function v = XtoVp( X ) % XtoVp obtain planar vector from small-angle transform. % XtoVp(X) interprets X as the coordinate transform from A to B % coordinates, and calculates the constant planar velocity of a third % frame, C(t), that travels from A to B in one time unit. Thus, C(0)=A, % C(1)=B and dC/dt is a constant. The return value is the planar velocity % of C. The calculation uses a small-angle approximation, and is therefore % only exact if A and B are parallel. The return value is an invariant of % X (i.e., v=X*v), and can therefore be regarded as being expressed in % either A or B coordinates. v = [ X(2,3); (X(3,1) + X(2,2)*X(3,1) + X(2,3)*X(2,1))/2; (-X(2,1) - X(2,2)*X(2,1) + X(2,3)*X(3,1))/2 ];