Introduction

Geometric primitives are represented by the following classes.

Twist and Wrench transformations: 3 different types of transformations do exist for the twists and wrenches.

*      1) Frame * Twist or Frame * Wrench :
*              this transforms both the velocity/force reference point
*             and the basis to which the twist/wrench are expressed.
*      2) Rotation * Twist or Rotation * Wrench :
*              this transforms the basis to which the twist/wrench are
*              expressed, but leaves the reference point intact.
*      3) Twist.RefPoint(v_base_AB) or Wrench.RefPoint(v_base_AB)
*              this transforms only the reference point. v is expressed
*              in the same base as the twist/wrench and points from the
*              old reference point to the new reference point.
*

Warning: Efficienty can be improved by writing p2 = A*(B*(C*p1))) instead of p2=A*B*C*p1

PROPOSED NAMING CONVENTION FOR FRAME-like OBJECTS

*      A naming convention of objects of the type defined in this file :
*          (1) Frame : F...
*              Rotation : R ...
*          (2) Twist    : T ...
*              Wrench   : W ...
*              Vector   : V ...
*      This prefix is followed by :
*      for category (1) :
*          F_A_B : w.r.t. frame A, frame B expressed
*          ( each column of F_A_B corresponds to an axis of B,
*            expressed w.r.t. frame A )
*          in mathematical convention :
*                   A
*         F_A_B ==    F
*                   B
*
*      for category (2) :
*          V_B   : a vector expressed w.r.t. frame B
*
*      This can also be prepended by a name :
*          e.g. : temporaryV_B
*
*      With this convention one can write :
*
*      F_A_B = F_B_A.Inverse();
*      F_A_C = F_A_B * F_B_C;
*      V_B   = F_B_C * V_C;    // both translation and rotation
*      V_B   = R_B_C * V_C;    // only rotation
*

CONVENTIONS FOR WHEN USED WITH ROBOTS :

*       world : represents the frame ([1 0 0,0 1 0,0 0 1],[0 0 0]')
*       mp    : represents mounting plate of a robot
*               (i.e. everything before MP is constructed by robot manufacturer
*                    everything after MP is tool )
*       tf    : represents task frame of a robot
*               (i.e. frame in which motion and force control is expressed)
*       sf    : represents sensor frame of a robot
*               (i.e. frame at which the forces measured by the force sensor
*               are expressed )
*
*          Frame F_world_mp=...;
*          Frame F_mp_sf(..)
*          Frame F_mp_tf(,.)
*
*          Wrench are measured in sensor frame SF, so one could write :
*                Wrench_tf = F_mp_tf.Inverse()* ( F_mp_sf * Wrench_sf );
*

CONVENTIONS REGARDING UNITS :: Typically we use the standard S.I. units: N, m, sec.