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+/*****************************************************************************
+ * \file
+ * provides inline functions of rrframes.h
+ *
+ * \author
+ * Erwin Aertbelien, Div. PMA, Dep. of Mech. Eng., K.U.Leuven
+ *
+ * \version
+ * ORO_Geometry V0.2
+ *
+ * \par History
+ * - $log$
+ *
+ * \par Release
+ * $Id: frameacc.inl 19905 2009-04-23 13:29:54Z ben2610 $
+ * $Name: $
+ ****************************************************************************/
+
+
+
+
+/////////////////// VectorAcc /////////////////////////////////////
+
+VectorAcc operator + (const VectorAcc& r1,const VectorAcc& r2) {
+ return VectorAcc(r1.p+r2.p,r1.v+r2.v,r1.dv+r2.dv);
+}
+
+VectorAcc operator - (const VectorAcc& r1,const VectorAcc& r2) {
+ return VectorAcc(r1.p-r2.p, r1.v-r2.v, r1.dv-r2.dv);
+}
+VectorAcc operator + (const Vector& r1,const VectorAcc& r2) {
+ return VectorAcc(r1+r2.p,r2.v,r2.dv);
+}
+
+VectorAcc operator - (const Vector& r1,const VectorAcc& r2) {
+ return VectorAcc(r1-r2.p, -r2.v, -r2.dv);
+}
+VectorAcc operator + (const VectorAcc& r1,const Vector& r2) {
+ return VectorAcc(r1.p+r2,r1.v,r1.dv);
+}
+
+VectorAcc operator - (const VectorAcc& r1,const Vector& r2) {
+ return VectorAcc(r1.p-r2, r1.v, r1.dv);
+}
+
+// unary -
+VectorAcc operator - (const VectorAcc& r) {
+ return VectorAcc(-r.p,-r.v,-r.dv);
+}
+
+// cross prod.
+VectorAcc operator * (const VectorAcc& r1,const VectorAcc& r2) {
+ return VectorAcc(r1.p*r2.p,
+ r1.p*r2.v+r1.v*r2.p,
+ r1.dv*r2.p+2*r1.v*r2.v+r1.p*r2.dv
+ );
+}
+
+VectorAcc operator * (const VectorAcc& r1,const Vector& r2) {
+ return VectorAcc(r1.p*r2, r1.v*r2, r1.dv*r2 );
+}
+
+VectorAcc operator * (const Vector& r1,const VectorAcc& r2) {
+ return VectorAcc(r1*r2.p, r1*r2.v, r1*r2.dv );
+}
+
+
+
+// scalar mult.
+VectorAcc operator * (double r1,const VectorAcc& r2) {
+ return VectorAcc(r1*r2.p, r1*r2.v, r1*r2.dv );
+}
+
+VectorAcc operator * (const VectorAcc& r1,double r2) {
+ return VectorAcc(r1.p*r2, r1.v*r2, r1.dv*r2 );
+}
+
+VectorAcc operator * (const doubleAcc& r1,const VectorAcc& r2) {
+ return VectorAcc(r1.t*r2.p,
+ r1.t*r2.v + r1.d*r2.p,
+ r1.t*r2.dv + 2*r1.d*r2.v + r1.dd*r2.p
+ );
+}
+
+VectorAcc operator * (const VectorAcc& r2,const doubleAcc& r1) {
+ return VectorAcc(r1.t*r2.p,
+ r1.t*r2.v + r1.d*r2.p,
+ r1.t*r2.dv + 2*r1.d*r2.v + r1.dd*r2.p
+ );
+}
+
+VectorAcc& VectorAcc::operator = (const VectorAcc& arg) {
+ p=arg.p;
+ v=arg.v;
+ dv=arg.dv;
+ return *this;
+}
+
+VectorAcc& VectorAcc::operator = (const Vector& arg) {
+ p=arg;
+ v=Vector::Zero();
+ dv=Vector::Zero();
+ return *this;
+}
+
+VectorAcc& VectorAcc::operator += (const VectorAcc& arg) {
+ p+=arg.p;
+ v+=arg.v;
+ dv+= arg.dv;
+ return *this;
+}
+VectorAcc& VectorAcc::operator -= (const VectorAcc& arg) {
+ p-=arg.p;
+ v-=arg.v;
+ dv-=arg.dv;
+ return *this;
+}
+
+VectorAcc VectorAcc::Zero() {
+ return VectorAcc(Vector::Zero(),Vector::Zero(),Vector::Zero());
+}
+
+void VectorAcc::ReverseSign() {
+ p.ReverseSign();
+ v.ReverseSign();
+ dv.ReverseSign();
+}
+
+doubleAcc VectorAcc::Norm() {
+ doubleAcc res;
+ res.t = p.Norm();
+ res.d = dot(p,v)/res.t;
+ res.dd = (dot(p,dv)+dot(v,v)-res.d*res.d)/res.t;
+ return res;
+}
+
+doubleAcc dot(const VectorAcc& lhs,const VectorAcc& rhs) {
+ return doubleAcc( dot(lhs.p,rhs.p),
+ dot(lhs.p,rhs.v)+dot(lhs.v,rhs.p),
+ dot(lhs.p,rhs.dv)+2*dot(lhs.v,rhs.v)+dot(lhs.dv,rhs.p)
+ );
+}
+
+doubleAcc dot(const VectorAcc& lhs,const Vector& rhs) {
+ return doubleAcc( dot(lhs.p,rhs),
+ dot(lhs.v,rhs),
+ dot(lhs.dv,rhs)
+ );
+}
+
+doubleAcc dot(const Vector& lhs,const VectorAcc& rhs) {
+ return doubleAcc( dot(lhs,rhs.p),
+ dot(lhs,rhs.v),
+ dot(lhs,rhs.dv)
+ );
+}
+
+
+bool Equal(const VectorAcc& r1,const VectorAcc& r2,double eps) {
+ return (Equal(r1.p,r2.p,eps)
+ && Equal(r1.v,r2.v,eps)
+ && Equal(r1.dv,r2.dv,eps)
+ );
+}
+
+bool Equal(const Vector& r1,const VectorAcc& r2,double eps) {
+ return (Equal(r1,r2.p,eps)
+ && Equal(Vector::Zero(),r2.v,eps)
+ && Equal(Vector::Zero(),r2.dv,eps)
+ );
+}
+
+bool Equal(const VectorAcc& r1,const Vector& r2,double eps) {
+ return (Equal(r1.p,r2,eps)
+ && Equal(r1.v,Vector::Zero(),eps)
+ && Equal(r1.dv,Vector::Zero(),eps)
+ );
+}
+
+VectorAcc operator / (const VectorAcc& r1,double r2) {
+ return r1*(1.0/r2);
+}
+
+VectorAcc operator / (const VectorAcc& r2,const doubleAcc& r1) {
+ return r2*(1.0/r1);
+}
+
+
+
+/////////////////// RotationAcc /////////////////////////////////////
+
+RotationAcc operator* (const RotationAcc& r1,const RotationAcc& r2) {
+ return RotationAcc( r1.R * r2.R,
+ r1.w + r1.R*r2.w,
+ r1.dw + r1.w*(r1.R*r2.w) + r1.R*r2.dw
+ );
+}
+
+RotationAcc operator* (const Rotation& r1,const RotationAcc& r2) {
+ return RotationAcc( r1*r2.R, r1*r2.w, r1*r2.dw);
+}
+
+RotationAcc operator* (const RotationAcc& r1,const Rotation& r2) {
+ return RotationAcc( r1.R*r2, r1.w, r1.dw );
+}
+
+RotationAcc& RotationAcc::operator = (const RotationAcc& arg) {
+ R=arg.R;
+ w=arg.w;
+ dw=arg.dw;
+ return *this;
+}
+RotationAcc& RotationAcc::operator = (const Rotation& arg) {
+ R = arg;
+ w = Vector::Zero();
+ dw = Vector::Zero();
+ return *this;
+}
+
+RotationAcc RotationAcc::Identity() {
+ return RotationAcc(Rotation::Identity(),Vector::Zero(),Vector::Zero());
+}
+
+RotationAcc RotationAcc::Inverse() const {
+ return RotationAcc(R.Inverse(),-R.Inverse(w),-R.Inverse(dw));
+}
+
+VectorAcc RotationAcc::Inverse(const VectorAcc& arg) const {
+ VectorAcc tmp;
+ tmp.p = R.Inverse(arg.p);
+ tmp.v = R.Inverse(arg.v - w * arg.p);
+ tmp.dv = R.Inverse(arg.dv - dw*arg.p - w*(arg.v+R*tmp.v));
+ return tmp;
+}
+
+VectorAcc RotationAcc::Inverse(const Vector& arg) const {
+ VectorAcc tmp;
+ tmp.p = R.Inverse(arg);
+ tmp.v = R.Inverse(-w*arg);
+ tmp.dv = R.Inverse(-dw*arg - w*(R*tmp.v));
+ return tmp;
+}
+
+
+VectorAcc RotationAcc::operator*(const VectorAcc& arg) const {
+ VectorAcc tmp;
+ tmp.p = R*arg.p;
+ tmp.dv = R*arg.v;
+ tmp.v = w*tmp.p + tmp.dv;
+ tmp.dv = dw*tmp.p + w*(tmp.v + tmp.dv) + R*arg.dv;
+ return tmp;
+}
+
+VectorAcc operator*(const Rotation& R,const VectorAcc& x) {
+ return VectorAcc(R*x.p,R*x.v,R*x.dv);
+}
+
+VectorAcc RotationAcc::operator*(const Vector& arg) const {
+ VectorAcc tmp;
+ tmp.p = R*arg;
+ tmp.v = w*tmp.p;
+ tmp.dv = dw*tmp.p + w*tmp.v;
+ return tmp;
+}
+
+/*
+ // = Rotations
+ // The Rot... static functions give the value of the appropriate rotation matrix back.
+ // The DoRot... functions apply a rotation R to *this,such that *this = *this * R.
+
+ void RRotation::DoRotX(const RDouble& angle) {
+ w+=R*Vector(angle.grad,0,0);
+ R.DoRotX(angle.t);
+ }
+RotationAcc RotationAcc::RotX(const doubleAcc& angle) {
+ return RotationAcc(Rotation::RotX(angle.t),
+ Vector(angle.d,0,0),
+ Vector(angle.dd,0,0)
+ );
+}
+
+ void RRotation::DoRotY(const RDouble& angle) {
+ w+=R*Vector(0,angle.grad,0);
+ R.DoRotY(angle.t);
+ }
+RotationAcc RotationAcc::RotY(const doubleAcc& angle) {
+ return RotationAcc(
+ Rotation::RotX(angle.t),
+ Vector(0,angle.d,0),
+ Vector(0,angle.dd,0)
+ );
+}
+
+ void RRotation::DoRotZ(const RDouble& angle) {
+ w+=R*Vector(0,0,angle.grad);
+ R.DoRotZ(angle.t);
+ }
+RotationAcc RotationAcc::RotZ(const doubleAcc& angle) {
+ return RotationAcc(
+ Rotation::RotZ(angle.t),
+ Vector(0,0,angle.d),
+ Vector(0,0,angle.dd)
+ );
+}
+
+
+ RRotation RRotation::Rot(const Vector& rotvec,const RDouble& angle)
+ // rotvec has arbitrary norm
+ // rotation around a constant vector !
+ {
+ Vector v = rotvec.Normalize();
+ return RRotation(Rotation::Rot2(v,angle.t),v*angle.grad);
+ }
+
+ RRotation RRotation::Rot2(const Vector& rotvec,const RDouble& angle)
+ // rotvec is normalized.
+ {
+ return RRotation(Rotation::Rot2(rotvec,angle.t),rotvec*angle.grad);
+ }
+
+*/
+
+bool Equal(const RotationAcc& r1,const RotationAcc& r2,double eps) {
+ return (Equal(r1.w,r2.w,eps) && Equal(r1.R,r2.R,eps) && Equal(r1.dw,r2.dw,eps) );
+}
+bool Equal(const Rotation& r1,const RotationAcc& r2,double eps) {
+ return (Equal(Vector::Zero(),r2.w,eps) && Equal(r1,r2.R,eps) &&
+ Equal(Vector::Zero(),r2.dw,eps) );
+}
+bool Equal(const RotationAcc& r1,const Rotation& r2,double eps) {
+ return (Equal(r1.w,Vector::Zero(),eps) && Equal(r1.R,r2,eps) &&
+ Equal(r1.dw,Vector::Zero(),eps) );
+}
+
+
+// Methods and operators related to FrameAcc
+// They all delegate most of the work to RotationAcc and VectorAcc
+FrameAcc& FrameAcc::operator = (const FrameAcc& arg) {
+ M=arg.M;
+ p=arg.p;
+ return *this;
+}
+
+FrameAcc FrameAcc::Identity() {
+ return FrameAcc(RotationAcc::Identity(),VectorAcc::Zero());
+}
+
+
+FrameAcc operator *(const FrameAcc& lhs,const FrameAcc& rhs)
+{
+ return FrameAcc(lhs.M*rhs.M,lhs.M*rhs.p+lhs.p);
+}
+FrameAcc operator *(const FrameAcc& lhs,const Frame& rhs)
+{
+ return FrameAcc(lhs.M*rhs.M,lhs.M*rhs.p+lhs.p);
+}
+FrameAcc operator *(const Frame& lhs,const FrameAcc& rhs)
+{
+ return FrameAcc(lhs.M*rhs.M,lhs.M*rhs.p+lhs.p);
+}
+
+VectorAcc FrameAcc::operator *(const VectorAcc & arg) const
+{
+ return M*arg+p;
+}
+VectorAcc FrameAcc::operator *(const Vector & arg) const
+{
+ return M*arg+p;
+}
+
+VectorAcc FrameAcc::Inverse(const VectorAcc& arg) const
+{
+ return M.Inverse(arg-p);
+}
+
+VectorAcc FrameAcc::Inverse(const Vector& arg) const
+{
+ return M.Inverse(arg-p);
+}
+
+FrameAcc FrameAcc::Inverse() const
+{
+ return FrameAcc(M.Inverse(),-M.Inverse(p));
+}
+
+FrameAcc& FrameAcc::operator =(const Frame & arg)
+{
+ M = arg.M;
+ p = arg.p;
+ return *this;
+}
+
+bool Equal(const FrameAcc& r1,const FrameAcc& r2,double eps) {
+ return (Equal(r1.M,r2.M,eps) && Equal(r1.p,r2.p,eps));
+}
+bool Equal(const Frame& r1,const FrameAcc& r2,double eps) {
+ return (Equal(r1.M,r2.M,eps) && Equal(r1.p,r2.p,eps));
+}
+bool Equal(const FrameAcc& r1,const Frame& r2,double eps) {
+ return (Equal(r1.M,r2.M,eps) && Equal(r1.p,r2.p,eps));
+}
+
+
+Frame FrameAcc::GetFrame() const {
+ return Frame(M.R,p.p);
+}
+
+
+Twist FrameAcc::GetTwist() const {
+ return Twist(p.v,M.w);
+}
+
+
+Twist FrameAcc::GetAccTwist() const {
+ return Twist(p.dv,M.dw);
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+TwistAcc TwistAcc::Zero()
+{
+ return TwistAcc(VectorAcc::Zero(),VectorAcc::Zero());
+}
+
+
+void TwistAcc::ReverseSign()
+{
+ vel.ReverseSign();
+ rot.ReverseSign();
+}
+
+TwistAcc TwistAcc::RefPoint(const VectorAcc& v_base_AB)
+ // Changes the reference point of the TwistAcc.
+ // The RVector v_base_AB is expressed in the same base as the TwistAcc
+ // The RVector v_base_AB is a RVector from the old point to
+ // the new point.
+ // Complexity : 6M+6A
+{
+ return TwistAcc(this->vel+this->rot*v_base_AB,this->rot);
+}
+
+TwistAcc& TwistAcc::operator-=(const TwistAcc& arg)
+{
+ vel-=arg.vel;
+ rot -=arg.rot;
+ return *this;
+}
+
+TwistAcc& TwistAcc::operator+=(const TwistAcc& arg)
+{
+ vel+=arg.vel;
+ rot +=arg.rot;
+ return *this;
+}
+
+
+TwistAcc operator*(const TwistAcc& lhs,double rhs)
+{
+ return TwistAcc(lhs.vel*rhs,lhs.rot*rhs);
+}
+
+TwistAcc operator*(double lhs,const TwistAcc& rhs)
+{
+ return TwistAcc(lhs*rhs.vel,lhs*rhs.rot);
+}
+
+TwistAcc operator/(const TwistAcc& lhs,double rhs)
+{
+ return TwistAcc(lhs.vel/rhs,lhs.rot/rhs);
+}
+
+
+TwistAcc operator*(const TwistAcc& lhs,const doubleAcc& rhs)
+{
+ return TwistAcc(lhs.vel*rhs,lhs.rot*rhs);
+}
+
+TwistAcc operator*(const doubleAcc& lhs,const TwistAcc& rhs)
+{
+ return TwistAcc(lhs*rhs.vel,lhs*rhs.rot);
+}
+
+TwistAcc operator/(const TwistAcc& lhs,const doubleAcc& rhs)
+{
+ return TwistAcc(lhs.vel/rhs,lhs.rot/rhs);
+}
+
+
+
+// addition of TwistAcc's
+TwistAcc operator+(const TwistAcc& lhs,const TwistAcc& rhs)
+{
+ return TwistAcc(lhs.vel+rhs.vel,lhs.rot+rhs.rot);
+}
+
+TwistAcc operator-(const TwistAcc& lhs,const TwistAcc& rhs)
+{
+ return TwistAcc(lhs.vel-rhs.vel,lhs.rot-rhs.rot);
+}
+
+// unary -
+TwistAcc operator-(const TwistAcc& arg)
+{
+ return TwistAcc(-arg.vel,-arg.rot);
+}
+
+
+
+
+
+TwistAcc RotationAcc::Inverse(const TwistAcc& arg) const
+{
+ return TwistAcc(Inverse(arg.vel),Inverse(arg.rot));
+}
+
+TwistAcc RotationAcc::operator * (const TwistAcc& arg) const
+{
+ return TwistAcc((*this)*arg.vel,(*this)*arg.rot);
+}
+
+TwistAcc RotationAcc::Inverse(const Twist& arg) const
+{
+ return TwistAcc(Inverse(arg.vel),Inverse(arg.rot));
+}
+
+TwistAcc RotationAcc::operator * (const Twist& arg) const
+{
+ return TwistAcc((*this)*arg.vel,(*this)*arg.rot);
+}
+
+
+TwistAcc FrameAcc::operator * (const TwistAcc& arg) const
+{
+ TwistAcc tmp;
+ tmp.rot = M*arg.rot;
+ tmp.vel = M*arg.vel+p*tmp.rot;
+ return tmp;
+}
+
+TwistAcc FrameAcc::operator * (const Twist& arg) const
+{
+ TwistAcc tmp;
+ tmp.rot = M*arg.rot;
+ tmp.vel = M*arg.vel+p*tmp.rot;
+ return tmp;
+}
+
+TwistAcc FrameAcc::Inverse(const TwistAcc& arg) const
+{
+ TwistAcc tmp;
+ tmp.rot = M.Inverse(arg.rot);
+ tmp.vel = M.Inverse(arg.vel-p*arg.rot);
+ return tmp;
+}
+
+TwistAcc FrameAcc::Inverse(const Twist& arg) const
+{
+ TwistAcc tmp;
+ tmp.rot = M.Inverse(arg.rot);
+ tmp.vel = M.Inverse(arg.vel-p*arg.rot);
+ return tmp;
+}
+
+Twist TwistAcc::GetTwist() const {
+ return Twist(vel.p,rot.p);
+}
+
+Twist TwistAcc::GetTwistDot() const {
+ return Twist(vel.v,rot.v);
+}
+
+bool Equal(const TwistAcc& a,const TwistAcc& b,double eps) {
+ return (Equal(a.rot,b.rot,eps)&&
+ Equal(a.vel,b.vel,eps) );
+}
+bool Equal(const Twist& a,const TwistAcc& b,double eps) {
+ return (Equal(a.rot,b.rot,eps)&&
+ Equal(a.vel,b.vel,eps) );
+}
+bool Equal(const TwistAcc& a,const Twist& b,double eps) {
+ return (Equal(a.rot,b.rot,eps)&&
+ Equal(a.vel,b.vel,eps) );
+}
+
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