Re: [Algorithms] Scaling Models

[<ro...@do...>]

Tom Hubina  wrote:

>I don't generally use scales on matrices this way (and the description is 
>atrocious from a math standpoint) so Ron can correct me here as needed, but 
>I seem to recall there being two ways to add a scale to a matrix. For a 
>non-uniform scale you can monkey with the different components to get what 
>ya need, or for a uniform scale you can insert the scale value directly 
>into the lower right corner of the matrix. 

Yes, for the uniform scale this is a trick that works in the context
of the 4x4 matrix, but it doesn't fall out until you do the
projection.  That is, you end up with points that have w != 1 before
projecting.  This is an ugly artifact of the 4x4 homogeneous
formulation, which I detest.  Part of its ugliness is that it doesn't
generalize to the non uniform scale.

>If you're doing a uniform scale, 
>and using homogenous matrices as I've described above you wouldn't need to 
>re-normalize the normal since the uniform scale would be ignored for 
>vectors (since the 4th component is zero). Vectors will still be affected 
>by the more traditional scales, and even if they're uniform, will need to 
>be normalized before they can be used in most lighting and environment 
>mapping situations.
>

And of course, in the case that the transformation contains within it
a non-uniform scale, you are completely wrong unless you
transpose(inverse(the upper 3x3)), before applying it to the normal
vectors. See my response to the original post of this thread.