150
where li, mi and ni are the components of the basis unit
vectors of the hand coordinate system, Hi are the
components of the hand position vector and i = x, y and z.
The position vector of point Ci with respect to OXYZ then
can be calculated from the following equation:
Ci = Tp m(Hi) (5.2)
where m(HCi) denotes the vector HCi with respect to the
moving coordinate system Hxyz. We can also find another
coordinate transformation matrix Ti, from oixiYizi to OXYZ,
which can be expressed as
Xix Yix Zix Ooix
Xiy Yiy Ziy Ooiy (5.3)
Ti = (5.3)
Xiz Yiz Ziz Ooiz
0 0 0 1
According to the relationship between the coordinate
systems, we can have the following equations:
OCi = TiCi (5.4)
or
ci = (Ti)-li (5.5)
where
Xix xiy Xiz -Ooi xi
(Ti)-1 Yix Yiy Yiz -oi Yi5.6)
Zix Ziy ziz -Ooi zi
0 0 0 1