Merge of itasc branch. Project files, scons and cmake should be working. Makefile updated but not tested. Comes with Eigen2 2.0.6 C++ matrix library.

1 files changed, 1390 insertions, 0 deletions

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+/***************************************************************************
+                        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                                *
+ *                                                                         *
+ ***************************************************************************/
+
+
+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(double* xyz)
+{
+        data[0]=xyz[0];data[1]=xyz[1];data[2]=xyz[2];
+}
+
+IMETHOD Vector::Vector(float* xyz)
+{
+        data[0]=xyz[0];data[1]=xyz[1];data[2]=xyz[2];
+}
+
+IMETHOD void Vector::GetValue(double* xyz) const
+{
+        xyz[0]=data[0];xyz[1]=data[1];xyz[2]=data[2];
+}
+
+
+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];
+}
+
+IMETHOD Vector Normalize(const Vector& a, double eps)
+{
+	double l=a.Norm();
+	return (l<eps) ? Vector(0.0,0.0,0.0) : a/l;
+}
+
+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);
+}
+
+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::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::setValue(float* oglmat)
+{
+    data[0] = *oglmat++; data[3] = *oglmat++; data[6] = *oglmat++; oglmat++;
+    data[1] = *oglmat++; data[4] = *oglmat++; data[7] = *oglmat++; oglmat++;
+    data[2] = *oglmat++; data[5] = *oglmat++; data[8] = *oglmat;
+	Ortho();
+}
+
+void Rotation::getValue(float* oglmat) const
+{
+	*oglmat++ = (float)data[0]; *oglmat++ = (float)data[3]; *oglmat++ = (float)data[6]; *oglmat++ = 0.f;
+	*oglmat++ = (float)data[1]; *oglmat++ = (float)data[4]; *oglmat++ = (float)data[7]; *oglmat++ = 0.f;
+	*oglmat++ = (float)data[2]; *oglmat++ = (float)data[5]; *oglmat++ = (float)data[8]; *oglmat++ = 0.f;
+	*oglmat++ = 0.f;            *oglmat++ = 0.f;            *oglmat++ = 0.f;            *oglmat   = 1.f;
+}
+
+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 Frame::setValue(float* oglmat)
+{
+	M.setValue(oglmat);
+	p.data[0] = oglmat[12];
+	p.data[1] = oglmat[13];
+	p.data[2] = oglmat[14];
+}
+
+void Frame::getValue(float* oglmat) const
+{
+	M.getValue(oglmat);
+	oglmat[12] = (float)p.data[0];
+	oglmat[13] = (float)p.data[1];
+	oglmat[14] = (float)p.data[2];
+}
+
+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(double* xy)
+{
+        data[0]=xy[0];data[1]=xy[1];
+}
+
+IMETHOD Vector2::Vector2(float* xy)
+{
+        data[0]=xy[0];data[1]=xy[1];
+}
+
+IMETHOD Vector2& Vector2::operator =(const Vector2 & arg)
+{
+    data[0] = arg.data[0];
+    data[1] = arg.data[1];
+    return *this;
+}
+
+IMETHOD void Vector2::GetValue(double* xy) const
+{
+        xy[0]=data[0];xy[1]=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,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 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 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::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)
+{
+    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;
+}
+
+/**
+ * \brief diff 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().
+ *
+ * \TODO represent a displacement twist and displacement rotational velocity with another
+ *       class, instead of Vector and Twist.
+ * \warning do not confuse displacement rotational velocities and velocities
+ * \warning do not confuse displacement twist and twist.
+ *
+IMETHOD Vector diff_displ(const Vector& a,const Vector& b,double dt) {
+	return diff(Rot(a),Rot(b),dt);
+}*/
+
+/**
+ * \brief diff operator for displacement twist.
+ *
+ * The Twist arguments here represent a displacement twist.  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().
+ *
+ * \warning do not confuse displacement rotational velocities and velocities
+ * \warning do not confuse displacement twist and twist.
+ *
+
+IMETHOD Twist diff_displ(const Twist& a,const Twist& b,double dt) {
+	return Twist(diff(a.vel,b.vel,dt),diff(Rot(a.rot),Rot(b.rot),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);
+}
+