I have to make a coordinates transformation between two reference systems (axes). For it, three matrices (3x3) have to be multiplied due to some intermediate axes are used. I have thought two approaches to resolve this:
method #1: Making the multiplication directly, i.e. v_f = R1*R2*R3*v_i
method #2: Split into steps.
step 1: v_3i = R3*v_i
step 2: v_23 = R2*v_3i
step 3: v_f = R1*v_23
where: R1, R2 and R3 are 3x3 matrices
v_f,v_i, v_3i, v_23 are 3x1 vectors
I would like to know what method is more efficient computationally (less time) to do the transformation (this will be made a lot of times).