Re: [Algorithms] C1 vs G1 (Was: "N-Patches")

[Charles B. <cb...@cb...>]

At 12:40 PM 7/28/2000 +0200, you wrote:
>Geometric continuity:
>"A curve is said to be Gr if there exists a regular reparametrization after
>which it is Cr"
>So what about C0 and G0 ?

There we go, that's the nice mathematical definition.  A curve

f:R -> R^d

(for a curve in d-dimensional space)
is Gn if there exists any remapping function

g:R -> R

(constraints on g below) such that

f(g()) is Cn

That means that C0 and G0 are the same.  I suspect
g must be 'reflexive' or whatever the math word is,
where it maps all values to unique other values,
and therefore is invertible.  I think g must also be C0
but not necessarily C1...


--------------------------------------
Charles Bloom           www.cbloom.com