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

[Tony C. <to...@mi...>]

>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...

The word you probably want is "bijection" which implies that for each value
y in R there exists one and only one x such that g(x) = y.

All is clear now.

Thanks,

Tony Cox - DirectX Luminary
Windows Gaming Developer Relations Group
http://msdn.microsoft.com/directx