Gvie you infomation the below.
C : Center
U : you could freely write in 3-D.
V : you could freely write in 3-D.
Youd could solve the local axes from the above.
u = normal(U) : normal vector of U.
v = normal(V) : normal vector of V.
w = cross( u, v ) : cross vector of u and v.
Threre is a arbitrary g in global position.
We define the formula in local axes.
g = au + bv + cw
a, b , c are scalar.
We could solve the below formula.
gx = aux + bvx + cwx ... (1)
gy = auy + bvy + cwy ... (2)
gz = auz + bvz + cwz ... (3)
u = ( ux , uy, uz )
v = ( vx , vy, vz )
w = ( wx , wy, wz )