Re: [Algorithms] Bicubic normals for a bicubic world

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

Actually, an (n-1) order polynomial can describe the tangent vectors in one
direction, so the normals would be the cross product of two (n-1) order
polynomials, one being the tangents in u and one in v.

Approximating the normals of a bicubic with a single quadratic would lead to
problems, however. Consider the 2D case, where a bicubic curve can make an
'S' shape, but a quadratic can't.

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: Friday, August 04, 2000 5:35 AM
Subject: RE: [Algorithms] Bicubic normals for a bicubic world


> I was under the impression that interpolating normals of an order-n
> polynomial surface only required an (n-1) order polynomial, i.e. a
> biquadratic Bezier patch in this case. But it's entirely possible I was
> wrong.
>
> Even if it's not strictly correct, I bet it would make a superb
> approximation in most cases.
>
> Tom Forsyth - Muckyfoot bloke.
> Whizzing and pasting and pooting through the day.
>
> > -----Original Message-----
> > From: John Sensebe [mailto:jse...@ho...]
> > Sent: 04 August 2000 01:02
> > To: gda...@li...
> > Subject: [Algorithms] Bicubic normals for a bicubic world
> >
> >
> > Hi! I'm new to this list, but already I'm asking questions... ;-)
> >
> > Does anyone here know how I can approximate the normals
> > across a bicubic
> > surface (i.e.: a Bezier patch) using another bicubic? I want
> > to use normals
> > for backface removal, and a simpler interpolation doesn't
> > help much. On the
> > other hand, an exact biquintic solution would be too
> > expensive to compute.
> >
> > 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!
> >
> >
> >
> >
> > _______________________________________________
> > GDAlgorithms-list mailing list
> > GDA...@li...
> > http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list
> >
>
> _______________________________________________
> GDAlgorithms-list mailing list
> GDA...@li...
> http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list
>