On Fri, 8 Jul 2005, Keean Schupke wrote:
Okay, this approach is starting to make sense to me... I can see now that Vectors are a different type of object to Matrices. Vectors represent points in N-Space and matrices represent operations on those points
That's what I wanted to express.
(say rotations or translations)... But it seems we can represent translations as adding vectors or matrix operations (although we need to introduce the 'extra' dimension W... and have an extra field in vectors that contains the value '1').
(3D translation)
[x,y,z,1] * [[0,0,0,0],[0,0,0,0],[0,0,0,0],[dx,dy,dz,dw]] = [x+dx,y+dy,z+dz,1+dw]
Do you mean [x,y,z,1] * [[1,0,0,0],[0,1,0,0],[0,0,1,0],[dx,dy,dz,dw+1]] ?
but how is this different from adding vectors? If we allow vector addition then we no longer have the nice separation between values and linear operators, as a value can also be a linear operator (a translation)?
???