RE: [Algorithms] Bicubic normals for a bicubic world

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

No - in the S shape, each component of the normal goes from value A to value
B and back to value A, which can be described by a quadratic.

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

> -----Original Message-----
> From: John Sensebe [mailto:jse...@ho...]
> Sent: 04 August 2000 14:41
> To: gda...@li...
> Subject: Re: [Algorithms] Bicubic normals for a bicubic world
> 
> 
> 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!