RE: [Algorithms] Bicubic normals for a bicubic world

[Tom F. <to...@mu...>]

Sorry - I wasn't suggesting that the normals _are_ biquadratic. But I was
suggesting that a biquadratic approximation was going to be pretty close in
most cases. Good enough to fool the eye, which really only _needs_ G0 for
lighting, and even a very rough-and-ready C/G1 reduces Mach banding to very
tolerable levels.

So all you need is a curve that can be reliably G0, and get pretty rough G1
at vertices, and not too far out on edges in non-extreme cases. Biquadratic
seems to fit the bill well.

Renormalisation is a pain, but you'd have to do that whatever function you
used (unless you used some astonishingly high-power function and use enough
control points to match the ideal curve, which is probably more expensive
than renormalisation).

Oh hang on - since _rational_ biquadratic surfaces can describe conic
sections (including spheres and sections of spheres), could you maybe use
them for your normals, and thus not have to renormalise - or at least get
close enough that the eye won't notice? Or maybe my brain can't visualise
the spacial equivalent of a unit-length normal well enough to see that a
rational biquadratic isn't good enough. Well, just a thought.

Tom Forsyth - Muckyfoot bloke.
Whizzing and pasting and pooting through the day.

> -----Original Message-----
> From: John Sensebe [mailto:jse...@ho...]
> Sent: 12 August 2000 04:39
> To: gda...@li...
> Subject: Re: [Algorithms] Bicubic normals for a bicubic world
> 
> 
> How are the normals biquadratic? And the two tangent surfaces can't be
> biquadratic, because you're only derivating in one parameter, 
> leaving the
> other as-is. You derive in u, it's still cubic in v, and vice-versa.
> 
> I really want to have a good solution to this, so please bear with me.
> 
> Thanks.
> 
> John Sensebe
> jse...@ho...
> Quantum mechanics is God's way of ensuring that we never 
> really know what's
> going on.
> 
> Check out http://members.home.com/jsensebe to see prophecies 
> for the coming
> Millennium!
> 
> 
> ----- Original Message -----
> From: "Conor Stokes" <cs...@tp...>
> To: <gda...@li...>
> Sent: Friday, August 11, 2000 9:58 PM
> Subject: Re: [Algorithms] Bicubic normals for a bicubic world
> 
> 
> >     Actually, if you think about it - The normals are 
> totally quadratic.
> And
> > if you do a derivitive in 2
> > directions (across S, and across T) you do get 2 
> quadratics. Not only
> that,
> > the cross product is
> > resiliant to transforms - So it remains the same. However, 
> normalisation
> > still needs to occur.
> >
> >     This is why I precalc my normals and reference them 
> from a map in most
> > cases.
> >
> > Conor Stokes
> >
> >
> 
> 
> 
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