text: /***************************************************************************
                          frames.inl -  description
                         -------------------------
      begin                : June 2006
      copyright            : (C) 2006 Erwin Aertbelien
      email                : firstname.lastname@mech.kuleuven.ac.be
  
   History (only major changes)( AUTHOR-Description ) :
   
   ***************************************************************************
   *   This library 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 2.1 of the License, or (at your option) any later version.    *
   *                                                                         *
   *   This library 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 for more details.                       *
   *                                                                         *
   *   You should have received a copy of the GNU Lesser General Public      *
   *   License along with this library; if not, write to the Free Software   *
   *   Foundation, Inc., 59 Temple Place,                                    *
   *   Suite 330, Boston, MA  02111-1307  USA                                *
   *                                                                         *
   ***************************************************************************/
  
  /**
   * \file frames.inl
   * Inlined member functions and global functions that relate to the classes in frames.cpp
   *
   */
  
  
  
  IMETHOD Vector::Vector(const Vector & arg)
  {
      data[0] = arg.data[0];
      data[1] = arg.data[1];
      data[2] = arg.data[2];
  }
  
  IMETHOD Vector::Vector(double x,double y, double z)
  {
          data[0]=x;data[1]=y;data[2]=z;
  }
  
  
  IMETHOD Vector& Vector::operator =(const Vector & arg)
  {
      data[0] = arg.data[0];
      data[1] = arg.data[1];
      data[2] = arg.data[2];
      return *this;
  }
  
  IMETHOD Vector operator +(const Vector & lhs,const Vector& rhs)
  {
      Vector tmp;
      tmp.data[0] = lhs.data[0]+rhs.data[0];
      tmp.data[1] = lhs.data[1]+rhs.data[1];
      tmp.data[2] = lhs.data[2]+rhs.data[2];
      return tmp;
  }
  
  IMETHOD Vector operator -(const Vector & lhs,const Vector& rhs)
  {
      Vector tmp;
      tmp.data[0] = lhs.data[0]-rhs.data[0];
      tmp.data[1] = lhs.data[1]-rhs.data[1];
      tmp.data[2] = lhs.data[2]-rhs.data[2];
      return tmp;
  }
  
  IMETHOD double Vector::x() const { return data[0]; }
  IMETHOD double Vector::y() const { return data[1]; }
  IMETHOD double Vector::z() const { return data[2]; }
  
  IMETHOD void Vector::x( double _x ) { data[0] = _x; }
  IMETHOD void Vector::y( double _y ) { data[1] = _y; }
  IMETHOD void Vector::z( double _z ) { data[2] = _z; }
  
  Vector operator *(const Vector& lhs,double rhs) 
  {
      Vector tmp;
      tmp.data[0] = lhs.data[0]*rhs;
      tmp.data[1] = lhs.data[1]*rhs;
      tmp.data[2] = lhs.data[2]*rhs;
      return tmp;
  }
  
  Vector operator *(double lhs,const Vector& rhs) 
  {
      Vector tmp;
      tmp.data[0] = lhs*rhs.data[0];
      tmp.data[1] = lhs*rhs.data[1];
      tmp.data[2] = lhs*rhs.data[2];
      return tmp;
  }
  
  Vector operator /(const Vector& lhs,double rhs) 
  {
      Vector tmp;
      tmp.data[0] = lhs.data[0]/rhs;
      tmp.data[1] = lhs.data[1]/rhs;
      tmp.data[2] = lhs.data[2]/rhs;
      return tmp;
  }
  
  Vector operator *(const Vector & lhs,const Vector& rhs)
  // Complexity : 6M+3A
  {
      Vector tmp;
      tmp.data[0] = lhs.data[1]*rhs.data[2]-lhs.data[2]*rhs.data[1];
      tmp.data[1] = lhs.data[2]*rhs.data[0]-lhs.data[0]*rhs.data[2];
      tmp.data[2] = lhs.data[0]*rhs.data[1]-lhs.data[1]*rhs.data[0];
      return tmp;
  }
  
  Vector& Vector::operator +=(const Vector & arg)
  // Complexity : 3A
  {
      data[0]+=arg.data[0];
      data[1]+=arg.data[1];
      data[2]+=arg.data[2];
      return *this;
  }
  
  Vector& Vector::operator -=(const Vector & arg)
  // Complexity : 3A
  {
      data[0]-=arg.data[0];
      data[1]-=arg.data[1];
      data[2]-=arg.data[2];
      return *this;
  }
  
  Vector Vector::Zero()
  {
      return Vector(0,0,0);
  }
  
  double Vector::operator()(int index) const {
      FRAMES_CHECKI((0<=index)&&(index<=2));
      return data[index];
  }
  
  double& Vector::operator () (int index)
  {
      FRAMES_CHECKI((0<=index)&&(index<=2));
      return data[index];
  }
  
  
  
  Wrench Frame::operator * (const Wrench& arg) const
  // Complexity : 24M+18A
  {
      Wrench tmp;
      tmp.force  = M*arg.force;
      tmp.torque = M*arg.torque + p*tmp.force;
      return tmp;
  }
  
  Wrench Frame::Inverse(const Wrench& arg) const
  {
      Wrench tmp;
      tmp.force =  M.Inverse(arg.force);
      tmp.torque = M.Inverse(arg.torque-p*arg.force);
      return tmp;
  }
  
  
  
  Wrench Rotation::Inverse(const Wrench& arg) const
  {
      return Wrench(Inverse(arg.force),Inverse(arg.torque));
  }
  
  Twist Rotation::Inverse(const Twist& arg) const
  {
      return Twist(Inverse(arg.vel),Inverse(arg.rot));
  }
  
  Wrench Wrench::Zero()
  {
      return Wrench(Vector::Zero(),Vector::Zero());
  }
  
  
  void Wrench::ReverseSign()
  {   
      torque.ReverseSign();
      force.ReverseSign();
  }
  
  Wrench Wrench::RefPoint(const Vector& v_base_AB) const
       // Changes the reference point of the Wrench.
       // The vector v_base_AB is expressed in the same base as the twist
       // The vector v_base_AB is a vector from the old point to
       // the new point.
  {
      return Wrench(this->force,
                    this->torque+this->force*v_base_AB
                    );
  }
  
  
  Wrench& Wrench::operator-=(const Wrench& arg)
  {
      torque-=arg.torque;
      force -=arg.force;
      return *this;
  }
  
  Wrench& Wrench::operator+=(const Wrench& arg)
  {
      torque+=arg.torque;
      force +=arg.force;
      return *this;
  }
  
  double& Wrench::operator()(int i)
  {
      // assert((0<=i)&&(i<6)); done by underlying routines
      if (i<3) 
          return force(i);
      else
          return torque(i-3);
  }
  
  double Wrench::operator()(int i) const
  {
      // assert((0<=i)&&(i<6)); done by underlying routines
      if (i<3) 
          return force(i);
      else
          return torque(i-3);
  }
  
  
  Wrench operator*(const Wrench& lhs,double rhs)
  {
      return Wrench(lhs.force*rhs,lhs.torque*rhs);
  }
  
  Wrench operator*(double lhs,const Wrench& rhs)
  {
      return Wrench(lhs*rhs.force,lhs*rhs.torque);
  }
  
  Wrench operator/(const Wrench& lhs,double rhs)
  {
      return Wrench(lhs.force/rhs,lhs.torque/rhs);
  }
  
  // addition of Wrench's
  Wrench operator+(const Wrench& lhs,const Wrench& rhs)
  {
      return Wrench(lhs.force+rhs.force,lhs.torque+rhs.torque);
  }
  
  Wrench operator-(const Wrench& lhs,const Wrench& rhs)
  {
      return Wrench(lhs.force-rhs.force,lhs.torque-rhs.torque);
  }
  
  // unary -
  Wrench operator-(const Wrench& arg) 
  {
      return Wrench(-arg.force,-arg.torque);
  }
  
  Twist Frame::operator * (const Twist& arg) const
  // Complexity : 24M+18A
  {
      Twist tmp;
      tmp.rot = M*arg.rot;
      tmp.vel = M*arg.vel+p*tmp.rot;
      return tmp;
  }
  Twist Frame::Inverse(const Twist& arg) const
  {
      Twist tmp;
      tmp.rot =  M.Inverse(arg.rot);
      tmp.vel = M.Inverse(arg.vel-p*arg.rot);
      return tmp;
  }
  
  Twist Twist::Zero()
  {
      return Twist(Vector::Zero(),Vector::Zero());
  }
  
  
  void Twist::ReverseSign()
  {   
      vel.ReverseSign();
      rot.ReverseSign();
  }
  
  Twist Twist::RefPoint(const Vector& v_base_AB) const
       // Changes the reference point of the twist.
       // The vector v_base_AB is expressed in the same base as the twist
       // The vector v_base_AB is a vector from the old point to
       // the new point.
       // Complexity : 6M+6A
  {
      return Twist(this->vel+this->rot*v_base_AB,this->rot);
  }
  
  Twist& Twist::operator-=(const Twist& arg)
  {
      vel-=arg.vel;
      rot -=arg.rot;
      return *this;
  }
  
  Twist& Twist::operator+=(const Twist& arg)
  {
      vel+=arg.vel;
      rot +=arg.rot;
      return *this;
  }
  
  double& Twist::operator()(int i)
  {
      // assert((0<=i)&&(i<6)); done by underlying routines
      if (i<3) 
          return vel(i);
      else
          return rot(i-3);
  }
  
  double Twist::operator()(int i) const
  {
      // assert((0<=i)&&(i<6)); done by underlying routines
      if (i<3) 
          return vel(i);
      else
          return rot(i-3);
  }
  
  
  Twist operator*(const Twist& lhs,double rhs)
  {
      return Twist(lhs.vel*rhs,lhs.rot*rhs);
  }
  
  Twist operator*(double lhs,const Twist& rhs)
  {
      return Twist(lhs*rhs.vel,lhs*rhs.rot);
  }
  
  Twist operator/(const Twist& lhs,double rhs)
  {
      return Twist(lhs.vel/rhs,lhs.rot/rhs);
  }
  
  // addition of Twist's
  Twist operator+(const Twist& lhs,const Twist& rhs)
  {
      return Twist(lhs.vel+rhs.vel,lhs.rot+rhs.rot);
  }
  
  Twist operator-(const Twist& lhs,const Twist& rhs)
  {
      return Twist(lhs.vel-rhs.vel,lhs.rot-rhs.rot);
  }
  
  // unary -
  Twist operator-(const Twist& arg) 
  {
      return Twist(-arg.vel,-arg.rot);
  }
  
  
  //Spatial products for twists
  Twist operator*(const Twist& lhs,const Twist& rhs)
  {
      return Twist(lhs.rot*rhs.vel+lhs.vel*rhs.rot,lhs.rot*rhs.rot);
  }
  Wrench operator*(const Twist& lhs,const Wrench& rhs)
  {
      return Wrench(lhs.rot*rhs.force,lhs.rot*rhs.torque+lhs.vel*rhs.force);
  }
  
  Frame::Frame(const Rotation & R)
  {
      M=R;
      p=Vector::Zero();
  }
  
  Frame::Frame(const Vector & V)
  {
      M = Rotation::Identity();
      p = V;
  }
  
  Frame::Frame(const Rotation & R, const Vector & V)
  {
      M = R;
      p = V;
  }
  
   Frame operator *(const Frame& lhs,const Frame& rhs)
  // Complexity : 36M+36A
  {
      return Frame(lhs.M*rhs.M,lhs.M*rhs.p+lhs.p);
  }
  
  Vector Frame::operator *(const Vector & arg) const
  {
      return M*arg+p;
  }
  
  Vector Frame::Inverse(const Vector& arg) const
  {
      return M.Inverse(arg-p);
  }
  
  Frame Frame::Inverse() const
  {
      return Frame(M.Inverse(),-M.Inverse(p));
  }
  
  
  Frame& Frame::operator =(const Frame & arg)
  { 
      M = arg.M;
      p = arg.p;
      return *this;
  }
  
  Frame::Frame(const Frame & arg) :
      p(arg.p),M(arg.M)
  {}
  
  
  void Vector::ReverseSign()
  {
      data[0] = -data[0];
      data[1] = -data[1];
      data[2] = -data[2];
  }
  
  
  
  Vector operator-(const Vector & arg)
  {
      Vector tmp;
      tmp.data[0]=-arg.data[0];
      tmp.data[1]=-arg.data[1];
      tmp.data[2]=-arg.data[2];
      return tmp;
  }
  
  void Vector::Set2DXY(const Vector2& v)
  // a 3D vector where the 2D vector v is put in the XY plane
  {
      data[0]=v(0);
      data[1]=v(1);
      data[2]=0;
  
  }
  void Vector::Set2DYZ(const Vector2& v)
  // a 3D vector where the 2D vector v is put in the YZ plane
  {
      data[1]=v(0);
      data[2]=v(1);
      data[0]=0;
  
  }
  
  void Vector::Set2DZX(const Vector2& v)
  // a 3D vector where the 2D vector v is put in the ZX plane
  {
      data[2]=v(0);
      data[0]=v(1);
      data[1]=0;
  
  }
  
  
  
  
  
  double& Rotation::operator()(int i,int j) {
      FRAMES_CHECKI((0<=i)&&(i<=2)&&(0<=j)&&(j<=2));
      return data[i*3+j];
  }
  
  double Rotation::operator()(int i,int j) const {
      FRAMES_CHECKI((0<=i)&&(i<=2)&&(0<=j)&&(j<=2));
      return data[i*3+j];
  }
  
  Rotation::Rotation( double Xx,double Yx,double Zx,
                              double Xy,double Yy,double Zy,
                              double Xz,double Yz,double Zz)
  {
      data[0] = Xx;data[1]=Yx;data[2]=Zx;
      data[3] = Xy;data[4]=Yy;data[5]=Zy;
      data[6] = Xz;data[7]=Yz;data[8]=Zz;
  }
  
  
  Rotation::Rotation(const Vector& x,const Vector& y,const Vector& z) 
  {
      data[0] = x.data[0];data[3] = x.data[1];data[6] = x.data[2];
      data[1] = y.data[0];data[4] = y.data[1];data[7] = y.data[2];
      data[2] = z.data[0];data[5] = z.data[1];data[8] = z.data[2];
  }
  
  Rotation::Rotation(const Rotation& arg) {
      int count=9;
      while (count--) data[count] = arg.data[count];
  }
  
  Rotation& Rotation::operator=(const Rotation& arg) {
      int count=9;
      while (count--) data[count] = arg.data[count];
      return *this;
  }
  
  Vector Rotation::operator*(const Vector& v) const {
  // Complexity : 9M+6A
      return Vector(
       data[0]*v.data[0] + data[1]*v.data[1] + data[2]*v.data[2],
       data[3]*v.data[0] + data[4]*v.data[1] + data[5]*v.data[2],
       data[6]*v.data[0] + data[7]*v.data[1] + data[8]*v.data[2] 
      );
  }
  
  Twist Rotation::operator * (const Twist& arg) const
       // Transformation of the base to which the twist is expressed.
       // look at Frame*Twist for a transformation that also transforms
       // the velocity reference point.
       // Complexity : 18M+12A
  {
      return Twist((*this)*arg.vel,(*this)*arg.rot);
  }
  
  Wrench Rotation::operator * (const Wrench& arg) const
       // Transformation of the base to which the wrench is expressed.
       // look at Frame*Twist for a transformation that also transforms
       // the force reference point.
  {
      return Wrench((*this)*arg.force,(*this)*arg.torque);
  }
  
  Rotation Rotation::Identity() {
          return Rotation(1,0,0,0,1,0,0,0,1);
  }
  // *this = *this * ROT(X,angle)
  void Rotation::DoRotX(double angle)
  {
      double cs = cos(angle);
      double sn = sin(angle);
      double x1,x2,x3;
      x1  = cs* (*this)(0,1) + sn* (*this)(0,2);
      x2  = cs* (*this)(1,1) + sn* (*this)(1,2);
      x3  = cs* (*this)(2,1) + sn* (*this)(2,2);
      (*this)(0,2) = -sn* (*this)(0,1) + cs* (*this)(0,2);
      (*this)(1,2) = -sn* (*this)(1,1) + cs* (*this)(1,2);
      (*this)(2,2) = -sn* (*this)(2,1) + cs* (*this)(2,2);
      (*this)(0,1) = x1;
      (*this)(1,1) = x2;
      (*this)(2,1) = x3;
  }
  
  void Rotation::DoRotY(double angle)
  {
      double cs = cos(angle);
      double sn = sin(angle);
      double x1,x2,x3;
      x1  = cs* (*this)(0,0) - sn* (*this)(0,2);
      x2  = cs* (*this)(1,0) - sn* (*this)(1,2);
      x3  = cs* (*this)(2,0) - sn* (*this)(2,2);
      (*this)(0,2) = sn* (*this)(0,0) + cs* (*this)(0,2);
      (*this)(1,2) = sn* (*this)(1,0) + cs* (*this)(1,2);
      (*this)(2,2) = sn* (*this)(2,0) + cs* (*this)(2,2);
      (*this)(0,0) = x1;
      (*this)(1,0) = x2;
      (*this)(2,0) = x3;
  }
  
  void Rotation::DoRotZ(double angle)
  {
      double cs = cos(angle);
      double sn = sin(angle);
      double x1,x2,x3;
      x1  = cs* (*this)(0,0) + sn* (*this)(0,1);
      x2  = cs* (*this)(1,0) + sn* (*this)(1,1);
      x3  = cs* (*this)(2,0) + sn* (*this)(2,1);
      (*this)(0,1) = -sn* (*this)(0,0) + cs* (*this)(0,1);
      (*this)(1,1) = -sn* (*this)(1,0) + cs* (*this)(1,1);
      (*this)(2,1) = -sn* (*this)(2,0) + cs* (*this)(2,1);
      (*this)(0,0) = x1;
      (*this)(1,0) = x2;
      (*this)(2,0) = x3;
  }
  
  
  Rotation Rotation::RotX(double angle) {
      double cs=cos(angle);
      double sn=sin(angle);
      return Rotation(1,0,0,0,cs,-sn,0,sn,cs);
  }
  Rotation Rotation::RotY(double angle) {
      double cs=cos(angle);
      double sn=sin(angle);
      return Rotation(cs,0,sn,0,1,0,-sn,0,cs);
  }
  Rotation Rotation::RotZ(double angle) {
      double cs=cos(angle);
      double sn=sin(angle);
      return Rotation(cs,-sn,0,sn,cs,0,0,0,1);
  }
  
  
  
  
  void Frame::Integrate(const Twist& t_this,double samplefrequency)
  {
      double n = t_this.rot.Norm()/samplefrequency;
      if (n<epsilon) {
          p += M*(t_this.vel/samplefrequency);
      } else {
          (*this) = (*this) * 
              Frame ( Rotation::Rot( t_this.rot, n ),
                      t_this.vel/samplefrequency
                  );
      }
  }
  
  Rotation Rotation::Inverse() const
  {
      Rotation tmp(*this);
      tmp.SetInverse();
      return tmp;
  }
  
  Vector Rotation::Inverse(const Vector& v) const {
      return Vector(
       data[0]*v.data[0] + data[3]*v.data[1] + data[6]*v.data[2],
       data[1]*v.data[0] + data[4]*v.data[1] + data[7]*v.data[2],
       data[2]*v.data[0] + data[5]*v.data[1] + data[8]*v.data[2] 
      );
  }
  
  
  void Rotation::SetInverse()
  {
      double tmp;
      tmp = data[1];data[1]=data[3];data[3]=tmp;
      tmp = data[2];data[2]=data[6];data[6]=tmp;
      tmp = data[5];data[5]=data[7];data[7]=tmp;
  }
  
  
  
  
  
  
  
  double Frame::operator()(int i,int j) {
      FRAMES_CHECKI((0<=i)&&(i<=3)&&(0<=j)&&(j<=3));
      if (i==3) {
          if (j==3)
              return 1.0;
          else
              return 0.0;
      } else {
          if (j==3) 
              return p(i);
          else
              return M(i,j);
  
      }
  }
  
  double Frame::operator()(int i,int j) const {
      FRAMES_CHECKI((0<=i)&&(i<=3)&&(0<=j)&&(j<=3));
          if (i==3) {
          if (j==3)
              return 1;
          else
              return 0;
      } else {
          if (j==3) 
              return p(i);
          else
              return M(i,j);
  
      }
  }
  
  
  Frame Frame::Identity() {
      return Frame(Rotation::Identity(),Vector::Zero());
  }
  
  
  
  
  void Vector::Set2DPlane(const Frame& F_someframe_XY,const Vector2& v_XY)
  // a 3D vector where the 2D vector v is put in the XY plane of the frame
  // F_someframe_XY.
  {
  Vector tmp_XY;
  tmp_XY.Set2DXY(v_XY);
  tmp_XY = F_someframe_XY*(tmp_XY);
  }
  
  
  
  
  
  
  
  
  
  //============ 2 dimensional version of the frames objects =============
  IMETHOD Vector2::Vector2(const Vector2 & arg)
  {
      data[0] = arg.data[0];
      data[1] = arg.data[1];
  }
  
  IMETHOD Vector2::Vector2(double x,double y)
  {
          data[0]=x;data[1]=y;
  }
  
  
  IMETHOD Vector2& Vector2::operator =(const Vector2 & arg)
  {
      data[0] = arg.data[0];
      data[1] = arg.data[1];
      return *this;
  }
  
  
  IMETHOD Vector2 operator +(const Vector2 & lhs,const Vector2& rhs)
  {
      return Vector2(lhs.data[0]+rhs.data[0],lhs.data[1]+rhs.data[1]);
  }
  
  IMETHOD Vector2 operator -(const Vector2 & lhs,const Vector2& rhs)
  {
      return Vector2(lhs.data[0]-rhs.data[0],lhs.data[1]-rhs.data[1]);
  }
  
  IMETHOD Vector2 operator *(const Vector2& lhs,double rhs) 
  {
      return Vector2(lhs.data[0]*rhs,lhs.data[1]*rhs);
  }
  
  IMETHOD Vector2 operator *(double lhs,const Vector2& rhs) 
  {
      return Vector2(lhs*rhs.data[0],lhs*rhs.data[1]);
  }
  
  IMETHOD Vector2 operator /(const Vector2& lhs,double rhs) 
  {
      return Vector2(lhs.data[0]/rhs,lhs.data[1]/rhs);
  }
  
  IMETHOD Vector2& Vector2::operator +=(const Vector2 & arg)
  {
      data[0]+=arg.data[0];
      data[1]+=arg.data[1];
      return *this;
  }
  
  IMETHOD Vector2& Vector2::operator -=(const Vector2 & arg)
  {
      data[0]-=arg.data[0];
      data[1]-=arg.data[1];
      return *this;
  }
  
  IMETHOD Vector2 Vector2::Zero() {
      return Vector2(0,0);
  }
  
  IMETHOD double Vector2::operator()(int index) const {
      FRAMES_CHECKI((0<=index)&&(index<=1));
      return data[index];
  }
  
  IMETHOD double& Vector2::operator () (int index)
  {
      FRAMES_CHECKI((0<=index)&&(index<=1));
      return data[index];
  }
  
  IMETHOD double Vector2::x() const { return data[0]; }
  IMETHOD double Vector2::y() const { return data[1]; }
  
  IMETHOD void Vector2::x( double _x ) { data[0] = _x; }
  IMETHOD void Vector2::y( double _y ) { data[1] = _y; }
  
  
  IMETHOD void Vector2::ReverseSign()
  {
      data[0] = -data[0];
      data[1] = -data[1];
  }
  
  
  IMETHOD Vector2 operator-(const Vector2 & arg)
  {
      return Vector2(-arg.data[0],-arg.data[1]);
  }
  
  
  IMETHOD void Vector2::Set3DXY(const Vector& v)
  // projects v in its XY plane, and sets *this to these values
  {
      data[0]=v(0);
      data[1]=v(1);
  }
  IMETHOD void Vector2::Set3DYZ(const Vector& v)
  // projects v in its XY plane, and sets *this to these values
  {
      data[0]=v(1);
      data[1]=v(2);
  }
  IMETHOD void Vector2::Set3DZX(const Vector& v)
  // projects v in its XY plane, and sets *this to these values
  {
      data[0]=v(2);
      data[1]=v(0);
  }
  
  IMETHOD void Vector2::Set3DPlane(const Frame& F_someframe_XY,const Vector& v_someframe) 
  // projects v in the XY plane of F_someframe_XY, and sets *this to these values
  // expressed wrt someframe.
  {
      Vector tmp = F_someframe_XY.Inverse(v_someframe);
      data[0]=tmp(0);
      data[1]=tmp(1);
  }
  
  IMETHOD Rotation2::Rotation2(const Rotation2& arg) {
      c=arg.c;s=arg.s;
  }
  
  IMETHOD Rotation2& Rotation2::operator=(const Rotation2& arg) {
      c=arg.c;s=arg.s;
      return *this;
  }
  
  IMETHOD Vector2 Rotation2::operator*(const Vector2& v) const {
      return Vector2(v.data[0]*c-v.data[1]*s,v.data[0]*s+v.data[1]*c);
  }
  
  IMETHOD double Rotation2::operator()(int i,int j) const {
      FRAMES_CHECKI((0<=i)&&(i<=1)&&(0<=j)&&(j<=1));
      if (i==j) return c;
      if (i==0) 
          return s;
      else
          return -s;
  }
  
  
  IMETHOD Rotation2 operator *(const Rotation2& lhs,const Rotation2& rhs) {
      return Rotation2(lhs.c*rhs.c-lhs.s*rhs.s,lhs.s*rhs.c+lhs.c*rhs.s);
  }
  
  IMETHOD void Rotation2::SetInverse() {
      s=-s;
  }
  
  IMETHOD Rotation2 Rotation2::Inverse() const {
      return Rotation2(c,-s);
  }
  
  IMETHOD Vector2 Rotation2::Inverse(const Vector2& v) const {
      return Vector2(v.data[0]*c+v.data[1]*s,-v.data[0]*s+v.data[1]*c);
  }
  
  IMETHOD Rotation2 Rotation2::Identity() {
      return Rotation2(1,0);
  }
       
  IMETHOD void Rotation2::SetIdentity()
  {
  	c = 1;
  	s = 0;
  }
  
  IMETHOD void Rotation2::SetRot(double angle) {
      c=cos(angle);s=sin(angle);
  }
  
  IMETHOD Rotation2 Rotation2::Rot(double angle) {
      return Rotation2(cos(angle),sin(angle));
  }
  
  IMETHOD double Rotation2::GetRot() const {
      return atan2(s,c);
  }
  
  
  IMETHOD Frame2::Frame2() {
  }
  
  IMETHOD Frame2::Frame2(const Rotation2 & R)
  {
      M=R;
      p=Vector2::Zero();
  }
  
  IMETHOD Frame2::Frame2(const Vector2 & V)
  {
      M = Rotation2::Identity();
      p = V;
  }
  
  IMETHOD Frame2::Frame2(const Rotation2 & R, const Vector2 & V)
  {
      M = R;
      p = V;
  }
  
  IMETHOD Frame2 operator *(const Frame2& lhs,const Frame2& rhs)
  {
      return Frame2(lhs.M*rhs.M,lhs.M*rhs.p+lhs.p);
  }
  
  IMETHOD Vector2 Frame2::operator *(const Vector2 & arg) const
  {
      return M*arg+p;
  }
  
  IMETHOD Vector2 Frame2::Inverse(const Vector2& arg) const
  {
      return M.Inverse(arg-p);
  }
  
  IMETHOD void Frame2::SetIdentity()
  {
  	M.SetIdentity();
  	p = Vector2::Zero();
  }
  
  IMETHOD void Frame2::SetInverse()
  {
      M.SetInverse();
      p = M*p;
      p.ReverseSign();
  }
  
  
  IMETHOD Frame2 Frame2::Inverse() const
  {
      Frame2 tmp(*this);
      tmp.SetInverse();
      return tmp;
  }
  
  IMETHOD Frame2& Frame2::operator =(const Frame2 & arg)
  { 
      M = arg.M;
      p = arg.p;
      return *this;
  }
  
  IMETHOD Frame2::Frame2(const Frame2 & arg) :
      p(arg.p), M(arg.M)
  {}
  
  
  IMETHOD double Frame2::operator()(int i,int j) {
      FRAMES_CHECKI((0<=i)&&(i<=2)&&(0<=j)&&(j<=2));
      if (i==2) {
          if (j==2)
              return 1;
          else
              return 0;
      } else {
          if (j==2) 
              return p(i);
          else
              return M(i,j);
  
      }
  }
  
  IMETHOD double Frame2::operator()(int i,int j) const {
      FRAMES_CHECKI((0<=i)&&(i<=2)&&(0<=j)&&(j<=2));
      if (i==2) {
          if (j==2)
              return 1;
          else
              return 0;
      } else {
          if (j==2) 
              return p(i);
          else
              return M(i,j);
  
      }
  }
  
  // Scalar products.
  
  IMETHOD double dot(const Vector& lhs,const Vector& rhs) {
      return rhs(0)*lhs(0)+rhs(1)*lhs(1)+rhs(2)*lhs(2);
  }
  
  IMETHOD double dot(const Twist& lhs,const Wrench& rhs) {
      return dot(lhs.vel,rhs.force)+dot(lhs.rot,rhs.torque);
  }
  
  IMETHOD double dot(const Wrench& rhs,const Twist& lhs) {
      return dot(lhs.vel,rhs.force)+dot(lhs.rot,rhs.torque);
  }
  
  
  
  
  
  // Equality operators
  
  
  
  IMETHOD bool Equal(const Vector& a,const Vector& b,double eps) {
          return (Equal(a.data[0],b.data[0],eps)&&
                  Equal(a.data[1],b.data[1],eps)&&
                  Equal(a.data[2],b.data[2],eps)   );
       }
       
  
  IMETHOD bool Equal(const Frame& a,const Frame& b,double eps) {
          return (Equal(a.p,b.p,eps)&&
                  Equal(a.M,b.M,eps)   );
  }
  
  IMETHOD bool Equal(const Wrench& a,const Wrench& b,double eps) {
          return (Equal(a.force,b.force,eps)&&
                  Equal(a.torque,b.torque,eps)  );
  }
  
  IMETHOD bool Equal(const Twist& a,const Twist& b,double eps) {
          return (Equal(a.rot,b.rot,eps)&&
                  Equal(a.vel,b.vel,eps)  );
  }
  
  IMETHOD bool Equal(const Vector2& a,const Vector2& b,double eps) {
          return (Equal(a.data[0],b.data[0],eps)&&
                  Equal(a.data[1],b.data[1],eps)   );
       }
       
  IMETHOD bool Equal(const Rotation2& a,const Rotation2& b,double eps) {
      return ( Equal(a.c,b.c,eps) && Equal(a.s,b.s,eps) );
  }
  
  IMETHOD bool Equal(const Frame2& a,const Frame2& b,double eps) {
          return (Equal(a.p,b.p,eps)&&
                  Equal(a.M,b.M,eps)   );
  }
  
  IMETHOD void SetToZero(Vector& v) {
      v=Vector::Zero();
  }
  IMETHOD void SetToZero(Twist& v) {
      SetToZero(v.rot);
      SetToZero(v.vel);
  }
  IMETHOD void SetToZero(Wrench& v) {
      SetToZero(v.force);
      SetToZero(v.torque);
  }
  
  IMETHOD void SetToZero(Vector2& v) {
      v = Vector2::Zero();
  }
  
  
  ////////////////////////////////////////////////////////////////
  // The following defines the operations
  //   diff
  //   addDelta
  //   random
  //   posrandom
  // on all the types defined in this library.
  // (mostly for uniform integration, differentiation and testing).
  // Defined as functions because double is not a class and a method
  // would brake uniformity when defined for a double.
  ////////////////////////////////////////////////////////////////
  
  
  
  
  
  
  /**
   * axis_a_b is a rotation vector, its norm is a rotation angle
   * axis_a_b rotates the a frame towards the b frame.
   * This routine returns the rotation matrix R_a_b
   */
  IMETHOD Rotation Rot(const Vector& axis_a_b) {
      // The formula is 
      // V.(V.tr) + st*[V x] + ct*(I-V.(V.tr))
      // can be found by multiplying it with an arbitrary vector p
      // and noting that this vector is rotated.
  	Vector rotvec = axis_a_b;
  	double angle = rotvec.Normalize(1E-10);
      double ct = ::cos(angle);
      double st = ::sin(angle);
      double vt = 1-ct;
      return Rotation(
          ct            +  vt*rotvec(0)*rotvec(0), 
          -rotvec(2)*st +  vt*rotvec(0)*rotvec(1), 
          rotvec(1)*st  +  vt*rotvec(0)*rotvec(2),
          rotvec(2)*st  +  vt*rotvec(1)*rotvec(0),
          ct            +  vt*rotvec(1)*rotvec(1),
          -rotvec(0)*st +  vt*rotvec(1)*rotvec(2),
          -rotvec(1)*st +  vt*rotvec(2)*rotvec(0),
          rotvec(0)*st  +  vt*rotvec(2)*rotvec(1),
          ct            +  vt*rotvec(2)*rotvec(2)
          );
      }
  IMETHOD Vector diff(const Vector& a,const Vector& b,double dt) {
  	return (b-a)/dt;
  }
  
  IMETHOD Vector diff(const Rotation& R_a_b1,const Rotation& R_a_b2,double dt) {
  	Rotation R_b1_b2(R_a_b1.Inverse()*R_a_b2);
  	return R_a_b1 * R_b1_b2.GetRot() / dt;
  }
  
  IMETHOD Twist diff(const Frame& F_a_b1,const Frame& F_a_b2,double dt) {
  	return Twist(
  			diff(F_a_b1.p,F_a_b2.p,dt),
  			diff(F_a_b1.M,F_a_b2.M,dt)
  			);
  }
  IMETHOD Twist diff(const Twist& a,const Twist& b,double dt) {
  	return Twist(diff(a.vel,b.vel,dt),diff(a.rot,b.rot,dt));
  }
  
  IMETHOD Wrench diff(const Wrench& a,const Wrench& b,double dt) {
  	return Wrench(
  			diff(a.force,b.force,dt),
  			diff(a.torque,b.torque,dt)
  			);
  }
  
  
  IMETHOD Vector addDelta(const Vector& a,const Vector&da,double dt) {
  	return a+da*dt;
  }
  
  IMETHOD Rotation addDelta(const Rotation& a,const Vector&da,double dt) {
  	return a*Rot(a.Inverse(da)*dt);
  }
  IMETHOD Frame addDelta(const Frame& a,const Twist& da,double dt) {
  	return Frame(
  			addDelta(a.M,da.rot,dt),
  			addDelta(a.p,da.vel,dt)
  		   );
  }
  IMETHOD Twist addDelta(const Twist& a,const Twist&da,double dt) {
  	return Twist(addDelta(a.vel,da.vel,dt),addDelta(a.rot,da.rot,dt));
  }
  IMETHOD Wrench addDelta(const Wrench& a,const Wrench&da,double dt) {
  	return Wrench(addDelta(a.force,da.force,dt),addDelta(a.torque,da.torque,dt));
  }
  
  
  /**
   * \brief addDelta operator for displacement rotational velocity.
   *
   * The Vector arguments here represent a displacement rotational velocity.  i.e. a rotation
   * around a fixed axis for a certain angle.  For this representation you cannot use diff() but
   * have to use diff_displ().
   *
   * \param a  : displacement rotational velocity
   * \param da : rotational velocity 
   * \return   displacement rotational velocity
   *
   * \warning do not confuse displacement rotational velocities and velocities
   * \warning do not confuse displacement twist and twist.
   *
  IMETHOD Vector addDelta_displ(const Vector& a,const Vector&da,double dt) {
      return getRot(addDelta(Rot(a),da,dt)); 
  }*/
  
  /**
   * \brief addDelta operator for displacement twist.
   *
   * The Vector arguments here represent a displacement rotational velocity.  i.e. a rotation
   * around a fixed axis for a certain angle.  For this representation you cannot use diff() but
   * have to use diff_displ().
   *
   * \param a  : displacement twist 
   * \param da : twist 
   * \return   displacement twist 
   *
   * \warning do not confuse displacement rotational velocities and velocities
   * \warning do not confuse displacement twist and twist.
   *
  IMETHOD Twist addDelta_displ(const Twist& a,const Twist&da,double dt) {
      return Twist(addDelta(a.vel,da.vel,dt),addDelta_displ(a.rot,da.rot,dt)); 
  }*/
  
  
  IMETHOD void random(Vector& a) {
  	random(a[0]);
  	random(a[1]);
  	random(a[2]);
  }
  IMETHOD void random(Twist& a) {
  	random(a.rot);
  	random(a.vel);
  }
  IMETHOD void random(Wrench& a) {
     	random(a.torque);
  	random(a.force);
  }
  
  IMETHOD void random(Rotation& R) {
  	double alfa;
  	double beta;
  	double gamma;
  	random(alfa);
  	random(beta);
  	random(gamma);
  	R = Rotation::EulerZYX(alfa,beta,gamma);
  }
  
  IMETHOD void random(Frame& F) {
  	random(F.M);
  	random(F.p);
  }
  
  IMETHOD void posrandom(Vector& a) {
  	posrandom(a[0]);
  	posrandom(a[1]);
  	posrandom(a[2]);
  }
  IMETHOD void posrandom(Twist& a) {
  	posrandom(a.rot);
  	posrandom(a.vel);
  }
  IMETHOD void posrandom(Wrench& a) {
     	posrandom(a.torque);
  	posrandom(a.force);
  }
  
  IMETHOD void posrandom(Rotation& R) {
  	double alfa;
  	double beta;
  	double gamma;
  	posrandom(alfa);
  	posrandom(beta);
  	posrandom(gamma);
  	R = Rotation::EulerZYX(alfa,beta,gamma);
  }
  
  IMETHOD void posrandom(Frame& F) {
  	random(F.M);
  	random(F.p);
  }
  
  
  
  
  IMETHOD bool operator==(const Frame& a,const Frame& b ) {
  #ifdef KDL_USE_EQUAL
      return Equal(a,b);
  #else
          return (a.p == b.p &&
                  a.M == b.M );
  #endif
  }
  
  IMETHOD bool operator!=(const Frame& a,const Frame& b) {
      return !operator==(a,b);
  }
  
  IMETHOD bool operator==(const Vector& a,const Vector& b) {
  #ifdef KDL_USE_EQUAL
      return Equal(a,b);
  #else
          return (a.data[0]==b.data[0]&&
                  a.data[1]==b.data[1]&&
                  a.data[2]==b.data[2] );
  #endif
       }
  
  IMETHOD bool operator!=(const Vector& a,const Vector& b) {
      return !operator==(a,b);
  }
  
  IMETHOD bool operator==(const Twist& a,const Twist& b) {
  #ifdef KDL_USE_EQUAL
      return Equal(a,b);
  #else
          return (a.rot==b.rot &&
                  a.vel==b.vel  );
  #endif
  }
  
  IMETHOD bool operator!=(const Twist& a,const Twist& b) {
      return !operator==(a,b);
  }
  
  IMETHOD bool operator==(const Wrench& a,const Wrench& b ) {
  #ifdef KDL_USE_EQUAL
      return Equal(a,b);
  #else
      return (a.force==b.force &&
              a.torque==b.torque );
  #endif
  }
  
  IMETHOD bool operator!=(const Wrench& a,const Wrench& b) {
      return !operator==(a,b);
  }
  IMETHOD bool operator!=(const Rotation& a,const Rotation& b) {
      return !operator==(a,b);
  }
  
  IMETHOD bool operator==(const Vector2& a,const Vector2& b) {
  #ifdef KDL_USE_EQUAL
      return Equal(a,b);
  #else
          return (a.data[0]==b.data[0]&&
                  a.data[1]==b.data[1] );
  #endif
       }
  
  IMETHOD bool operator!=(const Vector2& a,const Vector2& b) {
      return !operator==(a,b);
  }
  
  