Re: [Mesa3d-users] about glScale in Mesa

[Brian P. <br...@va...>]

Rouben Rostamian wrote:
> 
> Brian, thanks for your comments about Mesa's scaling routines.
> Re your remark:
> 
> > Also note that the regular GL_NORMALIZE operation isn't always
> > going to help with non-uniform scales either.  With shapes like
> > cylinders and cubes it just happens to do the job.  But with other
> > objects a non-uniform scale is going to transform normal vectors in
> > a way which is not consistent with the underlying surface geometry.
> 
> The correct transformation of normals under arbitrary scaling should
> not be hard to implement in Mesa.  I know how to do it mathematically,
> but I don't know enough about Mesa's internals to write a patch for
> its code.
> 
> When we transform the space with an arbitrary linear mapping
> P : R^3 -> R^3, i.e., y = P x, normals to surfaces transform
> according to:
> 
>          N'(y) = P' N(x)
> 
> where N(x) is the old normal, N'(y) is the new normal, and
> 
>          P' = inverse of transpose of P
> 
> Does GL_NORMALIZE apply this formula correctly?

Yes, that's what the OpenGL spec calls for.

I believe the transpose is just a technicality of whether you
represent normals as row or column vectors in the expression.


> Important:
>    1. In general N'(y) and N(x) are not parallel!
>    2. In general N'(y) is not of unit length.  Normalize
>       by dividing it by its own length.
> 
> > The behaviour with Mesa 3.2, 3.2.1, 3.3, 3.4, and 3.5 appears
> > identical.  With Mesa 3.1, however, the results are different
> > but I'm not sure it can be called better or worse.  It may
> > actually be that Mesa 3.1 was broken.
> 
> I don't think "better" or "worse" are the proper adjectives,
> since right or wrong is not a matter of degrees :-)
> 
> Actually, the behavior of Mesa-3.4 is correct and Mesa-3.1 is wrong.
> 
> For a simple demo program which I mentioned in my previous post,
> I can analytically calculate the exact location of the highlight.
> Mesa-3.4 puts the highlight in the theoretically correct place.
> Mesa-3.1's is off quite a bit.
> 
> But after the scene is scaled, both highlight are wrong :-(


It's been a long time since I worked through the arithmetic but
I seem to recall that transforming the normal by the transpose
of the modelview's inverse still isn't good enough to correctly
transform a surface normal when the modelview matrix has a non-
uniform scale.

That is, the transformed normal may not be exactly perpindicular to
the surface, as it was before the scale.

If I get a few minutes tonight I'll try going through the math
by hand to refresh my memory on this.

Maybe someone else here has an authoritive answer.

-Brian