// g2o - General Graph Optimization
// Copyright (C) 2011 H. Strasdat
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright notice,
//   this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
//   notice, this list of conditions and the following disclaimer in the
//   documentation and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
// IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
// PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
// TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

  Matrix3d skew(const Vector3d&v)
  {
    Matrix3d m;
    m.fill(0.);
    m(0,1)  = -v(2);
    m(0,2)  =  v(1);
    m(1,2)  = -v(0);
    m(1,0)  =  v(2);
    m(2,0) = -v(1);
    m(2,1) = v(0);
    return m;
  }

  Vector3d deltaR(const Matrix3d& R)
  {
    Vector3d v;
    v(0)=R(2,1)-R(1,2);
    v(1)=R(0,2)-R(2,0);
    v(2)=R(1,0)-R(0,1);
    return v;
  }

  Vector2d project(const Vector3d& v)
  {
    Vector2d res;
    res(0) = v(0)/v(2);
    res(1) = v(1)/v(2);
    return res;
  }

  Vector3d project(const Vector4d& v)
  {
    Vector3d res;
    res(0) = v(0)/v(3);
    res(1) = v(1)/v(3);
    res(2) = v(2)/v(3);
    return res;
  }

  Vector3d unproject(const Vector2d& v)
  {
    Vector3d res;
    res(0) = v(0);
    res(1) = v(1);
    res(2) = 1;
    return res;
  }

  Vector4d unproject(const Vector3d& v)
  {
    Vector4d res;
    res(0) = v(0);
    res(1) = v(1);
    res(2) = v(2);
    res(3) = 1;
    return res;
  }


