Re: [Algorithms] Bicubic normals for a bicubic world

[John S. <jse...@ho...>]

Well, as I've said in a previous post, I need to fool more than the eye,
since I want to cull backfacing subpatches (at least, as well as possible).

Therefore, since my patches are bicubic, I wanted to use a bicubic
approximation for the normals. It should be better than biquadratic, and it
fits well into my patch subdivision algorithm.

Having decided on the method, I'm having trouble figuring out what the
parameters should be. Should I just take the two tangent vectors at each
control point of a Bezier patch, cross them, and use the resulting vectors
as the control points of a Bezier patch describing the normals of the first?

BTW, I plan on letting D3D handle the normalization for me, so at least I
can let the hardware do it if it's doing T&L.

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: "Tom Forsyth" <to...@mu...>
To: <gda...@li...>
Sent: Saturday, August 12, 2000 4:42 AM
Subject: RE: [Algorithms] Bicubic normals for a bicubic world


> 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.
>