  inline static VectorType run(const Derived& src)
  {
    VectorType perp;
    /* Let us compute the crossed product of *this with a vector
     * that is not too close to being colinear to *this.
     */

    /* unless the x and y coords are both close to zero, we can
     * simply take ( -y, x, 0 ) and normalize it.
     */
    if((!ei_isMuchSmallerThan(src.x(), src.z()))
    || (!ei_isMuchSmallerThan(src.y(), src.z())))
    {
      Scalar invnm = Scalar(1)/src.template start<2>().norm();
      perp.template start<3>() << -ei_conj(src.y())*invnm, ei_conj(src.x())*invnm, 0;
    }
    /* if both x and y are close to zero, then the vector is close
     * to the z-axis, so it's far from colinear to the x-axis for instance.
     * So we take the crossed product with (1,0,0) and normalize it.
     */
    else
    {
      Scalar invnm = Scalar(1)/src.template end<2>().norm();
      perp.template start<3>() << 0, -ei_conj(src.z())*invnm, ei_conj(src.y())*invnm;
    }
    if (Derived::SizeAtCompileTime>3
    || (Derived::SizeAtCompileTime==Dynamic && src.size()>3))
      perp.end(src.size()-3).setZero();

    return perp;
   }
};

template<typename Derived>
struct ei_perpendicular_selector<Derived,2>
{
  typedef typename ei_eval<Derived>::type VectorType;
  inline static VectorType run(const Derived& src)
  { return VectorType(-ei_conj(src.y()), ei_conj(src.x())).normalized(); }
};

/** \Returns an orthogonal vector of \c *this
  *
  * The size of \c *this must be at least 2. If the size is exactly 2,
  * then the returned vector is a counter clock wise rotation of \c *this, \ie (-y,x).
  *
  * \sa cross()
  */
template<typename Derived>
typename ei_eval<Derived>::type
MatrixBase<Derived>::someOrthogonal() const
{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
  return ei_perpendicular_selector<Derived>::run(derived());
}

#endif // EIGEN_CROSS_H